College PhysicsCollection edited by: OpenStax CollegeContent authors: OpenStax College and College PhysicsOnline: <http://cnx.org/content/col11406/1.5>This selection and arrangement of content as a collection is copyrighted by Rice University.It is licensed under the Creative Commons Attribution License: http://creativecommons.org/licenses/by/3.0/Collection structure revised: 2012/03/30For copyright and attribution information for the modules contained in this collection, see the "Attributions" section at the end of the collection.

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Table of ContentsPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 01 Introduction: The Nature of Science and Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Physics: An Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Physical Quantities and Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Accuracy, Precision, and Significant Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Introduction to One-Dimensional Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Displacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Vectors, Scalars, and Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Time, Velocity, and Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Motion Equations for Constant Acceleration in One Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Problem-Solving Basics for One-Dimensional Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Falling Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Graphical Analysis of One-Dimensional Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3 Two-Dimensional Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Introduction to Two-Dimensional Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Kinematics in Two Dimensions: An Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Vector Addition and Subtraction: Graphical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Vector Addition and Subtraction: Analytical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Projectile Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Addition of Velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4 Dynamics: Force and Newton's Laws of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Introduction to Dynamics: Newton's Laws of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Development of Force Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Newton’s First Law of Motion: Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Newton’s Second Law of Motion: Concept of a System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Newton’s Third Law of Motion: Symmetry in Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Normal, Tension, and Other Examples of Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Problem-Solving Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Further Applications of Newton’s Laws of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Extended Topic: The Four Basic Forces—An Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5 Further Applications of Newton's Laws: Friction, Drag, and Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Introduction: Further Applications of Newton’s Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Drag Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Elasticity: Stress and Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

6 Uniform Circular Motion and Gravitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Introduction to Uniform Circular Motion and Gravitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Rotation Angle and Angular Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Centripetal Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Centripetal Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Fictitious Forces and Non-inertial Frames: The Corioluis Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Newton’s Universal Law of Gravitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Satellites and Kepler’s Laws: An Argument for Simplicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

7 Work, Energy, and Energy Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Introduction to Work, Energy, and Energy Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Work: The Scientific Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Kinetic Energy and the Work-Energy Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Gravitational Potential Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Conservative Forces and Potential Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Nonconservative Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Conservation of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Work, Energy, and Power in Humans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45World Energy Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

8 Linear Momentum and Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Introduction to Linear Momentum and Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Linear Momentum and Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Impulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Conservation of Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Elastic Collisions in One Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Inelastic Collisions in One Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Collisions of Point Masses in Two Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Introduction to Rocket Propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

9 Statics and Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Introduction to Statics and Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49The First Condition for Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49The Second Condition for Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3

Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Applications of Statistics, Including Problem-Solving Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Simple Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Forces and Torques in Muscles and Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

10 Rotational Motion and Angular Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Introduction to Rotational Motion and Angular Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Angular Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Kinematics of Rotational Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Dynamics of Rotational Motion: Rotational Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Rotational Kinetic Energy: Work-Energy Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Angular Momentum and Its Conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Collisions of Extended Bodies in Two Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Gyroscopic Effects: Vector Aspects of Angular Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

11 Fluid Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Introduction to Fluid Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53What Is a Fluid? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Variation of Pressure with Depth in a Fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Pascal’s Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Gauge Pressure, Absolute Pressure, and Pressure Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Archimedes’ Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Cohesion and Adhesion in Liquids: Surface Tension and Capillary Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Pressures in the Body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

12 Fluid Dynamics and Its Biological and Medical Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Introduction to Fluid Dynamics and Its Biological and Medical Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Flow Rate and Its Relation to Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Bernoulli’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55The Most General Applications of Bernoulli’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Viscosity and Laminar Flow: Poiseuille’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55The Onset of Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Motion of an Object in a Viscous Fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Molecular Transport Phenomena: Diffusion, Osmosis, and Related Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

13 Temperature, Kinetic Theory, and the Gas Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Introduction to Temperature, Kinetic Theory, and the Gas Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Thermal Expansion of Solids and Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57The Ideal Gas Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Kinetic Theory: Molecular Explanation of Pressure and Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Phase Changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Humidity, Evaporation, and Boiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

14 Heat and Heat Transfer Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Temperature Change and Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61Phase Change and Latent Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Heat Transfer Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

15 Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93Introduction to Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93The First Law of Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93The First Law of Thermodynamics and Some Simple Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93Introduction To The Second Law Of Thermodynamics: Heat Engines And Their Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . 93Carnot’s Perfect Heat Engine: The Second Law of Thermodynamics Restated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93Applications of Thermodynamics: Heat Pumps and Refrigerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy . . . . . . . . . . . . . . . . . . . . . . . . . 93Statistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation . . . . . . . . . . . . . . . . . . 93

16 Oscillatory Motion and Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Introduction to Oscillatory Motion and Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Hooke’s Law: Stress and Strain Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Period and Frequency in Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Simple Harmonic Motion: A Special Periodic Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95The Simple Pendulum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Energy and the Simple Harmonic Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Uniform Circular Motion and Simple Harmonic Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Damped Harmonic Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Forced Oscillations and Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Superposition and Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Energy in Waves: Intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

17 Physics of Hearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Introduction to the Physics of Hearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

4

Sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Speed of Sound, Frequency, and Wavelength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Sound Intensity and Sound Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Doppler Effect and Sonic Booms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Sound Interference and Resonance: Standing Waves in Air Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Hearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Ultrasound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

18 Electric Charge and Electric Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Introduction to Electric Charge and Electric Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Static Electricity and Charge: Conservation of Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Conductors and Insulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Coulomb’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Electric Field: Concept of a Field Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Electric Field Lines: Multiple Charges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Electric Forces in Biology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Conductors and Electric Fields in Static Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Applications of Electrostatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

19 Electric Potential and Electric Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Introduction to Electric Potential and Electric Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Electric Potential Energy: Potential Difference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Electric Potential in a Uniform Electric Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Electric Potential due to a Point Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Equipotential Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Capacitors and Dielectrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Capacitors in Series and Parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Energy Stored in Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

20 Electric Current, Resistance, and Ohm's Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103Introduction to Electric Current, Resistance, and Ohm's Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103Ohm’s Law: Resistance and Simple Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103Resistance and Resistivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103Electric Power and Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103Alternating Current versus Direct Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103Electric Hazards and the Human Body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103Nerve Conduction-Electrocardiograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

21 Circuits, Bioelectricity, and DC Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105Introduction to Circuits, Bioelectricity, and DC Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105Resistors in Series and Parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105Electromotive Force: Terminal Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105Kirchhoff’s Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105DC Voltmeters and Ammeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105Null Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105DC Circuits Containing Resistors and Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

22 Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Introduction to Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Magnets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Ferromagnets and Electromagnets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Magnetic Fields and Magnetic Field Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Magnetic Field Strength B: Force on a Moving Charge in a Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Force on a Moving Charge in a Magnetic Field: Examples and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107The Hall Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Magnetic Force on a Current-Carrying Conductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Torque on a Current Loop: Motors and Meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Magnetic Fields Produced by Currents: Ampere’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Magnetic Force Between Two Parallel Conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107More Applications of Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

23 Electromagnetic Induction, AC Circuits, and Electrical Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Introduction to Electromagnetic Induction: AC Circuits, and Electrical Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Induced Emf and Magnetic Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Faraday’s Law of Induction: Lenz’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Motional Emf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Eddy Currents and Magnetic Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Electric Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Back Emf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Electrical Safety: Systems and Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109RL Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Reactance, Inductive and Capacitive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109RLC Series AC Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

24 Electromagnetic Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111Introduction to Electromagnetic Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111Maxwell’s Equations: Electromagnetic Waves Predicted and Observed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

5

Production of Electromagnetic Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111The Electromagnetic Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111Energy in Electromagnetic Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

25 Geometric Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Introduction to Geometric Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113The Ray Aspect of Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113The Law of Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113The Law of Refraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Total Internal Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Dispersion: The Rainbow and Prisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Image Formation by Lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Image Formation by Mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

26 Vision and Optical Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Introduction to Vision and Optical Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Physics of the Eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Vision Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Color and Color Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Microscopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Aberrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

27 Wave Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Introduction to Wave Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117The Wave Aspect of Light: Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Huygen’s Principle: Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Young’s Double Slit Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Multiple Slit Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Single Slit Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Limits of Resolution: The Rayleigh Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Thin Film Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117*Extended Topic* Microscopy Enhanced by the Wave Characteristics of Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

28 Special Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119Introduction to Special Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119Einstein’s Postulates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119Simultaneity and Time Dilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119Length Contraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119Relativistic Addition of Velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119Relativistic Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119Relativistic Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

29 Introduction to Quantum Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121Introduction to Quantum Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121Quantization of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121The Photoelectric Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121Photon Energies and the Electromagnetic Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121Photon Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121The Particle-Wave Duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121The Wave Nature of Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121Probability: The Heisenberg Uncertainty Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121The Particle-Wave Duality Reviewed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

30 Atomic Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123Introduction to Atomic Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123Discovery of the Atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123Discovery of the Parts of the Atom: Electrons and Nuclei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123Bohr’s Theory of the Hydrogen Atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123X-Rays: Atomic Origins and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123Applications of Atomic Excitations and De-Excitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123The Wave Nature of Matter Causes Quantization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123Patterns in Spectra Reveal More Quantization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123Quantum Numbers and Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123The Pauli Exclusion Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

31 Radioactivity and Nuclear Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Introduction to Radioactivity and Nuclear Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Nuclear Radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Radiation Detection and Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Substructure of the Nucleus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Nuclear Decay and Conservation Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Half-Life and Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Binding Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Tunneling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

32 Medical Applications of Nuclear Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127Introduction to Applications of Nuclear Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127Medical Imaging and Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127Biological Effects of Ionizing Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

6

Therapeutic Uses of Ionizing Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127Food Irradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127Fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127Fission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127Nuclear Weapons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

33 Particle Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Introduction to Particle Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129The Yukawa Particle and the Heinsenberg Uncertainty Principle Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129The Four Basic Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Accelerators Create Matter from Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Particles, Patterns, and Conservation Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Quarks: Is That All There Is? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129GUTs, the Unification of Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

34 Frontiers of Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Introduction to Frontiers of Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Cosmology and Particle Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131General Relativity and Quantum Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Superstrings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Dark Matter and Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Complexity and Chaos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131High-Temperature Superconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Some Questions We Know to Ask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

35 Appendix A: Atomic Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0

36 Appendix B: Selected Radioactive Isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0

37 Appendix C: Useful Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0

38 Appendix CO: Missions of Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0

39 Appendix G: Glossary of Key Symbols and Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

7

PREFACEOur StoryWelcome to College Physics, an OpenStax College resource created with several goals in mind: accessibility, affordability, customization, and studentengagement—all while encouraging learners toward high levels of learning. Instructors and students alike will find that this textbook offers a strongfoundation in introductory physics, with algebra as a prerequisite... and is free online and available in low- cost print options.

OpenStax CollegeOpenStax College strives to create learning resources that make higher education accessible to all. Created by a team of educators, editors, subject-matter experts, and professional writers, the OpenStax College resources are built specifically to address student learning needs in physics. Unliketraditional textbooks, the OpenStax College resources live online and are owned by the community of educators using them. We encourage you tomake suggestions for improvement by contacting us at info@openstaxcollege.org. Community curation is important; therefore, you will find the statusof the project, as well as alternate versions, corrections, etc., on the StaxDash that can be found at http://openstaxcollege.org(http://openstaxcollege.org) . OpenStax College provides essential supplemental resources; however, we have pared down the number ofsupplements available to keep costs low.

College Physics can also be easily customized for your course. Simply select the content most relevant to your curricula and create a textbook thatspeaks directly to the needs of your class. The resource is developed under a CC-BY creative commons license that makes texts open and availableto students and their instructors. Grounded in emerging development of open-source materials, OpenStax College strives to create a textbook thatcan be easily updated and refined. Because this type of resource is owned by the community of educators using it, scholars are invited to submitexamples, emerging research, and other feedback to enhance and strengthen each module, keeping content current and relevant for today’sstudents. All of the content and art found within the OpenStax College textbooks are completely open and reusable in any form.

To the StudentThis book is written for you. It is based on the teaching and research experience of numerous physicists and influenced by a strong recollection oftheir own struggles as students. After reading this book, we hope you see that physics is visible everywhere. Applications range from driving a car tolaunching a rocket, from a skater whirling on ice to a neutron star spinning in space, and from taking your temperature to taking a chest X-ray.

To the InstructorThis text is intended for one-year introductory courses requiring algebra and some trigonometry, but no calculus. It is written for both the students andinstructors of today.

General ApproachAlthough this text can be modified and reorganized to suit your needs, the standard version is organized such that topics are introduced conceptuallywith a steady progression to precise definitions and analytical applications. The analytical aspect (problem solving) is tied back to the conceptualbefore moving on to another topic. Each introductory module, for example, opens with an engaging photograph relevant to the subject of the chapterand interesting applications that are easy for most students to visualize. Starting with familiar applications, there is a progression from conceptual toanalytical, which is tied back to the conceptual at the end.

Organization, Level, and ContentThere is considerable latitude on the part of the instructor regarding the use, organization, level, and content of this book. By choosing the types ofproblems assigned, the instructor can determine the level of sophistication required of the student. As well, in the Connexions system, professorsmay either assign certain portions of the book as they would any other text, or they may edit and republish the book in whole or in part to suit theneeds of a particular class.

Concepts and CalculationsAn ability to calculate does not guarantee conceptual understanding. In order to unify conceptual, analytical, and calculation skills within the learningprocess, we have integrated them throughout the text.

Modern PerspectiveThe chapters on modern physics are more complete than most, with an entire chapter devoted to medical applications of nuclear physics and anotherto particle physics. The final chapter of the text, “Frontiers of Physics,” is devoted to the most exciting endeavors in physics. It ends with a moduletitled “Some Questions We Know to Ask.”

SupplementsAccompanying the main text are a Student Solutions Manual and an Instructor Solutions Manual. The Student Solutions Manual provides worked-outsolutions to select end-of-module Conceptual Questions and Exercises. The Instructor Solutions Manual provides worked-out solutions to allExercises.

Features of OpenStax College PhysicsThe following briefly describes the special features of this text.

8 PREFACE | PREFACE

Modularity

This collection is organized into subcollections and modules that can be rearranged and modified to suit the needs of a particular professor or class.That being said, modules often contain references to content in other modules, as most topics in physics cannot be discussed in isolation.

Learning Objectives

Every module begins with a set of learning objectives. These objectives are designed to guide the instructor in deciding what content to include orassign, and to guide the student with respect to what he or she can expect to learn. After completing the module and end-of-module exercises,students should be able to demonstrate mastery of the learning objectives.

Call-Outs

Key definitions, concepts, and equations are called out with a special design treatment. Call-outs are designed to catch readers’ attention, to make itclear that a specific term, concept, or equation is particularly important, and to provide easy reference for a student reviewing content.

Key Terms

Key terms are in bold and are followed by a definition in context. Definitions of key terms are also listed in the Glossary, which appears at the end ofthe module.

Worked Examples

Worked examples have four distinct parts to promote both analytical and conceptual skills. Worked examples are introduced in words, always usingsome application that should be of interest. This is followed by a Strategy section that emphasizes the concepts involved and how solving theproblem relates to those concepts. This is followed by the mathematical solution and discussion.

Many worked examples contain multiple-part problems to help the students learn how to approach normal situations, in which problems tend to havemultiple parts. Finally, worked examples employ the techniques of the problem-solving strategies so that students can see how those strategiessucceed in practice as well as in theory.

Problem-Solving Strategies

Problem solving strategies are first presented in a special section and subsequently appear at crucial points in the text where students can benefitmost from them. Problem-solving strategies have a logical structure that is reinforced in the worked examples and supported in certain places by linedrawings that illustrate various steps.

Misconception Alerts

Students come to physics with preconceptions from everyday experiences and from previous courses. Some of these preconceptions aremisconceptions, and many are very common among students and the general public. Some are inadvertently picked up through misunderstandingsof lectures and texts. The Misconception Alerts feature is designed to point these out and correct them explicitly.

Take Home Investigations

Take Home Investigations provide the opportunity for students to apply or explore what they have learned with a hands-on activity.

Things Great and Small

In these special topic essays, macroscopic phenomena (such as air pressure) are explained with submicroscopic phenomena (such as atomsbouncing off walls). These essays support the modern perspective by describing aspects of modern physics before they are formally treated in laterchapters. Connections are also made between apparently disparate phenomena.

Simulations

Where applicable, students are directed to physics simulations developed by the University of Colorado. There they can further explore the physicsconcepts they have learned about in the module.

Summary

Module summaries are thorough and functional and present all important definitions and equations. Students are able to find the definitions of allterms and symbols as well as their physical relationships. The structure of the summary makes plain the fundamental principles of the module orcollection and will serve as a useful study guide.

Glossary

At the end of every module or collection is a glossary containing definitions of all of the key terms in the module or collection.

End-of-Module Problems

At the end of every chapter is a set of Conceptual Questions and/or skills-based Problems & Exercises. Conceptual Questions challenge students’ability to explain what they have learned conceptually, independent of the mathematical details. Problems & Exercises challenge students to applyboth concepts and skills to solve mathematical physics problems. Every other problem includes an answer that students can reveal immediately byclicking on a “Show Solution” button. Fully worked solutions to select problems are available in the Student Solutions Manual and the TeacherSolutions Manual.

In addition to traditional skills-based problems, there are three special types of end-of-module problems: Integrated Concept Problems, UnreasonableResults Problems, and Construct Your Own Problems. All of these problems are indicated with a subtitle preceding the problem.

Integrated Concept Problems

Integrated Concept Problems require the student to apply not only those concepts addressed in the particular module or chapter, but those of otherchapters as well. Many would say that a central tenet of physics is its underlying unity and connections. Although topics are necessarily introducedseparately, we have written numerous Integrated Concept Problems to encourage students to apply principles broadly.

PREFACE | PREFACE 9

Unreasonable Results

In Unreasonable Results Problems, students are challenged to not only apply concepts and skills to solve a problem, but also to analyze the answerwith respect to how likely or realistic it really is. These problems contain a premise that produces an unreasonable answer and are designed to furtheremphasize that properly applied physics must describe nature accurately and is not simply the process of solving equations.

Construct Your Own Problem

These problems require students to construct the details of a problem, justify their starting assumptions, show specific steps in the problem’s solution,and finally discuss the meaning of the result. These types of problems relate well to both conceptual and analytical aspects of physics, emphasizingthat physics must describe nature. Often they involve an integration of topics from more than one chapter. Unlike other problems, solutions are notprovided since there is no single correct answer. Instructors should feel free to direct students regarding the level and scope of their considerations.Whether the problem is solved and described correctly will depend on initial assumptions.

Appendices

Appendix A: Atomic MassesAppendix B: Selected Radioactive IsotopesAppendix C: Useful InformationAppendix G: Glossary of Key Symbols and Notation

AcknowledgementsThis text is based on the work completed by Dr. Paul Peter Urone in collaboration with Roger Hinrichs, Kim Dirks, and Manjula Sharma. We wouldlike to thank the authors as well as the numerous professors (a partial list follows) who have contributed their time and energy to review and providefeedback on the manuscript. Their input has been critical in maintaining the pedagogical integrity and accuracy of the text.

Senior Contributing AuthorsDr. Paul Peter Urone,Dr. Roger Hinrichs, State University of New York, College at Oswego

Contributing AuthorsKim Dirks, University of Auckland, New ZealandDr. Manjula Sharma, University of Sydney, Australia

Expert ReviewersErik Christensen, P.E, South Florida Community CollegeUlrich Zurcher, Ph.D., Cleveland State UniversityEric Kincanon, Ph.D., Gonzaga UniversityDonald Franceschetti, Ph.D., University of MemphisDouglas Ingram, Ph.D, Texas Christian UniversityLee H. LaRue, Paris Junior CollegeMarc Sher, College of William and Mary

The SupplementsStudent’s Solutions ManualInstructor’s Solutions Manual

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1 INTRODUCTION: THE NATURE OF SCIENCE ANDPHYSICS

Figure 1.1 Galaxies are as immense as atoms are small. Yet the same laws of physics describe both, and all the rest of nature—an indication of the underlying unity in theuniverse. The laws of physics are surprisingly few in number, implying an underlying simplicity to nature’s apparent complexity. (credit: NASA, JPL-Caltech, P. Barmby,Harvard-Smithsonian Center for Astrophysics)

Introduction to Science and the Realm of Physics, Physical Quantities, and UnitsWhat is your first reaction when you hear the word “physics”? Did you imagine working through difficult equations or memorizing formulas that seemto have no real use in life outside the physics classroom? Many people come to the subject of physics with a bit of fear. But as you begin yourexploration of this broad-ranging subject, you may soon come to realize that physics plays a much larger role in your life than you first thought, nomatter your life goals or career choice.

For example, take a look at the image above. This image is of the Andromeda Galaxy, which contains billions of individual stars, huge clouds of gas,and dust. Two smaller galaxies are also visible as bright blue spots in the background. At a staggering 2.5 million light years from the Earth, thisgalaxy is the nearest one to our own galaxy (which is called the Milky Way). The stars and planets that make up Andromeda might seem to be thefurthest thing from most people’s regular, everyday lives. But Andromeda is a great starting point to think about the forces that hold together theuniverse. The forces that cause Andromeda to act as it does are the same forces we contend with here on Earth, whether we are planning to send arocket into space or simply raise the walls for a new home. The same gravity that causes the stars of Andromeda to rotate and revolve also causeswater to flow over hydroelectric dams here on Earth. Tonight, take a moment to look up at the stars. The forces out there are the same as the oneshere on Earth. Through a study of physics, you may gain a greater understanding of the interconnectedness of everything we can see and know inthis universe.

Think now about all of the technological devices that you use on a regular basis. Computers, smart phones, GPS systems, MP3 players, and satelliteradio might come to mind. Next, think about the most exciting modern technologies that you have heard about in the news, such as trains that levitateabove tracks, “invisibility cloaks” that bend light around them, and microscopic robots that fight cancer cells in our bodies. All of these groundbreakingadvancements, commonplace or unbelievable, rely on the principles of physics. Aside from playing a significant role in technology, professionals suchas engineers, pilots, physicians, physical therapists, electricians, and computer programmers apply physics concepts in their daily work. For example,a pilot must understand how wind forces affect a flight path and a physical therapist must understand how the muscles in the body experience forcesas they move and bend. As you will learn in this text, physics principles are propelling new, exciting technologies, and these principles are applied ina wide range of careers.

In this text, you will begin to explore the history of the formal study of physics, beginning with natural philosophy and the ancient Greeks, and leadingup through a review of Sir Isaac Newton and the laws of physics that bear his name. You will also be introduced to the standards scientists use whenthey study physical quantities and the interrelated system of measurements most of the scientific community uses to communicate in a singlemathematical language. Finally, you will study the limits of our ability to be accurate and precise, and the reasons scientists go to painstaking lengthsto be as clear as possible regarding their own limitations.

Learning Objectives1.1 Physics: An Introduction

Explain the difference between a principle and a law.Explain the difference between a model and a theory.

1.2 Physical Quantities and UnitsPerform unit conversions both in the SI and English units.Explain the most common prefixes in the SI units and be able to write them in scientific notation.

1.3 Accuracy, Precision, and Significant FiguresDetermine the appropriate number of significant figures in both addition and subtraction, as well as multiplication and division calculations.Calculate the percent uncertainty of a measurement.

1.4 ApproximationMake reasonable approximations based on given data.

CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS 11

1.1 Physics: An Introduction

Figure 1.2 The flight formations of migratory birds such as Canada geese are governed by the laws of physics. (credit: David Merrett)

The physical universe is enormously complex in its detail. Every day, each of us observes a great variety of objects and phenomena. Over thecenturies, the curiosity of the human race has led us collectively to explore and catalog a tremendous wealth of information. From the flight of birds tothe colors of flowers, from lightning to gravity, from quarks to clusters of galaxies, from the flow of time to the mystery of the creation of the universe,we have asked questions and assembled huge arrays of facts. In the face of all these details, we have discovered that a surprisingly small andunified set of physical laws can explain what we observe. As humans, we make generalizations and seek order. We have found that nature isremarkably cooperative—it exhibits the underlying order and simplicity we so value.

It is the underlying order of nature that makes science in general, and physics in particular, so enjoyable to study. For example, what do a bag ofchips and a car battery have in common? Both contain energy that can be converted to other forms. The law of conservation of energy (which saysthat energy can change form but is never lost) ties together such topics as food calories, batteries, heat, light, and watch springs. Understanding thislaw makes it easier to learn about the various forms energy takes and how they relate to one another. Apparently unrelated topics are connectedthrough broadly applicable physical laws, permitting an understanding beyond just the memorization of lists of facts.

The unifying aspect of physical laws and the basic simplicity of nature form the underlying themes of this text. In learning to apply these laws, you will,of course, study the most important topics in physics. More importantly, you will gain analytical abilities that will enable you to apply these laws farbeyond the scope of what can be included in a single book. These analytical skills will help you to excel academically, and they will also help you tothink critically in any professional career you choose to pursue. This module discusses the realm of physics (to define what physics is), someapplications of physics (to illustrate its relevance to other disciplines), and more precisely what constitutes a physical law (to illuminate the importanceof experimentation to theory).

Science and the Realm of PhysicsScience consists of the theories and laws that are the general truths of nature as well as the body of knowledge they encompass. Scientists arecontinually trying to expand this body of knowledge and to perfect the expression of the laws that describe it. Physics is concerned with describingthe interactions of energy, matter, space, and time, and it is especially interested in what fundamental mechanisms underlie every phenomenon. Theconcern for describing the basic phenomena in nature essentially defines the realm of physics .

Physics aims to describe the function of everything around us, from the movement of tiny charged particles to the motion of people, cars, andspaceships. In fact, almost everything around you can be described quite accurately by the laws of physics. Consider a smart phone (Figure 1.3).Physics describes how electricity interacts with the various circuits inside the device. This knowledge helps engineers select the appropriate materialsand circuit layout when building the smart phone. Next, consider a GPS system. Physics describes the relationship between the speed of an object,the distance over which it travels, and the time it takes to travel that distance. When you use a GPS device in a vehicle, it utilizes these physicsequations to determine the travel time from one location to another.

Figure 1.3 The Apple “iPhone” is a common smart phone with a GPS function. Physics describes the way that electricity flows through the circuits of this device. Engineersuse their knowledge of physics to construct an iPhone with features that consumers will enjoy. One specific feature of an iPhone is the GPS function. GPS uses physicsequations to determine the driving time between two locations on a map. (credit: @gletham GIS, Social, Mobile Tech Images)

12 CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS

Applications of PhysicsYou need not be a scientist to use physics. On the contrary, knowledge of physics is useful in everyday situations as well as in nonscientificprofessions. It can help you understand how microwave ovens work, why metals should not be put into them, and why they might affect pacemakers.(See Figure 1.4 and Figure 1.5.) Physics allows you to understand the hazards of radiation and rationally evaluate these hazards more easily.Physics also explains the reason why a black car radiator helps remove heat in a car engine, and it explains why a white roof helps keep the inside ofa house cool. Similarly, the operation of a car’s ignition system as well as the transmission of electrical signals through our body’s nervous system aremuch easier to understand when you think about them in terms of basic physics.

Physics is the foundation of many important disciplines and contributes directly to others. Chemistry, for example—since it deals with the interactionsof atoms and molecules—is rooted in atomic and molecular physics. Most branches of engineering are applied physics. In architecture, physics is atthe heart of structural stability, and is involved in the acoustics, heating, lighting, and cooling of buildings. Parts of geology rely heavily on physics,such as radioactive dating of rocks, earthquake analysis, and heat transfer in the Earth. Some disciplines, such as biophysics and geophysics, arehybrids of physics and other disciplines.

Physics has many applications in the biological sciences. On the microscopic level, it helps describe the properties of cell walls and cell membranes(Figure 1.6 and Figure 1.7). On the macroscopic level, it can explain the heat, work, and power associated with the human body. Physics is involvedin medical diagnostics, such as x-rays, magnetic resonance imaging (MRI), and ultrasonic blood flow measurements. Medical therapy sometimesdirectly involves physics; for example, cancer radiotherapy uses ionizing radiation. Physics can also explain sensory phenomena, such as howmusical instruments make sound, how the eye detects color, and how lasers can transmit information.

It is not necessary to formally study all applications of physics. What is most useful is knowledge of the basic laws of physics and a skill in theanalytical methods for applying them. The study of physics also can improve your problem-solving skills. Furthermore, physics has retained the mostbasic aspects of science, so it is used by all of the sciences, and the study of physics makes other sciences easier to understand.

Figure 1.4 The laws of physics help us understand how common appliances work. For example, the laws of physics can help explain how microwave ovens heat up food, andthey also help us understand why it is dangerous to place metal objects in a microwave oven. (credit: MoneyBlogNewz)

Figure 1.5 These two applications of physics have more in common than meets the eye. Microwave ovens use electromagnetic waves to heat food. Magnetic resonanceimaging (MRI) also uses electromagnetic waves to yield an image of the brain, from which the exact location of tumors can be determined. (credit: Rashmi Chawla, DanielSmith, and Paul E. Marik)

Figure 1.6 Physics, chemistry, and biology help describe the properties of cell walls in plant cells, such as the onion cells seen here. (credit: Umberto Salvagnin)

CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS 13

Figure 1.7 An artist’s rendition of the the structure of a cell membrane. Membranes form the boundaries of animal cells and are complex in structure and function. Many of themost fundamental properties of life, such as the firing of nerve cells, are related to membranes. The disciplines of biology, chemistry, and physics all help us understand themembranes of animal cells. (credit: Mariana Ruiz)

Models, Theories, and Laws; The Role of ExperimentationThe laws of nature are concise descriptions of the universe around us; they are human statements of the underlying laws or rules that all naturalprocesses follow. Such laws are intrinsic to the universe; humans did not create them and so cannot change them. We can only discover andunderstand them. Their discovery is a very human endeavor, with all the elements of mystery, imagination, struggle, triumph, and disappointmentinherent in any creative effort. (See Figure 1.8 and Figure 1.9.) The cornerstone of discovering natural laws is observation; science must describethe universe as it is, not as we may imagine it to be.

Figure 1.8 Isaac Newton (1642–1727) was very reluctant to publish his revolutionary work and had to be convinced to do so. In his later years, he stepped down from hisacademic post and became exchequer of the Royal Mint. He took this post seriously, inventing reeding (or creating ridges) on the edge of coins to prevent unscrupulouspeople from trimming the silver off of them before using them as currency. (credit: Arthur Shuster and Arthur E. Shipley: Britain’s Heritage of Science. London, 1917.)

Figure 1.9 Marie Curie (1867–1934) sacrificed monetary assets to help finance her early research and damaged her physical well-being with radiation exposure. She is theonly person to win Nobel prizes in both physics and chemistry. One of her daughters also won a Nobel Prize. (credit: Wikimedia Commons)

14 CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS

We all are curious to some extent. We look around, make generalizations, and try to understand what we see—for example, we look up and wonderwhether one type of cloud signals an oncoming storm. As we become serious about exploring nature, we become more organized and formal incollecting and analyzing data. We attempt greater precision, perform controlled experiments (if we can), and write down ideas about how the datamay be organized and unified. We then formulate models, theories, and laws based on the data we have collected and analyzed to generalize andcommunicate the results of these experiments.

A model is a representation of something that is often too difficult (or impossible) to display directly. While a model is justified with experimental proof,it is only accurate under limited situations. An example is the planetary model of the atom in which electrons are pictured as orbiting the nucleus,analogous to the way planets orbit the Sun. (See Figure 1.10.) We cannot observe electron orbits directly, but the mental image helps explain theobservations we can make, such as the emission of light from hot gases (atomic spectra). Physicists use models for a variety of purposes. Forexample, models can help physicists analyze a scenario and perform a calculation, or they can be used to represent a situation in the form of acomputer simulation. A theory is an explanation for patterns in nature that is supported by scientific evidence and verified multiple times by variousgroups of researchers. Some theories include models to help visualize phenomena, whereas others do not. Newton’s theory of gravity, for example,does not require a model or mental image, because we can observe the objects directly with our own senses. The kinetic theory of gases, on theother hand, is a model in which a gas is viewed as being composed of atoms and molecules. Atoms and molecules are too small to be observeddirectly with our senses—thus, we picture them mentally to understand what our instruments tell us about the behavior of gases.

A law uses concise language to describe a generalized pattern in nature that is supported by scientific evidence and repeated experiments. Often, alaw can be expressed in the form of a single mathematical equation. Laws and theories are similar in that they are both scientific statements thatresult from a tested hypothesis and are supported by scientific evidence. However, the designation law is reserved for a concise and very generalstatement that describes phenomena in nature, such as the law that energy is conserved during any process, or Newton’s second law of motion,which relates force, mass, and acceleration by the simple equation F =ma . A theory, in contrast, is a less concise statement of observedphenomena. For example, the Theory of Evolution and the Theory of Relativity cannot be expressed concisely enough to be considered a law. Thebiggest difference between a law and a theory is that a theory is much more complex and dynamic. A law describes a single action, whereas a theoryexplains an entire group of related phenomena. And, whereas a law is a postulate that forms the foundation of the scientific method, a theory is theend result of that process.

Less broadly applicable statements are usually called principles (such as Pascal’s principle, which is applicable only in fluids), but the distinctionbetween laws and principles often is not carefully made.

Figure 1.10 What is a model? This planetary model of the atom shows electrons orbiting the nucleus. It is a drawing that we use to form a mental image of the atom that wecannot see directly with our eyes because it is too small.

Models, Theories, and Laws

Models, theories, and laws are used to help scientists analyze the data they have already collected. However, often after a model, theory, or lawhas been developed, it points scientists toward new discoveries they would not otherwise have made.

The models, theories, and laws we devise sometimes imply the existence of objects or phenomena as yet unobserved. These predictions areremarkable triumphs and tributes to the power of science. It is the underlying order in the universe that enables scientists to make such spectacularpredictions. However, if experiment does not verify our predictions, then the theory or law is wrong, no matter how elegant or convenient it is. Lawscan never be known with absolute certainty because it is impossible to perform every imaginable experiment in order to confirm a law in everypossible scenario. Physicists operate under the assumption that all scientific laws and theories are valid until a counterexample is observed. If agood-quality, verifiable experiment contradicts a well-established law, then the law must be modified or overthrown completely.

The study of science in general and physics in particular is an adventure much like the exploration of uncharted ocean. Discoveries are made;models, theories, and laws are formulated; and the beauty of the physical universe is made more sublime for the insights gained.

The Scientific Method

As scientists inquire and gather information about the world, they follow a process called the scientific method . This process typically beginswith an observation and question that the scientist will research. Next, the scientist typically performs some research about the topic and thendevises a hypothesis. Then, the scientist will test the hypothesis by performing an experiment. Finally, the scientist analyzes the results of theexperiment and draws a conclusion. Note that the scientific method can be applied to many situations that are not limited to science, and thismethod can be modified to suit the situation.

Consider an example. Let us say that you try to turn on your car, but it will not start. You undoubtedly wonder: Why will the car not start? You canfollow a scientific method to answer this question. First off, you may perform some research to determine a variety of reasons why the car will notstart. Next, you will state a hypothesis. For example, you may believe that the car is not starting because it has no engine oil. To test this, youopen the hood of the car and examine the oil level. You observe that the oil is at an acceptable level, and you thus conclude that the oil level isnot contributing to your car issue. To troubleshoot the issue further, you may devise a new hypothesis to test and then repeat the process again.

CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS 15

The Evolution of Natural Philosophy into Modern PhysicsPhysics was not always a separate and distinct discipline. It remains connected to other sciences to this day. The word physics comes from Greek,meaning nature. The study of nature came to be called “natural philosophy.” From ancient times through the Renaissance, natural philosophyencompassed many fields, including astronomy, biology, chemistry, physics, mathematics, and medicine. Over the last few centuries, the growth ofknowledge has resulted in ever-increasing specialization and branching of natural philosophy into separate fields, with physics retaining the mostbasic facets. (See Figure 1.11, Figure 1.12, and Figure 1.13.) Physics as it developed from the Renaissance to the end of the 19th century is calledclassical physics . It was transformed into modern physics by revolutionary discoveries made starting at the beginning of the 20th century.

Figure 1.11 Over the centuries, natural philosophy has evolved into more specialized disciplines, as illustrated by the contributions of some of the greatest minds in history.The Greek philosopher Aristotle (384–322 B.C.) wrote on a broad range of topics including physics, animals, the soul, politics, and poetry. (credit: Jastrow (2006)/LudovisiCollection)

Figure 1.12 Galileo Galilei (1564–1642) laid the foundation of modern experimentation and made contributions in mathematics, physics, and astronomy. (credit: DomenicoTintoretto)

Figure 1.13 Niels Bohr (1885–1962) made fundamental contributions to the development of quantum mechanics, one part of modern physics. (credit: United States Library ofCongress Prints and Photographs Division)

Classical physics is not an exact description of the universe, but it is an excellent approximation under the following conditions: Matter must bemoving at speeds less than about 1% of the speed of light, the objects dealt with must be large enough to be seen with a microscope, and only weakgravitational fields, such as the field generated by the Earth, can be involved. Because humans live under such circumstances, classical physicsseems intuitively reasonable, while many aspects of modern physics seem bizarre. This is why models are so useful in modern physics—they let usconceptualize phenomena we do not ordinarily experience. We can relate to models in human terms and visualize what happens when objects move

16 CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS

at high speeds or imagine what objects too small to observe with our senses might be like. For example, we can understand an atom’s propertiesbecause we can picture it in our minds, although we have never seen an atom with our eyes. New tools, of course, allow us to better picturephenomena we cannot see. In fact, new instrumentation has allowed us in recent years to actually “picture” the atom.

Limits on the Laws of Classical Physics

For the laws of classical physics to apply, the following criteria must be met: Matter must be moving at speeds less than about 1% of the speedof light, the objects dealt with must be large enough to be seen with a microscope, and only weak gravitational fields (such as the field generatedby the Earth) can be involved.

Figure 1.14 Using a scanning tunneling microscope (STM), scientists can see the individual atoms that compose this sheet of gold. (credit: Erwinrossen)

Some of the most spectacular advances in science have been made in modern physics. Many of the laws of classical physics have been modified orrejected, and revolutionary changes in technology, society, and our view of the universe have resulted. Like science fiction, modern physics is filledwith fascinating objects beyond our normal experiences, but it has the advantage over science fiction of being very real. Why, then, is the majority ofthis text devoted to topics of classical physics? There are two main reasons: Classical physics gives an extremely accurate description of theuniverse under a wide range of everyday circumstances, and knowledge of classical physics is necessary to understand modern physics.

Modern physics itself consists of the two revolutionary theories, relativity and quantum mechanics. These theories deal with the very fast and thevery small, respectively. Relativity must be used whenever an object is traveling at greater than about 1% of the speed of light or experiences astrong gravitational field such as that near the Sun. Quantum mechanics must be used for objects smaller than can be seen with a microscope. Thecombination of these two theories is relativistic quantum mechanics, and it describes the behavior of small objects traveling at high speeds orexperiencing a strong gravitational field. Relativistic quantum mechanics is the best universally applicable theory we have. Because of itsmathematical complexity, it is used only when necessary, and the other theories are used whenever they will produce sufficiently accurate results. Wewill find, however, that we can do a great deal of modern physics with the algebra and trigonometry used in this text.

Check Your Understanding

A friend tells you he has learned about a new law of nature. What can you know about the information even before your friend describes the law?How would the information be different if your friend told you he had learned about a scientific theory rather than a law?

SolutionWithout knowing the details of the law, you can still infer that the information your friend has learned conforms to the requirements of all laws ofnature: it will be a concise description of the universe around us; a statement of the underlying rules that all natural processes follow. If theinformation had been a theory, you would be able to infer that the information will be a large-scale, broadly applicable generalization.

Equation Grapher

Figure 1.15 Equation Grapher (http://cnx.org/content/m42092/1.2/equation-grapher_en.jar)

Learn about graphing polynomials. The shape of the curve changes as the constants are adjusted. View the curves for the individual terms (e.g.y= bx ) to see how they add to generate the polynomial curve.

CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS 17

1.2 Physical Quantities and Units

Figure 1.16 The distance from Earth to the Moon may seem immense, but it is just a tiny fraction of the distances from Earth to other celestial bodies. (credit: NASA)

The range of objects and phenomena studied in physics is immense. From the incredibly short lifetime of a nucleus to the age of the Earth, from thetiny sizes of sub-nuclear particles to the vast distance to the edges of the known universe, from the force exerted by a jumping flea to the forcebetween Earth and the Sun, there are enough factors of 10 to challenge the imagination of even the most experienced scientist. Giving numericalvalues for physical quantities and equations for physical principles allows us to understand nature much more deeply than does qualitativedescription alone. To comprehend these vast ranges, we must also have accepted units in which to express them. And we shall find that (even in thepotentially mundane discussion of meters, kilograms, and seconds) a profound simplicity of nature appears—all physical quantities can be expressedas combinations of only four fundamental physical quantities: length, mass, time, and electric charge.

We define a physical quantity either by specifying how it is measured or by stating how it is calculated from other measurements. For example, wedefine distance and time by specifying methods for measuring them, whereas we define average speed by stating that it is calculated as distancetraveled divided by time of travel.

Measurements of physical quantities are expressed in terms of units , which are standardized values. For example, the length of a race, which is aphysical quantity, can be expressed in units of meters (for sprinters) or kilometers (for distance runners). Without standardized units, it would beextremely difficult for scientists to express and compare measured values in a meaningful way. (See Figure 1.17.)

Figure 1.17 Distances given in unknown units are maddeningly useless.

There are two major systems of units used in the world: SI units (also known as the metric system) and English units (also known as the customaryor imperial system). English units were historically used in nations once ruled by the British Empire and are still widely used in the United States.Virtually every other country in the world now uses SI units as the standard; the metric system is also the standard system agreed upon by scientistsand mathematicians. The acronym “SI” is derived from the French Système International.

SI Units: Fundamental and Derived UnitsTable 1.1 gives the fundamental SI units that are used throughout this textbook. This text uses non-SI units in a few applications where they are invery common use, such as the measurement of blood pressure in millimeters of mercury (mm Hg). Whenever non-SI units are discussed, they will betied to SI units through conversions.

Table 1.1 Fundamental SI UnitsLength Mass Time Electric charge

meter (m) kilogram (kg) second (s) coulomb (C)

It is an intriguing fact that some physical quantities are more fundamental than others and that the most fundamental physical quantities can bedefined only in terms of the procedure used to measure them. The units in which they are measured are thus called fundamental units . In thistextbook, the fundamental physical quantities are taken to be length, mass, time, and electric charge. (Note that electric charge will not be introduceduntil much later in this text.) All other physical quantities, such as force and electric current, can be expressed as algebraic combinations of length,mass, time, and charge (for example, speed is length divided by time); these units are called derived units .

18 CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS

Units of Time, Length, and Mass: The Second, Meter, and Kilogram

The Second

The SI unit for time, the second (abbreviated s), has a long history. For many years it was defined as 1/86,400 of a mean solar day. More recently, anew standard was adopted to gain greater accuracy and to define the second in terms of a non-varying, or constant, physical phenomenon (becausethe solar day is getting longer due to very gradual slowing of the Earth’s rotation). Cesium atoms can be made to vibrate in a very steady way, andthese vibrations can be readily observed and counted. In 1967 the second was redefined as the time required for 9,192,631,770 of these vibrations.(See Figure 1.18.) Accuracy in the fundamental units is essential, because all measurements are ultimately expressed in terms of fundamental unitsand can be no more accurate than are the fundamental units themselves.

Figure 1.18 An atomic clock such as this one uses the vibrations of cesium atoms to keep time to a precision of better than a microsecond per year. The fundamental unit oftime, the second, is based on such clocks. This image is looking down from the top of an atomic fountain nearly 30 feet tall! (credit: Steve Jurvetson/Flickr)

The Meter

The SI unit for length is the meter (abbreviated m); its definition has also changed over time to become more accurate and precise. The meter wasfirst defined in 1791 as 1/10,000,000 of the distance from the equator to the North Pole. This measurement was improved in 1889 by redefining themeter to be the distance between two engraved lines on a platinum-iridium bar now kept near Paris. By 1960, it had become possible to define themeter even more accurately in terms of the wavelength of light, so it was again redefined as 1,650,763.73 wavelengths of orange light emitted bykrypton atoms. In 1983, the meter was given its present definition (partly for greater accuracy) as the distance light travels in a vacuum in1/299,792,458 of a second. (See Figure 1.19.) This change defines the speed of light to be exactly 299,792,458 meters per second. The length ofthe meter will change if the speed of light is someday measured with greater accuracy.

The Kilogram

The SI unit for mass is the kilogram (abbreviated kg); it is defined to be the mass of a platinum-iridium cylinder kept with the old meter standard atthe International Bureau of Weights and Measures near Paris. Exact replicas of the standard kilogram are also kept at the United States’ NationalInstitute of Standards and Technology, or NIST, located in Gaithersburg, Maryland outside of Washington D.C., and at other locations around theworld. The determination of all other masses can be ultimately traced to a comparison with the standard mass.

Figure 1.19 The meter is defined to be the distance light travels in 1/299,792,458 of a second in a vacuum. Distance traveled is speed multiplied by time.

Electric charge and its accompanying unit, the coulomb, will be introduced in the chapter Section 18.2 when electricity and magnetism are covered.The initial modules in this textbook are concerned with mechanics, fluids, heat, and waves. In these subjects all pertinent physical quantities can beexpressed in terms of the fundamental units of length, mass, and time.

Metric PrefixesSI units are part of the metric system . The metric system is convenient for scientific and engineering calculations because the units are categorizedby factors of 10. Table 1.2 gives metric prefixes and symbols used to denote various factors of 10.

Metric systems have the advantage that conversions of units involve only powers of 10. There are 100 centimeters in a meter, 1000 meters in akilometer, and so on. In nonmetric systems, such as the system of U.S. customary units, the relationships are not as simple—there are 12 inches in afoot, 5280 feet in a mile, and so on. Another advantage of the metric system is that the same unit can be used over extremely large ranges of valuessimply by using an appropriate metric prefix. For example, distances in meters are suitable in construction, while distances in kilometers areappropriate for air travel, and the tiny measure of nanometers are convenient in optical design. With the metric system there is no need to invent newunits for particular applications.

The term order of magnitude refers to the scale of a value expressed in the metric system. Each power of 10 in the metric system represents a

different order of magnitude. For example, 101 ,102 ,103 , and so forth are all different orders of magnitude. All quantities that can be expressed as

a product of a specific power of 10 are said to be of the same order of magnitude. For example, the number 800 can be written as 8×102 , and

CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS 19

the number 450 can be written as 4.5×102 . Thus, the numbers 800 and 450 are of the same order of magnitude: 102 . Order of magnitude

can be thought of as a ballpark estimate for the scale of a value. The diameter of an atom is on the order of 10−9 m , while the diameter of the Sun

is on the order of 109 m .

The Quest for Microscopic Standards for Basic Units

The fundamental units described in this chapter are those that produce the greatest accuracy and precision in measurement. There is a senseamong physicists that, because there is an underlying microscopic substructure to matter, it would be most satisfying to base our standards ofmeasurement on microscopic objects and fundamental physical phenomena such as the speed of light. A microscopic standard has beenaccomplished for the standard of time, which is based on the oscillations of the cesium atom.

The standard for length was once based on the wavelength of light (a small-scale length) emitted by a certain type of atom, but it has beensupplanted by the more precise measurement of the speed of light. If it becomes possible to measure the mass of atoms or a particulararrangement of atoms such as a silicon sphere to greater precision than the kilogram standard, it may become possible to base massmeasurements on the small scale. There are also possibilities that electrical phenomena on the small scale may someday allow us to base theunit of charge on that of electrons and protons, but at present charge is related to large-scale currents and forces between wires.

Table 1.2 METRIC PREFIXES FOR POWERS OF 10 AND THEIR SYMBOLSPrefix Symbol Value[1] Example (some are approximate)

exa E 1018 exameter Em 1018 m distance light travels in a century

peta P 1015 petasecond Ps 1015 s 30 million years

tera T 1012 terawatt TW 1012 W powerful laser output

giga G 109 gigahertz GHz 109 Hz a microwave frequency

mega M 106 megacurie MCi 106 Ci high radioactivity

kilo k 103 kilometer km 103 m about 6/10 mile

hecto h 102 hectoliter hL 102 L 26 gallons

deka da 101 dekagram dag 101 g teaspoon of butter

— — 100 (=1)

deci d 10−1 deciliter dL 10−1 L less than half a soda

centi c 10−2 centimeter cm 10−2 m fingertip thickness

milli m 10−3 millimeter mm 10−3 m flea at its shoulders

micro µ 10−6 micrometer µm 10−6 m detail in microscope

nano n 10−9 nanogram ng 10−9 g small speck of dust

pico p 10−12 picofarad pF 10−12 F small capacitor in radio

femto f 10−15 femtometer fm 10−15 m size of a proton

atto a 10−18 attosecond as 10−18 s time light crosses an atom

Known Ranges of Length, Mass, and TimeThe vastness of the universe and the breadth over which physics applies are illustrated by the wide range of examples of known lengths, masses,and times in Table 1.3. Examination of this table will give you some feeling for the range of possible topics and numerical values. (See Figure 1.20and Figure 1.21.)

1. See Appendix A for a discussion of powers of 10.

20 CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS

Figure 1.20 Tiny phytoplankton swims among crystals of ice in the Antarctic Sea. They range from a few micrometers to as much as 2 millimeters in length. (credit: Prof.Gordon T. Taylor, Stony Brook University; NOAA Corps Collections)

Figure 1.21 Galaxies collide 2.4 billion light years away from Earth. The tremendous range of observable phenomena in nature challenges the imagination. (credit: NASA/CXC/UVic./A. Mahdavi et al. Optical/lensing: CFHT/UVic./H. Hoekstra et al.)

Unit Conversion and Dimensional AnalysisIt is often necessary to convert from one type of unit to another. For example, if you are reading a European cookbook, some quantities may beexpressed in units of liters and you need to convert them to cups. Or, perhaps you are reading walking directions from one location to another andyou are interested in how many miles you will be walking. In this case, you will need to convert units of feet to miles.

Let us consider a simple example of how to convert units. Let us say that we want to convert 80 meters (m) to kilometers (km).

The first thing to do is to list the units that you have and the units that you want to convert to. In this case, we have units in meters and we want toconvert to kilometers .

Next, we need to determine a conversion factor relating meters to kilometers. A conversion factor is a ratio expressing how many of one unit areequal to another unit. For example, there are 12 inches in 1 foot, 100 centimeters in 1 meter, 60 seconds in 1 minute, and so on. In this case, weknow that there are 1,000 meters in 1 kilometer.

Now we can set up our unit conversion. We will write the units that we have and then multiply them by the conversion factor so that the units cancelout, as shown:

(1.1)80m× 1 km1000m = 0.080 km.

Note that the unwanted m unit cancels, leaving only the desired km unit. You can use this method to convert between any types of unit.

Click Section 37.1 for a more complete list of conversion factors.

CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS 21

Table 1.3 APPROXIMATE VALUES OF LENGTH, MASS, AND TIME

Lengths in meters Masses in kilograms (more precisevalues in parentheses)

Times in seconds (more precisevalues in parentheses)

10−18 Present experimental limit to smallestobservable detail 10−30

Mass of an electron⎛⎝9.11×10−31 kg⎞⎠ 10−23 Time for light to cross a proton

10−15 Diameter of a proton 10−27Mass of a hydrogen atom⎛⎝1.67×10−27 kg⎞⎠ 10−22 Mean life of an extremely unstable

nucleus

10−14 Diameter of a uranium nucleus 10−15 Mass of a bacterium 10−15 Time for one oscillation of visiblelight

10−10 Diameter of a hydrogen atom 10−5 Mass of a mosquito 10−13 Time for one vibration of an atomin a solid

10−8 Thickness of membranes in cells of livingorganisms 10−2 Mass of a hummingbird 10−8 Time for one oscillation of an FM

radio wave

10−6 Wavelength of visible light 1 Mass of a liter of water (about aquart) 10−3 Duration of a nerve impulse

10−3 Size of a grain of sand 102 Mass of a person 1 Time for one heartbeat

1 Height of a 4-year-old child 103 Mass of a car 105 One day ⎛⎝8.64×104s⎞⎠

102 Length of a football field 108 Mass of a large ship 107 One year (y) ⎛⎝3.16×107s⎞⎠

104 Greatest ocean depth 1012 Mass of a large iceberg 109 About half the life expectancy of ahuman

107 Diameter of the Earth 1015 Mass of the nucleus of a comet 1011 Recorded history

1011 Distance from the Earth to the Sun 1023 Mass of the Moon ⎛⎝7.35×1022 kg⎞⎠ 1017 Age of the Earth

1016 Distance traveled by light in 1 year (a lightyear) 1025 Mass of the Earth ⎛⎝5.97×1024 kg⎞⎠ 1018 Age of the universe

1021 Diameter of the Milky Way galaxy 1030 Mass of the Sun ⎛⎝1.99×1030 kg⎞⎠

1022 Distance from the Earth to the nearest largegalaxy (Andromeda) 1042 Mass of the Milky Way galaxy

(current upper limit)

1026 Distance from the Earth to the edges of theknown universe 1053 Mass of the known universe (current

upper limit)

Example 1.1 Unit Conversions: A Short Drive Home

Suppose that you drive the 10.0 km from your university to home in 20.0 min. Calculate your average speed (a) in kilometers per hour (km/h) and(b) in meters per second (m/s). (Note: Average speed is distance traveled divided by time of travel.)

Strategy

First we calculate the average speed using the given units. Then we can get the average speed into the desired units by picking the correctconversion factor and multiplying by it. The correct conversion factor is the one that cancels the unwanted unit and leaves the desired unit in itsplace.

Solution for (a)

(1) Calculate average speed. Average speed is distance traveled divided by time of travel. (Take this definition as a given for now—averagespeed and other motion concepts will be covered in a later module.) In equation form,

(1.2)average speed = distancetime .

(2) Substitute the given values for distance and time.

(1.3)average speed = 10.0 km20.0 min = 0.500 km

min.

(3) Convert km/min to km/h: multiply by the conversion factor that will cancel minutes and leave hours. That conversion factor is 60 min/hr .Thus,

(1.4)average speed =0.500 km min×60 min

1 h = 30.0 km h .

22 CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS

Discussion for (a)

To check your answer, consider the following:

(1) Be sure that you have properly cancelled the units in the unit conversion. If you have written the unit conversion factor upside down, the unitswill not cancel properly in the equation. If you accidentally get the ratio upside down, then the units will not cancel; rather, they will give you thewrong units as follows:

(1.5) kmmin× 1 hr

60 min = 160

km ⋅ hr min2 ,

which are obviously not the desired units of km/h.

(2) Check that the units of the final answer are the desired units. The problem asked us to solve for average speed in units of km/h and we haveindeed obtained these units.

(3) Check the significant figures. Because each of the values given in the problem has three significant figures, the answer should also havethree significant figures. The answer 30.0 km/hr does indeed have three significant figures, so this is appropriate. Note that the significant figuresin the conversion factor are not relevant because an hour is defined to be 60 minutes, so the precision of the conversion factor is perfect.

(4) Next, check whether the answer is reasonable. Let us consider some information from the problem—if you travel 10 km in a third of an hour(20 min), you would travel three times that far in an hour. The answer does seem reasonable.

Solution for (b)

There are several ways to convert the average speed into meters per second.

(1) Start with the answer to (a) and convert km/h to m/s. Two conversion factors are needed—one to convert hours to seconds, and another toconvert kilometers to meters.

(2) Multiplying by these yields

(1.6)Average speed = 30.0kmh × 1 h

3,600 s×1,000 m1 km ,

(1.7)Average speed = 8.33ms .

Discussion for (b)

If we had started with 0.500 km/min, we would have needed different conversion factors, but the answer would have been the same: 8.33 m/s.

You may have noted that the answers in the worked example just covered were given to three digits. Why? When do you need to be concernedabout the number of digits in something you calculate? Why not write down all the digits your calculator produces? The module Section 1.3 willhelp you answer these questions.

Nonstandard Units

While there are numerous types of units that we are all familiar with, there are others that are much more obscure. For example, a firkin is a unitof volume that was once used to measure beer. One firkin equals about 34 liters. To learn more about nonstandard units, use a dictionary orencyclopedia to research different “weights and measures.” Take note of any unusual units, such as a barleycorn, that are not listed in the text.Think about how the unit is defined and state its relationship to SI units.

Check Your Understanding

Some hummingbirds beat their wings more than 50 times per second. A scientist is measuring the time it takes for a hummingbird to beat itswings once. Which fundamental unit should the scientist use to describe the measurement? Which factor of 10 is the scientist likely to use todescribe the motion precisely? Identify the metric prefix that corresponds to this factor of 10.

SolutionThe scientist will measure the time between each movement using the fundamental unit of seconds. Because the wings beat so fast, the scientist

will probably need to measure in milliseconds, or 10−3 seconds. (50 beats per second corresponds to 20 milliseconds per beat.)

Check Your Understanding

One cubic centimeter is equal to one milliliter. What does this tell you about the different units in the SI metric system?

SolutionThe fundamental unit of length (meter) is probably used to create the derived unit of volume (liter). The measure of a milliliter is dependent on themeasure of a centimeter.

CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS 23

1.3 Accuracy, Precision, and Significant Figures

Figure 1.22 A double-pan mechanical balance is used to compare different masses. Usually an object with unknown mass is placed in one pan and objects of known mass areplaced in the other pan. When the bar that connects the two pans is horizontal, then the masses in both pans are equal. The “known masses” are typically metal cylinders ofstandard mass such as 1 gram, 10 grams, and 100 grams. (credit: Serge Melki)

Figure 1.23 Many mechanical balances, such as double-pan balances, have been replaced by digital scales, which can typically measure the mass of an object moreprecisely. Whereas a mechanical balance may only read the mass of an object to the nearest tenth of a gram, many digital scales can measure the mass of an object up to thenearest thousandth of a gram. (credit: Karel Jakubec)

Accuracy and Precision of a MeasurementScience is based on observation and experiment—that is, on measurements. Accuracy is how close a measurement is to the correct value for thatmeasurement. For example, let us say that you are measuring the length of standard computer paper. The packaging in which you purchased thepaper states that it is 11.0 inches long. You measure the length of the paper three times and obtain the following measurements: 11.1 in., 11.2 in., and10.9 in. These measurements are quite accurate because they are very close to the correct value of 11.0 inches. In contrast, if you had obtained ameasurement of 12 inches, your measurement would not be very accurate.

The precision of a measurement system is refers to how close the agreement is between repeated measurements (which are repeated under thesame conditions). Consider the example of the paper measurements. The precision of the measurements refers to the spread of the measuredvalues. One way to analyze the precision of the measurements would be to determine the range, or difference, between the lowest and the highestmeasured values. In that case, the lowest value was 10.9 in. and the highest value was 11.2 in. Thus, the measured values deviated from each otherby at most 0.3 in. These measurements were relatively precise because they did not vary too much in value. However, if the measured values hadbeen 10.9, 11.1, and 11.9, then the measurements would not be very precise because there would be significant variation from one measurement toanother.

The measurements in the paper example are both accurate and precise, but in some cases, measurements are accurate but not precise, or they areprecise but not accurate. Let us consider an example of a GPS system that is attempting to locate the position of a restaurant in a city. Think of therestaurant location as existing at the center of a bull’s-eye target, and think of each GPS attempt to locate the restaurant as a black dot. In Figure1.24, you can see that the GPS measurements are spread out far apart from each other, but they are all relatively close to the actual location of therestaurant at the center of the target. This indicates a low precision, high accuracy measuring system. However, in Figure 1.25, the GPSmeasurements are concentrated quite closely to one another, but they are far away from the target location. This indicates a high precision, lowaccuracy measuring system.

24 CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS

Figure 1.24 A GPS system attempts to locate a restaurant at the center of the bull’s-eye. The black dots represent each attempt to pinpoint the location of the restaurant. Thedots are spread out quite far apart from one another, indicating low precision, but they are each rather close to the actual location of the restaurant, indicating high accuracy.(credit: Dark Evil)

Figure 1.25 In this figure, the dots are concentrated rather closely to one another, indicating high precision, but they are rather far away from the actual location of therestaurant, indicating low accuracy. (credit: Dark Evil)

Accuracy, Precision, and UncertaintyThe degree of accuracy and precision of a measuring system are related to the uncertainty in the measurements. Uncertainty is a quantitativemeasure of how much your measured values deviate from a standard or expected value. If your measurements are not very accurate or precise, thenthe uncertainty of your values will be very high. In more general terms, uncertainty can be thought of as a disclaimer for your measured values. Forexample, if someone asked you to provide the mileage on your car, you might say that it is 45,000 miles, plus or minus 500 miles. The plus or minusamount is the uncertainty in your value. That is, you are indicating that the actual mileage of your car might be as low as 44,500 miles or as high as45,500 miles, or anywhere in between. All measurements contain some amount of uncertainty. In our example of measuring the length of the paper,we might say that the length of the paper is 11 in., plus or minus 0.2 in. The uncertainty in a measurement, A , is often denoted as δA (“delta A ”),

so the measurement result would be recorded as A ± δA . In our paper example, the length of the paper could be expressed as 11 in. ± 0.2.

The factors contributing to uncertainty in a measurement include:

1. Limitations of the measuring device,2. The skill of the person making the measurement,3. Irregularities in the object being measured,4. Any other factors that affect the outcome (highly dependent on the situation).

In our example, such factors contributing to the uncertainty could be the following: the smallest division on the ruler is 0.1 in., the person using theruler has bad eyesight, or one side of the paper is slightly longer than the other. At any rate, the uncertainty in a measurement must be based on acareful consideration of all the factors that might contribute and their possible effects.

Making Connections: Real-World Connections – Fevers or Chills?

Uncertainty is a critical piece of information, both in physics and in many other real-world applications. Imagine you are caring for a sick child.You suspect the child has a fever, so you check his or her temperature with a thermometer. What if the uncertainty of the thermometer were3.0°C ? If the child’s temperature reading was 37.0°C (which is normal body temperature), the “true” temperature could be anywhere from a

hypothermic 34.0°C to a dangerously high 40.0°C . A thermometer with an uncertainty of 3.0°C would be useless.

Percent Uncertainty

One method of expressing uncertainty is as a percent of the measured value. If a measurement A is expressed with uncertainty, δA , the percentuncertainty (%unc) is defined to be

(1.8)% unc =δAA ×100%.

CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS 25

Example 1.2 Calculating Percent Uncertainty: A Bag of Apples

A grocery store sells 5-lb bags of apples. You purchase four bags over the course of a month and weigh the apples each time. You obtain thefollowing measurements:

• Week 1 weight: 4.8 lb• Week 2 weight: 5.3 lb• Week 3 weight: 4.9 lb• Week 4 weight: 5.4 lb

You determine that the weight of the 5-lb bag has an uncertainty of ±0.4 lb . What is the percent uncertainty of the bag’s weight?

Strategy

First, observe that the expected value of the bag’s weight, A , is 5 lb. The uncertainty in this value, δA , is 0.4 lb. We can use the followingequation to determine the percent uncertainty of the weight:

(1.9)% unc =δAA ×100%.

Solution

Plug the known values into the equation:

(1.10)% unc =0.4 lb5 lb ×100% = 8%.

Discussion

We can conclude that the weight of the apple bag is 5 lb ± 8% . Consider how this percent uncertainty would change if the bag of apples were

half as heavy, but the uncertainty in the weight remained the same. Hint for future calculations: when calculating percent uncertainty, alwaysremember that you must multiply the fraction by 100%. If you do not do this, you will have a decimal quantity, not a percent value.

Uncertainties in Calculations

There is an uncertainty in anything calculated from measured quantities. For example, the area of a floor calculated from measurements of its lengthand width has an uncertainty because the length and width have uncertainties. How big is the uncertainty in something you calculate by multiplicationor division? If the measurements going into the calculation have small uncertainties (a few percent or less), then the method of adding percents canbe used for multiplication or division. This method says that the percent uncertainty in a quantity calculated by multiplication or division is the sum ofthe percent uncertainties in the items used to make the calculation . For example, if a floor has a length of 4.00 m and a width of 3.00 m , with

uncertainties of 2% and 1% , respectively, then the area of the floor is 12.0 m2 and has an uncertainty of 3% . (Expressed as an area this is

0.36 m2 , which we round to 0.4 m2 since the area of the floor is given to a tenth of a square meter.)

Check Your Understanding

A high school track coach has just purchased a new stopwatch. The stopwatch manual states that the stopwatch has an uncertainty of ±0.05 s. Runners on the track coach’s team regularly clock 100-m sprints of 11.49 s to 15.01 s . At the school’s last track meet, the first-place sprinter

came in at 12.04 s and the second-place sprinter came in at 12.07 s . Will the coach’s new stopwatch be helpful in timing the sprint team?Why or why not?

SolutionNo, the uncertainty in the stopwatch is too great to effectively differentiate between the sprint times.

Precision of Measuring Tools and Significant FiguresAn important factor in the accuracy and precision of measurements involves the precision of the measuring tool. In general, a precise measuring toolis one that can measure values in very small increments. For example, a standard ruler can measure length to the nearest millimeter, while a calipercan measure length to the nearest 0.01 millimeter. The caliper is a more precise measuring tool because it can measure extremely small differencesin length. The more precise the measuring tool, the more precise and accurate the measurements can be.

When we express measured values, we can only list as many digits as we initially measured with our measuring tool. For example, if you use astandard ruler to measure the length of a stick, you may measure it to be 36.7 cm . You could not express this value as 36.71 cm because yourmeasuring tool was not precise enough to measure a hundredth of a centimeter. It should be noted that the last digit in a measured value has beenestimated in some way by the person performing the measurement. For example, the person measuring the length of a stick with a ruler notices thatthe stick length seems to be somewhere in between 36.6 cm and 36.7 cm , and he or she must estimate the value of the last digit. Using themethod of significant figures , the rule is that the last digit written down in a measurement is the first digit with some uncertainty . In order todetermine the number of significant digits in a value, start with the first measured value at the left and count the number of digits through the last digitwritten on the right. For example, the measured value 36.7 cm has three digits, or significant figures. Significant figures indicate the precision of ameasuring tool that was used to measure a value.

26 CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS

Zeros

Special consideration is given to zeros when counting significant figures. The zeros in 0.053 are not significant, because they are only placekeepersthat locate the decimal point. There are two significant figures in 0.053. The zeros in 10.053 are not placekeepers but are significant—this numberhas five significant figures. The zeros in 1300 may or may not be significant depending on the style of writing numbers. They could mean the numberis known to the last digit, or they could be placekeepers. So 1300 could have two, three, or four significant figures. (To avoid this ambiguity, write1300 in scientific notation.) Zeros are significant except when they serve only as placekeepers .

Check Your Understanding

Determine the number of significant figures in the following measurements:

a. 0.0009b. 15,450.0

c. 6×103

d. 87.990e. 30.42

Solution

(a) 1; the zeros in this number are placekeepers that indicate the decimal point

(b) 6; here, the zeros indicate that a measurement was made to the 0.1 decimal point, so the zeros are significant

(c) 1; the value 103 signifies the decimal place, not the number of measured values

(d) 5; the final zero indicates that a measurement was made to the 0.001 decimal point, so it is significant

(e) 4; any zeros located in between significant figures in a number are also significant

Significant Figures in Calculations

When combining measurements with different degrees of accuracy and precision, the number of significant digits in the final answer can be nogreater than the number of significant digits in the least precise measured value . There are two different rules, one for multiplication and division andthe other for addition and subtraction, as discussed below.

1. For multiplication and division: The result should have the same number of significant figures as the quantity having the least significant figures

entering into the calculation . For example, the area of a circle can be calculated from its radius using A= πr2 . Let us see how many significant

figures the area has if the radius has only two—say, r = 1.2 m . Then,

(1.11)A= πr2 = (3.1415927...)×(1.2 m)2 = 4.5238934 m2

is what you would get using a calculator that has an eight-digit output. But because the radius has only two significant figures, it limits the calculatedquantity to two significant figures or

(1.12)A=4.5 m2,

even though π is good to at least eight digits.

2. For addition and subtraction: The answer can contain no more decimal places than the least precise measurement . Suppose that you buy7.56-kg of potatoes in a grocery store as measured with a scale with precision 0.01 kg. Then you drop off 6.052-kg of potatoes at your laboratory asmeasured by a scale with precision 0.001 kg. Finally, you go home and add 13.7 kg of potatoes as measured by a bathroom scale with precision 0.1kg. How many kilograms of potatoes do you now have, and how many significant figures are appropriate in the answer? The mass is found by simpleaddition and subtraction:

(1.13)7.56 kg- 6.052 kg+13.7 kg

15.208 kg = 15.2 kg.

Next, we identify the least precise measurement: 13.7 kg. This measurement is expressed to the 0.1 decimal place, so our final answer must also beexpressed to the 0.1 decimal place. Thus, the answer is rounded to the tenths place, giving us 15.2 kg.

Significant Figures in this Text

In this text, most numbers are assumed to have three significant figures. Furthermore, consistent numbers of significant figures are used in all workedexamples. You will note that an answer given to three digits is based on input good to at least three digits, for example. If the input has fewersignificant figures, the answer will also have fewer significant figures. Care is also taken that the number of significant figures is reasonable for thesituation posed. In some topics, particularly in optics, more accurate numbers are needed and more than three significant figures will be used. Finally,if a number is exact , such as the two in the formula for the circumference of a circle, c= 2πr , it does not affect the number of significant figures in acalculation.

Check Your Understanding

Perform the following calculations and express your answer using the correct number of significant digits.

CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS 27

(a) A woman has two bags weighing 13.5 pounds and one bag with a weight of 10.2 pounds. What is the total weight of the bags?

(b) The force F on an object is equal to its mass m multiplied by its acceleration a . If a wagon with mass 55 kg accelerates at a rate of

0.0255 m/s2 , what is the force on the wagon? (The unit of force is called the newton, and it is expressed with the symbol N.)

Solution

(a) 37.2 pounds; Because the number of bags is an exact value, it is not considered in the significant figures.

(b) 1.4 N; Because the value 55 kg has only two significant figures, the final value must also contain two significant figures.

Estimation

Explore size estimation in one, two, and three dimensions! Multiple levels of difficulty allow for progressive skill improvement.

Figure 1.26 Estimation (http://cnx.org/content/m42120/1.3/estimation_en.jar)

1.4 ApproximationOn many occasions, physicists, other scientists, and engineers need to make approximations or “guesstimates” for a particular quantity. What is thedistance to a certain destination? What is the approximate density of a given item? About how large a current will there be in a circuit? Manyapproximate numbers are based on formulae in which the input quantities are known only to a limited accuracy. As you develop problem-solving skills(that can be applied to a variety of fields through a study of physics), you will also develop skills at approximating. You will develop these skillsthrough thinking more quantitatively, and by being willing to take risks. As with any endeavor, experience helps, as well as familiarity with units. Theseapproximations allow us to rule out certain scenarios or unrealistic numbers. Approximations also allow us to challenge others and guide us in ourapproaches to our scientific world. Let us do two examples to illustrate this concept.

Example 1.3 Approximate the Height of a Building

Can you approximate the height of one of the buildings on your campus, or in your neighborhood? Let us make an approximation based uponthe height of a person. In this example, we will calculate the height of a 39-story building.

Strategy

Think about the average height of an adult male. We can approximate the height of the building by scaling up from the height of a person.

Solution

Based on information in the example, we know there are 39 stories in the building. If we use the fact that the height of one story is approximatelyequal to about the length of two adult humans (each human is about 2-m tall), then we can estimate the total height of the building to be

(1.14)2 m1 person×2 person

1 story ×39 stories = 156 m.

Discussion

You can use known quantities to determine an approximate measurement of unknown quantities. If your hand measures 10 cm across, howmany hand lengths equal the width of your desk? What other measurements can you approximate besides length?

28 CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS

Example 1.4 Approximating Vast Numbers: a Trillion Dollars

Figure 1.27 A bank stack contains one-hundred $100 bills, and is worth $10,000. How many bank stacks make up a trillion dollars? (credit: Andrew Magill)

The U.S. federal deficit in the 2008 fiscal year was a little greater than $10 trillion. Most of us do not have any concept of how much even onetrillion actually is. Suppose that you were given a trillion dollars in $100 bills. If you made 100-bill stacks and used them to evenly cover a footballfield (between the end zones), make an approximation of how high the money pile would become. (We will use feet/inches rather than metershere because football fields are measured in yards.) One of your friends says 3 in., while another says 10 ft. What do you think?

Strategy

When you imagine the situation, you probably envision thousands of small stacks of 100 wrapped $100 bills, such as you might see in movies orat a bank. Since this is an easy-to-approximate quantity, let us start there. We can find the volume of a stack of 100 bills, find out how manystacks make up one trillion dollars, and then set this volume equal to the area of the football field multiplied by the unknown height.

Solution

(1) Calculate the volume of a stack of 100 bills. The dimensions of a single bill are approximately 3 in. by 6 in. A stack of 100 of these is about0.5 in. thick. So the total volume of a stack of 100 bills is:

(1.15)volume of stack = length×width×height,volume of stack = 6 in.×3 in.×0.5 in.,volume of stack = 9 in.3 .

(2) Calculate the number of stacks. Note that a trillion dollars is equal to $1×1012 , and a stack of one-hundred $100 bills is equal to

$10,000, or $1×104 . The number of stacks you will have is:

(1.16)$1×1012(a trillion dollars)/ $1×104 per stack = 1×108 stacks.

(3) Calculate the area of a football field in square inches. The area of a football field is 100 yd×50 yd , which gives 5,000 yd2 . Because we

are working in inches, we need to convert square yards to square inches:

(1.17)Area = 5,000 yd2× 3 ft1 yd× 3 ft

1 yd×12 in.1 ft ×12 in.

1 ft = 6,480,000 in.2 ,

Area ≈ 6×106 in.2 .

This conversion gives us 6×106in.2 for the area of the field. (Note that we are using only one significant figure in these calculations.)

(4) Calculate the total volume of the bills. The volume of all the $100 -bill stacks is 9 in.3 / stack×108 stacks = 9×108 in.3 .

(5) Calculate the height. To determine the height of the bills, use the equation:

(1.18)volume of bills = area of field×height of money:

Height of money = volume of billsarea of field ,

Height of money = 9×108in.3

6×106in.2 = 1.33×102 in.,

Height of money ≈ 1×102 in. = 100 in.

The height of the money will be about 100 in. high. Converting this value to feet gives

(1.19)100 in.× 1 ft12 in. = 8.33 ft ≈ 8 ft.

Discussion

CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS 29

accuracy :

approximation :

classical physics :

conversion factor :

derived units :

English units :

fundamental units :

kilogram :

law :

meter :

method of adding percents :

metric system :

model :

modern physics :

order of magnitude :

percent uncertainty :

physical quantity :

physics :

precision :

quantum mechanics :

relativity :

SI units :

scientific method :

second :

significant figures :

theory :

uncertainty :

The final approximate value is much higher than the early estimate of 3 in., but the other early estimate of 10 ft (120 in.) was roughly correct.How did the approximation measure up to your first guess? What can this exercise tell you in terms of rough “guesstimates” versus carefullycalculated approximations?

Check Your Understanding

Using mental math and your understanding of fundamental units, approximate the area of a regulation basketball court. Describe the processyou used to arrive at your final approximation.

SolutionAn average male is about two meters tall. It would take approximately 15 men laid out end to end to cover the length, and about 7 to cover the

width. That gives an approximate area of 420 m2 .

Glossarythe degree to which a measured value agrees with correct value for that measurement

an estimated value based on prior experience and reasoning

physics that was developed from the Renaissance to the end of the 19th century

a ratio expressing how many of one unit are equal to another unit

units that can be calculated using algebraic combinations of the fundamental units

system of measurement used in the United States; includes units of measurement such as feet, gallons, and pounds

units that can only be expressed relative to the procedure used to measure them

the SI unit for mass, abbreviated (kg)

a description, using concise language or a mathematical formula, a generalized pattern in nature that is supported by scientific evidence andrepeated experiments

the SI unit for length, abbreviated (m)

the percent uncertainty in a quantity calculated by multiplication or division is the sum of the percent uncertainties inthe items used to make the calculation

a system in which values can be calculated in factors of 10

representation of something that is often too difficult (or impossible) to display directly

the study of relativity, quantum mechanics, or both

refers to the size of a quantity as it relates to a power of 10

the ratio of the uncertainty of a measurement to the measured value, expressed as a percentage.

a characteristic or property of an object that can be measured or calculated from other measurements

the science concerned with describing the interactions of energy, matter, space, and time; it is especially interested in what fundamentalmechanisms underlie every phenomenon

the degree to which repeated measurements agree with each other

the study of objects smaller than can be seen with a microscope

the study of objects moving at speeds greater than about 1% of the speed of light, or of objects being affected by a strong gravitationalfield

the international system of units that scientists in most countries have agreed to use; includes units such as meters, liters, and grams

a method that typically begins with an observation and question that the scientist will research; next, the scientist typicallyperforms some research about the topic and then devises a hypothesis; then, the scientist will test the hypothesis by performing anexperiment; finally, the scientist analyzes the results of the experiment and draws a conclusion

the SI unit for time, abbreviated (s)

express the precision of a measuring tool used to measure a value

an explanation for patterns in nature that is supported by scientific evidence and verified multiple times by various groups of researchers

a quantitative measure of how much your measured values deviate from a standard or expected value

30 CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS

units : a standard used for expressing and comparing measurements

Section Summary

1.1 Physics: An Introduction• Science seeks to discover and describe the underlying order and simplicity in nature.• Physics is the most basic of the sciences, concerning itself with energy, matter, space and time, and their interactions.• Scientific laws and theories express the general truths of nature and the body of knowledge they encompass. These laws of nature are rules

that all natural processes appear to follow.

1.2 Physical Quantities and Units• Physical quantities are a characteristic or property of an object that can be measured or calculated from other measurements.• Units are standards for expressing and comparing the measurement of physical quantities. All units can be expressed as combinations of four

fundamental units.• The four fundamental units we will use in this text are the meter (for length), the kilogram (for mass), the second (for time), and the coulomb (for

electric charge). These units are part of the metric system, which uses powers of 10 to relate quantities over the vast ranges encountered innature.

• The four fundamental units are abbreviated as follows: meter, m; kilogram, kg; second, s; and coulomb, C. The metric system also uses astandard set of prefixes to denote each order of magnitude greater than or lesser than the fundamental unit itself.

• Unit conversions involve changing a value expressed in one type of unit to another type of unit. This is done by using conversion factors, whichare ratios relating equal quantities of different units.

1.3 Accuracy, Precision, and Significant Figures• Accuracy of a measured value refers to how close a measurement is to the correct value. The uncertainty in a measurement is an estimate of

the amount by which the measurement result may differ from this value.• Precision of measured values refers to how close the agreement is between repeated measurements.• The precision of a measuring tool is related to the size of its measurement increments. The smaller the measurement increment, the more

precise the tool.• Significant figures express the precision of a measuring tool.• When multiplying or dividing measured values, the final answer can contain only as many significant figures as the least precise value.• When adding or subtracting measured values, the final answer cannot contain more decimal places than the least precise value.

1.4 ApproximationScientists often approximate the values of quantities to perform calculations and analyze systems.

Conceptual Questions

1.1 Physics: An Introduction1. Models are particularly useful in relativity and quantum mechanics, where conditions are outside those normally encountered by humans. What is amodel?

2. How does a model differ from a theory?

3. If two different theories describe experimental observations equally well, can one be said to be more valid than the other (assuming both useaccepted rules of logic)?

4. What determines the validity of a theory?

5. Certain criteria must be satisfied if a measurement or observation is to be believed. Will the criteria necessarily be as strict for an expected resultas for an unexpected result?

6. Can the validity of a model be limited, or must it be universally valid? How does this compare to the required validity of a theory or a law?

7. Classical physics is a good approximation to modern physics under certain circumstances. What are they?

8. When is it necessary to use relativistic quantum mechanics?

9. Can classical physics be used to accurately describe a satellite moving at a speed of 7500 m/s? Explain why or why not.

1.2 Physical Quantities and Units10. Identify some advantages of metric units.

1.3 Accuracy, Precision, and Significant Figures11. What is the relationship between the accuracy and uncertainty of a measurement?

12. Prescriptions for vision correction are given in units called diopters (D). Determine the meaning of that unit. Obtain information (perhaps by callingan optometrist or performing an internet search) on the minimum uncertainty with which corrections in diopters are determined and the accuracy withwhich corrective lenses can be produced. Discuss the sources of uncertainties in both the prescription and accuracy in the manufacture of lenses.

CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS 31

Problems & Exercises

1.2 Physical Quantities and Units1. The speed limit on some interstate highways is roughly 100 km/h. (a)What is this in meters per second? (b) How many miles per hour is this?

2. A car is traveling at a speed of 33 m/s . (a) What is its speed in

kilometers per hour? (b) Is it exceeding the 90 km/h speed limit?

3. Show that 1.0 m/s = 3.6 km/h . Hint: Show the explicit steps involved

in converting 1.0 m/s = 3.6 km/h .

4. American football is played on a 100-yd-long field, excluding the endzones. How long is the field in meters? (Assume that 1 meter equals3.281 feet.)

5. Soccer fields vary in size. A large soccer field is 115 m long and 85 mwide. What are its dimensions in feet and inches? (Assume that 1 meterequals 3.281 feet.)

6. What is the height in meters of a person who is 6 ft 1.0 in. tall?(Assume that 1 meter equals 39.37 in.)

7. Mount Everest, at 29,028 feet, is the tallest mountain on the Earth.What is its height in kilometers? (Assume that 1 kilometer equals 3,281feet.)

8. The speed of sound is measured to be 342 m/s on a certain day.What is this in km/h?

9. Tectonic plates are large segments of the Earth’s crust that moveslowly. Suppose that one such plate has an average speed of 4.0 cm/year. (a) What distance does it move in 1 s at this speed? (b) What is itsspeed in kilometers per million years?

10. (a) Refer to Table 1.3 to determine the average distance between theEarth and the Sun. Then calculate the average speed of the Earth in itsorbit in kilometers per second. (b) What is this in meters per second?

1.3 Accuracy, Precision, and Significant FiguresExpress your answers to problems in this section to the correctnumber of significant figures and proper units.

11. Suppose that your bathroom scale reads your mass as 65 kg with a 3uncertainty. What is the uncertainty in your mass (in kilograms)?

12. A good-quality measuring tape can be off by 0.50 cm over a distanceof 20 m. What is its percent uncertainty?

13. (a) A car speedometer has a 5.0% uncertainty. What is the range of

possible speeds when it reads 90 km/h ? (b) Convert this range to miles

per hour. (1 km = 0.6214 mi)

14. An infant’s pulse rate is measured to be 130 ± 5 beats/min. What is

the percent uncertainty in this measurement?

15. (a) Suppose that a person has an average heart rate of 72.0 beats/min. How many beats does he or she have in 2.0 y? (b) In 2.00 y? (c) In2.000 y?

16. A can contains 375 mL of soda. How much is left after 308 mL isremoved?

17. State how many significant figures are proper in the results of the

following calculations: (a) (106.7)(98.2) / (46.210)(1.01) (b) (18.7)2

(c) ⎛⎝1.60×10−19⎞⎠(3712) .

18. (a) How many significant figures are in the numbers 99 and 100? (b)If the uncertainty in each number is 1, what is the percent uncertainty ineach? (c) Which is a more meaningful way to express the accuracy ofthese two numbers, significant figures or percent uncertainties?

19. (a) If your speedometer has an uncertainty of 2.0 km/h at a speed

of 90 km/h , what is the percent uncertainty? (b) If it has the same

percent uncertainty when it reads 60 km/h , what is the range of speedsyou could be going?

20. (a) A person’s blood pressure is measured to be 120 ± 2 mm Hg .

What is its percent uncertainty? (b) Assuming the same percentuncertainty, what is the uncertainty in a blood pressure measurement of80 mm Hg ?

21. A person measures his or her heart rate by counting the number ofbeats in 30 s . If 40 ± 1 beats are counted in 30.0 ± 0.5 s , what is

the heart rate and its uncertainty in beats per minute?

22. What is the area of a circle 3.102 cm in diameter?

23. If a marathon runner averages 9.5 mi/h, how long does it take him orher to run a 26.22-mi marathon?

24. A marathon runner completes a 42.188-km course in 2 h , 30 min,

and 12 s . There is an uncertainty of 25 m in the distance traveled andan uncertainty of 1 s in the elapsed time. (a) Calculate the percentuncertainty in the distance. (b) Calculate the uncertainty in the elapsedtime. (c) What is the average speed in meters per second? (d) What isthe uncertainty in the average speed?

25. The sides of a small rectangular box are measured to be1.80 ± 0.01 cm , 2.05 ± 0.02 cm, and 3.1 ± 0.1 cm long.

Calculate its volume and uncertainty in cubic centimeters.

26. When non-metric units were used in the United Kingdom, a unit ofmass called the pound-mass (lbm) was employed, where1 lbm = 0.4539 kg . (a) If there is an uncertainty of 0.0001 kg in the

pound-mass unit, what is its percent uncertainty? (b) Based on thatpercent uncertainty, what mass in pound-mass has an uncertainty of 1 kgwhen converted to kilograms?

27. The length and width of a rectangular room are measured to be3.955 ± 0.005 m and 3.050 ± 0.005 m . Calculate the area of the

room and its uncertainty in square meters.

28. A car engine moves a piston with a circular cross section of7.500 ± 0.002 cm diameter a distance of 3.250 ± 0.001 cm to

compress the gas in the cylinder. (a) By what amount is the gasdecreased in volume in cubic centimeters? (b) Find the uncertainty in thisvolume.

1.4 Approximation29. How many heartbeats are there in a lifetime?

30. A generation is about one-third of a lifetime. Approximately how manygenerations have passed since the year 0 AD?

31. How many times longer than the mean life of an extremely unstableatomic nucleus is the lifetime of a human? (Hint: The lifetime of an

unstable atomic nucleus is on the order of 10−22 s .)

32. Calculate the approximate number of atoms in a bacterium. Assumethat the average mass of an atom in the bacterium is ten times the massof a hydrogen atom. (Hint: The mass of a hydrogen atom is on the order

of 10−27 kg and the mass of a bacterium is on the order of 10−15 kg.)

32 CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS

Figure 1.28 This color-enhanced photo shows Salmonella typhimurium (red)attacking human cells. These bacteria are commonly known for causing foodborneillness. Can you estimate the number of atoms in each bacterium? (credit: RockyMountain Laboratories, NIAID, NIH)

33. Approximately how many atoms thick is a cell membrane, assumingall atoms there average about twice the size of a hydrogen atom?

34. (a) What fraction of Earth’s diameter is the greatest ocean depth? (b)The greatest mountain height?

35. (a) Calculate the number of cells in a hummingbird assuming themass of an average cell is ten times the mass of a bacterium. (b) Makingthe same assumption, how many cells are there in a human?

36. Assuming one nerve impulse must end before another can begin,what is the maximum firing rate of a nerve in impulses per second?

CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS 33

34 CHAPTER 1 | INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS

2 KINEMATICSLearning Objectives

2.1 Introduction to One-Dimensional Kinematics2.2 Displacement2.3 Vectors, Scalars, and Coordinate Systems2.4 Time, Velocity, and Speed2.5 Acceleration2.6 Motion Equations for Constant Acceleration in One Dimension2.7 Problem-Solving Basics for One-Dimensional Kinematics2.8 Falling Objects2.9 Graphical Analysis of One-Dimensional Motion

2.1 Introduction to One-Dimensional Kinematics

2.2 Displacement

2.3 Vectors, Scalars, and Coordinate Systems

2.4 Time, Velocity, and Speed

2.5 Acceleration

2.6 Motion Equations for Constant Acceleration in One Dimension

2.7 Problem-Solving Basics for One-Dimensional Kinematics

2.8 Falling Objects

2.9 Graphical Analysis of One-Dimensional Motion

CHAPTER 2 | KINEMATICS 35

36 CHAPTER 2 | KINEMATICS

3 TWO-DIMENSIONAL KINEMATICSLearning Objectives

3.1 Introduction to Two-Dimensional Kinematics3.2 Kinematics in Two Dimensions: An Introduction3.3 Vector Addition and Subtraction: Graphical Methods3.4 Vector Addition and Subtraction: Analytical Methods3.5 Projectile Motion3.6 Addition of Velocities

3.1 Introduction to Two-Dimensional Kinematics

3.2 Kinematics in Two Dimensions: An Introduction

3.3 Vector Addition and Subtraction: Graphical Methods

3.4 Vector Addition and Subtraction: Analytical Methods

3.5 Projectile Motion

3.6 Addition of Velocities

CHAPTER 3 | TWO-DIMENSIONAL KINEMATICS 37

38 CHAPTER 3 | TWO-DIMENSIONAL KINEMATICS

4 DYNAMICS: FORCE AND NEWTON'S LAWS OFMOTION

Learning Objectives4.1 Introduction to Dynamics: Newton's Laws of Motion4.2 Development of Force Concept4.3 Newton’s First Law of Motion: Inertia4.4 Newton’s Second Law of Motion: Concept of a System4.5 Newton’s Third Law of Motion: Symmetry in Forces4.6 Normal, Tension, and Other Examples of Forces4.7 Problem-Solving Strategies4.8 Further Applications of Newton’s Laws of Motion4.9 Extended Topic: The Four Basic Forces—An Introduction

4.1 Introduction to Dynamics: Newton's Laws of Motion

4.2 Development of Force Concept

4.3 Newton’s First Law of Motion: Inertia

4.4 Newton’s Second Law of Motion: Concept of a System

4.5 Newton’s Third Law of Motion: Symmetry in Forces

4.6 Normal, Tension, and Other Examples of Forces

4.7 Problem-Solving Strategies

4.8 Further Applications of Newton’s Laws of Motion

4.9 Extended Topic: The Four Basic Forces—An Introduction

CHAPTER 4 | DYNAMICS: FORCE AND NEWTON'S LAWS OF MOTION 39

40 CHAPTER 4 | DYNAMICS: FORCE AND NEWTON'S LAWS OF MOTION

5 FURTHER APPLICATIONS OF NEWTON'S LAWS:FRICTION, DRAG, AND ELASTICITY

Learning Objectives5.1 Introduction: Further Applications of Newton’s Laws5.2 Friction5.3 Drag Forces5.4 Elasticity: Stress and Strain

5.1 Introduction: Further Applications of Newton’s Laws

5.2 Friction

5.3 Drag Forces

5.4 Elasticity: Stress and Strain

CHAPTER 5 | FURTHER APPLICATIONS OF NEWTON'S LAWS: FRICTION, DRAG, AND ELASTICITY 41

42 CHAPTER 5 | FURTHER APPLICATIONS OF NEWTON'S LAWS: FRICTION, DRAG, AND ELASTICITY

6 UNIFORM CIRCULAR MOTION AND GRAVITATIONLearning Objectives

6.1 Introduction to Uniform Circular Motion and Gravitation6.2 Rotation Angle and Angular Velocity6.3 Centripetal Acceleration6.4 Centripetal Force6.5 Fictitious Forces and Non-inertial Frames: The Corioluis Force6.6 Newton’s Universal Law of Gravitation6.7 Satellites and Kepler’s Laws: An Argument for Simplicity

6.1 Introduction to Uniform Circular Motion and Gravitation

6.2 Rotation Angle and Angular Velocity

6.3 Centripetal Acceleration

6.4 Centripetal Force

6.5 Fictitious Forces and Non-inertial Frames: The Corioluis Force

6.6 Newton’s Universal Law of Gravitation

6.7 Satellites and Kepler’s Laws: An Argument for Simplicity

CHAPTER 6 | UNIFORM CIRCULAR MOTION AND GRAVITATION 43

44 CHAPTER 6 | UNIFORM CIRCULAR MOTION AND GRAVITATION

7 WORK, ENERGY, AND ENERGY RESOURCESLearning Objectives

7.1 Introduction to Work, Energy, and Energy Resources7.2 Work: The Scientific Definition7.3 Kinetic Energy and the Work-Energy Theorem7.4 Gravitational Potential Energy7.5 Conservative Forces and Potential Energy7.6 Nonconservative Forces7.7 Conservation of Energy7.8 Power7.9 Work, Energy, and Power in Humans7.10 World Energy Use

7.1 Introduction to Work, Energy, and Energy Resources

7.2 Work: The Scientific Definition

7.3 Kinetic Energy and the Work-Energy Theorem

7.4 Gravitational Potential Energy

7.5 Conservative Forces and Potential Energy

7.6 Nonconservative Forces

7.7 Conservation of Energy

7.8 Power

7.9 Work, Energy, and Power in Humans

7.10 World Energy Use

CHAPTER 7 | WORK, ENERGY, AND ENERGY RESOURCES 45

46 CHAPTER 7 | WORK, ENERGY, AND ENERGY RESOURCES

8 LINEAR MOMENTUM AND COLLISIONSLearning Objectives

8.1 Introduction to Linear Momentum and Collisions8.2 Linear Momentum and Force8.3 Impulse8.4 Conservation of Momentum8.5 Elastic Collisions in One Dimension8.6 Inelastic Collisions in One Dimension8.7 Collisions of Point Masses in Two Dimensions8.8 Introduction to Rocket Propulsion

8.1 Introduction to Linear Momentum and Collisions

8.2 Linear Momentum and Force

8.3 Impulse

8.4 Conservation of Momentum

8.5 Elastic Collisions in One Dimension

8.6 Inelastic Collisions in One Dimension

8.7 Collisions of Point Masses in Two Dimensions

8.8 Introduction to Rocket Propulsion

CHAPTER 8 | LINEAR MOMENTUM AND COLLISIONS 47

48 CHAPTER 8 | LINEAR MOMENTUM AND COLLISIONS

9 STATICS AND TORQUELearning Objectives

9.1 Introduction to Statics and Torque9.2 The First Condition for Equilibrium9.3 The Second Condition for Equilibrium9.4 Stability9.5 Applications of Statistics, Including Problem-Solving Strategies9.6 Simple Machines9.7 Forces and Torques in Muscles and Joints

9.1 Introduction to Statics and Torque

9.2 The First Condition for Equilibrium

9.3 The Second Condition for Equilibrium

9.4 Stability

9.5 Applications of Statistics, Including Problem-Solving Strategies

9.6 Simple Machines

9.7 Forces and Torques in Muscles and Joints

CHAPTER 9 | STATICS AND TORQUE 49

50 CHAPTER 9 | STATICS AND TORQUE

10 ROTATIONAL MOTION AND ANGULARMOMENTUM

Learning Objectives10.1 Introduction to Rotational Motion and Angular Momentum10.2 Angular Acceleration10.3 Kinematics of Rotational Motion10.4 Dynamics of Rotational Motion: Rotational Inertia10.5 Rotational Kinetic Energy: Work-Energy Revisited10.6 Angular Momentum and Its Conservation10.7 Collisions of Extended Bodies in Two Dimensions10.8 Gyroscopic Effects: Vector Aspects of Angular Momentum

10.1 Introduction to Rotational Motion and Angular Momentum

10.2 Angular Acceleration

10.3 Kinematics of Rotational Motion

10.4 Dynamics of Rotational Motion: Rotational Inertia

10.5 Rotational Kinetic Energy: Work-Energy Revisited

10.6 Angular Momentum and Its Conservation

10.7 Collisions of Extended Bodies in Two Dimensions

10.8 Gyroscopic Effects: Vector Aspects of Angular Momentum

CHAPTER 10 | ROTATIONAL MOTION AND ANGULAR MOMENTUM 51

52 CHAPTER 10 | ROTATIONAL MOTION AND ANGULAR MOMENTUM

11 FLUID STATICSLearning Objectives

11.1 Introduction to Fluid Statics11.2 What Is a Fluid?11.3 Density11.4 Pressure11.5 Variation of Pressure with Depth in a Fluid11.6 Pascal’s Principle11.7 Gauge Pressure, Absolute Pressure, and Pressure Measurement11.8 Archimedes’ Principle11.9 Cohesion and Adhesion in Liquids: Surface Tension and Capillary Action11.10 Pressures in the Body

11.1 Introduction to Fluid Statics

11.2 What Is a Fluid?

11.3 Density

11.4 Pressure

11.5 Variation of Pressure with Depth in a Fluid

11.6 Pascal’s Principle

11.7 Gauge Pressure, Absolute Pressure, and Pressure Measurement

11.8 Archimedes’ Principle

11.9 Cohesion and Adhesion in Liquids: Surface Tension and Capillary Action

11.10 Pressures in the Body

CHAPTER 11 | FLUID STATICS 53

54 CHAPTER 11 | FLUID STATICS

12 FLUID DYNAMICS AND ITS BIOLOGICAL ANDMEDICAL APPLICATIONS

Learning Objectives12.1 Introduction to Fluid Dynamics and Its Biological and Medical Applications12.2 Flow Rate and Its Relation to Velocity12.3 Bernoulli’s Equation12.4 The Most General Applications of Bernoulli’s Equation12.5 Viscosity and Laminar Flow: Poiseuille’s Law12.6 The Onset of Turbulence12.7 Motion of an Object in a Viscous Fluid12.8 Molecular Transport Phenomena: Diffusion, Osmosis, and Related Processes

12.1 Introduction to Fluid Dynamics and Its Biological and Medical Applications

12.2 Flow Rate and Its Relation to Velocity

12.3 Bernoulli’s Equation

12.4 The Most General Applications of Bernoulli’s Equation

12.5 Viscosity and Laminar Flow: Poiseuille’s Law

12.6 The Onset of Turbulence

12.7 Motion of an Object in a Viscous Fluid

12.8 Molecular Transport Phenomena: Diffusion, Osmosis, and Related Processes

CHAPTER 12 | FLUID DYNAMICS AND ITS BIOLOGICAL AND MEDICAL APPLICATIONS 55

56 CHAPTER 12 | FLUID DYNAMICS AND ITS BIOLOGICAL AND MEDICAL APPLICATIONS

13 TEMPERATURE, KINETIC THEORY, AND THEGAS LAWS

Learning Objectives13.1 Introduction to Temperature, Kinetic Theory, and the Gas Laws13.2 Temperature13.3 Thermal Expansion of Solids and Liquids13.4 The Ideal Gas Law13.5 Kinetic Theory: Molecular Explanation of Pressure and Temperature13.6 Phase Changes13.7 Humidity, Evaporation, and Boiling

13.1 Introduction to Temperature, Kinetic Theory, and the Gas Laws

13.2 Temperature

13.3 Thermal Expansion of Solids and Liquids

13.4 The Ideal Gas Law

13.5 Kinetic Theory: Molecular Explanation of Pressure and Temperature

13.6 Phase Changes

13.7 Humidity, Evaporation, and Boiling

CHAPTER 13 | TEMPERATURE, KINETIC THEORY, AND THE GAS LAWS 57

58 CHAPTER 13 | TEMPERATURE, KINETIC THEORY, AND THE GAS LAWS

14 HEAT AND HEAT TRANSFER METHODS

Figure 14.1 (a) The chilling effect of a clear breezy night is produced by the wind and by radiative heat transfer to cold outer space. (b) There was once great controversyabout the Earth’s age, but it is now generally accepted to be about 4.5 billion years old. Much of the debate is centered on the Earth’s molten interior. According to ourunderstanding of heat transfer, if the Earth is really that old, its center should have cooled off long ago. The discovery of radioactivity in rocks revealed the source of energythat keeps the Earth’s interior molten, despite heat transfer to the surface, and from there to cold outer space.

Introduction to Heat and Heat Transfer MethodsEnergy can exist in many forms and heat is one of the most intriguing. Heat is often hidden, as it only exists when in transit, and is transferred by anumber of distinctly different methods. Heat transfer touches every aspect of our lives and helps us understand how the universe functions. Itexplains the chill we feel on a clear breezy night, or why Earth’s core has yet to cool. This chapter defines and explores heat transfer, its effects, andthe methods by which heat is transferred. These topics are fundamental, as well as practical, and will often be referred to in the chapters ahead.

CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS 59

Learning Objectives14.1 Heat

Define heat as transfer of energy.Explain Joule’s experiment.

14.2 Temperature Change and Heat CapacityObserve heat transfer and change in temperature and mass.Calculate temperature change due to work done and overheating.Study specific heats of various substances.Calculate final temperature after heat transfer between two objects.

14.3 Phase Change and Latent HeatExamine heat transfer.Calculate latent heat coefficients.Study heats of fusion, vaporization, and sublimation.Calculate final temperature from heat transfer.

14.4 Heat Transfer MethodsDiscuss the different methods of heat transfer.

14.5 ConductionCalculate thermal conductivity.Observe conduction of heat in collisions.Calculate heat transfer rate through conduction.Study thermal conductivities of common substances.Calculate the temperature difference maintained by the heat transfer.

14.6 ConvectionDiscuss the method of heat transfer by convection.Discuss the case of convection accompanied by a phase change.

14.7 RadiationDiscuss heat transfer by radiation.Explain the heat absorbing power of different materials.

14.1 HeatIn Work, Energy, and Energy Resources, we defined work as force times distance and learned that work done on an object changes its kineticenergy. We also saw in Temperature, Kinetic Theory, and the Gas Laws that temperature is proportional to the (average) kinetic energy of atomsand molecules. We say that a thermal system has a certain internal energy: its internal energy is higher if the temperature is higher. If two objects atdifferent temperatures are brought in contact with each other, energy is transferred from the hotter to the colder object until equilibrium is reached andthe bodies reach thermal equilibrium (i.e., they are at the same temperature). No work is done by either object, because no force acts through adistance. The transfer of energy is caused by the temperature difference, and ceases once the temperatures are equal. These observations lead tothe following definition of heat : Heat is the spontaneous transfer of energy due to a temperature difference.

As noted in Temperature, Kinetic Theory, and the Gas Laws, heat is often confused with temperature. For example, we may say the heat wasunbearable, when we actually mean that the temperature was high. Heat is a form of energy, whereas temperature is not. The misconception arisesbecause we are sensitive to the flow of heat, rather than the temperature.

Owing to the fact that heat is a form of energy, it has the SI unit of joule (J). The calorie (cal) is a common unit of energy, defined as the energyneeded to change the temperature of 1.00 g of water by 1.00°C —specifically, between 14.5°C and 15.5°C , since there is a slight temperaturedependence. Perhaps the most common unit of heat is the kilocalorie (kcal), which is the energy needed to change the temperature of 1.00 kg ofwater by 1.00°C . Since mass is most often specified in kilograms, kilocalorie is commonly used. Food calories (given the notation Cal, and

sometimes called “big calorie”) are actually kilocalories ( 1 kilocalorie = 1000 calories ), a fact not easily determined from package labeling.

Figure 14.2 In figure (a) the soft drink and the ice have different temperatures, T1 and T2 , and are not in thermal equilibrium. In figure (b), when the soft drink and ice are

allowed to interact, energy is transferred until they reach the same temperature T' , achieving equilibrium. Heat transfer occurs due to the difference in temperatures. In fact,since the soft drink and ice are both in contact with the surrounding air and bench, the equilibrium temperature will be the same for both.

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Mechanical Equivalent of HeatIt is also possible to change the temperature of a substance by doing work. Work can transfer energy into or out of a system. This realization helpedestablish the fact that heat is a form of energy. James Prescott Joule (1818–1889) performed many experiments to establish the mechanicalequivalent of heat —the work needed to produce the same effects as heat transfer. In terms of the units used for these two terms, the best modernvalue for this equivalence is

(14.1)1.000 kcal = 4186 J.We consider this equation as the conversion between two different units of energy.

Figure 14.3 Schematic depiction of Joule’s experiment that established the equivalence of heat and work.

The figure above shows one of Joule’s most famous experimental setups for demonstrating the mechanical equivalent of heat. It demonstrated thatwork and heat can produce the same effects, and helped establish the principle of conservation of energy. Gravitational potential energy (PE) (workdone by the gravitational force) is converted into kinetic energy (KE), and then randomized by viscosity and turbulence into increased average kineticenergy of atoms and molecules in the system, producing a temperature increase. His contributions to the field of thermodynamics were so significantthat the SI unit of energy was named after him.

Heat added or removed from a system changes its internal energy and thus its temperature. Such a temperature increase is observed while cooking.However, adding heat does not necessarily increase the temperature. An example is melting of ice; that is, when a substance changes from onephase to another. Work done on the system or by the system can also change the internal energy of the system. Joule demonstrated that thetemperature of a system can be increased by stirring. If an ice cube is rubbed against a rough surface, work is done by the frictional force. A systemhas a well-defined internal energy, but we cannot say that it has a certain “heat content” or “work content”. We use the phrase “heat transfer” toemphasize its nature.

Check Your Understanding

Two samples (A and B) of the same substance are kept in a lab. Someone adds 10 kilojoules (kJ) of heat to one sample, while 10 kJ of work isdone on the other sample. How can you tell to which sample the heat was added?

SolutionHeat and work both change the internal energy of the substance. However, the properties of the sample only depend on the internal energy sothat it is impossible to tell whether heat was added to sample A or B.

14.2 Temperature Change and Heat CapacityOne of the major effects of heat transfer is temperature change: heating increases the temperature while cooling decreases it. We assume that thereis no phase change and that no work is done on or by the system. Experiments show that the transferred heat depends on three factors—the changein temperature, the mass of the system, and the substance and phase of the substance.

CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS 61

Figure 14.4 The heat Q transferred to cause a temperature change depends on the magnitude of the temperature change, the mass of the system, and the substance and

phase involved. (a) The amount of heat transferred is directly proportional to the temperature change. To double the temperature change of a mass m , you need to add twicethe heat. (b) The amount of heat transferred is also directly proportional to the mass. To cause an equivalent temperature change in a doubled mass, you need to add twice theheat. (c) The amount of heat transferred depends on the substance and its phase. If it takes an amount Q of heat to cause a temperature change ΔT in a given mass of

copper, it will take 10.8 times that amount of heat to cause the equivalent temperature change in the same mass of water assuming no phase change in either substance.

The dependence on temperature change and mass are easily understood. Owing to the fact that the (average) kinetic energy of an atom or moleculeis proportional to the absolute temperature, the internal energy of a system is proportional to the absolute temperature and the number of atoms ormolecules. Owing to the fact that the transferred heat is equal to the change in the internal energy, the heat is proportional to the mass of thesubstance and the temperature change. The transferred heat also depends on the substance so that, for example, the heat necessary to raise thetemperature is less for alcohol than for water. For the same substance, the transferred heat also depends on the phase (gas, liquid, or solid).

Heat Transfer and Temperature Change

The quantitative relationship between heat transfer and temperature change contains all three factors:

(14.2)Q=mcΔT,

where Q is the symbol for heat transfer, m is the mass of the substance, and ΔT is the change in temperature. The symbol c stands for

specific heat and depends on the material and phase. The specific heat is the amount of heat necessary to change the temperature of 1.00 kgof mass by 1.00°C . The specific heat c is a property of the substance; its SI unit is J/(kg ⋅ K) or J/(kg ⋅ °C) . Recall that the temperature

change (ΔT) is the same in units of kelvin and degrees Celsius. If heat transfer is measured in kilocalories, then the unit of specific heat is

kcal/(kg ⋅ °C) .

Values of specific heat must generally be looked up in tables, because there is no simple way to calculate them. In general, the specific heat alsodepends on the temperature. Table 14.1 lists representative values of specific heat for various substances. Except for gases, the temperature andvolume dependence of the specific heat of most substances is weak. We see from this table that the specific heat of water is five times that of glassand ten times that of iron, which means that it takes five times as much heat to raise the temperature of water the same amount as for glass and tentimes as much heat to raise the temperature of water as for iron. In fact, water has one of the largest specific heats of any material, which is importantfor sustaining life on Earth.

Example 14.1 Calculating the Required Heat: Heating Water in an Aluminum Pan

A 0.500 kg aluminum pan on a stove is used to heat 0.250 liters of water from 20.0°C to 80.0°C . (a) How much heat is required? Whatpercentage of the heat is used to raise the temperature of (b) the pan and (c) the water?

Strategy

The pan and the water are always at the same temperature. When you put the pan on the stove, the temperature of the water and the pan isincreased by the same amount. We use the equation for the heat transfer for the given temperature change and mass of water and aluminum.The specific heat values for water and aluminum are given in Table 14.1.

Solution

Because water is in thermal contact with the aluminum, the pan and the water are at the same temperature.

1. Calculate the temperature difference:(14.3)ΔT =Tf − Ti = 60.0°C.

62 CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS

2. Calculate the mass of water. Because the density of water is 1000 kg/m3 , one liter of water has a mass of 1 kg, and the mass of 0.250

liters of water is mw = 0.250 kg .

3. Calculate the heat transferred to the water. Use the specific heat of water in Table 14.1:(14.4)Qw =mwcwΔT = ⎛

⎝0.250 kg⎞⎠⎛⎝4186 J/kg°C⎞⎠(60.0°C) = 62.8 kJ.4. Calculate the heat transferred to the aluminum. Use the specific heat for aluminum in Table 14.1:

(14.5)QAl =mAlcAl ΔT = ⎛⎝0.500 kg⎞⎠⎛⎝900 J/kg°C⎞⎠(60.0°C)= 27.0 × 104J = 27.0 kJ.

5. Compare the percentage of heat going into the pan versus that going into the water. First, find the total transferred heat:(14.6)QTotal =QW + QAl = 62.8 kJ + 27.0 kJ = 89.8 kJ.

Thus, the amount of heat going into heating the pan is

(14.7)27.0 kJ89.8 kJ×100% = 30.1%,

and the amount going into heating the water is

(14.8)62.8 kJ89.8 kJ×100% = 69.9%.

Discussion

In this example, the heat transferred to the container is a significant fraction of the total transferred heat. Although the mass of the pan is twicethat of the water, the specific heat of water is over four times greater than that of aluminum. Therefore, it takes a bit more than twice the heat toachieve the given temperature change for the water as compared to the aluminum pan.

Figure 14.5 The smoking brakes on this truck are a visible evidence of the mechanical equivalent of heat.

Example 14.2 Calculating the Temperature Increase from the Work Done on a Substance: Truck BrakesOverheat on Downhill Runs

Truck brakes used to control speed on a downhill run do work, converting gravitational potential energy into increased internal energy (highertemperature) of the brake material. This conversion prevents the gravitational potential energy from being converted into kinetic energy of thetruck. The problem is that the mass of the truck is large compared with that of the brake material absorbing the energy, and the temperatureincrease may occur too fast for sufficient heat to transfer from the brakes to the environment.

Calculate the temperature increase of 100 kg of brake material with an average specific heat of 800 J/kg ⋅ °C if the material retains 10% of the

energy from a 10,000-kg truck descending 75.0 m (in vertical displacement) at a constant speed.

Strategy

If the brakes are not applied, gravitational potential energy is converted into kinetic energy. When brakes are applied, gravitational potentialenergy is converted into internal energy of the brake material. We first calculate the gravitational potential energy (Mgh) that the entire truck

loses in its descent and then find the temperature increase produced in the brake material alone.

Solution

1. Calculate the change in gravitational potential energy as the truck goes downhill(14.9)Mgh= ⎛

⎝10,000kg⎞⎠⎛⎝9.80m/s2⎞⎠(75.0m)=7.35×106J.

2. Calculate the temperature from the heat transferred using Q=Mgh and

(14.10)ΔT = Qmc,

CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS 63

where m is the mass of the brake material. Insert the values m= 100 kg and c= 800 J/kg ⋅ °C to find

(14.11)ΔT =

⎛⎝7.35×106J⎞⎠

⎛⎝100 kg⎞⎠⎛⎝800 J/kg°C⎞⎠

= 92°C.

Discussion

This temperature is close to the boiling point of water. If the truck had been traveling for some time, then just before the descent, the braketemperature would likely be higher than the ambient temperature. The temperature increase in the descent would likely raise the temperature ofthe brake material above the boiling point of water, so this technique is not practical. However, the same idea underlies the recent hybridtechnology of cars, where mechanical energy (gravitational potential energy) is converted by the brakes into electrical energy (battery).

Table 14.1 Specific Heats[1] of Various SubstancesSubstances Specific heat (c)

Solids J/kg ⋅ °C kcal/kg ⋅ °C [2]

Aluminum 900 0.215

Asbestos 800 0.19

Concrete, granite (average) 840 0.20

Copper 387 0.0924

Glass 840 0.20

Gold 129 0.0308

Human body (average at 37 °C) 3500 0.83

Ice (average, -50°C to 0°C) 2090 0.50

Iron, steel 452 0.108

Lead 128 0.0305

Silver 235 0.0562

Wood 1700 0.4

Liquids

Benzene 1740 0.415

Ethanol 2450 0.586

Glycerin 2410 0.576

Mercury 139 0.0333

Water (15.0 °C) 4186 1.000

Gases [3]

Air (dry) 721 (1015) 0.172 (0.242)

Ammonia 1670 (2190) 0.399 (0.523)

Carbon dioxide 638 (833) 0.152 (0.199)

Nitrogen 739 (1040) 0.177 (0.248)

Oxygen 651 (913) 0.156 (0.218)

Steam (100°C) 1520 (2020) 0.363 (0.482)

Note that Example 14.2 is an illustration of the mechanical equivalent of heat. Alternatively, the temperature increase could be produced by a blowtorch instead of mechanically.

Example 14.3 Calculating the Final Temperature When Heat Is Transferred Between Two Bodies: Pouring ColdWater in a Hot Pan

Suppose you pour 0.250 kg of 20.0°C water (about a cup) into a 0.500-kg aluminum pan off the stove with a temperature of 150°C . Assumethat the pan is placed on an insulated pad and that a negligible amount of water boils off. What is the temperature when the water and pan reachthermal equilibrium a short time later?

1. The values for solids and liquids are at constant volume and at 25°C , except as noted.

2. These values are identical in units of cal/g ⋅ °C .

3. cv at constant volume and at 20.0°C , except as noted, and at 1.00 atm average pressure. Values in parentheses are cp at a constant pressure of

1.00 atm.

64 CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS

Strategy

The pan is placed on an insulated pad so that little heat transfer occurs with the surroundings. Originally the pan and water are not in thermalequilibrium: the pan is at a higher temperature than the water. Heat transfer then restores thermal equilibrium once the water and pan are incontact. Because heat transfer between the pan and water takes place rapidly, the mass of evaporated water is negligible and the magnitude ofthe heat lost by the pan is equal to the heat gained by the water. The exchange of heat stops once a thermal equilibrium between the pan andthe water is achieved. The heat exchange can be written as ∣Qhot ∣ =Qcold .

Solution

1. Use the equation for heat transfer Q=mcΔT to express the heat lost by the aluminum pan in terms of the mass of the pan, the specific

heat of aluminum, the initial temperature of the pan, and the final temperature:(14.12)Qhot =mAlcAl

⎛⎝Tf − 150°C⎞⎠.

2. Express the heat gained by the water in terms of the mass of the water, the specific heat of water, the initial temperature of the water andthe final temperature:

(14.13)Qcold =mWcW⎛⎝Tf − 20.0° C⎞⎠.

3. Note that Qhot < 0 and Qcold > 0 and that they must sum to zero because the heat lost by the hot pan must be the same as the heat

gained by the cold water:(14.14)Qcold +Qhot = 0,

Qcold =-Qhot,mW cW

⎛⎝Tf − 20.0°C⎞⎠= −mAlcAl

⎛⎝Tf − 150°C⎞⎠.

4. This an equation for the unknown final temperature, Tf5. Bring all terms involving Tf on the left hand side and all other terms on the right hand side. Solve for Tf ,

(14.15)Tf = mAl cAl (150°C) + mWcW(20.0°C)

mAl cAl + mWcW,

and insert the numerical values:(14.16)

Tf =⎛⎝0.500 kg⎞⎠⎛⎝900 J/kg°C⎞⎠(150°C)+⎛⎝0.250 kg⎞⎠⎛⎝4186 J/kg°C⎞⎠(20.0°C)

⎛⎝0.500 kg⎞⎠⎛⎝900 J/kg°C⎞⎠+ ⎛

⎝0.250 kg⎞⎠⎛⎝4186 J/kg°C⎞⎠= 88430 J

1496.5 J/°C= 59.1°C

.

Discussion

This is a typical calorimetry problem—two bodies at different temperatures are brought in contact with each other and exchange heat until acommon temperature is reached. Why is the final temperature so much closer to 20.0°C than 150°C ? The reason is that water has a greaterspecific heat than most common substances and thus undergoes a small temperature change for a given heat transfer. A large body of water,such as a lake, requires a large amount of heat to increase its temperature appreciably. This explains why the temperature of a lake staysrelatively constant during a day even when the temperature change of the air is large. However, the water temperature does change over longertimes (e.g., summer to winter).

Take-Home Experiment: Temperature Change of Land and Water

What heats faster, land or water?

To study differences in heat capacity:

• Place equal masses of dry sand (or soil) and water at the same temperature into two small jars. (The average density of soil or sand isabout 1.6 times that of water, so you can achieve approximately equal masses by using 50% more water by volume.)

• Heat both (using an oven or a heat lamp) for the same amount of time.• Record the final temperature of the two masses.• Now bring both jars to the same temperature by heating for a longer period of time.• Remove the jars from the heat source and measure their temperature every 5 minutes for about 30 minutes.

Which sample cools off the fastest? This activity replicates the phenomena responsible for land breezes and sea breezes.

Check Your Understanding

If 25 kJ is necessary to raise the temperature of a block from 25°C to 30°C , how much heat is necessary to heat the block from 45°C to

50°C ?

SolutionThe heat transfer depends only on the temperature difference. Since the temperature differences are the same in both cases, the same 25 kJ isnecessary in the second case.

CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS 65

14.3 Phase Change and Latent HeatSo far we have discussed temperature change due to heat transfer. No temperature change occurs from heat transfer if ice melts and becomes liquidwater (i.e., during a phase change). For example, consider water dripping from icicles melting on a roof warmed by the Sun. Conversely, waterfreezes in an ice tray cooled by lower-temperature surroundings.

Figure 14.6 Heat from the air transfers to the ice causing it to melt. (credit: Mike Brand)

Energy is required to melt a solid because the cohesive bonds between the molecules in the solid must be broken apart such that, in the liquid, themolecules can move around at comparable kinetic energies; thus, there is no rise in temperature. Similarly, energy is needed to vaporize a liquid,because molecules in a liquid interact with each other via attractive forces. There is no temperature change until a phase change is complete. Thetemperature of a cup of soda initially at 0°C stays at 0°C until all the ice has melted. Conversely, energy is released during freezing andcondensation, usually in the form of thermal energy. Work is done by cohesive forces when molecules are brought together. The correspondingenergy must be given off (dissipated) to allow them to stay together Figure 14.7.

The energy involved in a phase change depends on two major factors: the number and strength of bonds or force pairs. The number of bonds isproportional to the number of molecules and thus to the mass of the sample. The strength of forces depends on the type of molecules. The heat Qrequired to change the phase of a sample of mass m is given by

(14.17)Q=mL f (melting/freezing),(14.18)Q=mLv (vaporization/condensation),

where the latent heat of fusion, Lf , and latent heat of vaporization, Lv , are material constants that are determined experimentally. See (Table

14.2).

Figure 14.7 (a) Energy is required to partially overcome the attractive forces between molecules in a solid to form a liquid. That same energy must be removed for freezing totake place. (b) Molecules are separated by large distances when going from liquid to vapor, requiring significant energy to overcome molecular attraction. The same energymust be removed for condensation to take place. There is no temperature change until a phase change is complete.

66 CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS

Latent heat is measured in units of J/kg. Both Lf and Lv depend on the substance, particularly on the strength of its molecular forces as noted

earlier. Lf and Lv are collectively called latent heat coefficients . They are latent, or hidden, because in phase changes, energy enters or leaves

a system without causing a temperature change in the system; so, in effect, the energy is hidden. Table 14.2 lists representative values of Lf and

Lv , together with melting and boiling points.

The table shows that significant amounts of energy are involved in phase changes. Let us look, for example, at how much energy is needed to melt akilogram of ice at 0°C to produce a kilogram of water at 0°C . Using the equation for a change in temperature and the value for water from Table14.2, we find that Q=mLf = (1.0 kg)(334 kJ/kg) = 334 kJ is the energy to melt a kilogram of ice. This is a lot of energy as it represents the same

amount of energy needed to raise the temperature of 1 kg of liquid water from 0°C to 79.8°C . Even more energy is required to vaporize water; it

would take 2256 kJ to change 1 kg of liquid water at the normal boiling point ( 100°C at atmospheric pressure) to steam (water vapor). This exampleshows that the energy for a phase change is enormous compared to energy associated with temperature changes without a phase change.

Table 14.2 Heats of Fusion and Vaporization [4]

Lf Lv

Substance Melting point (°C) kJ/kg kcal/kg Boiling point (°C) kJ/kg kcal/kg

Helium −269.7 5.23 1.25 −268.9 20.9 4.99

Hydrogen −259.3 58.6 14.0 −252.9 452 108

Nitrogen −210.0 25.5 6.09 −195.8 201 48.0

Oxygen −218.8 13.8 3.30 −183.0 213 50.9

Ethanol −114 104 24.9 78.3 854 204

Ammonia −75 108 −33.4 1370 327

Mercury −38.9 11.8 2.82 357 272 65.0

Water 0.00 334 79.8 100.0 2256[5] 539[6]

Sulfur 119 38.1 9.10 444.6 326 77.9

Lead 327 24.5 5.85 1750 871 208

Antimony 631 165 39.4 1440 561 134

Aluminum 660 380 90 2450 11400 2720

Silver 961 88.3 21.1 2193 2336 558

Gold 1063 64.5 15.4 2660 1578 377

Copper 1083 134 32.0 2595 5069 1211

Uranium 1133 84 20 3900 1900 454

Tungsten 3410 184 44 5900 4810 1150

Phase changes can have a tremendous stabilizing effect even on temperatures that are not near the melting and boiling points, because evaporationand condensation (conversion of a gas into a liquid state) occur even at temperatures below the boiling point. Take, for example, the fact that airtemperatures in humid climates rarely go above 35.0°C , which is because most heat transfer goes into evaporating water into the air. Similarly,temperatures in humid weather rarely fall below the dew point because enormous heat is released when water vapor condenses.

We examine the effects of phase change more precisely by considering adding heat into a sample of ice at −20°C (Figure 14.8). The temperature

of the ice rises linearly, absorbing heat at a constant rate of 0.50 cal/g ⋅ °C until it reaches 0°C . Once at this temperature, the ice begins to melt

until all the ice has melted, absorbing 79.8 cal/g of heat. The temperature remains constant at 0°C during this phase change. Once all the ice has

melted, the temperature of the liquid water rises, absorbing heat at a new constant rate of 1.00 cal/g ⋅ °C . At 100°C , the water begins to boil and

the temperature again remains constant while the water absorbs 539 cal/g of heat during this phase change. When all the liquid has become steamvapor, the temperature rises again, absorbing heat at a rate of 0.482 cal/g ⋅ °C .

4. Values quoted at the normal melting and boiling temperatures at standard atmospheric pressure (1 atm).5. At 37.0°C (body temperature), the heat of vaporization Lv for water is 2430 kJ/kg or 580 kcal/kg

6. At 37.0°C (body temperature), the heat of vaporization Lv for water is 2430 kJ/kg or 580 kcal/kg

CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS 67

Figure 14.8 A graph of temperature versus energy added. The system is constructed so that no vapor evaporates while ice warms to become liquid water, and so that, whenvaporization occurs, the vapor remains in of the system. The long stretches of constant temperature values at 0°C and 100°C reflect the large latent heat of melting andvaporization, respectively.

Water can evaporate at temperatures below the boiling point. More energy is required than at the boiling point, because the kinetic energy of watermolecules at temperatures below 100°C is less than that at 100°C , hence less energy is available from random thermal motions. Take, forexample, the fact that, at body temperature, perspiration from the skin requires a heat input of 2428 kJ/kg, which is about 10 percent higher than thelatent heat of vaporization at 100°C . This heat comes from the skin, and thus provides an effective cooling mechanism in hot weather. Highhumidity inhibits evaporation, so that body temperature might rise, leaving unevaporated sweat on your brow.

Example 14.4 Calculate Final Temperature from Phase Change: Cooling Soda with Ice Cubes

Three ice cubes are used to chill a soda at 20°C with mass msoda = 0.25 kg . The ice is at 0°C and each ice cube has a mass of 6.0 g.

Assume that the soda is kept in a foam container so that heat loss can be ignored. Assume the soda has the same heat capacity as water. Findthe final temperature when all ice has melted.

Strategy

The ice cubes are at the melting temperature of 0°C . Heat is transferred from the soda to the ice for melting. Melting of ice occurs in two steps:first the phase change occurs and solid (ice) transforms into liquid water at the melting temperature, then the temperature of this water rises.Melting yields water at 0°C , so more heat is transferred from the soda to this water until the water plus soda system reaches thermalequilibrium,

(14.19)Qice = −Qsoda.

The heat transferred to the ice is Qice =miceLf + micecW(Tf − 0°C) . The heat given off by the soda is Qsoda =msoda cW(Tf − 20°C) .

Since no heat is lost, Qice = −Qsoda , so that

(14.20)miceLf + micecW⎛⎝Tf − 0°C⎞⎠= - msodacW

⎛⎝Tf − 20°C⎞⎠.

Bring all terms involving Tf on the left-hand-side and all other terms on the right-hand-side. Solve for the unknown quantity Tf :

(14.21)Tf = msoda cW (20°C) − miceLf

(msoda + mice)cW.

Solution

1. Identify the known quantities. The mass of ice is mice = 3×6.0 g = 0.018 kg and the mass of soda is msoda = 0.25 kg .

2. Calculate the terms in the numerator:(14.22)msoda cW (20°C) = ⎛

⎝0.25 kg⎞⎠⎛⎝4186 J/kg ⋅ °C⎞⎠(20°C)=20,930 Jand

(14.23)miceLf = ⎛⎝0.018 kg⎞⎠⎛⎝334,000 J/kg⎞⎠=6012 J.

3. Calculate the denominator:(14.24)(msoda + mice)cW = ⎛

⎝0.25 kg + 0.018 kg⎞⎠⎛⎝4186 K/(kg ⋅ °C⎞⎠=1122 J/°C.4. Calculate the final temperature:

(14.25)Tf = 20,930 J − 6012 J1122 J/°C = 13°C.

Discussion

This example illustrates the enormous energies involved during a phase change. The mass of ice is about 7 percent the mass of water but leadsto a noticeable change in the temperature of soda. Although we assumed that the ice was at the freezing temperature, this is incorrect: the

68 CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS

typical temperature is −6°C . However, this correction gives a final temperature that is essentially identical to the result we found. Can youexplain why?

We have seen that vaporization requires heat transfer to a liquid from the surroundings, so that energy is released by the surroundings.Condensation is the reverse process, increasing the temperature of the surroundings. This increase may seem surprising, since we associatecondensation with cold objects—the glass in the figure, for example. However, energy must be removed from the condensing molecules to make avapor condense. The energy is exactly the same as that required to make the phase change in the other direction, from liquid to vapor, and so it canbe calculated from Q=mLv .

Figure 14.9 Condensation forms on this glass of iced tea because the temperature of the nearby air is reduced to below the dew point. The air cannot hold as much water as itdid at room temperature, and so water condenses. Energy is released when the water condenses, speeding the melting of the ice in the glass. (credit: Jenny Downing)

Real-World Application

Energy is also released when a liquid freezes. This phenomenon is used by fruit growers in Florida to protect oranges when the temperature isclose to the freezing point (0°C) . Growers spray water on the plants in orchards so that the water freezes and heat is released to the growing

oranges on the trees. This prevents the temperature inside the orange from dropping below freezing, which would damage the fruit.

Figure 14.10 The ice on these trees released large amounts of energy when it froze, helping to prevent the temperature of the trees from dropping below 0°C . Water isintentionally sprayed on orchards to help prevent hard frosts. (credit: Hermann Hammer)

Sublimation is the transition from solid to vapor phase. You may have noticed that snow can disappear into thin air without a trace of liquid water, orthe disappearance of ice cubes in a freezer. The reverse is also true: Frost can form on very cold windows without going through the liquid stage. Apopular effect is the making of “smoke” from dry ice, which is solid carbon dioxide. Sublimation occurs because the equilibrium vapor pressure ofsolids is not zero. Certain air fresheners use the sublimation of a solid to inject a perfume into the room. Moth balls are a slightly toxic example of aphenol (an organic compound) that sublimates, while some solids, such as osmium tetroxide, are so toxic that they must be kept in sealed containersto prevent human exposure to their sublimation-produced vapors.

CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS 69

Figure 14.11 Direct transitions between solid and vapor are common, sometimes useful, and even beautiful. (a) Dry ice sublimates directly to carbon dioxide gas. The visiblevapor is made of water droplets. (credit: Windell Oskay) (b) Frost forms patterns on a very cold window, an example of a solid formed directly from a vapor. (credit: Liz West)

All phase transitions involve heat. In the case of direct solid-vapor transitions, the energy required is given by the equation Q=mL s , where Ls is

the heat of sublimation , which is the energy required to change 1.00 kg of a substance from the solid phase to the vapor phase. Ls is analogous

to Lf and Lv , and its value depends on the substance. Sublimation requires energy input, so that dry ice is an effective coolant, whereas the

reverse process (i.e., frosting) releases energy. The amount of energy required for sublimation is of the same order of magnitude as that for otherphase transitions.

The material presented in this section and the preceding section allows us to calculate any number of effects related to temperature and phasechange. In each case, it is necessary to identify which temperature and phase changes are taking place and then to apply the appropriate equation.Keep in mind that heat transfer and work can cause both temperature and phase changes.

Problem-Solving Strategies for the Effects of Heat Transfer1. Examine the situation to determine that there is a change in the temperature or phase. Is there heat transfer into or out of the system? When

the presence or absence of a phase change is not obvious, you may wish to first solve the problem as if there were no phase changes, andexamine the temperature change obtained. If it is sufficient to take you past a boiling or melting point, you should then go back and do theproblem in steps—temperature change, phase change, subsequent temperature change, and so on.

2. Identify and list all objects that change temperature and phase.3. Identify exactly what needs to be determined in the problem (identify the unknowns). A written list is useful.4. Make a list of what is given or what can be inferred from the problem as stated (identify the knowns).5. Solve the appropriate equation for the quantity to be determined (the unknown). If there is a temperature change, the transferred heat depends

on the specific heat (see Table 14.1) whereas, for a phase change, the transferred heat depends on the latent heat. See Table 14.2.6. Substitute the knowns along with their units into the appropriate equation and obtain numerical solutions complete with units. You will need to

do this in steps if there is more than one stage to the process (such as a temperature change followed by a phase change).7. Check the answer to see if it is reasonable: Does it make sense? As an example, be certain that the temperature change does not also cause a

phase change that you have not taken into account.

Check Your Understanding

Why does snow remain on mountain slopes even when daytime temperatures are higher than the freezing temperature?

SolutionSnow is formed from ice crystals and thus is the solid phase of water. Because enormous heat is necessary for phase changes, it takes a certainamount of time for this heat to be accumulated from the air, even if the air is above 0°C . The warmer the air is, the faster this heat exchangeoccurs and the faster the snow melts.

14.4 Heat Transfer MethodsEqually as interesting as the effects of heat transfer on a system are the methods by which this occurs. Whenever there is a temperature difference,heat transfer occurs. Heat transfer may occur rapidly, such as through a cooking pan, or slowly, such as through the walls of a picnic ice chest. Wecan control rates of heat transfer by choosing materials (such as thick wool clothing for the winter), controlling air movement (such as the use ofweather stripping around doors), or by choice of color (such as a white roof to reflect summer sunlight). So many processes involve heat transfer, sothat it is hard to imagine a situation where no heat transfer occurs. Yet every process involving heat transfer takes place by only three methods:

70 CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS

1. Conduction is heat transfer through stationary matter by physical contact. (The matter is stationary on a macroscopic scale—we know there isthermal motion of the atoms and molecules at any temperature above absolute zero.) Heat transferred between the electric burner of a stoveand the bottom of a pan is transferred by conduction.

2. Convection is the heat transfer by the macroscopic movement of a fluid. This type of transfer takes place in a forced-air furnace and in weathersystems, for example.

3. Heat transfer by radiation occurs when microwaves, infrared radiation, visible light, or another form of electromagnetic radiation is emitted orabsorbed. An obvious example is the warming of the Earth by the Sun. A less obvious example is thermal radiation from the human body.

Figure 14.12 In a fireplace, heat transfer occurs by all three methods: conduction, convection, and radiation. Radiation is responsible for most of the heat transferred into theroom. Heat transfer also occurs through conduction into the room, but at a much slower rate. Heat transfer by convection also occurs through cold air entering the room aroundwindows and hot air leaving the room by rising up the chimney.

We examine these methods in some detail in the three following modules. Each method has unique and interesting characteristics, but all three dohave one thing in common: they transfer heat solely because of a temperature difference Figure 14.12.

Check Your Understanding

Name an example from daily life (different from the text) for each mechanism of heat transfer.

Solution

Conduction: Heat transfers into your hands as you hold a hot cup of coffee.

Convection: Heat transfers as the barista “steams” cold milk to make hot cocoa.

Radiation: Reheating a cold cup of coffee in a microwave oven.

14.5 Conduction

Figure 14.13 Insulation is used to limit the conduction of heat from the inside to the outside (in winters) and from the outside to the inside (in summers). (credit: Giles Douglas)

Your feet feel cold as you walk barefoot across the living room carpet in your cold house and then step onto the kitchen tile floor. This result isintriguing, since the carpet and tile floor are both at the same temperature. The different sensation you feel is explained by the different rates of heattransfer: the heat loss during the same time interval is greater for skin in contact with the tiles than with the carpet, so the temperature drop is greateron the tiles.

Some materials conduct thermal energy faster than others. In general, good conductors of electricity (metals like copper, aluminum, gold, and silver)are also good heat conductors, whereas insulators of electricity (wood, plastic, and rubber) are poor heat conductors. Figure 14.14 shows molecules

CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS 71

in two bodies at different temperatures. The (average) kinetic energy of a molecule in the hot body is higher than in the colder body. If two moleculescollide, an energy transfer from the hot to the cold molecule occurs. The cumulative effect from all collisions results in a net flux of heat from the hotbody to the colder body. The heat flux thus depends on the temperature difference ΔΤ =Τhot − Tcold . Therefore, you will get a more severe burn

from boiling water than from hot tap water. Conversely, if the temperatures are the same, the net heat transfer rate falls to zero, and equilibrium isachieved. Owing to the fact that the number of collisions increases with increasing area, heat conduction depends on the cross-sectional area. If youtouch a cold wall with your palm, your hand cools faster than if you just touch it with your fingertip.

Figure 14.14 The molecules in two bodies at different temperatures have different average kinetic energies. Collisions occurring at the contact surface tend to transfer energyfrom high-temperature regions to low-temperature regions. In this illustration, a molecule in the lower temperature region (right side) has low energy before collision, but itsenergy increases after colliding with the contact surface. In contrast, a molecule in the higher temperature region (left side) has high energy before collision, but its energydecreases after colliding with the contact surface.

A third factor in the mechanism of conduction is the thickness of the material through which heat transfers. The figure below shows a slab of materialwith different temperatures on either side. Suppose that T2 is greater than T1 , so that heat is transferred from left to right. Heat transfer from the

left side to the right side is accomplished by a series of molecular collisions. The thicker the material, the more time it takes to transfer the sameamount of heat. This model explains why thick clothing is warmer than thin clothing in winters, and why Arctic mammals protect themselves with thickblubber.

Figure 14.15 Heat conduction occurs through any material, represented here by a rectangular bar, whether window glass or walrus blubber. The temperature of the material isT2 on the left and T1 on the right, where T2 is greater than T1 . The rate of heat transfer by conduction is directly proportional to the surface area A , the temperature

difference T2 − T1 , and the substance’s conductivity k . The rate of heat transfer is inversely proportional to the thickness d .

Lastly, the heat transfer rate depends on the material properties described by the coefficient of thermal conductivity. All four factors are included in asimple equation that was deduced from and is confirmed by experiments. The rate of conductive heat transfer through a slab of material, such asthe one in Figure 14.15, is given by

(14.26)Qt = kA(T2 − T1)

d ,

where Q / t is the rate of heat transfer in watts or kilocalories per second, k is the thermal conductivity of the material, A and d are its surface

area and thickness, as shown in Figure 14.15, and (T2 − T1) is the temperature difference across the slab. Table 14.3 gives representative values

of thermal conductivity.

72 CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS

Example 14.5 Calculating Heat Transfer Through Conduction: Conduction Rate Through an Ice Box

A Styrofoam ice box has a total area of 0.950 m2 and walls with an average thickness of 2.50 cm. The box contains ice, water, and canned

beverages at 0°C . The inside of the box is kept cold by melting ice. How much ice melts in one day if the ice box is kept in the trunk of a car at

35.0°C ?

Strategy

This question involves both heat for a phase change (melting of ice) and the transfer of heat by conduction. To find the amount of ice melted, wemust find the net heat transferred. This value can be obtained by calculating the rate of heat transfer by conduction and multiplying by time.

Solution

1. Identify the knowns.(14.27)A= 0.950 m2 ; d = 2.50 cm = 0.0250 m; T1 = 0°C; T2 = 35.0°C, t= 1 day = 24 hours = 86,400 s.

2. Identify the unknowns. We need to solve for the mass of the ice, m . We will also need to solve for the net heat transferred to melt the ice,

Q .

3. Determine which equations to use. The rate of heat transfer by conduction is given by(14.28)Q

t = kA(T2 − T1)d .

4. The heat is used to melt the ice: Q=mLf.5. Insert the known values:

(14.29)Qt =

(0.010 J/s ⋅ m ⋅ °C)⎛⎝0.950 m2⎞⎠(35.0°C − 0°C)0.0250 m = 13.3 J/s.

6. Multiply the rate of heat transfer by the time ( 1 day = 86,400 s ):

(14.30)Q= ⎛⎝Q / t⎞⎠t= (13.3 J/s)(86,400 s) = 1.15×106 J.

7. Set this equal to the heat transferred to melt the ice: Q=mLf . Solve for the mass m :

(14.31)m= Q

Lf= 1.15×106 J

334 ×103 J/kg= 3.44kg.

Discussion

The result of 3.44 kg, or about 7.6 lbs, seems about right, based on experience. You might expect to use about a 4 kg (7–10 lb) bag of ice perday. A little extra ice is required if you add any warm food or beverages.

Inspecting the conductivities in Table 14.3 shows that Styrofoam is a very poor conductor and thus a good insulator. Other good insulatorsinclude fiberglass, wool, and goose-down feathers. Like Styrofoam, these all incorporate many small pockets of air, taking advantage of air’spoor thermal conductivity.

CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS 73

Table 14.3 Thermal Conductivities of Common Substances[7]

Substance Thermal conductivity k(J/s⋅m⋅°C)

Silver 420

Copper 390

Gold 318

Aluminum 220

Steel iron 80

Steel (stainless) 14

Ice 2.2

Glass (average) 0.84

Concrete brick 0.84

Water 0.6

Fatty tissue (without blood) 0.2

Asbestos 0.16

Plasterboard 0.16

Wood 0.08–0.16

Snow (dry) 0.10

Cork 0.042

Glass wool 0.042

Wool 0.04

Down feathers 0.025

Air 0.023

Styrofoam 0.010

A combination of material and thickness is often manipulated to develop good insulators—the smaller the conductivity k and the larger the thickness

d , the better. The ratio of d / k will thus be large for a good insulator. The ratio d / k is called the R factor . The rate of conductive heat transfer is

inversely proportional to R . The larger the value of R , the better the insulation. R factors are most commonly quoted for household insulation,

refrigerators, and the like—unfortunately, it is still in non-metric units of ft2·°F·h/Btu, although the unit usually goes unstated (1 British thermal unit[Btu] is the amount of energy needed to change the temperature of 1.0 lb of water by 1.0 °F). A couple of representative values are an R factor of 11

for 3.5-in-thick fiberglass batts (pieces) of insulation and an R factor of 19 for 6.5-in-thick fiberglass batts. Walls are usually insulated with 3.5-inbatts, while ceilings are usually insulated with 6.5-in batts. In cold climates, thicker batts may be used in ceilings and walls.

Figure 14.16 The fiberglass batt is used for insulation of walls and ceilings to prevent heat transfer between the inside of the building and the outside environment.

Note that in Table 14.3, the best thermal conductors—silver, copper, gold, and aluminum—are also the best electrical conductors, again related to thedensity of free electrons in them. Cooking utensils are typically made from good conductors.

Example 14.6 Calculating the Temperature Difference Maintained by a Heat Transfer: Conduction Through anAluminum Pan

Water is boiling in an aluminum pan placed on an electrical element on a stovetop. The sauce pan has a bottom that is 0.800 cm thick and 14.0cm in diameter. The boiling water is evaporating at the rate of 1.00 g/s. What is the temperature difference across (through) the bottom of thepan?

Strategy

Conduction through the aluminum is the primary method of heat transfer here, and so we use the equation for the rate of heat transfer and solvefor the temperature difference.

7. At temperatures near 0°C.

74 CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS

(14.32)T2 − T1 = Qt⎛⎝ dkA⎞⎠.

Solution

1. Identify the knowns and convert them to the SI units.

The thickness of the pan, d = 0.800 cm = 8.0×10−3 m, the area of the pan, A= π(0.14 / 2)2 m2 = 1.54×10−2 m2 , and the thermal

conductivity, k= 220 J/s ⋅ m⋅°C.2. Calculate the necessary heat of vaporization of 1 g of water:

(14.33)Q=mLv = ⎛⎝1.00×10−3 kg⎞⎠⎛⎝2256×103 J/kg⎞⎠= 2256 J.

3. Calculate the rate of heat transfer given that 1 g of water melts in one second:(14.34)Q / t= 2256 J/s or 2.26 kW.

4. Insert the knowns into the equation and solve for the temperature difference:(14.35)

T2 − T1 = Qt⎛⎝ dkA⎞⎠= (2256 J/s) 8.00 × 10−3m

(220 J/s ⋅ m ⋅ °C)⎛⎝1.54×10−2 m2⎞⎠= 5.33°C.

Discussion

The value for the heat transfer Q / t = 2.26kW or 2256 J/s is typical for an electric stove. This value gives a remarkably small temperature

difference between the stove and the pan. Consider that the stove burner is red hot while the inside of the pan is nearly 100°C because of itscontact with boiling water. This contact effectively cools the bottom of the pan in spite of its proximity to the very hot stove burner. Aluminum issuch a good conductor that it only takes this small temperature difference to produce a heat transfer of 2.26 kW into the pan.

Conduction is caused by the random motion of atoms and molecules. As such, it is an ineffective mechanism for heat transport over macroscopicdistances and short time distances. Take, for example, the temperature on the Earth, which would be unbearably cold during the night andextremely hot during the day if heat transport in the atmosphere was to be only through conduction. In another example, car engines wouldoverheat unless there was a more efficient way to remove excess heat from the pistons.

Check Your Understanding

How does the rate of heat transfer by conduction change when all spatial dimensions are doubled?

Solution

Because area is the product of two spatial dimensions, it increases by a factor of four when each dimension is doubled⎛⎝Afinal = (2d)2 = 4d2 = 4Ainitial

⎞⎠ . The distance, however, simply doubles. Because the temperature difference and the coefficient of thermal

conductivity are independent of the spatial dimensions, the rate of heat transfer by conduction increases by a factor of four divided by two, ortwo:

(14.36)⎛⎝Qt⎞⎠final = kAfinal

⎛⎝T2 − T1

⎞⎠

dfinal= k⎛⎝4Ainitial

⎞⎠⎛⎝T2 − T1

⎞⎠

2dinitial= 2kAinitial

⎛⎝T2 − T1

⎞⎠

dinitial= 2⎛⎝

Qt⎞⎠initial.

14.6 ConvectionConvection is driven by large-scale flow of matter. In the case of Earth, the atmospheric circulation is caused by the flow of hot air from the tropics tothe poles, and the flow of cold air from the poles toward the tropics. (Note that Earth’s rotation causes the observed easterly flow of air in the northernhemisphere). Car engines are kept cool by the flow of water in the cooling system, with the water pump maintaining a flow of cool water to thepistons. The circulatory system is used the body: when the body overheats, the blood vessels in the skin expand (dilate), which increases the bloodflow to the skin where it can be cooled by sweating. These vessels become smaller when it is cold outside and larger when it is hot (so more fluidflows, and more energy is transferred).

The body also loses a significant fraction of its heat through the breathing process.

While convection is usually more complicated than conduction, we can describe convection and do some straightforward, realistic calculations of itseffects. Natural convection is driven by buoyant forces: hot air rises because density decreases as temperature increases. The house in Figure 14.17is kept warm in this manner, as is the pot of water on the stove in Figure 14.18. Ocean currents and large-scale atmospheric circulation transferenergy from one part of the globe to another. Both are examples of natural convection.

CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS 75

Figure 14.17 Air heated by the so-called gravity furnace expands and rises, forming a convective loop that transfers energy to other parts of the room. As the air is cooled atthe ceiling and outside walls, it contracts, eventually becoming denser than room air and sinking to the floor. A properly designed heating system using natural convection, likethis one, can be quite efficient in uniformly heating a home.

Figure 14.18 Convection plays an important role in heat transfer inside this pot of water. Once conducted to the inside, heat transfer to other parts of the pot is mostly byconvection. The hotter water expands, decreases in density, and rises to transfer heat to other regions of the water, while colder water sinks to the bottom. This process keepsrepeating.

Take-Home Experiment: Convection Rolls in a Heated Pan

Take two small pots of water and use an eye dropper to place a drop of food coloring near the bottom of each. Leave one on a bench top andheat the other over a stovetop. Watch how the color spreads and how long it takes the color to reach the top. Watch how convective loops form.

Example 14.7 Calculating Heat Transfer by Convection: Convection of Air Through the Walls of a House

Most houses are not airtight: air goes in and out around doors and windows, through cracks and crevices, following wiring to switches andoutlets, and so on. The air in a typical house is completely replaced in less than an hour. Suppose that a moderately-sized house has insidedimensions 12.0m×18.0m×3.00m high, and that all air is replaced in 30.0 min. Calculate the heat transfer per unit time in watts needed to

warm the incoming cold air by 10.0°C , thus replacing the heat transferred by convection alone.

Strategy

Heat is used to raise the temperature of air so that Q=mcΔT . The rate of heat transfer is then Q / t , where t is the time for air turnover. We

are given that ΔT is 10.0°C , but we must still find values for the mass of air and its specific heat before we can calculate Q . The specific

heat of air is a weighted average of the specific heats of nitrogen and oxygen, which gives c= cp ≅ 1000 J/kg ⋅ °C from Table 14.4 (note that

the specific heat at constant pressure must be used for this process).

Solution

1. Determine the mass of air from its density and the given volume of the house. The density is given from the density ρ and the volume

(14.37)m= ρV = ⎛⎝1.29 kg/m3⎞⎠(12.0 m×18.0 m×3.00 m) = 836 kg.

2. Calculate the heat transferred from the change in air temperature: Q=mcΔT so that

(14.38)Q= ⎛⎝836 kg⎞⎠⎛⎝1000 J/kg ⋅ °C⎞⎠(10.0°C)=8.36×106J.

3. Calculate the heat transfer from the heat Q and the turnover time t . Since air is turned over in t= 0.500 h = 1800 s , the heat

transferred per unit time is

76 CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS

(14.39)Qt = 8.36×106 J

1800 s = 4.64 kW.

Discussion

This rate of heat transfer is equal to the power consumed by about forty-six 100-W light bulbs. Newly constructed homes are designed for aturnover time of 2 hours or more, rather than 30 minutes for the house of this example. Weather stripping, caulking, and improved window sealsare commonly employed. More extreme measures are sometimes taken in very cold (or hot) climates to achieve a tight standard of more than 6hours for one air turnover. Still longer turnover times are unhealthy, because a minimum amount of fresh air is necessary to supply oxygen forbreathing and to dilute household pollutants. The term used for the process by which outside air leaks into the house from cracks aroundwindows, doors, and the foundation is called “air infiltration.”

A cold wind is much more chilling than still cold air, because convection combines with conduction in the body to increase the rate at which energy istransferred away from the body. The table below gives approximate wind-chill factors, which are the temperatures of still air that produce the samerate of cooling as air of a given temperature and speed. Wind-chill factors are a dramatic reminder of convection’s ability to transfer heat faster thanconduction. For example, a 15.0 m/s wind at 0°C has the chilling equivalent of still air at about −18°C .

Table 14.4 Wind-Chill FactorsMoving air temperature Wind speed (m/s)

(°C) 2 5 10 15 20

5 3 −1 −8 −10 −12

2 0 −7 −12 −16 −18

0 −2 −9 −15 −18 −20

−5 −7 −15 −22 −26 −29

−10 −12 −21 −29 −34 −36

−20 −23 −34 −44 −50 −52

−10 −12 −21 −29 −34 −36

−20 −23 −34 −44 −50 −52

−40 −44 −59 −73 −82 −84

Although air can transfer heat rapidly by convection, it is a poor conductor and thus a good insulator. The amount of available space for airflowdetermines whether air acts as an insulator or conductor. The space between the inside and outside walls of a house, for example, is about 9 cm (3.5in) —large enough for convection to work effectively. The addition of wall insulation prevents airflow, so heat loss (or gain) is decreased. Similarly, thegap between the two panes of a double-paned window is about 1 cm, which prevents convection and takes advantage of air’s low conductivity toprevent greater loss. Fur, fiber, and fiberglass also take advantage of the low conductivity of air by trapping it in spaces too small to supportconvection, as shown in the figure. Fur and feathers are lightweight and thus ideal for the protection of animals.

Figure 14.19 Fur is filled with air, breaking it up into many small pockets. Convection is very slow here, because the loops are so small. The low conductivity of air makes fur avery good lightweight insulator.

Some interesting phenomena happen when convection is accompanied by a phase change. It allows us to cool off by sweating, even if thetemperature of the surrounding air exceeds body temperature. Heat from the skin is required for sweat to evaporate from the skin, but without air flow,the air becomes saturated and evaporation stops. Air flow caused by convection replaces the saturated air by dry air and evaporation continues.

CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS 77

Example 14.8 Calculate the Flow of Mass during Convection: Sweat-Heat Transfer away from the Body

The average person produces heat at the rate of about 120 W when at rest. At what rate must water evaporate from the body to get rid of all thisenergy? (This evaporation might occur when a person is sitting in the shade and surrounding temperatures are the same as skin temperature,eliminating heat transfer by other methods.)

Strategy

Energy is needed for a phase change ( Q=mLv ). Thus, the energy loss per unit time is

(14.40)Qt = mLv

t = 120 W = 120J/s.

We divide both sides of the equation by Lv to find that the mass evaporated per unit time is

(14.41)mt = 120 J/s

Lv.

Solution

(1) Insert the value of the latent heat from Table 14.2, Lv = 2430 kJ/kg = 2430 J/g . This yields

(14.42)mt = 120 J/s

2430 J/g = 0.0494 g/s = 2.96 g/min.

Discussion

Evaporating about 3 g/min seems reasonable. This would be about 180 g (about 7 oz) per hour. If the air is very dry, the sweat may evaporatewithout even being noticed. A significant amount of evaporation also takes place in the lungs and breathing passages.

Another important example of the combination of phase change and convection occurs when water evaporates from the oceans. Heat is removedfrom the ocean when water evaporates. If the water vapor condenses in liquid droplets as clouds form, heat is released in the atmosphere. Thus,there is an overall transfer of heat from the ocean to the atmosphere. This process is the driving power behind thunderheads, those great cumulusclouds that rise as much as 20.0 km into the stratosphere. Water vapor carried in by convection condenses, releasing tremendous amounts ofenergy. This energy causes the air to expand and rise, where it is colder. More condensation occurs in these colder regions, which in turn drives thecloud even higher. Such a mechanism is called positive feedback, since the process reinforces and accelerates itself. These systems sometimesproduce violent storms, with lightning and hail, and constitute the mechanism driving hurricanes.

Figure 14.20 Cumulus clouds are caused by water vapor that rises because of convection. The rise of clouds is driven by a positive feedback mechanism. (credit: Mike Love)

78 CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS

Figure 14.21 Convection accompanied by a phase change releases the energy needed to drive this thunderhead into the stratosphere. (credit: Gerardo García Moretti )

Figure 14.22 The phase change that occurs when this iceberg melts involves tremendous heat transfer. (credit: Dominic Alves)

The movement of icebergs is another example of convection accompanied by a phase change. Suppose an iceberg drifts from Greenland intowarmer Atlantic waters. Heat is removed from the warm ocean water when the ice melts and heat is released to the land mass when the icebergforms on Greenland.

Check Your Understanding

Explain why using a fan in the summer feels refreshing!

SolutionUsing a fan increases the flow of air: warm air near your body is replaced by cooler air from elsewhere. Convection increases the rate of heattransfer so that moving air “feels” cooler than still air.

14.7 RadiationYou can feel the heat transfer from a fire and from the Sun. Similarly, you can sometimes tell that the oven is hot without touching its door or lookinginside—it may just warm you as you walk by. The space between the Earth and the Sun is largely empty, without any possibility of heat transfer byconvection or conduction. In these examples, heat is transferred by radiation. That is, the hot body emits electromagnetic waves that are absorbed byour skin: no medium is required for electromagnetic waves to propagate. Different names are used for electromagnetic waves of differentwavelengths: radio waves, microwaves, infrared radiation , visible light, ultraviolet radiation, X-rays, and gamma rays.

CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS 79

Figure 14.23 Most of the heat transfer from this fire to the observers is through infrared radiation. The visible light, although dramatic, transfers relatively little thermal energy.Convection transfers energy away from the observers as hot air rises, while conduction is negligibly slow here. Skin is very sensitive to infrared radiation, so that you cansense the presence of a fire without looking at it directly. (credit: Daniel X. O’Neil)

The energy of electromagnetic radiation depends on the wavelength (color) and varies over a wide range: a smaller wavelength (or higher frequency)corresponds to a higher energy. Because more heat is radiated at higher temperatures, a temperature change is accompanied by a color change.Take, for example, an electrical element on a stove, which glows from red to orange, while the higher-temperature steel in a blast furnace glows fromyellow to white. The radiation you feel is mostly infrared, which corresponds to a lower temperature than that of the electrical element and the steel.The radiated energy depends on its intensity, which is represented in the figure below by the height of the distribution.

Electromagnetic Waves explains more about the electromagnetic spectrum and Introduction to Quantum Physics discusses how the decrease inwavelength corresponds to an increase in energy.

Figure 14.24 (a) A graph of the spectra of electromagnetic waves emitted from an ideal radiator at three different temperatures. The intensity or rate of radiation emissionincreases dramatically with temperature, and the spectrum shifts toward the visible and ultraviolet parts of the spectrum. The shaded portion denotes the visible part of thespectrum. It is apparent that the shift toward the ultraviolet with temperature makes the visible appearance shift from red to white to blue as temperature increases. (b) Note thevariations in color corresponding to variations in flame temperature. (credit: Tuohirulla)

All objects absorb and emit electromagnetic radiation. The rate of heat transfer by radiation is largely determined by the color of the object. Black isthe most effective, and white is the least effective. People living in hot climates generally avoid wearing black clothing, for instance (see ???).Similarly, black asphalt in a parking lot will be hotter than adjacent gray sidewalk on a summer day, because black absorbs better than gray. Thereverse is also true—black radiates better than gray. Thus, on a clear summer night, the asphalt will be colder than the gray sidewalk, because blackradiates the energy more rapidly than gray. An ideal radiator is the same color as an ideal absorber, and captures all the radiation that falls on it. Incontrast, white is a poor absorber and is also a poor radiator. A white object reflects all radiation, like a mirror. (A perfect, polished white surface ismirror-like in appearance, and a crushed mirror looks white.)

Figure 14.25 This illustration shows that the darker pavement is hotter than the lighter pavement (much more of the ice on the right has melted), although both have been inthe sunlight for the same time. The thermal conductivities of the pavements are the same.

80 CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS

Gray objects have a uniform ability to absorb all parts of the electromagnetic spectrum. Colored objects behave in similar but more complex ways,which gives them a particular color in the visible range and may make them special in other ranges of the nonvisible spectrum. Take, for example, thestrong absorption of infrared radiation by the skin, which allows us to be very sensitive to it.

Figure 14.26 A black object is a good absorber and a good radiator, while a white (or silver) object is a poor absorber and a poor radiator. It is as if radiation from the inside isreflected back into the silver object, whereas radiation from the inside of the black object is “absorbed” when it hits the surface and finds itself on the outside and is stronglyemitted.

The rate of heat transfer by emitted radiation is determined by the Stefan-Boltzmann law of radiation :

(14.43)Qt = σeAT 4,

where σ = 5.67×10−8J/s ⋅ m2 ⋅ K4 is the Stefan-Boltzmann constant, A is the surface area of the object, and T is its absolute temperature inkelvin. The symbol e stands for the emissivity of the object, which is a measure of how well it radiates. An ideal jet-black (or black body) radiator

has e= 1 , whereas a perfect reflector has e= 0 . Real objects fall between these two values. Take, for example, tungsten light bulb filaments which

have an e of about 0.5 , and carbon black (a material used in printer toner), which has the (greatest known) emissivity of about 0.99 .

The radiation rate is directly proportional to the fourth power of the absolute temperature—a remarkably strong temperature dependence.Furthermore, the radiated heat is proportional to the surface area of the object. If you knock apart the coals of a fire, there is a noticeable increase inradiation due to an increase in radiating surface area.

Figure 14.27 A thermograph of part of a building shows temperature variations, indicating where heat transfer to the outside is most severe. Windows are a major region ofheat transfer to the outside of homes. (credit: U.S. Army)

Skin is a remarkably good absorber and emitter of infrared radiation, having an emissivity of 0.97 in the infrared spectrum. Thus, we are all nearly(jet) black in the infrared, in spite of the obvious variations in skin color. This high infrared emissivity is why we can so easily feel radiation on our skin.It is also the basis for the use of night scopes used by law enforcement and the military to detect human beings. Even small temperature variations

can be detected because of the T 4 dependence. Images, called thermographs, can be used medically to detect regions of abnormally high

CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS 81

temperature in the body, perhaps indicative of disease. Similar techniques can be used to detect heat leaks in homes Figure 14.27, optimizeperformance of blast furnaces, improve comfort levels in work environments, and even remotely map the Earth’s temperature profile.

All objects emit and absorb radiation. The net rate of heat transfer by radiation (absorption minus emission) is related to both the temperature of theobject and the temperature of its surroundings. Assuming that an object with a temperature T1 is surrounded by an environment with uniform

temperature T2 , the net rate of heat transfer by radiation is

(14.44)Qnett = σeA⎛⎝T2

4 − T14⎞⎠,

where e is the emissivity of the object alone. In other words, it does not matter whether the surroundings are white, gray, or black; the balance of

radiation into and out of the object depends on how well it emits and absorbs radiation. When T2 >T1 , the quantity Qnet / t is positive; that is, the

net heat transfer is from hot to cold.

Take-Home Experiment: Temperature in the Sun

Place a thermometer out in the sunshine and shield it from direct sunlight using an aluminum foil. What is the reading? Now remove the shield,and note what the thermometer reads. Take a handkerchief soaked in nail polish remover, wrap it around the thermometer and place it in thesunshine. What does the thermometer read?

Example 14.9 Calculate the Net Heat Transfer of a Person: Heat Transfer by Radiation

What is the rate of heat transfer by radiation, with an unclothed person standing in a dark room whose ambient temperature is 22.0°C . The

person has a normal skin temperature of 33.0°C and a surface area of 1.50m2 . The emissivity of skin is 0.97 in the infrared, where theradiation takes place.

Strategy

We can solve this by using the equation for the rate of radiative heat transfer.

Solution

Insert the temperatures values T2 = 295K and T1 = 306K , so that

(14.45)Qt =σeA⎛⎝T2

4 − T14⎞⎠

(14.46)= ⎛⎝5.67×10−8 J/s ⋅ m2 ⋅ K 4⎞⎠(0.97)⎛⎝1.50 m2⎞⎠

⎡⎣(295 K)4 − (306 K)4⎤⎦

(14.47)= −99 J/s = −99 W.Discussion

This value is a significant rate of heat transfer to the environment (note the minus sign), considering that a person at rest may produce energy atthe rate of 125 W and that conduction and convection will also be transferring energy to the environment. Indeed, we would probably expect thisperson to feel cold. Clothing significantly reduces heat transfer to the environment by many methods, because clothing slows down bothconduction and convection, and has a lower emissivity (especially if it is white) than skin.

The Earth receives almost all its energy from radiation of the Sun and reflects some of it back into outer space. Because the Sun is hotter than theEarth, the net energy flux is from the Sun to the Earth. However, the rate of energy transfer is less than the equation for the radiative heat transferwould predict because the Sun does not fill the sky. The average emissivity ( e ) of the Earth is about 0.65, but the calculation of this value iscomplicated by the fact that the highly reflective cloud coverage varies greatly from day to day. There is a negative feedback (one in which a changeproduces an effect that opposes that change) between clouds and heat transfer; greater temperatures evaporate more water to form more clouds,which reflect more radiation back into space, reducing the temperature. The often mentioned greenhouse effect is directly related to the variation ofthe Earth’s emissivity with radiation type (see the figure given below). The greenhouse effect is a natural phenomenon responsible for providingtemperatures suitable for life on Earth. The Earth’s relatively constant temperature is a result of the energy balance between the incoming solarradiation and the energy radiated from the Earth. Most of the infrared radiation emitted from the Earth is absorbed by carbon dioxide ( CO2 ) and

water ( H2 O ) in the atmosphere and then re-radiated back to the Earth or into outer space. Re-radiation back to the Earth maintains its surface

temperature about 40°C higher than it would be if there was no atmosphere, similar to the way glass increases temperatures in a greenhouse.

82 CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS

Figure 14.28 The greenhouse effect is a name given to the trapping of energy in the Earth’s atmosphere by a process similar to that used in greenhouses. The atmosphere,like window glass, is transparent to incoming visible radiation and most of the Sun’s infrared. These wavelengths are absorbed by the Earth and re-emitted as infrared. SinceEarth’s temperature is much lower than that of the Sun, the infrared radiated by the Earth has a much longer wavelength. The atmosphere, like glass, traps these longerinfrared rays, keeping the Earth warmer than it would otherwise be. The amount of trapping depends on concentrations of trace gases like carbon dioxide, and a change in theconcentration of these gases is believed to affect the Earth’s surface temperature.

The greenhouse effect is also central to the discussion of global warming due to emission of carbon dioxide and methane (and other so-calledgreenhouse gases) into the Earth’s atmosphere from industrial production and farming. Changes in global climate could lead to more intense storms,precipitation changes (affecting agriculture), reduction in rain forest biodiversity, and rising sea levels.

Heating and cooling are often significant contributors to energy use in individual homes. Current research efforts into developing environmentallyfriendly homes quite often focus on reducing conventional heating and cooling through better building materials, strategically positioning windows tooptimize radiation gain from the Sun, and opening spaces to allow convection. It is possible to build a zero-energy house that allows for comfortableliving in most parts of the United States with hot and humid summers and cold winters.

Figure 14.29 This simple but effective solar cooker uses the greenhouse effect and reflective material to trap and retain solar energy. Made of inexpensive, durable materials,it saves money and labor, and is of particular economic value in energy-poor developing countries. (credit: E.B. Kauai)

Conversely, dark space is very cold, about 3K(−454°F) , so that the Earth radiates energy into the dark sky. Owing to the fact that clouds have

lower emissivity than either oceans or land masses, they reflect some of the radiation back to the surface, greatly reducing heat transfer into darkspace, just as they greatly reduce heat transfer into the atmosphere during the day. The rate of heat transfer from soil and grasses can be so rapidthat frost may occur on clear summer evenings, even in warm latitudes.

Check Your Understanding

What is the change in the rate of the radiated heat by a body at the temperature T1 = 20°C compared to when the body is at the temperature

T2 = 40°C ?

SolutionThe radiated heat is proportional to the fourth power of the absolute temperature. Because T1 = 293 K and T2 = 313 K , the rate of heat

transfer increases by about 30 percent of the original rate.

Career Connection: Energy Conservation Consultation

The cost of energy is generally believed to remain very high for the foreseeable future. Thus, passive control of heat loss in both commercial anddomestic housing will become increasingly important. Energy consultants measure and analyze the flow of energy into and out of houses andensure that a healthy exchange of air is maintained inside the house. The job prospects for an energy consultant are strong.

CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS 83

conduction:

convection:

emissivity:

greenhouse effect:

heat of sublimation:

heat:

kilocalorie:

latent heat coefficient:

mechanical equivalent of heat:

net rate of heat transfer by radiation:

radiation:

radiation:

rate of conductive heat transfer:

Stefan-Boltzmann law of radiation:

specific heat:

sublimation:

thermal conductivity:

Problem-Solving Strategies for the Methods of Heat Transfer1. Examine the situation to determine what type of heat transfer is involved.2. Identify the type(s) of heat transfer—conduction, convection, or radiation.3. Identify exactly what needs to be determined in the problem (identify the unknowns). A written list is very useful.4. Make a list of what is given or can be inferred from the problem as stated (identify the knowns).5. Solve the appropriate equation for the quantity to be determined (the unknown).

6. For conduction, equationQt = kA(T2 − T1)

d is appropriate. Table 14.3 lists thermal conductivities. For convection, determine the amount

of matter moved and use equation Q=mcΔT , to calculate the heat transfer involved in the temperature change of the fluid. If a phase

change accompanies convection, equation Q=mLf or Q=mLv is appropriate to find the heat transfer involved in the phase change.

Table 14.2 lists information relevant to phase change. For radiation, equationQnett = σeA⎛⎝T2

4 − T14⎞⎠ gives the net heat transfer rate.

7. Insert the knowns along with their units into the appropriate equation and obtain numerical solutions complete with units.8. Check the answer to see if it is reasonable. Does it make sense?

Glossaryheat transfer through stationary matter by physical contact

heat transfer by the macroscopic movement of fluid

measure of how well an object radiates

warming of the Earth that is due to gases such as carbon dioxide and methane that absorb infrared radiation from the Earth’ssurface and reradiate it in all directions, thus sending a fraction of it back toward the surface of the Earth

the energy required to change a substance from the solid phase to the vapor phase

the spontaneous transfer of energy due to a temperature difference

1 kilocalorie = 1000 calories

a physical constant equal to the amount of heat transferred for every 1 kg of a substance during the change in phase ofthe substance

the work needed to produce the same effects as heat transfer

isQnett = σeA⎛⎝T2

4 − T14⎞⎠

heat transfer which occurs when microwaves, infrared radiation, visible light, or other electromagnetic radiation is emitted or absorbed

energy transferred by electromagnetic waves directly as a result of a temperature difference

rate of heat transfer from one material to another

Qt = σeAT 4 ,

the amount of heat necessary to change the temperature of 1.00 kg of a substance by 1.00 °C

the transition from the solid phase to the vapor phase

the property of a material’s ability to conduct heat

Section Summary

14.1 Heat• Heat and work are the two distinct methods of energy transfer.• Heat is energy transferred solely due to a temperature difference.• Any energy unit can be used for heat transfer, and the most common are kilocalorie (kcal) and joule (J).• Kilocalorie is defined to be the energy needed to change the temperature of 1.00 kg of water between 14.5°C and 15.5°C .

• The mechanical equivalent of this heat transfer is 1.00 kcal = 4186 J .

14.2 Temperature Change and Heat Capacity• The transfer of heat Q that leads to a change ΔT in the temperature of a body with mass m is Q=mcΔT , where c is the specific heat of

the material. This relationship can also be considered as the definition of specific heat.

14.3 Phase Change and Latent Heat• Most substances can exist either in solid, liquid, and gas forms, which are referred to as “phases.”

84 CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS

• Phase changes occur at fixed temperatures for a given substance at a given pressure, and these temperatures are called boiling and freezing(or melting) points.

• During phase changes, heat absorbed or released is given by:(14.29)Q=mL,

where L is the latent heat coefficient.

14.4 Heat Transfer Methods• Heat is transferred by three different methods: conduction, convection, and radiation.

14.5 Conduction• Heat conduction is the transfer of heat between two objects in direct contact with each other.• The rate of heat transfer Q / t (energy per unit time) is proportional to the temperature difference T2 − T1 and the contact area A and

inversely proportional to the distance d between the objects:(14.41)Q

t = kA⎛⎝T2 − T1⎞⎠

d .

14.6 Convection• Convection is heat transfer by the macroscopic movement of mass. Convection can be natural or forced and generally transfers thermal energy

faster than conduction. Table 14.4 gives wind-chill factors, indicating that moving air has the same chilling effect of much colder stationary air.Convection that occurs along with a phase change can transfer energy from cold regions to warm ones.

14.7 Radiation• Radiation is the rate of heat transfer through the emission or absorption of electromagnetic waves.• The rate of heat transfer depends on the surface area and the fourth power of the absolute temperature:

(14.53)Qt = σeAT 4 ,

where σ = 5.67×10−8J/s ⋅ m2 ⋅ K4 is the Stefan-Boltzmann constant and e is the emissivity of the body. For a black body, e= 1 whereas

a shiny white or perfect reflector has e= 0 , with real objects having values of e between 1 and 0. The net rate of heat transfer by radiation is(14.54)Qnet

t = σeA⎛⎝T24 − T1

4⎞⎠where T1 is the temperature of an object surrounded by an environment with uniform temperature T2 and e is the emissivity of the object.

Conceptual Questions

14.1 Heat1. How is heat transfer related to temperature?

2. Describe a situation in which heat transfer occurs. What are the resulting forms of energy?

3. When heat transfers into a system, is the energy stored as heat? Explain briefly.

14.2 Temperature Change and Heat Capacity4. What three factors affect the heat transfer that is necessary to change an object’s temperature?

5. The brakes in a car increase in temperature by ΔT when bringing the car to rest from a speed v . How much greater would ΔT be if the carinitially had twice the speed? You may assume the car to stop sufficiently fast so that no heat transfers out of the brakes.

14.3 Phase Change and Latent Heat6. Heat transfer can cause temperature and phase changes. What else can cause these changes?

7. How does the latent heat of fusion of water help slow the decrease of air temperatures, perhaps preventing temperatures from falling significantlybelow 0°C , in the vicinity of large bodies of water?

8. What is the temperature of ice right after it is formed by freezing water?

9. If you place 0°C ice into 0°C water in an insulated container, what will happen? Will some ice melt, will more water freeze, or will neither takeplace?

10. What effect does condensation on a glass of ice water have on the rate at which the ice melts? Will the condensation speed up the meltingprocess or slow it down?

11. In very humid climates where there are numerous bodies of water, such as in Florida, it is unusual for temperatures to rise above about35°C(95°F) . In deserts, however, temperatures can rise far above this. Explain how the evaporation of water helps limit high temperatures in humid

climates.

12. In winters, it is often warmer in San Francisco than in nearby Sacramento, 150 km inland. In summers, it is nearly always hotter in Sacramento.Explain how the bodies of water surrounding San Francisco moderate its extreme temperatures.

13. Putting a lid on a boiling pot greatly reduces the heat transfer necessary to keep it boiling. Explain why.

14. Freeze-dried foods have been dehydrated in a vacuum. During the process, the food freezes and must be heated to facilitate dehydration.Explain both how the vacuum speeds up dehydration and why the food freezes as a result.

CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS 85

15. When still air cools by radiating at night, it is unusual for temperatures to fall below the dew point. Explain why.

16. In a physics classroom demonstration, an instructor inflates a balloon by mouth and then cools it in liquid nitrogen. When cold, the shrunkenballoon has a small amount of light blue liquid in it, as well as some snow-like crystals. As it warms up, the liquid boils, and part of the crystalssublimate, with some crystals lingering for awhile and then producing a liquid. Identify the blue liquid and the two solids in the cold balloon. Justifyyour identifications using data from Table 14.2.

14.4 Heat Transfer Methods17. What are the main methods of heat transfer from the hot core of Earth to its surface? From Earth’s surface to outer space?

When our bodies get too warm, they respond by sweating and increasing blood circulation to the surface to transfer thermal energy away from thecore. What effect will this have on a person in a 40.0°C hot tub?

Figure 14.30 shows a cut-away drawing of a thermos bottle (also known as a Dewar flask), which is a device designed specifically to slow down allforms of heat transfer. Explain the functions of the various parts, such as the vacuum, the silvering of the walls, the thin-walled long glass neck, therubber support, the air layer, and the stopper.

Figure 14.30 The construction of a thermos bottle is designed to inhibit all methods of heat transfer.

14.5 Conduction18. Some electric stoves have a flat ceramic surface with heating elements hidden beneath. A pot placed over a heating element will be heated, whileit is safe to touch the surface only a few centimeters away. Why is ceramic, with a conductivity less than that of a metal but greater than that of agood insulator, an ideal choice for the stove top?

19. Loose-fitting white clothing covering most of the body is ideal for desert dwellers, both in the hot Sun and during cold evenings. Explain how suchclothing is advantageous during both day and night.

Figure 14.31 A jellabiya is worn by many men in Egypt. (credit: Zerida)

14.6 Convection20. One way to make a fireplace more energy efficient is to have an external air supply for the combustion of its fuel. Another is to have room aircirculate around the outside of the fire box and back into the room. Detail the methods of heat transfer involved in each.

86 CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS

21. On cold, clear nights horses will sleep under the cover of large trees. How does this help them keep warm?

14.7 Radiation22. When watching a daytime circus in a large, dark-colored tent, you sense significant heat transfer from the tent. Explain why this occurs.

23. Satellites designed to observe the radiation from cold (3 K) dark space have sensors that are shaded from the Sun, Earth, and Moon and that arecooled to very low temperatures. Why must the sensors be at low temperature?

24. Why are cloudy nights generally warmer than clear ones?

25. Why are thermometers that are used in weather stations shielded from the sunshine? What does a thermometer measure if it is shielded from thesunshine and also if it is not?

26. On average, would Earth be warmer or cooler without the atmosphere? Explain your answer.

CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS 87

Problems & Exercises

14.2 Temperature Change and Heat Capacity1. On a hot day, the temperature of an 80,000-L swimming poolincreases by 1.50°C . What is the net heat transfer during this heating?Ignore any complications, such as loss of water by evaporation.

2. Show that 1 cal/g ⋅ °C = 1 kcal/kg ⋅ °C .

3. To sterilize a 50.0-g glass baby bottle, we must raise its temperaturefrom 22.0°C to 95.0°C . How much heat transfer is required?

4. The same heat transfer into identical masses of different substancesproduces different temperature changes. Calculate the final temperaturewhen 1.00 kcal of heat transfers into 1.00 kg of the following, originally at20.0°C : (a) water; (b) concrete; (c) steel; and (d) mercury.

5. Rubbing your hands together warms them by converting work intothermal energy. If a woman rubs her hands back and forth for a total of20 rubs, at a distance of 7.50 cm per rub, and with an average frictionalforce of 40.0 N, what is the temperature increase? The mass of tissueswarmed is only 0.100 kg, mostly in the palms and fingers.

6. A 0.250-kg block of a pure material is heated from 20.0°C to

65.0°C by the addition of 4.35 kJ of energy. Calculate its specific heatand identify the substance of which it is most likely composed.

7. Suppose identical amounts of heat transfer into different masses ofcopper and water, causing identical changes in temperature. What is theratio of the mass of copper to water?

8. (a) The number of kilocalories in food is determined by calorimetrytechniques in which the food is burned and the amount of heat transfer ismeasured. How many kilocalories per gram are there in a 5.00-g peanutif the energy from burning it is transferred to 0.500 kg of water held in a0.100-kg aluminum cup, causing a 54.9°C temperature increase? (b)Compare your answer to labeling information found on a package ofpeanuts and comment on whether the values are consistent.

9. Following vigorous exercise, the body temperature of an 80.0-kgperson is 40.0°C . At what rate in watts must the person transfer thermal

energy to reduce the the body temperature to 37.0°C in 30.0 min,assuming the body continues to produce energy at the rate of 150 W?⎛⎝1 watt = 1 joule/second or 1 W = 1 J/s ⎞⎠ .

10. Even when shut down after a period of normal use, a largecommercial nuclear reactor transfers thermal energy at the rate of 150MW by the radioactive decay of fission products. This heat transfercauses a rapid increase in temperature if the cooling system fails(1watt=1 joule/second or 1 W=1 J/s and 1 MW=1 megawatt) . (a)

Calculate the rate of temperature increase in degrees Celsius per second

(°C/s) if the mass of the reactor core is 1.60×105kg and it has an

average specific heat of 0.3349 kJ/kg ⋅ °C . (b) How long would it take

to obtain a temperature increase of 2000°C , which could cause somemetals holding the radioactive materials to melt? (The initial rate oftemperature increase would be greater than that calculated here becausethe heat transfer is concentrated in a smaller mass. Later, however, the

temperature increase would slow down because the 5×105-kg steel

containment vessel would also begin to heat up.)

Figure 14.32 Radioactive spent-fuel pool at a nuclear power plant. Spent fuel stayshot for a long time. (credit: U.S. Department of Energy)

14.3 Phase Change and Latent Heat11. How much heat transfer (in kilocalories) is required to thaw a0.450-kg package of frozen vegetables originally at 0°C if their heat offusion is the same as that of water?

12. A bag containing 0°C ice is much more effective in absorbing

energy than one containing the same amount of 0°C water.

(a) How much heat transfer is necessary to raise the temperature of0.800 kg of water from 0°C to 30.0°C ?

(b) How much heat transfer is required to first melt 0.800 kg of 0°C iceand then raise its temperature?

(c) Explain how your answer supports the contention that the ice is moreeffective.

13. (a) How much heat transfer is required to raise the temperature of a0.750-kg aluminum pot containing 2.50 kg of water from 30.0°C to theboiling point and then boil away 0.750 kg of water? (b) How long doesthis take if the rate of heat transfer is 500 W1 watt = 1 joule/second (1 W = 1 J/s) ?

14. The formation of condensation on a glass of ice water causes the iceto melt faster than it would otherwise. If 8.00 g of condensation forms ona glass containing both water and 200 g of ice, how many grams of theice will melt as a result? Assume no other heat transfer occurs.

On a trip, you notice that a 3.50-kg bag of ice lasts an average of one dayin your cooler. What is the average power in watts entering the ice if itstarts at 0°C and completely melts to 0°C water in exactly one day

1 watt = 1 joule/second (1 W = 1 J/s) ?

15. On a certain dry sunny day, a swimming pool’s temperature wouldrise by 1.50°C if not for evaporation. What fraction of the water mustevaporate to carry away precisely enough energy to keep thetemperature constant?

(a) How much heat transfer is necessary to raise the temperature of a0.200-kg piece of ice from −20.0°C to 130°C , including the energyneeded for phase changes?

(b) How much time is required for each stage, assuming a constant 20.0kJ/s rate of heat transfer?

(c) Make a graph of temperature versus time for this process.

88 CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS

16. In 1986, a gargantuan iceberg broke away from the Ross Ice Shelf inAntarctica. It was approximately a rectangle 160 km long, 40.0 km wide,and 250 m thick.

(a) What is the mass of this iceberg, given that the density of ice is

917 kg/m3 ?

(b) How much heat transfer (in joules) is needed to melt it?

(c) How many years would it take sunlight alone to melt ice this thick, if

the ice absorbs an average of 100 W/m2 , 12.00 h per day?

17. How many grams of coffee must evaporate from 350 g of coffee in a100-g glass cup to cool the coffee from 95.0°C to 45.0°C ? You mayassume the coffee has the same thermal properties as water and that theaverage heat of vaporization is 2340 kJ/kg (560 cal/g). (You may neglectthe change in mass of the coffee as it cools, which will give you ananswer that is slightly larger than correct.)

18. (a) It is difficult to extinguish a fire on a crude oil tanker, because

each liter of crude oil releases 2.80×107J of energy when burned. Toillustrate this difficulty, calculate the number of liters of water that must beexpended to absorb the energy released by burning 1.00 L of crude oil, ifthe water has its temperature raised from 20.0°C to 100°C , it boils,

and the resulting steam is raised to 300°C . (b) Discuss additionalcomplications caused by the fact that crude oil has a smaller density thanwater.

19. The energy released from condensation in thunderstorms can be verylarge. Calculate the energy released into the atmosphere for a smallstorm of radius 1 km, assuming that 1.0 cm of rain is precipitateduniformly over this area.

20. To help prevent frost damage, 4.00 kg of 0°C water is sprayed ontoa fruit tree.

(a) How much heat transfer occurs as the water freezes?

(b) How much would the temperature of the 200-kg tree decrease if thisamount of heat transferred from the tree? Take the specific heat to be3.35 kJ/kg ⋅ °C , and assume that no phase change occurs.

21. A 0.250-kg aluminum bowl holding 0.800 kg of soup at 25.0°C isplaced in a freezer. What is the final temperature if 377 kJ of energy istransferred from the bowl and soup, assuming the soup’s thermalproperties are the same as that of water? Explicitly show how you followthe steps in the Problem-Solving Strategies for the Effects of HeatTransfer.

22. A 0.0500-kg ice cube at −30.0°C is placed in 0.400 kg of 35.0°Cwater in a very well-insulated container. What is the final temperature?

23. If you pour 0.0100 kg of 20.0°C water onto a 1.20-kg block of ice

(which is initially at −15.0°C ), what is the final temperature? You mayassume that the water cools so rapidly that effects of the surroundingsare negligible.

24. Indigenous people sometimes cook in watertight baskets by placinghot rocks into water to bring it to a boil. What mass of 500°C rock must

be placed in 4.00 kg of 15.0°C water to bring its temperature to

100°C , if 0.0250 kg of water escapes as vapor from the initial sizzle?You may neglect the effects of the surroundings and take the averagespecific heat of the rocks to be that of granite.

25. What would be the final temperature of the pan and water inCalculating the Final Temperature When Heat Is TransferredBetween Two Bodies: Pouring Cold Water in a Hot Pan if 0.260 kg ofwater was placed in the pan and 0.0100 kg of the water evaporatedimmediately, leaving the remainder to come to a common temperaturewith the pan?

26. In some countries, liquid nitrogen is used on dairy trucks instead ofmechanical refrigerators. A 3.00-hour delivery trip requires 200 L of liquid

nitrogen, which has a density of 808 kg/m3 .

(a) Calculate the heat transfer necessary to evaporate this amount ofliquid nitrogen and raise its temperature to 3.00°C . (Use c p and

assume it is constant over the temperature range.) This value is theamount of cooling the liquid nitrogen supplies.

(b) What is this heat transfer rate in kilowatt-hours?

(c) Compare the amount of cooling obtained from melting an identicalmass of 0°C ice with that from evaporating the liquid nitrogen.

27. Some gun fanciers make their own bullets, which involves meltingand casting the lead slugs. How much heat transfer is needed to raisethe temperature and melt 0.500 kg of lead, starting from 25.0°C ?

14.5 Conduction28. (a) Calculate the rate of heat conduction through house walls that are13.0 cm thick and that have an average thermal conductivity twice that ofglass wool. Assume there are no windows or doors. The surface area of

the walls is 120 m2 and their inside surface is at 18.0°C , while their

outside surface is at 5.00°C . (b) How many 1-kW room heaters wouldbe needed to balance the heat transfer due to conduction?

29. The rate of heat conduction out of a window on a winter day is rapidenough to chill the air next to it. To see just how rapidly the windowstransfer heat by conduction, calculate the rate of conduction in watts

through a 3.00-m2 window that is 0.635 cm thick (1/4 in) if the

temperatures of the inner and outer surfaces are 5.00°C and

−10.0°C , respectively. This rapid rate will not be maintained—the innersurface will cool, and even result in frost formation.

Calculate the rate of heat conduction out of the human body, assumingthat the core internal temperature is 37.0°C , the skin temperature is

34.0°C , the thickness of the tissues between averages 1.00 cm , and

the surface area is 1.40 m2 .

30. Suppose you stand with one foot on ceramic flooring and one foot on

a wool carpet, making contact over an area of 80.0 cm2 with each foot.

Both the ceramic and the carpet are 2.00 cm thick and are 10.0°C ontheir bottom sides. At what rate must heat transfer occur from each footto keep the top of the ceramic and carpet at 33.0°C ?

31. A man consumes 3000 kcal of food in one day, converting most of itto maintain body temperature. If he loses half this energy by evaporatingwater (through breathing and sweating), how many kilograms of waterevaporate?

32. (a) A firewalker runs across a bed of hot coals without sustainingburns. Calculate the heat transferred by conduction into the sole of onefoot of a firewalker given that the bottom of the foot is a 3.00-mm-thickcallus with a conductivity at the low end of the range for wood and its

density is 300 kg/m3 . The area of contact is 25.0 cm2 , the

temperature of the coals is 700°C , and the time in contact is 1.00 s.

(b) What temperature increase is produced in the 25.0 cm3 of tissueaffected?

(c) What effect do you think this will have on the tissue, keeping in mindthat a callus is made of dead cells?

33. (a) What is the rate of heat conduction through the 3.00-cm-thick fur

of a large animal having a 1.40-m2 surface area? Assume that the

animal’s skin temperature is 32.0°C , that the air temperature is

−5.00°C , and that fur has the same thermal conductivity as air. (b)What food intake will the animal need in one day to replace this heattransfer?

34. A walrus transfers energy by conduction through its blubber at therate of 150 W when immersed in −1.00°C water. The walrus’s internal

core temperature is 37.0°C , and it has a surface area of 2.00 m2 .

CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS 89

What is the average thickness of its blubber, which has the conductivityof fatty tissues without blood?

Figure 14.33 Walrus on ice. (credit: Captain Budd Christman, NOAA Corps)

35. Compare the rate of heat conduction through a 13.0-cm-thick wall

that has an area of 10.0 m2 and a thermal conductivity twice that ofglass wool with the rate of heat conduction through a window that is

0.750 cm thick and that has an area of 2.00 m2 , assuming the sametemperature difference across each.

36. Suppose a person is covered head to foot by wool clothing withaverage thickness of 2.00 cm and is transferring energy by conductionthrough the clothing at the rate of 50.0 W. What is the temperature

difference across the clothing, given the surface area is 1.40 m2 ?

37. Some stove tops are smooth ceramic for easy cleaning. If theceramic is 0.600 cm thick and heat conduction occurs through the samearea and at the same rate as computed in Example 14.6, what is thetemperature difference across it? Ceramic has the same thermalconductivity as glass and brick.

38. One easy way to reduce heating (and cooling) costs is to add extrainsulation in the attic of a house. Suppose the house already had 15 cmof fiberglass insulation in the attic and in all the exterior surfaces. If youadded an extra 8.0 cm of fiberglass to the attic, then by what percentagewould the heating cost of the house drop? Take the single story house tobe of dimensions 10 m by 15 m by 3.0 m. Ignore air infiltration and heatloss through windows and doors.

39. (a) Calculate the rate of heat conduction through a double-paned

window that has a 1.50-m2 area and is made of two panes of0.800-cm-thick glass separated by a 1.00-cm air gap. The inside surfacetemperature is 15.0°C , while that on the outside is −10.0°C . (Hint:There are identical temperature drops across the two glass panes. Firstfind these and then the temperature drop across the air gap. Thisproblem ignores the increased heat transfer in the air gap due toconvection.)

(b) Calculate the rate of heat conduction through a 1.60-cm-thick windowof the same area and with the same temperatures. Compare your answerwith that for part (a).

40. Many decisions are made on the basis of the payback period: thetime it will take through savings to equal the capital cost of an investment.Acceptable payback times depend upon the business or philosophy onehas. (For some industries, a payback period is as small as two years.)Suppose you wish to install the extra insulation in previous problem. Ifenergy cost $1.00 per million joules and the insulation was $4.00 persquare meter, then calculate the simple payback time. Take the averageΔT for the 120 day heating season to be 15.0°C .

41. For the human body, what is the rate of heat transfer by conductionthrough the body’s tissue with the following conditions: the tissuethickness is 3.00 cm, the change in temperature is 2.00°C , and the skin

area is 1.50 m2 . How does this compare with the average heat transferrate to the body resulting from an energy intake of about 2400 kcal perday? (No exercise is included.)

14.6 Convection

42. At what wind speed does −10°C air cause the same chill factor as

still air at −29°C ?

43. At what temperature does still air cause the same chill factor as−5°C air moving at 15 m/s?

44. The “steam” above a freshly made cup of instant coffee is really watervapor droplets condensing after evaporating from the hot coffee. What isthe final temperature of 250 g of hot coffee initially at 90.0°C if 2.00 gevaporates from it? The coffee is in a Styrofoam cup, so other methodsof heat transfer can be neglected.

45. (a) How many kilograms of water must evaporate from a 60.0-kgwoman to lower her body temperature by 0.750°C ?

(b) Is this a reasonable amount of water to evaporate in the form ofperspiration, assuming the relative humidity of the surrounding air is low?

46. On a hot dry day, evaporation from a lake has just enough heat

transfer to balance the 1.00 kW/m2 of incoming heat from the Sun.What mass of water evaporates in 1.00 h from each square meter?Explicitly show how you follow the steps in the Problem-SolvingStrategies for the Effects of Heat Transfer.

47. One winter day, the climate control system of a large university

classroom building malfunctions. As a result, 500 m3 of excess cold airis brought in each minute. At what rate in kilowatts must heat transferoccur to warm this air by 10.0°C (that is, to bring the air to roomtemperature)?

48. The Kilauea volcano in Hawaii is the world’s most active, disgorging

about 5×105 m3 of 1200°C lava per day. What is the rate of heattransfer out of Earth by convection if this lava has a density of

2700 kg/m3 and eventually cools to 30°C ? Assume that the specific

heat of lava is the same as that of granite.

Figure 14.34 Lava flow on Kilauea volcano in Hawaii. (credit: J. P. Eaton, U.S.Geological Survey)

49. During heavy exercise, the body pumps 2.00 L of blood per minute tothe surface, where it is cooled by 2.00°C . What is the rate of heattransfer from this forced convection alone, assuming blood has the same

specific heat as water and its density is 1050 kg/m3 ?

50. A person inhales and exhales 2.00 L of 37.0°C air, evaporating

4.00×10−2 g of water from the lungs and breathing passages with

each breath.

(a) How much heat transfer occurs due to evaporation in each breath?

(b) What is the rate of heat transfer in watts if the person is breathing at amoderate rate of 18.0 breaths per minute?

(c) If the inhaled air had a temperature of 20.0°C , what is the rate ofheat transfer for warming the air?

(d) Discuss the total rate of heat transfer as it relates to typical metabolicrates. Will this breathing be a major form of heat transfer for this person?

90 CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS

51. A glass coffee pot has a circular bottom with a 9.00-cm diameter incontact with a heating element that keeps the coffee warm with acontinuous heat transfer rate of 50.0 W

(a) What is the temperature of the bottom of the pot, if it is 3.00 mm thickand the inside temperature is 60.0°C ?

(b) If the temperature of the coffee remains constant and all of the heattransfer is removed by evaporation, how many grams per minuteevaporate? Take the heat of vaporization to be 2340 kJ/kg.

14.7 Radiation

52. At what net rate does heat radiate from a 275-m2 black roof on a

night when the roof’s temperature is 30.0°C and the surrounding

temperature is 15.0°C ? The emissivity of the roof is 0.900.

53. (a) Cherry-red embers in a fireplace are at 850°C and have an

exposed area of 0.200 m2 and an emissivity of 0.980. The surrounding

room has a temperature of 18.0°C . If 50% of the radiant energy entersthe room, what is the net rate of radiant heat transfer in kilowatts? (b)Does your answer support the contention that most of the heat transferinto a room by a fireplace comes from infrared radiation?

54. Radiation makes it impossible to stand close to a hot lava flow.

Calculate the rate of heat transfer by radiation from 1.00 m2 of

1200°C fresh lava into 30.0°C surroundings, assuming lava’semissivity is 1.00.

55. (a) Calculate the rate of heat transfer by radiation from a car radiatorat 110°C into a 50.0°C environment, if the radiator has an emissivity

of 0.750 and a 1.20-m2 surface area. (b) Is this a significant fraction ofthe heat transfer by an automobile engine? To answer this, assume ahorsepower of 200 hp(1.5 kW) and the efficiency of automobile

engines as 25%.

56. Find the net rate of heat transfer by radiation from a skier standing inthe shade, given the following. She is completely clothed in white (headto foot, including a ski mask), the clothes have an emissivity of 0.200 anda surface temperature of 10.0°C , the surroundings are at −15.0°C ,

and her surface area is 1.60 m2 .

57. Suppose you walk into a sauna that has an ambient temperature of50.0°C . (a) Calculate the rate of heat transfer to you by radiation given

your skin temperature is 37.0°C , the emissivity of skin is 0.98, and the

surface area of your body is 1.50 m2 . (b) If all other forms of heattransfer are balanced (the net heat transfer is zero), at what rate will yourbody temperature increase if your mass is 75.0 kg?

58. Thermography is a technique for measuring radiant heat anddetecting variations in surface temperatures that may be medically,environmentally, or militarily meaningful.(a) What is the percent increasein the rate of heat transfer by radiation from a given area at atemperature of 34.0°C compared with that at 33.0°C , such as on aperson’s skin? (b) What is the percent increase in the rate of heattransfer by radiation from a given area at a temperature of 34.0°Ccompared with that at 20.0°C , such as for warm and cool automobilehoods?

59.

Figure 14.35 Artist’s rendition of a thermograph of a patient’s upper body, showingthe distribution of heat represented by different colors.

60. The Sun radiates like a perfect black body with an emissivity ofexactly 1. (a) Calculate the surface temperature of the Sun, given that it

is a sphere with a 7.00×108-m radius that radiates 3.80×1026 Winto 3-K space. (b) How much power does the Sun radiate per squaremeter of its surface? (c) How much power in watts per square meter is

that value at the distance of Earth, 1.50×1011 m away? (This numberis called the solar constant.)

61. A large body of lava from a volcano has stopped flowing and is slowlycooling. The interior of the lava is at 1200°C , its surface is at 450°C ,

and the surroundings are at 27.0°C . (a) Calculate the rate at which

energy is transferred by radiation from 1.00 m2 of surface lava into thesurroundings, assuming the emissivity is 1.00. (b) Suppose heatconduction to the surface occurs at the same rate. What is the thicknessof the lava between the 450°C surface and the 1200°C interior,assuming that the lava’s conductivity is the same as that of brick?

62. Calculate the temperature the entire sky would have to be in order to

transfer energy by radiation at 1000 W/m2 —about the rate at whichthe Sun radiates when it is directly overhead on a clear day. This value isthe effective temperature of the sky, a kind of average that takes accountof the fact that the Sun occupies only a small part of the sky but is muchhotter than the rest. Assume that the body receiving the energy has atemperature of 27.0°C .

63. (a) A shirtless rider under a circus tent feels the heat radiating fromthe sunlit portion of the tent. Calculate the temperature of the tent canvasbased on the following information: The shirtless rider’s skin temperatureis 34.0°C and has an emissivity of 0.970. The exposed area of skin is

0.400 m2 . He receives radiation at the rate of 20.0 W—half what youwould calculate if the entire region behind him was hot. The rest of thesurroundings are at 34.0°C . (b) Discuss how this situation wouldchange if the sunlit side of the tent was nearly pure white and if the riderwas covered by a white tunic.

64. Integrated Concepts

One 30.0°C day the relative humidity is 75.0% , and that evening the

temperature drops to 20.0°C , well below the dew point. (a) How manygrams of water condense from each cubic meter of air? (b) How muchheat transfer occurs by this condensation? (c) What temperatureincrease could this cause in dry air?

65. Integrated Concepts

Large meteors sometimes strike the Earth, converting most of theirkinetic energy into thermal energy. (a) What is the kinetic energy of a

109 kg meteor moving at 25.0 km/s? (b) If this meteor lands in a deep

ocean and 80% of its kinetic energy goes into heating water, how many

kilograms of water could it raise by 5.0°C? (c) Discuss how the energy

CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS 91

of the meteor is more likely to be deposited in the ocean and the likelyeffects of that energy.

66. Integrated Concepts

Frozen waste from airplane toilets has sometimes been accidentallyejected at high altitude. Ordinarily it breaks up and disperses over a largearea, but sometimes it holds together and strikes the ground. Calculatethe mass of 0°C ice that can be melted by the conversion of kinetic and

gravitational potential energy when a 20.0 kg piece of frozen waste is

released at 12.0 km altitude while moving at 250 m/s and strikes theground at 100 m/s (since less than 20.0 kg melts, a significant messresults).

67. Integrated Concepts

(a) A large electrical power facility produces 1600 MW of “waste heat,”which is dissipated to the environment in cooling towers by warming airflowing through the towers by 5.00°C . What is the necessary flow rate

of air in m3 /s ? (b) Is your result consistent with the large cooling towersused by many large electrical power plants?

68. Integrated Concepts

(a) Suppose you start a workout on a Stairmaster, producing power at thesame rate as climbing 116 stairs per minute. Assuming your mass is 76.0kg and your efficiency is 20.0% , how long will it take for your body

temperature to rise 1.00ºC if all other forms of heat transfer in and outof your body are balanced? (b) Is this consistent with your experience ingetting warm while exercising?

69. Integrated Concepts

A 76.0-kg person suffering from hypothermia comes indoors and shiversvigorously. How long does it take the heat transfer to increase theperson’s body temperature by 2.00ºC if all other forms of heat transferare balanced?

70. Integrated Concepts

In certain large geographic regions, the underlying rock is hot. Wells canbe drilled and water circulated through the rock for heat transfer for thegeneration of electricity. (a) Calculate the heat transfer that can be

extracted by cooling 1.00 km3 of granite by 100°C . (b) How long willit take for heat transfer at the rate of 300 MW, assuming no heat transfers

back into the 1.00 km3 of rock by its surroundings?

71. Integrated Concepts

Heat transfers from your lungs and breathing passages by evaporatingwater. (a) Calculate the maximum number of grams of water that can beevaporated when you inhale 1.50 L of 37 ° C air with an original relative

humidity of 40.0%. (Assume that body temperature is also 37 ° C .) (b)How many joules of energy are required to evaporate this amount? (c)What is the rate of heat transfer in watts from this method, if you breatheat a normal resting rate of 10.0 breaths per minute?

72. Integrated Concepts

(a) What is the temperature increase of water falling 55.0 m over NiagaraFalls? (b) What fraction must evaporate to keep the temperatureconstant?

73. Integrated Concepts

Hot air rises because it has expanded. It then displaces a greater volumeof cold air, which increases the buoyant force on it. (a) Calculate the ratio

of the buoyant force to the weight of 50.0 ° C air surrounded by

20.0 ° C air. (b) What energy is needed to cause 1.00 m3 of air to go

from 20.0 ° C to 50.0 ° C ? (c) What gravitational potential energy isgained by this volume of air if it rises 1.00 m? Will this cause a significantcooling of the air?

74. Unreasonable Results

(a) What is the temperature increase of an 80.0 kg person whoconsumes 2500 kcal of food in one day with 95.0% of the energytransferred as heat to the body? (b) What is unreasonable about thisresult? (c) Which premise or assumption is responsible?

75. Unreasonable Results

A slightly deranged Arctic inventor surrounded by ice thinks it would bemuch less mechanically complex to cool a car engine by melting ice on itthan by having a water-cooled system with a radiator, water pump,antifreeze, and so on. (a) If 80.0% of the energy in 1.00 gal of gasolineis converted into “waste heat” in a car engine, how many kilograms of0°C ice could it melt? (b) Is this a reasonable amount of ice to carryaround to cool the engine for 1.00 gal of gasoline consumption? (c) Whatpremises or assumptions are unreasonable?

76. Unreasonable Results

(a) Calculate the rate of heat transfer by conduction through a window

with an area of 1.00 m2 that is 0.750 cm thick, if its inner surface is at

22.0°C and its outer surface is at 35.0°C . (b) What is unreasonableabout this result? (c) Which premise or assumption is responsible?

77. Unreasonable Results

A meteorite 1.20 cm in diameter is so hot immediately after penetratingthe atmosphere that it radiates 20.0 kW of power. (a) What is itstemperature, if the surroundings are at 20.0°C and it has an emissivityof 0.800? (b) What is unreasonable about this result? (c) Which premiseor assumption is responsible?

78. Construct Your Own Problem

Consider a new model of commercial airplane having its brakes tested asa part of the initial flight permission procedure. The airplane is brought totakeoff speed and then stopped with the brakes alone. Construct aproblem in which you calculate the temperature increase of the brakesduring this process. You may assume most of the kinetic energy of theairplane is converted to thermal energy in the brakes and surroundingmaterials, and that little escapes. Note that the brakes are expected tobecome so hot in this procedure that they ignite and, in order to pass thetest, the airplane must be able to withstand the fire for some time withouta general conflagration.

79. Construct Your Own Problem

Consider a person outdoors on a cold night. Construct a problem inwhich you calculate the rate of heat transfer from the person by all threeheat transfer methods. Make the initial circumstances such that at restthe person will have a net heat transfer and then decide how muchphysical activity of a chosen type is necessary to balance the rate of heattransfer. Among the things to consider are the size of the person, type ofclothing, initial metabolic rate, sky conditions, amount of waterevaporated, and volume of air breathed. Of course, there are many otherfactors to consider and your instructor may wish to guide you in theassumptions made as well as the detail of analysis and method ofpresenting your results.

92 CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS

15 THERMODYNAMICSLearning Objectives

15.1 Introduction to Thermodynamics15.2 The First Law of Thermodynamics15.3 The First Law of Thermodynamics and Some Simple Processes15.4 Introduction To The Second Law Of Thermodynamics: Heat Engines And Their Efficiency15.5 Carnot’s Perfect Heat Engine: The Second Law of Thermodynamics Restated15.6 Applications of Thermodynamics: Heat Pumps and Refrigerators15.7 Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy15.8 Statistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation

15.1 Introduction to Thermodynamics

15.2 The First Law of Thermodynamics

15.3 The First Law of Thermodynamics and Some Simple Processes

15.4 Introduction To The Second Law Of Thermodynamics: Heat Engines And Their Efficiency

15.5 Carnot’s Perfect Heat Engine: The Second Law of Thermodynamics Restated

15.6 Applications of Thermodynamics: Heat Pumps and Refrigerators

15.7 Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability ofEnergy

15.8 Statistical Interpretation of Entropy and the Second Law of Thermodynamics: TheUnderlying Explanation

CHAPTER 15 | THERMODYNAMICS 93

94 CHAPTER 15 | THERMODYNAMICS

16 OSCILLATORY MOTION AND WAVESLearning Objectives

16.1 Introduction to Oscillatory Motion and Waves16.2 Hooke’s Law: Stress and Strain Revisited16.3 Period and Frequency in Oscillations16.4 Simple Harmonic Motion: A Special Periodic Motion16.5 The Simple Pendulum16.6 Energy and the Simple Harmonic Oscillator16.7 Uniform Circular Motion and Simple Harmonic Motion16.8 Damped Harmonic Motion16.9 Forced Oscillations and Resonance16.10 Waves16.11 Superposition and Interference16.12 Energy in Waves: Intensity

16.1 Introduction to Oscillatory Motion and Waves

16.2 Hooke’s Law: Stress and Strain Revisited

16.3 Period and Frequency in Oscillations

16.4 Simple Harmonic Motion: A Special Periodic Motion

16.5 The Simple Pendulum

16.6 Energy and the Simple Harmonic Oscillator

16.7 Uniform Circular Motion and Simple Harmonic Motion

16.8 Damped Harmonic Motion

16.9 Forced Oscillations and Resonance

16.10 Waves

16.11 Superposition and Interference

16.12 Energy in Waves: Intensity

CHAPTER 16 | OSCILLATORY MOTION AND WAVES 95

96 CHAPTER 16 | OSCILLATORY MOTION AND WAVES

17 PHYSICS OF HEARINGLearning Objectives

17.1 Introduction to the Physics of Hearing17.2 Sound17.3 Speed of Sound, Frequency, and Wavelength17.4 Sound Intensity and Sound Level17.5 Doppler Effect and Sonic Booms17.6 Sound Interference and Resonance: Standing Waves in Air Columns17.7 Hearing17.8 Ultrasound

17.1 Introduction to the Physics of Hearing

17.2 Sound

17.3 Speed of Sound, Frequency, and Wavelength

17.4 Sound Intensity and Sound Level

17.5 Doppler Effect and Sonic Booms

17.6 Sound Interference and Resonance: Standing Waves in Air Columns

17.7 Hearing

17.8 Ultrasound

CHAPTER 17 | PHYSICS OF HEARING 97

98 CHAPTER 17 | PHYSICS OF HEARING

18 ELECTRIC CHARGE AND ELECTRIC FIELDLearning Objectives

18.1 Introduction to Electric Charge and Electric Field18.2 Static Electricity and Charge: Conservation of Charge18.3 Conductors and Insulators18.4 Coulomb’s Law18.5 Electric Field: Concept of a Field Revisited18.6 Electric Field Lines: Multiple Charges18.7 Electric Forces in Biology18.8 Conductors and Electric Fields in Static Equilibrium18.9 Applications of Electrostatics

18.1 Introduction to Electric Charge and Electric Field

18.2 Static Electricity and Charge: Conservation of Charge

18.3 Conductors and Insulators

18.4 Coulomb’s Law

18.5 Electric Field: Concept of a Field Revisited

18.6 Electric Field Lines: Multiple Charges

18.7 Electric Forces in Biology

18.8 Conductors and Electric Fields in Static Equilibrium

18.9 Applications of Electrostatics

CHAPTER 18 | ELECTRIC CHARGE AND ELECTRIC FIELD 99

100 CHAPTER 18 | ELECTRIC CHARGE AND ELECTRIC FIELD

19 ELECTRIC POTENTIAL AND ELECTRIC FIELDLearning Objectives

19.1 Introduction to Electric Potential and Electric Energy19.2 Electric Potential Energy: Potential Difference19.3 Electric Potential in a Uniform Electric Field19.4 Electric Potential due to a Point Change19.5 Equipotential Lines19.6 Capacitors and Dielectrics19.7 Capacitors in Series and Parallel19.8 Energy Stored in Capacitors

19.1 Introduction to Electric Potential and Electric Energy

19.2 Electric Potential Energy: Potential Difference

19.3 Electric Potential in a Uniform Electric Field

19.4 Electric Potential due to a Point Change

19.5 Equipotential Lines

19.6 Capacitors and Dielectrics

19.7 Capacitors in Series and Parallel

19.8 Energy Stored in Capacitors

CHAPTER 19 | ELECTRIC POTENTIAL AND ELECTRIC FIELD 101

102 CHAPTER 19 | ELECTRIC POTENTIAL AND ELECTRIC FIELD

20 ELECTRIC CURRENT, RESISTANCE, AND OHM'SLAW

Learning Objectives20.1 Introduction to Electric Current, Resistance, and Ohm's Law20.2 Current20.3 Ohm’s Law: Resistance and Simple Circuits20.4 Resistance and Resistivity20.5 Electric Power and Energy20.6 Alternating Current versus Direct Current20.7 Electric Hazards and the Human Body20.8 Nerve Conduction-Electrocardiograms

20.1 Introduction to Electric Current, Resistance, and Ohm's Law

20.2 Current

20.3 Ohm’s Law: Resistance and Simple Circuits

20.4 Resistance and Resistivity

20.5 Electric Power and Energy

20.6 Alternating Current versus Direct Current

20.7 Electric Hazards and the Human Body

20.8 Nerve Conduction-Electrocardiograms

CHAPTER 20 | ELECTRIC CURRENT, RESISTANCE, AND OHM'S LAW 103

104 CHAPTER 20 | ELECTRIC CURRENT, RESISTANCE, AND OHM'S LAW

21 CIRCUITS, BIOELECTRICITY, AND DCINSTRUMENTS

Learning Objectives21.1 Introduction to Circuits, Bioelectricity, and DC Instruments21.2 Resistors in Series and Parallel21.3 Electromotive Force: Terminal Voltage21.4 Kirchhoff’s Rules21.5 DC Voltmeters and Ammeters21.6 Null Measurements21.7 DC Circuits Containing Resistors and Capacitors

21.1 Introduction to Circuits, Bioelectricity, and DC Instruments

21.2 Resistors in Series and Parallel

21.3 Electromotive Force: Terminal Voltage

21.4 Kirchhoff’s Rules

21.5 DC Voltmeters and Ammeters

21.6 Null Measurements

21.7 DC Circuits Containing Resistors and Capacitors

CHAPTER 21 | CIRCUITS, BIOELECTRICITY, AND DC INSTRUMENTS 105

106 CHAPTER 21 | CIRCUITS, BIOELECTRICITY, AND DC INSTRUMENTS

22 MAGNETISMLearning Objectives

22.1 Introduction to Magnetism22.2 Magnets22.3 Ferromagnets and Electromagnets22.4 Magnetic Fields and Magnetic Field Lines22.5 Magnetic Field Strength B: Force on a Moving Charge in a Magnetic Field22.6 Force on a Moving Charge in a Magnetic Field: Examples and Applications22.7 The Hall Effect22.8 Magnetic Force on a Current-Carrying Conductor22.9 Torque on a Current Loop: Motors and Meters22.10 Magnetic Fields Produced by Currents: Ampere’s Law22.11 Magnetic Force Between Two Parallel Conductors22.12 More Applications of Magnetism

22.1 Introduction to Magnetism

22.2 Magnets

22.3 Ferromagnets and Electromagnets

22.4 Magnetic Fields and Magnetic Field Lines

22.5 Magnetic Field Strength B: Force on a Moving Charge in a Magnetic Field

22.6 Force on a Moving Charge in a Magnetic Field: Examples and Applications

22.7 The Hall Effect

22.8 Magnetic Force on a Current-Carrying Conductor

22.9 Torque on a Current Loop: Motors and Meters

22.10 Magnetic Fields Produced by Currents: Ampere’s Law

22.11 Magnetic Force Between Two Parallel Conductors

22.12 More Applications of Magnetism

CHAPTER 22 | MAGNETISM 107

108 CHAPTER 22 | MAGNETISM

23 ELECTROMAGNETIC INDUCTION, AC CIRCUITS,AND ELECTRICAL TECHNOLOGIES

Learning Objectives23.1 Introduction to Electromagnetic Induction: AC Circuits, and Electrical Technologies23.2 Induced Emf and Magnetic Flux23.3 Faraday’s Law of Induction: Lenz’s Law23.4 Motional Emf23.5 Eddy Currents and Magnetic Damping23.6 Electric Generators23.7 Back Emf23.8 Transformers23.9 Electrical Safety: Systems and Devices23.10 Inductance23.11 RL Circuits23.12 Reactance, Inductive and Capacitive23.13 RLC Series AC Circuits

23.1 Introduction to Electromagnetic Induction: AC Circuits, and Electrical Technologies

23.2 Induced Emf and Magnetic Flux

23.3 Faraday’s Law of Induction: Lenz’s Law

23.4 Motional Emf

23.5 Eddy Currents and Magnetic Damping

23.6 Electric Generators

23.7 Back Emf

23.8 Transformers

23.9 Electrical Safety: Systems and Devices

23.10 Inductance

23.11 RL Circuits

23.12 Reactance, Inductive and Capacitive

23.13 RLC Series AC Circuits

CHAPTER 23 | ELECTROMAGNETIC INDUCTION, AC CIRCUITS, AND ELECTRICAL TECHNOLOGIES 109

110 CHAPTER 23 | ELECTROMAGNETIC INDUCTION, AC CIRCUITS, AND ELECTRICAL TECHNOLOGIES

24 ELECTROMAGNETIC WAVESLearning Objectives

24.1 Introduction to Electromagnetic Waves24.2 Maxwell’s Equations: Electromagnetic Waves Predicted and Observed24.3 Production of Electromagnetic Waves24.4 The Electromagnetic Spectrum24.5 Energy in Electromagnetic Waves

24.1 Introduction to Electromagnetic Waves

24.2 Maxwell’s Equations: Electromagnetic Waves Predicted and Observed

24.3 Production of Electromagnetic Waves

24.4 The Electromagnetic Spectrum

24.5 Energy in Electromagnetic Waves

CHAPTER 24 | ELECTROMAGNETIC WAVES 111

112 CHAPTER 24 | ELECTROMAGNETIC WAVES

25 GEOMETRIC OPTICSLearning Objectives

25.1 Introduction to Geometric Optics25.2 The Ray Aspect of Light25.3 The Law of Reflection25.4 The Law of Refraction25.5 Total Internal Reflection25.6 Dispersion: The Rainbow and Prisms25.7 Image Formation by Lenses25.8 Image Formation by Mirrors

25.1 Introduction to Geometric Optics

25.2 The Ray Aspect of Light

25.3 The Law of Reflection

25.4 The Law of Refraction

25.5 Total Internal Reflection

25.6 Dispersion: The Rainbow and Prisms

25.7 Image Formation by Lenses

25.8 Image Formation by Mirrors

CHAPTER 25 | GEOMETRIC OPTICS 113

114 CHAPTER 25 | GEOMETRIC OPTICS

26 VISION AND OPTICAL INSTRUMENTSLearning Objectives

26.1 Introduction to Vision and Optical Instruments26.2 Physics of the Eye26.3 Vision Correction26.4 Color and Color Vision26.5 Microscopes26.6 Telescopes26.7 Aberrations

26.1 Introduction to Vision and Optical Instruments

26.2 Physics of the Eye

26.3 Vision Correction

26.4 Color and Color Vision

26.5 Microscopes

26.6 Telescopes

26.7 Aberrations

CHAPTER 26 | VISION AND OPTICAL INSTRUMENTS 115

116 CHAPTER 26 | VISION AND OPTICAL INSTRUMENTS

27 WAVE OPTICSLearning Objectives

27.1 Introduction to Wave Optics27.2 The Wave Aspect of Light: Interference27.3 Huygen’s Principle: Diffraction27.4 Young’s Double Slit Experiment27.5 Multiple Slit Diffraction27.6 Single Slit Diffraction27.7 Limits of Resolution: The Rayleigh Criterion27.8 Thin Film Interference27.9 Polarization27.10 *Extended Topic* Microscopy Enhanced by the Wave Characteristics of Light

27.1 Introduction to Wave Optics

27.2 The Wave Aspect of Light: Interference

27.3 Huygen’s Principle: Diffraction

27.4 Young’s Double Slit Experiment

27.5 Multiple Slit Diffraction

27.6 Single Slit Diffraction

27.7 Limits of Resolution: The Rayleigh Criterion

27.8 Thin Film Interference

27.9 Polarization

27.10 *Extended Topic* Microscopy Enhanced by the Wave Characteristics of Light

CHAPTER 27 | WAVE OPTICS 117

118 CHAPTER 27 | WAVE OPTICS

28 SPECIAL RELATIVITYLearning Objectives

28.1 Introduction to Special Relativity28.2 Einstein’s Postulates28.3 Simultaneity and Time Dilation28.4 Length Contraction28.5 Relativistic Addition of Velocities28.6 Relativistic Momentum28.7 Relativistic Energy

28.1 Introduction to Special Relativity

28.2 Einstein’s Postulates

28.3 Simultaneity and Time Dilation

28.4 Length Contraction

28.5 Relativistic Addition of Velocities

28.6 Relativistic Momentum

28.7 Relativistic Energy

CHAPTER 28 | SPECIAL RELATIVITY 119

120 CHAPTER 28 | SPECIAL RELATIVITY

29 INTRODUCTION TO QUANTUM PHYSICSLearning Objectives

29.1 Introduction to Quantum Physics29.2 Quantization of Energy29.3 The Photoelectric Effect29.4 Photon Energies and the Electromagnetic Spectrum29.5 Photon Momentum29.6 The Particle-Wave Duality29.7 The Wave Nature of Matter29.8 Probability: The Heisenberg Uncertainty Principle29.9 The Particle-Wave Duality Reviewed

29.1 Introduction to Quantum Physics

29.2 Quantization of Energy

29.3 The Photoelectric Effect

29.4 Photon Energies and the Electromagnetic Spectrum

29.5 Photon Momentum

29.6 The Particle-Wave Duality

29.7 The Wave Nature of Matter

29.8 Probability: The Heisenberg Uncertainty Principle

29.9 The Particle-Wave Duality Reviewed

CHAPTER 29 | INTRODUCTION TO QUANTUM PHYSICS 121

122 CHAPTER 29 | INTRODUCTION TO QUANTUM PHYSICS

30 ATOMIC PHYSICSLearning Objectives

30.1 Introduction to Atomic Physics30.2 Discovery of the Atom30.3 Discovery of the Parts of the Atom: Electrons and Nuclei30.4 Bohr’s Theory of the Hydrogen Atom30.5 X-Rays: Atomic Origins and Applications30.6 Applications of Atomic Excitations and De-Excitations30.7 The Wave Nature of Matter Causes Quantization30.8 Patterns in Spectra Reveal More Quantization30.9 Quantum Numbers and Rules30.10 The Pauli Exclusion Principle

30.1 Introduction to Atomic Physics

30.2 Discovery of the Atom

30.3 Discovery of the Parts of the Atom: Electrons and Nuclei

30.4 Bohr’s Theory of the Hydrogen Atom

30.5 X-Rays: Atomic Origins and Applications

30.6 Applications of Atomic Excitations and De-Excitations

30.7 The Wave Nature of Matter Causes Quantization

30.8 Patterns in Spectra Reveal More Quantization

30.9 Quantum Numbers and Rules

30.10 The Pauli Exclusion Principle

CHAPTER 30 | ATOMIC PHYSICS 123

124 CHAPTER 30 | ATOMIC PHYSICS

31 RADIOACTIVITY AND NUCLEAR PHYSICSLearning Objectives

31.1 Introduction to Radioactivity and Nuclear Physics31.2 Nuclear Radioactivity31.3 Radiation Detection and Detectors31.4 Substructure of the Nucleus31.5 Nuclear Decay and Conservation Laws31.6 Half-Life and Activity31.7 Binding Energy31.8 Tunneling

31.1 Introduction to Radioactivity and Nuclear Physics

31.2 Nuclear Radioactivity

31.3 Radiation Detection and Detectors

31.4 Substructure of the Nucleus

31.5 Nuclear Decay and Conservation Laws

31.6 Half-Life and Activity

31.7 Binding Energy

31.8 Tunneling

CHAPTER 31 | RADIOACTIVITY AND NUCLEAR PHYSICS 125

126 CHAPTER 31 | RADIOACTIVITY AND NUCLEAR PHYSICS

32 MEDICAL APPLICATIONS OF NUCLEAR PHYSICSLearning Objectives

32.1 Introduction to Applications of Nuclear Physics32.2 Medical Imaging and Diagnostics32.3 Biological Effects of Ionizing Radiation32.4 Therapeutic Uses of Ionizing Radiation32.5 Food Irradiation32.6 Fusion32.7 Fission32.8 Nuclear Weapons

32.1 Introduction to Applications of Nuclear Physics

32.2 Medical Imaging and Diagnostics

32.3 Biological Effects of Ionizing Radiation

32.4 Therapeutic Uses of Ionizing Radiation

32.5 Food Irradiation

32.6 Fusion

32.7 Fission

32.8 Nuclear Weapons

CHAPTER 32 | MEDICAL APPLICATIONS OF NUCLEAR PHYSICS 127

128 CHAPTER 32 | MEDICAL APPLICATIONS OF NUCLEAR PHYSICS

33 PARTICLE PHYSICSLearning Objectives

33.1 Introduction to Particle Physics33.2 The Yukawa Particle and the Heinsenberg Uncertainty Principle Revisited33.3 The Four Basic Forces33.4 Accelerators Create Matter from Energy33.5 Particles, Patterns, and Conservation Laws33.6 Quarks: Is That All There Is?33.7 GUTs, the Unification of Forces

33.1 Introduction to Particle Physics

33.2 The Yukawa Particle and the Heinsenberg Uncertainty Principle Revisited

33.3 The Four Basic Forces

33.4 Accelerators Create Matter from Energy

33.5 Particles, Patterns, and Conservation Laws

33.6 Quarks: Is That All There Is?

33.7 GUTs, the Unification of Forces

CHAPTER 33 | PARTICLE PHYSICS 129

130 CHAPTER 33 | PARTICLE PHYSICS

34 FRONTIERS OF PHYSICSLearning Objectives

34.1 Introduction to Frontiers of Physics34.2 Cosmology and Particle Physics34.3 General Relativity and Quantum Gravity34.4 Superstrings34.5 Dark Matter and Closure34.6 Complexity and Chaos34.7 High-Temperature Superconductors34.8 Some Questions We Know to Ask

34.1 Introduction to Frontiers of Physics

34.2 Cosmology and Particle Physics

34.3 General Relativity and Quantum Gravity

34.4 Superstrings

34.5 Dark Matter and Closure

34.6 Complexity and Chaos

34.7 High-Temperature Superconductors

34.8 Some Questions We Know to Ask

CHAPTER 34 | FRONTIERS OF PHYSICS 131

132 CHAPTER 34 | FRONTIERS OF PHYSICS

35 APPENDIX A: ATOMIC MASSESLearning Objectives35.1

CHAPTER 35 | APPENDIX A: ATOMIC MASSES 133

134 CHAPTER 35 | APPENDIX A: ATOMIC MASSES

36 APPENDIX B: SELECTED RADIOACTIVEISOTOPES

Learning Objectives36.1

CHAPTER 36 | APPENDIX B: SELECTED RADIOACTIVE ISOTOPES 135

136 CHAPTER 36 | APPENDIX B: SELECTED RADIOACTIVE ISOTOPES

37 APPENDIX C: USEFUL INFORMATIONLearning Objectives37.1

CHAPTER 37 | APPENDIX C: USEFUL INFORMATION 137

138 CHAPTER 37 | APPENDIX C: USEFUL INFORMATION

38 APPENDIX CO: MISSIONS OF EXPLORATIONLearning Objectives38.1

CHAPTER 38 | APPENDIX CO: MISSIONS OF EXPLORATION 139

140 CHAPTER 38 | APPENDIX CO: MISSIONS OF EXPLORATION

39 APPENDIX G: GLOSSARY OF KEY SYMBOLSAND NOTATION

Learning Objectives39.1

CHAPTER 39 | APPENDIX G: GLOSSARY OF KEY SYMBOLS AND NOTATION 141

Index

A

Accuracy , 24accuracy , 30approximation , 30approximations , 28

C

classical physics , 16, 30Conduction , 70conduction , 84Convection , 70convection , 84conversion factor , 21, 30

D

derived units , 18, 30

E

emissivity , 79, 84English units , 18, 30

F

fundamental units , 18, 30

G

greenhouse effect , 79, 84

H

heat , 60, 84heat of sublimation , 66, 84

K

kilocalorie , 60, 84kilogram , 19, 30

L

latent heat coefficient , 84latent heat coefficients , 66law , 14, 30

M

mechanical equivalent of heat , 61, 84meter , 19, 30method of adding percents , 26, 30metric system , 19, 30model , 14, 30Modern physics , 16modern physics , 30

N

net rate of heat transfer by radiation , 79,84

O

order of magnitude , 19, 30

P

percent uncertainty , 25, 30physical quantity , 18, 30Physics , 12physics , 30precision , 24, 30

Q

Quantum mechanics , 16quantum mechanics , 30

R

R 2 R R factor , 71radiation , 70, 79, 84rate of conductive heat transfer , 71, 84Relativity , 16relativity , 30

S

scientific method , 14, 30second , 19, 30SI units , 18, 30significant figures , 26, 30specific heat , 61, 84Stefan-Boltzmann law of radiation , 79,84Sublimation , 66sublimation , 84

T

theory , 14, 30thermal conductivity , 71, 84

U

uncertainty , 25, 30units , 18, 30

142 INDEX

ATTRIBUTIONSCollection: College PhysicsEdited by: OpenStax CollegeURL: http://cnx.org/content/col11406/1.5/Copyright: Rice UniversityLicense: http://creativecommons.org/licenses/by/3.0/

Module: Preface to College PhysicsBy: OpenStax CollegeURL: http://cnx.org/content/m42955/1.3/Copyright: Rice UniversityLicense: http://creativecommons.org/licenses/by/3.0/

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Module: Addition of VelocitiesBy: College PhysicsURL: http://cnx.org/content/m42045/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to Dynamics: Newton's Laws of MotionBy: College PhysicsURL: http://cnx.org/content/m42129/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

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Module: Newton’s First Law of Motion: InertiaBy: College PhysicsURL: http://cnx.org/content/m42130/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Newton’s Second Law of Motion: Concept of a SystemBy: College PhysicsURL: http://cnx.org/content/m42073/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Newton’s Third Law of Motion: Symmetry in ForcesBy: College PhysicsURL: http://cnx.org/content/m42074/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

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Module: Problem-Solving StrategiesBy: College PhysicsURL: http://cnx.org/content/m42076/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Further Applications of Newton’s Laws of MotionBy: College PhysicsURL: http://cnx.org/content/m42132/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Extended Topic: The Four Basic Forces—An IntroductionBy: College PhysicsURL: http://cnx.org/content/m42137/1.1/Copyright: College Physics

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Module: Introduction: Further Applications of Newton’s LawsBy: College PhysicsURL: http://cnx.org/content/m42138/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: FrictionBy: College PhysicsURL: http://cnx.org/content/m42139/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

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Module: Introduction to Uniform Circular Motion and GravitationBy: College PhysicsURL: http://cnx.org/content/m42140/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

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URL: http://cnx.org/content/m42144/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to Work, Energy, and Energy ResourcesBy: College PhysicsURL: http://cnx.org/content/m42145/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Work: The Scientific DefinitionBy: College PhysicsURL: http://cnx.org/content/m42146/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

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Module: PowerBy: College PhysicsURL: http://cnx.org/content/m42152/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Work, Energy, and Power in HumansBy: College PhysicsURL: http://cnx.org/content/m42153/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: World Energy UseBy: College PhysicsURL: http://cnx.org/content/m42154/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

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Module: Introduction to Linear Momentum and CollisionsBy: College PhysicsURL: http://cnx.org/content/m42155/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Linear Momentum and ForceBy: College PhysicsURL: http://cnx.org/content/m42156/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: ImpulseBy: College PhysicsURL: http://cnx.org/content/m42159/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Conservation of MomentumBy: College PhysicsURL: http://cnx.org/content/m42162/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Elastic Collisions in One DimensionBy: College PhysicsURL: http://cnx.org/content/m42163/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Inelastic Collisions in One DimensionBy: College PhysicsURL: http://cnx.org/content/m42164/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Collisions of Point Masses in Two DimensionsBy: College PhysicsURL: http://cnx.org/content/m42165/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

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148 INDEX

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Module: StabilityBy: College PhysicsURL: http://cnx.org/content/m42172/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

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Module: Forces and Torques in Muscles and JointsBy: College PhysicsURL: http://cnx.org/content/m42175/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to Rotational Motion and Angular MomentumBy: College PhysicsURL: http://cnx.org/content/m42176/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

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Module: Collisions of Extended Bodies in Two Dimensions

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By: College PhysicsURL: http://cnx.org/content/m42183/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Gyroscopic Effects: Vector Aspects of Angular MomentumBy: College PhysicsURL: http://cnx.org/content/m42184/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

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Module: Cohesion and Adhesion in Liquids: Surface Tension and Capillary ActionBy: College PhysicsURL: http://cnx.org/content/m42197/1.1/Copyright: College Physics

150 INDEX

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Module: Pressures in the BodyBy: College PhysicsURL: http://cnx.org/content/m42199/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

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Module: The Onset of TurbulenceBy: College PhysicsURL: http://cnx.org/content/m42210/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Motion of an Object in a Viscous FluidBy: College PhysicsURL: http://cnx.org/content/m42211/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Molecular Transport Phenomena: Diffusion, Osmosis, and Related ProcessesBy: College PhysicsURL: http://cnx.org/content/m42212/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to Temperature, Kinetic Theory, and the Gas LawsBy: College PhysicsURL: http://cnx.org/content/m42213/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: TemperatureBy: College Physics

INDEX 151

URL: http://cnx.org/content/m42214/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Thermal Expansion of Solids and LiquidsBy: College PhysicsURL: http://cnx.org/content/m42215/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: The Ideal Gas LawBy: College PhysicsURL: http://cnx.org/content/m42216/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Kinetic Theory: Molecular Explanation of Pressure and TemperatureBy: College PhysicsURL: http://cnx.org/content/m42217/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Phase ChangesBy: College PhysicsURL: http://cnx.org/content/m42218/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Humidity, Evaporation, and BoilingBy: College PhysicsURL: http://cnx.org/content/m42219/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to Heat and Heat Transfer MethodsBy: OpenStax CollegeURL: http://cnx.org/content/m42221/1.2/Copyright: Rice UniversityLicense: http://creativecommons.org/licenses/by/3.0/

Module: HeatBy: OpenStax CollegeURL: http://cnx.org/content/m42223/1.2/Copyright: Rice UniversityLicense: http://creativecommons.org/licenses/by/3.0/

Module: Temperature Change and Heat CapacityBy: OpenStax CollegeURL: http://cnx.org/content/m42224/1.2/Copyright: Rice UniversityLicense: http://creativecommons.org/licenses/by/3.0/

Module: Phase Change and Latent HeatBy: OpenStax CollegeURL: http://cnx.org/content/m42225/1.2/Copyright: Rice UniversityLicense: http://creativecommons.org/licenses/by/3.0/

Module: Heat Transfer MethodsBy: OpenStax CollegeURL: http://cnx.org/content/m42226/1.2/Copyright: Rice UniversityLicense: http://creativecommons.org/licenses/by/3.0/

152 INDEX

Module: ConductionBy: OpenStax CollegeURL: http://cnx.org/content/m42228/1.2/Copyright: Rice UniversityLicense: http://creativecommons.org/licenses/by/3.0/

Module: ConvectionBy: OpenStax CollegeURL: http://cnx.org/content/m42229/1.2/Copyright: Rice UniversityLicense: http://creativecommons.org/licenses/by/3.0/

Module: RadiationBy: OpenStax CollegeURL: http://cnx.org/content/m42230/1.2/Copyright: Rice UniversityLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to ThermodynamicsBy: College PhysicsURL: http://cnx.org/content/m42231/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: The First Law of ThermodynamicsBy: College PhysicsURL: http://cnx.org/content/m42232/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: The First Law of Thermodynamics and Some Simple ProcessesBy: College PhysicsURL: http://cnx.org/content/m42233/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction To The Second Law Of Thermodynamics: Heat Engines And Their EfficiencyBy: College PhysicsURL: http://cnx.org/content/m42234/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Carnot’s Perfect Heat Engine: The Second Law of Thermodynamics RestatedBy: College PhysicsURL: http://cnx.org/content/m42235/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Applications of Thermodynamics: Heat Pumps and RefrigeratorsBy: College PhysicsURL: http://cnx.org/content/m42236/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of EnergyBy: College PhysicsURL: http://cnx.org/content/m42237/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Statistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying ExplanationBy: College PhysicsURL: http://cnx.org/content/m42238/1.1/

INDEX 153

Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to Oscillatory Motion and WavesBy: College PhysicsURL: http://cnx.org/content/m42239/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Hooke’s Law: Stress and Strain RevisitedBy: College PhysicsURL: http://cnx.org/content/m42240/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Period and Frequency in OscillationsBy: College PhysicsURL: http://cnx.org/content/m42241/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Simple Harmonic Motion: A Special Periodic MotionBy: College PhysicsURL: http://cnx.org/content/m42242/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: The Simple PendulumBy: College PhysicsURL: http://cnx.org/content/m42243/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Energy and the Simple Harmonic OscillatorBy: College PhysicsURL: http://cnx.org/content/m42244/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Uniform Circular Motion and Simple Harmonic MotionBy: College PhysicsURL: http://cnx.org/content/m42245/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Damped Harmonic MotionBy: College PhysicsURL: http://cnx.org/content/m42246/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Forced Oscillations and ResonanceBy: College PhysicsURL: http://cnx.org/content/m42247/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: WavesBy: College PhysicsURL: http://cnx.org/content/m42248/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Superposition and Interference

154 INDEX

By: College PhysicsURL: http://cnx.org/content/m42249/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Energy in Waves: IntensityBy: College PhysicsURL: http://cnx.org/content/m42250/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to the Physics of HearingBy: College PhysicsURL: http://cnx.org/content/m42254/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: SoundBy: College PhysicsURL: http://cnx.org/content/m42255/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Speed of Sound, Frequency, and WavelengthBy: College PhysicsURL: http://cnx.org/content/m42256/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Sound Intensity and Sound LevelBy: College PhysicsURL: http://cnx.org/content/m42257/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Doppler Effect and Sonic BoomsBy: College PhysicsURL: http://cnx.org/content/m42712/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Sound Interference and Resonance: Standing Waves in Air ColumnsUsed here as: Sound Interference and Resonance: Standing Waves in Air ColumnsBy: College PhysicsURL: http://cnx.org/content/m42296/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: HearingBy: College PhysicsURL: http://cnx.org/content/m42297/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: UltrasoundBy: College PhysicsURL: http://cnx.org/content/m42298/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to Electric Charge and Electric FieldUsed here as: Introduction to Electric Charge and Electric FieldBy: College Physics

INDEX 155

URL: http://cnx.org/content/m42299/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Static Electricity and Charge: Conservation of ChargeBy: College PhysicsURL: http://cnx.org/content/m42300/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Conductors and InsulatorsBy: College PhysicsURL: http://cnx.org/content/m42306/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Coulomb’s LawBy: College PhysicsURL: http://cnx.org/content/m42308/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Electric Field: Concept of a Field RevisitedUsed here as: Electric Field: Concept of a Field RevisitedBy: College PhysicsURL: http://cnx.org/content/m42310/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Electric Field Lines: Multiple ChargesUsed here as: Electric Field Lines: Multiple ChargesBy: College PhysicsURL: http://cnx.org/content/m42312/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Electric Forces in BiologyBy: College PhysicsURL: http://cnx.org/content/m42315/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Conductors and Electric Fields in Static EquilibriumUsed here as: Conductors and Electric Fields in Static EquilibriumBy: College PhysicsURL: http://cnx.org/content/m42317/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Applications of ElectrostaticsBy: College PhysicsURL: http://cnx.org/content/m42329/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to Electric Potential and Electric EnergyUsed here as: Introduction to Electric Potential and Electric EnergyBy: College PhysicsURL: http://cnx.org/content/m42320/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Electric Potential Energy: Potential Difference

156 INDEX

Used here as: Electric Potential Energy: Potential DifferenceBy: College PhysicsURL: http://cnx.org/content/m42324/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Electric Potential in a Uniform Electric FieldUsed here as: Electric Potential in a Uniform Electric FieldBy: College PhysicsURL: http://cnx.org/content/m42326/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Electric Potential due to a Point ChangeUsed here as: Electric Potential due to a Point ChangeBy: College PhysicsURL: http://cnx.org/content/m42328/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Equipotential LinesBy: College PhysicsURL: http://cnx.org/content/m42331/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Capacitors and DielectricsBy: College PhysicsURL: http://cnx.org/content/m42333/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Capacitors in Series and ParallelUsed here as: Capacitors in Series and ParallelBy: College PhysicsURL: http://cnx.org/content/m42336/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Energy Stored in CapacitorsBy: College PhysicsURL: http://cnx.org/content/m42395/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to Electric Current, Resistance, and Ohm's LawUsed here as: Introduction to Electric Current, Resistance, and Ohm's LawBy: College PhysicsURL: http://cnx.org/content/m42339/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: CurrentBy: College PhysicsURL: http://cnx.org/content/m42341/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Ohm’s Law: Resistance and Simple CircuitsBy: College PhysicsURL: http://cnx.org/content/m42344/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

INDEX 157

Module: Resistance and ResistivityBy: College PhysicsURL: http://cnx.org/content/m42346/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Electric Power and EnergyBy: College PhysicsURL: http://cnx.org/content/m42714/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Alternating Current versus Direct CurrentUsed here as: Alternating Current versus Direct CurrentBy: College PhysicsURL: http://cnx.org/content/m42348/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Electric Hazards and the Human BodyUsed here as: Electric Hazards and the Human BodyBy: College PhysicsURL: http://cnx.org/content/m42350/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Nerve Conduction-ElectrocardiogramsUsed here as: Nerve Conduction-ElectrocardiogramsBy: College PhysicsURL: http://cnx.org/content/m42352/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to Circuits, Bioelectricity, and DC InstrumentsUsed here as: Introduction to Circuits, Bioelectricity, and DC InstrumentsBy: College PhysicsURL: http://cnx.org/content/m42354/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Resistors in Series and ParallelBy: College PhysicsURL: http://cnx.org/content/m42356/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Electromotive Force: Terminal VoltageUsed here as: Electromotive Force: Terminal VoltageBy: College PhysicsURL: http://cnx.org/content/m42357/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Kirchhoff’s RulesBy: College PhysicsURL: http://cnx.org/content/m42359/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: DC Voltmeters and AmmetersBy: College PhysicsURL: http://cnx.org/content/m42360/1.1/Copyright: College Physics

158 INDEX

License: http://creativecommons.org/licenses/by/3.0/

Module: Null MeasurementsBy: College PhysicsURL: http://cnx.org/content/m42362/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: DC Circuits Containing Resistors and CapacitorsBy: College PhysicsURL: http://cnx.org/content/m42363/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to MagnetismBy: College PhysicsURL: http://cnx.org/content/m42365/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: MagnetsBy: College PhysicsURL: http://cnx.org/content/m42366/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Ferromagnets and ElectromagnetsBy: College PhysicsURL: http://cnx.org/content/m42368/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Magnetic Fields and Magnetic Field LinesUsed here as: Magnetic Fields and Magnetic Field LinesBy: College PhysicsURL: http://cnx.org/content/m42370/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Magnetic Field Strength B: Force on a Moving Charge in a Magnetic FieldUsed here as: Magnetic Field Strength B: Force on a Moving Charge in a Magnetic FieldBy: College PhysicsURL: http://cnx.org/content/m42372/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Force on a Moving Charge in a Magnetic Field: Examples and ApplicationsUsed here as: Force on a Moving Charge in a Magnetic Field: Examples and ApplicationsBy: College PhysicsURL: http://cnx.org/content/m42375/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: The Hall EffectBy: College PhysicsURL: http://cnx.org/content/m42377/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Magnetic Force on a Current-Carrying ConductorUsed here as: Magnetic Force on a Current-Carrying ConductorBy: College PhysicsURL: http://cnx.org/content/m42398/1.1/

INDEX 159

Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Torque on a Current Loop: Motors and MetersBy: College PhysicsURL: http://cnx.org/content/m42380/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Magnetic Fields Produced by Currents: Ampere’s LawUsed here as: Magnetic Fields Produced by Currents: Ampere’s LawBy: College PhysicsURL: http://cnx.org/content/m42382/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Magnetic Force Between Two Parallel ConductorsUsed here as: Magnetic Force Between Two Parallel ConductorsBy: College PhysicsURL: http://cnx.org/content/m42386/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: More Applications of MagnetismBy: College PhysicsURL: http://cnx.org/content/m42388/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to Electromagnetic Induction: AC Circuits, and Electrical TechnologiesUsed here as: Introduction to Electromagnetic Induction: AC Circuits, and Electrical TechnologiesBy: College PhysicsURL: http://cnx.org/content/m42389/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Induced Emf and Magnetic FluxBy: College PhysicsURL: http://cnx.org/content/m42390/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Faraday’s Law of Induction: Lenz’s LawUsed here as: Faraday’s Law of Induction: Lenz’s LawBy: College PhysicsURL: http://cnx.org/content/m42392/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Motional EmfBy: College PhysicsURL: http://cnx.org/content/m42400/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Eddy Currents and Magnetic DampingBy: College PhysicsURL: http://cnx.org/content/m42404/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Electric GeneratorsBy: College Physics

160 INDEX

URL: http://cnx.org/content/m42408/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Back EmfBy: College PhysicsURL: http://cnx.org/content/m42411/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: TransformersBy: College PhysicsURL: http://cnx.org/content/m42414/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Electrical Safety: Systems and DevicesUsed here as: Electrical Safety: Systems and DevicesBy: College PhysicsURL: http://cnx.org/content/m42416/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: InductanceBy: College PhysicsURL: http://cnx.org/content/m42420/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: RL CircuitsBy: College PhysicsURL: http://cnx.org/content/m42425/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Reactance, Inductive and CapacitiveUsed here as: Reactance, Inductive and CapacitiveBy: College PhysicsURL: http://cnx.org/content/m42427/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: RLC Series AC CircuitsBy: College PhysicsURL: http://cnx.org/content/m42431/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to Electromagnetic WavesUsed here as: Introduction to Electromagnetic WavesBy: College PhysicsURL: http://cnx.org/content/m42434/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Maxwell’s Equations: Electromagnetic Waves Predicted and ObservedUsed here as: Maxwell’s Equations: Electromagnetic Waves Predicted and ObservedBy: College PhysicsURL: http://cnx.org/content/m42437/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Production of Electromagnetic Waves

INDEX 161

Used here as: Production of Electromagnetic WavesBy: College PhysicsURL: http://cnx.org/content/m42440/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: The Electromagnetic SpectrumBy: College PhysicsURL: http://cnx.org/content/m42444/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Energy in Electromagnetic WavesBy: College PhysicsURL: http://cnx.org/content/m42446/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to Geometric OpticsBy: College PhysicsURL: http://cnx.org/content/m42449/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: The Ray Aspect of LightBy: College PhysicsURL: http://cnx.org/content/m42452/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: The Law of ReflectionBy: College PhysicsURL: http://cnx.org/content/m42456/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: The Law of RefractionBy: College PhysicsURL: http://cnx.org/content/m42459/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Total Internal ReflectionBy: College PhysicsURL: http://cnx.org/content/m42462/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Dispersion: The Rainbow and PrismsUsed here as: Dispersion: The Rainbow and PrismsBy: College PhysicsURL: http://cnx.org/content/m42466/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Image Formation by LensesBy: College PhysicsURL: http://cnx.org/content/m42470/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Image Formation by MirrorsBy: College Physics

162 INDEX

URL: http://cnx.org/content/m42474/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to Vision and Optical InstrumentsUsed here as: Introduction to Vision and Optical InstrumentsBy: College PhysicsURL: http://cnx.org/content/m42478/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Physics of the EyeBy: College PhysicsURL: http://cnx.org/content/m42482/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Vision CorrectionBy: College PhysicsURL: http://cnx.org/content/m42484/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Color and Color VisionBy: College PhysicsURL: http://cnx.org/content/m42487/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: MicroscopesBy: College PhysicsURL: http://cnx.org/content/m42491/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: TelescopesBy: College PhysicsURL: http://cnx.org/content/m42493/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: AberrationsBy: College PhysicsURL: http://cnx.org/content/m42292/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to Wave OpticsBy: College PhysicsURL: http://cnx.org/content/m42496/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: The Wave Aspect of Light: InterferenceUsed here as: The Wave Aspect of Light: InterferenceBy: College PhysicsURL: http://cnx.org/content/m42501/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Huygen’s Principle: DiffractionBy: College PhysicsURL: http://cnx.org/content/m42505/1.1/

INDEX 163

Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Young’s Double Slit ExperimentBy: College PhysicsURL: http://cnx.org/content/m42508/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Multiple Slit DiffractionBy: College PhysicsURL: http://cnx.org/content/m42512/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Single Slit DiffractionBy: College PhysicsURL: http://cnx.org/content/m42515/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Limits of Resolution: The Rayleigh CriterionBy: College PhysicsURL: http://cnx.org/content/m42517/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Thin Film InterferenceBy: College PhysicsURL: http://cnx.org/content/m42519/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: PolarizationBy: College PhysicsURL: http://cnx.org/content/m42522/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: *Extended Topic* Microscopy Enhanced by the Wave Characteristics of LightUsed here as: *Extended Topic* Microscopy Enhanced by the Wave Characteristics of LightBy: College PhysicsURL: http://cnx.org/content/m42290/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to Special RelativityUsed here as: Introduction to Special RelativityBy: College PhysicsURL: http://cnx.org/content/m42525/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Einstein’s PostulatesBy: College PhysicsURL: http://cnx.org/content/m42528/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Simultaneity and Time DilationBy: College PhysicsURL: http://cnx.org/content/m42531/1.1/Copyright: College Physics

164 INDEX

License: http://creativecommons.org/licenses/by/3.0/

Module: Length ContractionBy: College PhysicsURL: http://cnx.org/content/m42535/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Relativistic Addition of VelocitiesUsed here as: Relativistic Addition of VelocitiesBy: College PhysicsURL: http://cnx.org/content/m42540/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Relativistic MomentumBy: College PhysicsURL: http://cnx.org/content/m42542/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Relativistic EnergyBy: College PhysicsURL: http://cnx.org/content/m42546/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to Quantum PhysicsBy: College PhysicsURL: http://cnx.org/content/m42550/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Quantization of EnergyBy: College PhysicsURL: http://cnx.org/content/m42554/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: The Photoelectric EffectBy: College PhysicsURL: http://cnx.org/content/m42558/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Photon Energies and the Electromagnetic SpectrumBy: College PhysicsURL: http://cnx.org/content/m42563/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Photon MomentumBy: College PhysicsURL: http://cnx.org/content/m42568/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: The Particle-Wave DualityBy: College PhysicsURL: http://cnx.org/content/m42573/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: The Wave Nature of Matter

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By: College PhysicsURL: http://cnx.org/content/m42576/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Probability: The Heisenberg Uncertainty PrincipleBy: College PhysicsURL: http://cnx.org/content/m42579/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: The Particle-Wave Duality ReviewedBy: College PhysicsURL: http://cnx.org/content/m42581/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to Atomic PhysicsBy: College PhysicsURL: http://cnx.org/content/m42585/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Discovery of the AtomBy: College PhysicsURL: http://cnx.org/content/m42589/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Discovery of the Parts of the Atom: Electrons and NucleiUsed here as: Discovery of the Parts of the Atom: Electrons and NucleiBy: College PhysicsURL: http://cnx.org/content/m42592/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Bohr’s Theory of the Hydrogen AtomBy: College PhysicsURL: http://cnx.org/content/m42596/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: X-Rays: Atomic Origins and ApplicationsBy: College PhysicsURL: http://cnx.org/content/m42599/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Applications of Atomic Excitations and De-ExcitationsUsed here as: Applications of Atomic Excitations and De-ExcitationsBy: College PhysicsURL: http://cnx.org/content/m42602/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: The Wave Nature of Matter Causes QuantizationBy: College PhysicsURL: http://cnx.org/content/m42606/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Patterns in Spectra Reveal More QuantizationBy: College Physics

166 INDEX

URL: http://cnx.org/content/m42609/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Quantum Numbers and RulesBy: College PhysicsURL: http://cnx.org/content/m42614/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: The Pauli Exclusion PrincipleBy: College PhysicsURL: http://cnx.org/content/m42618/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to Radioactivity and Nuclear PhysicsBy: College PhysicsURL: http://cnx.org/content/m42620/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Nuclear RadioactivityBy: College PhysicsURL: http://cnx.org/content/m42623/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Radiation Detection and DetectorsBy: College PhysicsURL: http://cnx.org/content/m42627/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Substructure of the NucleusBy: College PhysicsURL: http://cnx.org/content/m42631/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Nuclear Decay and Conservation LawsBy: College PhysicsURL: http://cnx.org/content/m42633/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Half-Life and ActivityBy: College PhysicsURL: http://cnx.org/content/m42636/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Binding EnergyBy: College PhysicsURL: http://cnx.org/content/m42640/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: TunnelingBy: College PhysicsURL: http://cnx.org/content/m42644/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

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Module: Introduction to Applications of Nuclear PhysicsBy: College PhysicsURL: http://cnx.org/content/m42646/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Medical Imaging and DiagnosticsBy: College PhysicsURL: http://cnx.org/content/m42649/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Biological Effects of Ionizing RadiationBy: College PhysicsURL: http://cnx.org/content/m42652/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Therapeutic Uses of Ionizing RadiationBy: College PhysicsURL: http://cnx.org/content/m42654/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Food IrradiationBy: College PhysicsURL: http://cnx.org/content/m42656/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: FusionBy: College PhysicsURL: http://cnx.org/content/m42659/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: FissionBy: College PhysicsURL: http://cnx.org/content/m42662/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Nuclear WeaponsBy: College PhysicsURL: http://cnx.org/content/m42665/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to Particle PhysicsBy: College PhysicsURL: http://cnx.org/content/m42667/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: The Yukawa Particle and the Heinsenberg Uncertainty Principle RevisitedUsed here as: The Yukawa Particle and the Heinsenberg Uncertainty Principle RevisitedBy: College PhysicsURL: http://cnx.org/content/m42669/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: The Four Basic ForcesBy: College Physics

168 INDEX

URL: http://cnx.org/content/m42671/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Accelerators Create Matter from EnergyBy: College PhysicsURL: http://cnx.org/content/m42718/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Particles, Patterns, and Conservation LawsBy: College PhysicsURL: http://cnx.org/content/m42674/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Quarks: Is That All There Is?By: College PhysicsURL: http://cnx.org/content/m42678/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: GUTs, the Unification of ForcesBy: College PhysicsURL: http://cnx.org/content/m42680/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Introduction to Frontiers of PhysicsBy: College PhysicsURL: http://cnx.org/content/m42683/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Cosmology and Particle PhysicsBy: College PhysicsURL: http://cnx.org/content/m42686/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: General Relativity and Quantum GravityBy: College PhysicsURL: http://cnx.org/content/m42689/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: SuperstringsBy: College PhysicsURL: http://cnx.org/content/m42691/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Dark Matter and ClosureBy: College PhysicsURL: http://cnx.org/content/m42692/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Complexity and ChaosBy: College PhysicsURL: http://cnx.org/content/m42694/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

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Module: High-Temperature SuperconductorsBy: College PhysicsURL: http://cnx.org/content/m42696/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Some Questions We Know to AskBy: College PhysicsURL: http://cnx.org/content/m42704/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Appendix A: Atomic MassesBy: College PhysicsURL: http://cnx.org/content/m42699/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Appendix B: Selected Radioactive IsotopesBy: College PhysicsURL: http://cnx.org/content/m42702/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Appendix C: Useful InformationBy: College PhysicsURL: http://cnx.org/content/m42720/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Appendix CO: Missions of ExplorationBy: College PhysicsURL: http://cnx.org/content/m42706/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

Module: Appendix G: Glossary of Key Symbols and NotationBy: College PhysicsURL: http://cnx.org/content/m42709/1.1/Copyright: College PhysicsLicense: http://creativecommons.org/licenses/by/3.0/

170 INDEX

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