MACMILLAN COLLEGE WORK OUT SERIES

Heat

and

Thermodynamics Michael Sprackling

150eh YEAR

M

Contents

Preface viii

1 Basic Concepts in Thermodynamics 1.1 Introduction 1 1.2 Some Definitions 1 1.3 The First Stages in Problem-Solving With Closed Systems 3 1.4 Worked Example 4

2 Work 2.1 Definition of Work 5 2.2 Problem-Solving 6 2.3 Electrical Work 6 2.4 Worked Examples on Electrical Work 6 2.5 Work to Change the Volume of a Closed Hydrostatic System 8 2.6 Worked Examples on Pressure-Volume Work 8 2.7 Work to Change the Length of an Elastic Rod 12 2.8 Worked Examples on Work and Elastic Deformation 12 2.9 Exercises 14

3 Gases and the Ideal Gas Scale of Temperature 3.1 Boyle's Law 15 3.2 Ideal Gases 16 3.3 Problem-Solving 16 3.4 Worked Examples on Boyle's Law 16 3.5 The Ideal Gas Scale of Temperature and the Ideal Gas Equation 20 3.6 Worked Examples on the Ideal Gas Equation 21 3.7 Exercises 25

4 The First Law of Thermodynamics 4.1 Internal Energy 26 4.2 The First Law of Thermodynamics 27 4.3 Problem-Solving 27 4.4 Worked Examples on the First Law of Thermodynamics 27 4.5 Reversible Processes 29 4.6 Worked Examples on Reversible Processes 30 4.7 Heat Capacities 31 4.8 Worked Examples on Heat Capacities 33 4.9 Exercises 42

5 The Second Law of Thermodynamics 5.1 The Clausius Statement of the Second Law 43 5.2 Heat Engines 43 5.3 Worked Examples on Heat Engines 44 5.4 Kelvin's Statement of The Second Law 48

5.5 Carnot's Theorem and its Corollary 48 5.6 Universal Temperatures 49 5.7 Thermodynamic Temperature 49 5.8 Worked Examples on Heat Engines and Thermodynamic Temperature 50 5.9 Celsius Temperature 53 5.10 Problem-Solving 53 5.11 Worked Examples on Heat Engines and the Second Law of Thermodynamics 53 5.12 Exercises 60

6 Entropy 6.1 The Inequality of Clausius 61 6.2 Entropy 61 6.3 Worked Examples on Entropy 62 6.4 Entropy and Work 66 6.5 Worked Examples on Entropy and Work 67 6.6 The Entropy Form of the First Law 68 6.7 Worked Examples on the Entropy Form of the First Law 69 6.8 Entropy and Irreversible Processes 71 6.9 Worked Examples on the Law of the Increase of Entropy 71 6.10 Maxwell's Relations 75 6.11 Some Useful Mathematical Relations 75 6.12 Problem-Solving 75 6.13 Worked Examples on Entropy 76 6.14 Exercises 81

7 Thermodynamic Potential Functions 7.1 The Helmholtz Function (Helmholtz Free Energy) 82 7.2 Worked Examples on the Helmholtz Function 83 7.3 The Gibbs Function (Gibbs Free Energy) 86 7.4 Worked Examples on the Gibbs Function 87 7.5 Useful Work and Availability 90 7.6 Worked Examples on Availability 91 7.7 Exercises 100

8 Some Simple Thermodynamic Systems 8.1 Closed Hydrostatic Systems 101 8.2 Worked Examples on Closed Hydrostatic Systems 102 8.3 Ideal Gases 111 8.4 Worked Examples on Ideal Gases 112 8.5 Perfectly Elastic Solids 119 8.6 Worked Examples on Perfectly Elastic Solids 120 8.7 Voltaic Cells 126 8.8 Worked Example on Voltaic Cells 127 8.9 Exercises 128

9 Heat Capacities and Equations of State 9.1 Introduction 130 9.2 Heat Capacities 130 9.3 Worked Examples on Heat Capacities 131 9.4 Equations of State 139 9.5 Worked Examples on Equations of State 141 9.6 Exercises 145

10 Phase Changes 10.1 The Enthalpy of a Phase Change (Latent Heat) 147 10.2 Worked Examples on the Enthalpy of a Phase Change 148 10.3 The Clapeyron-Clausius Equation 153

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10.4 Worked Examples on the Clapeyron-Clausius Equation 154 10.5 The Equation of Clausius 157 10.6 Worked Example on the Equation of Clausius 158 10.7 Exercises 159

11 The Third Law of Thermodynamics 11.1 The Third Law of Thermodynamics 161 11.2 Worked Examples on the Third Law 161 11.3 Planck's and Simon's Versions of the Third Law 164 11.4 Worked Example on Absolute Entropy 165 11.5 Allotropic Transformations 165 11.6 Worked Example on Allotropic Transformations 166 11.7 Exercises 167

12 Irreversible Processes 12.1 Irreversible Processes and Thermodynamics 168 12.2 The Joule Process 168 12.3 Worked Examples on the Joule Process 169 12.4 The Joule-Thomson Process 173 12.5 Worked Examples on the Joule-Thomson Process 174 12.6 Exercises 182

13 A Simple Kinetic Theory of Gases 13.1 A Simple Kinetic Theory of Gases 183 13.2 Worked Examples on a Kinetic Theory of Gases 185 13.3 Exercises 190

14 Heat Transfer 14.1 Introduction 191 14.2 Heat Conduction 191 14.3 A General Approach to Solving Heat Conduction Problems 192 14.4 Worked Examples on Heat Conduction 193 14.5 Heat Convection 197 14.6 Worked Examples on Heat Convection 198 14.7 Thermal Radiation 202 14.8 Worked Examples on Thermal Radiation 204 14.9 Exercises 208

Recommended Reading 210 Index 211

VII