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PHYSICS 1401
SEMESTER EXAM REVIEW
1.1 MeasurementsVernier caliper
%)100( valueltheoretica
valuealexperiment - valueltheoretica error %
Micrometer
Photogate (millisec)
1.2 Resultant and Equilibrant
2.4 Motion Graphs
2.4 Equations of Kinematics for Constant Acceleration
Equations of Kinematics for Constant Acceleration
POSITION, VELOCITY & ACCELERATION
tvvx o 21
221 attvx o
atvv o
axvv o 222
3.2 Equations of Kinematics in Two Dimensions
tavv xoxx tvvx xox 21
xavv xoxx 222 221 tatvx xox
3.2 Equations of Kinematics in Two Dimensions
tavv yoyy
221 tatvy yoy
tvvy yoy 21
yavv yoyy 222
3.3 Projectile Motion
Under the influence of gravity alone, an object near the surface of the Earth will accelerate downwards at 9.80 m/s2.
2sm80.9ya
0xa
constant oxx vv
3.3 Projectile Motion
Objects falling in a vacuum will experience the same speed.
Galileo started experimenting totest the theories of otherscientists such as Aristotle.
3.3 Projectile Motion
Properties of Projectile Motion
1. Horizontal velocity stays constant.2. No vertical velocity when object is thrown horizontally
from the top of hill. 3. When object is launched from the ground, velocity
has horizontal and vertical components. 4. At the top of the trajectory, no vertical velocity, but
there is acceleration due to gravity. 5. The time for a projectile to reach the top is equal to
the time for it to go back to the ground. 6. The initial launching velocity is equal to the final
lvelocity just before it hits the ground.
3.3 Projectile Motion
y ay vy voy t-1050 m -9.80 m/s2 ? 0 m/s 14.6 s
3.3 Projectile Motion
y ay vy voy t? -9.80 m/s2 0 14 m/s
3.3 Projectile Motion
Example 7 The Time of Flight of a Kickoff
What is the time of flight between kickoff and landing?
3.3 Projectile Motion
y ay vy voy t0 -9.80 m/s2 14 m/s ?
3.3 Projectile Motion
y ay vy voy t0 -9.80 m/s2 14 m/s ?
221 tatvy yoy
2221 sm80.9sm140 tt
t2sm80.9sm1420
s 9.2t
3.3 Projectile Motion
Example 8 The Range of a Kickoff
Calculate the range R of the projectile.
m 49s 9.2sm17
221
tvtatvx oxxox
4.2 Newton’s First Law of Motion
An object continues in a state of restor in a state of motion at a constant speed along a straight line, unless compelled to change that state by a net force.
The net force is the vector sum of allof the forces acting on an object.
If the vector sum is equal to zero, then the system is in equilibrium.
4.2 Newton’s First Law of Motion
Inertia is the natural tendency of anobject to remain at rest in motion ata constant speed along a straight line.
The mass of an object is a quantitativemeasure of inertia.
SI Unit of Mass: kilogram (kg)
4.3 Newton’s Second Law of Motion
Newton’s Second Law
When a net external force acts on an objectof mass m, the acceleration that results is directly proportional to the net force and hasa magnitude that is inversely proportional tothe mass. The direction of the acceleration isthe same as the direction of the net force.
m F
a
aF
m
4.3 Newton’s Second Law of Motion
SI Unit for Force
22 s
mkg
s
mkg
This combination of units is called a newton (N).
4.4 The Vector Nature of Newton’s Second Law
xx maFyy maF
The direction of force and acceleration vectorscan be taken into account by using x and ycomponents.
aF
m
is equivalent to
4.5 Newton’s Third Law of Motion
Newton’s Third Law of Motion
Whenever one body exerts a force on a second body, the second body exerts an oppositely directed force of equal magnitude on the first body.
It involves TWO objects to form an action-reaction pair.
4.6 Types of Forces: An Overview
In nature there are two general types of forces,fundamental and nonfundamental.
Fundamental Forces
1. Gravitational force
2. Strong Nuclear force
3. Electroweak force
4.6 Types of Forces: An Overview
Examples of nonfundamental forces:
friction
tension in a rope
normal or support forces
4.7 The Gravitational Force
Newton’s Law of Universal Gravitation
Every particle in the universe exerts an attractive force on everyother particle.
He said gravity is universal.
The force that each exerts on the other is directed along the linejoining the particles.
4.7 The Gravitational Force
For two particles that have masses m1 and m2 and are separated by a distance r, the force has a magnitude given by
221
r
mmGF
2211 kgmN10673.6 G
4.7 The Gravitational Force
N 104.1
m 1.2
kg 25kg 12kgmN1067.6
8
22211
221
r
mmGF
4.7 The Gravitational Force
4.9 Static and Kinetic Frictional Forces
When the two surfaces are not sliding across one anotherthe friction is called static friction.
4.9 Static and Kinetic Frictional Forces
The magnitude of the static frictional force can have any valuefrom zero up to a maximum value.
MAXss ff
NsMAXs Ff
10 s is called the coefficient of static friction.
4.9 Static and Kinetic Frictional Forces
Note that the magnitude of the frictional force doesNOT depend on the contact area of the surfaces.
4.9 Static and Kinetic Frictional Forces
Static friction opposes the impending relative motion betweentwo objects.
Kinetic friction opposes the relative sliding motion motions thatactually does occur.
Nkk Ff
10 k is called the coefficient of kinetic friction.
4.9 Static and Kinetic Frictional Forces
4.10 The Tension Force
Cables and ropes transmit forces through tension.
4.11 Equilibrium Application of Newton’s Laws of Motion
Definition of EquilibriumAn object is in equilibrium when it has zero acceleration.
0xF
0yF
4.12 Nonequilibrium Application of Newton’s Laws of Motion
xx maF
yy maF
When an object is accelerating, it is not in equilibrium.
5.1 Uniform Circular Motion
Let T be the time it takes for the object totravel once around the circle.
vr
T
2
r
5.2 Centripetal Acceleration
The direction of the centripetal acceleration is towards the center of the circle; in the same direction as the change in velocity.
r
vac
2
5.3 Centripetal Force
aF
m
m F
a
Recall Newton’s Second Law
When a net external force acts on an objectof mass m, the acceleration that results is directly proportional to the net force and hasa magnitude that is inversely proportional tothe mass. The direction of the acceleration isthe same as the direction of the net force.
5.3 Centripetal Force
Thus, in uniform circular motion there must be a netforce to produce the centripetal acceleration.
The centripetal force is the name given to the net force required to keep an object moving on a circular path.
The direction of the centripetal force always points towardthe center of the circle and continually changes direction as the object moves.
r
vmmaF cc
2
5.7 Vertical Circular Motion
r
vmmgFN
21
1
r
vmmgFN
23
3
r
vmFN
22
2
r
vmFN
24
4
6.1 Work Done by a Constant Force
FsW J joule 1 mN 1
6.1 Work Done by a Constant Force
sFW cos1180cos
090cos
10cos
6.1 Work Done by a Constant Force
FssFW 0cos
FssFW 180cos
6.2 The Work-Energy Theorem and Kinetic Energy
THE WORK-ENERGY THEOREM
When a net external force does work on and object, the kineticenergy of the object changes according to
2212
f21
of KEKE omvmvW
6.3 Gravitational Potential Energy
sFW cos
fo hhmgW gravity
6.3 Gravitational Potential Energy
fo hhmgW gravity
6.3 Gravitational Potential Energy
fo mghmghW gravity
DEFINITION OF GRAVITATIONAL POTENTIAL ENERGY
The gravitational potential energy PE is the energy that anobject of mass m has by virtue of its position relative to thesurface of the earth. That position is measured by the heighth of the object relative to an arbitrary zero level:
mghPE
J joule 1 mN 1
6.3 Gravitational Potential Energy
2212
f21W omvmv
fo hhmgW gravity
221
ofo mvhhmg
foo hhgv 2
sm40.8m 80.4m 20.1sm80.92 2 ov
6.4 Conservative Versus Nonconservative Forces
Version 1 A force is conservative when the work it doeson a moving object is independent of the path between theobject’s initial and final positions.
fo hhmgW gravity
6.4 Conservative Versus Nonconservative Forces
Version 2 A force is conservative when it does no work on an object moving around a closed path, starting andfinishing at the same point.
fo hh fo hhmgW gravity
6.5 The Conservation of Mechanical Energy
THE PRINCIPLE OF CONSERVATION OF MECHANICAL ENERGY
The total mechanical energy (E = KE + PE) of an objectremains constant as the object moves, provided that the network done by external nonconservative forces is zero.
6.5 The Conservation of Mechanical Energy
6.5 The Conservation of Mechanical Energy
of EE
2212
21
ooff mvmghmvmgh
2212
21
ooff vghvgh
6.7 Power
DEFINITION OF AVERAGE POWER
Average power is the rate at which work is done, and itis obtained by dividing the work by the time required to perform the work.
t
WP
Time
Work
(W)watt sjoule
6.7 Power
Time
energyin ChangeP
watts745.7 secondpoundsfoot 550 horsepower 1
vFP
6.8 Other Forms of Energy and the Conservation of Energy
THE PRINCIPLE OF CONSERVATION OF ENERGYEnergy can neither be created nor destroyed, but can only be converted from one form to another.
6.9 Work Done by a Variable Force
sFW cos
Constant Force
Variable Force
2211 coscos sFsFW
7.1 The Impulse-Momentum Theorem
There are many situations when the force on an object is not constant.
7.1 The Impulse-Momentum Theorem
DEFINITION OF IMPULSE
The impulse of a force is the product of the averageforce and the time interval during which the force acts:
tFJ
Impulse is a vector quantity and has the same directionas the average force.
s)(N secondsnewton
7.1 The Impulse-Momentum Theorem
tFJ
7.1 The Impulse-Momentum Theorem
DEFINITION OF LINEAR MOMENTUM
The linear momentum of an object is the product of the object’s mass times its velocity:
vp
m
Linear momentum is a vector quantity and has the same direction as the velocity.
m/s)(kg ndmeter/secokilogram
7.1 The Impulse-Momentum Theorem
t
of vva
aF
m
t
mm
of vvF
of vvF
mmt
7.1 The Impulse-Momentum Theorem
of vvF
mmt
final momentum initial momentum
IMPULSE-MOMENTUM THEOREM
When a net force acts on an object, the impulse ofthis force is equal to the change in the momentumof the object
impulse
7.2 The Principle of Conservation of Linear Momentum
of PP
tforces external average of sum
If the sum of the external forces is zero, then
of PP
0 of PP
PRINCIPLE OF CONSERVATION OF LINEAR MOMENTUM
The total linear momentum of an isolated system is constant(conserved). An isolated system is one for which the sum ofthe average external forces acting on the system is zero.
7.3 Collisions in One Dimension
The total linear momentum is conserved when two objectscollide, provided they constitute an isolated system.
Elastic collision -- One in which the total kinetic energy of the system after the collision is equal to the total kinetic energy before the collision. Momentum and KE are constant.
Inelastic collision -- One in which the total kinetic energy of the system after the collision is not equal to the total kinetic energy before the collision; if the objects stick together after colliding, the collision is said to be completely inelastic.
Momentum is constant but not KE.
7.2 The Principle of Conservation of Linear Momentum
of PP
02211 ff vmvm
2
112 m
vmv ff
sm5.1
kg 88
sm5.2kg 542
fv
7.3 Perfectly Inelastic Collision
Momentum is conserved. Kinetic energy is NOT conserved.
7.5 Center of Mass
The center of mass is a point that represents the average location forthe total mass of a system.
21
2211
mm
xmxmxcm
7.5 Center of Mass
21
2211
mm
xmxmxcm
21
2211
mm
vmvmvcm
7.5 Center of Mass
21
2211
mm
vmvmvcm
In an isolated system, the total linear momentum does not change,therefore the velocity of the center of mass does not change.
7.5 Center of Mass
021
2211
mm
vmvmvcm
BEFORE
AFTER
0002.0
kg 54kg 88
sm5.2kg 54sm5.1kg 88
cmv
8.1 Rotational Motion and Angular Displacement
r
s
Radius
length Arcradians)(in
For a full revolution:
360rad 2 rad 22
r
r
8.1 Rotational Motion and Angular Displacement
rad 0349.0deg360
rad 2deg00.2
miles) (920 m1048.1
rad 0349.0m1023.46
7
rs
r
s
Radius
length Arcradians)(in
8.2 Angular Velocity and Angular Acceleration
DEFINITION OF AVERAGE ANGULAR VELOCITY
timeElapsed
ntdisplacemeAngular locity angular ve Average
ttt o
o
SI Unit of Angular Velocity: radian per second (rad/s)
8.2 Angular Velocity and Angular Acceleration
Example 3 Gymnast on a High Bar
A gymnast on a high bar swings throughtwo revolutions in a time of 1.90 s.
Find the average angular velocityof the gymnast.
8.2 Angular Velocity and Angular Acceleration
rad 6.12rev 1
rad 2rev 00.2
srad63.6s 90.1
rad 6.12
8.2 Angular Velocity and Angular Acceleration
Changing angular velocity means that an angular acceleration is occurring.
DEFINITION OF AVERAGE ANGULAR ACCELERATION
ttt o
o
timeElapsed
locityangular vein Change on acceleratiangular Average
SI Unit of Angular acceleration: radian per second squared (rad/s2)
8.3 The Equations of Rotational Kinematics
8.3 The Equations of Rotational Kinematics
Example 5 Blending with a Blender
The blades are whirling with an angular velocity of +375 rad/s whenthe “puree” button is pushed in.
When the “blend” button is pushed,the blades accelerate and reach agreater angular velocity after the blades have rotated through anangular displacement of +44.0 rad.
The angular acceleration has a constant value of +1740 rad/s2.
Find the final angular velocity of the blades.
8.3 The Equations of Rotational Kinematics
θ α ω ωo t
+44.0 rad +1740 rad/s2 ? +375 rad/s
222 o
srad542rad0.44srad17402srad375
2
22
2
o
8.4 Angular Variables and Tangential Variables
velocityl tangentiaTv
speed l tangentiaTv
8.4 Angular Variables and Tangential Variables
t
rt
r
t
svT
t
rad/s)in ( rvT
8.4 Angular Variables and Tangential Variables
Tctotal aaa
Total acceleration is the vector sum of centripetal acceleration and tangential acceleration.
8.4 Angular Variables and Tangential Variables
t
rt
rr
t
vva oToTT
0
to
)rad/sin ( 2raT
8.4 Angular Variables and Tangential Variables
Example 6 A Helicopter Blade
A helicopter blade has an angular speed of 6.50 rev/s and anangular acceleration of 1.30 rev/s2.For point 1 on the blade, findthe magnitude of (a) thetangential speed and (b) thetangential acceleration.
8.4 Angular Variables and Tangential Variables
srad 8.40rev 1
rad 2
s
rev 50.6
sm122srad8.40m 3.00 rvT
8.4 Angular Variables and Tangential Variables
22 sm5.24srad17.8m 3.00 raT
22
srad 17.8rev 1
rad 2
s
rev 30.1
9.1 The Action of Forces and Torques on Rigid Objects
In pure translational motion, all points on anobject travel on parallel paths.
The most general motion is a combination oftranslation and rotation.
9.1 The Action of Forces and Torques on Rigid Objects
According to Newton’s second law, a net force causes anobject to have an acceleration.
What causes an object to have an angular acceleration?
TORQUE
9.1 The Action of Forces and Torques on Rigid Objects
DEFINITION OF TORQUE
Magnitude of Torque = (Magnitude of the force) x (Lever arm)
FDirection: The torque is positive when the force tends to produce a counterclockwise rotation about the axis.
SI Unit of Torque: newton x meter (N·m)
9.1 The Action of Forces and Torques on Rigid Objects
790 N
F
m106.355cos
2
mN 15
55cosm106.3N 720 2
9.2 Rigid Objects in Equilibrium
EQUILIBRIUM OF A RIGID BODY
A rigid body is in equilibrium if it has zero translationalacceleration and zero angular acceleration. In equilibrium,the sum of the externally applied forces is zero, and thesum of the externally applied torques is zero.
0 0yF0 xF
9.2 Rigid Objects in Equilibrium
022 WWF
N 1480
m 1.40
m 90.3N 5302 F
22
WWF
9.2 Rigid Objects in Equilibrium
021 WFFFy
0N 530N 14801 F
N 9501 F
9.2 Rigid Objects in Equilibrium
Example 5 Bodybuilding
The arm is horizontal and weighs 31.0 N. The deltoid muscle can supply1840 N of force. What is the weight of the heaviest dumbbell he can hold?
9.2 Rigid Objects in Equilibrium
0 Mddaa MWW
0.13sinm 150.0M
9.2 Rigid Objects in Equilibrium
N 1.86
m 620.0
0.13sinm 150.0N 1840m 280.0N 0.31
d
Maad
MWW
9.3 Center of Gravity
When an object has a symmetrical shape and its weight is distributed uniformly, the center of gravity lies at its geometrical center.
9.3 Center of Gravity
21
2211
WW
xWxWxcg
9.6 Angular Momentum
DEFINITION OF ANGULAR MOMENTUM
The angular momentum L of a body rotating about a fixed axis is the product of the body’s moment of inertia and its angular velocity with respect to thataxis:
IL
Requirement: The angular speed mustbe expressed in rad/s.
SI Unit of Angular Momentum: kg·m2/s
9.6 Angular Momentum
PRINCIPLE OF CONSERVATION OF ANGULAR MOMENTUM
The angular momentum of a system remains constant (is conserved) if the net external torque acting on the system is zero.
9.6 Angular Momentum
Conceptual Example 14 A Spinning Skater
An ice skater is spinning with botharms and a leg outstretched. Shepulls her arms and leg inward andher spinning motion changesdramatically.
Use the principle of conservationof angular momentum to explainhow and why her spinning motionchanges.
10.1 The Ideal Spring and Simple Harmonic Motion
xkF Appliedx
spring constant
Units: N/m
10.1 The Ideal Spring and Simple Harmonic Motion
HOOKE’S LAW: RESTORING FORCE OF AN IDEAL SPRING
The restoring force on an ideal spring is xkFx
10.2 Simple Harmonic Motion and the Reference Circle
period T: the time required to complete one cycle
frequency f: the number of cycles per second (measured in Hz)
Tf
1
Tf
22
amplitude A: the maximum displacement
10.3 Energy and Simple Harmonic Motion
DEFINITION OF ELASTIC POTENTIAL ENERGY
The elastic potential energy is the energy that a springhas by virtue of being stretched or compressed. For anideal spring, the elastic potential energy is
221
elasticPE kx
SI Unit of Elastic Potential Energy: joule (J)
10.3 Energy and Simple Harmonic Motion
Example 8 Changing the Mass of a Simple Harmonic Oscillator
A 0.20-kg ball is attached to a vertical spring. The spring constantis 28 N/m. When released from rest, how far does the ball fallbefore being brought to a momentary stop by the spring?
10.3 Energy and Simple Harmonic Motion
of EE
2212
212
212
21
ooofff kymghmvkymghmv
oo mghkh 221
m 14.0
mN28
sm8.9kg 20.02
2
2
k
mgho
10.4 The Pendulum
Example 10 Keeping Time
Determine the length of a simple pendulum that willswing back and forth in simple harmonic motion with a period of 1.00 s.
2
2L
g
Tf
m 248.0
4
sm80.9s 00.1
4 2
22
2
2
gTL
2
2
4gT
L
Period of simple pendulum isg
LT
22
11.1 Mass Density
DEFINITION OF MASS DENSITY
The mass density of a substance is CONSTANT andis the mass of a substance divided by its volume:
V
m
SI Unit of Mass Density: kg/m3
11.1 Mass Density
11.2 Pressure
A
FP
SI Unit of Pressure: 1 N/m2 = 1Pa
Pascal
11.2 Pressure
Atmospheric Pressure at Sea Level: 1.013x105 Pa = 1 atmosphere
11.3 Pressure and Depth in a Static Fluid
VgAPAP 12
AhV
AhgAPAP 12
hgPP 12
11.3 Pressure and Depth in a Static Fluid
Pa 1055.1
m 50.5sm80.9mkg1000.1Pa 1001.15
233
pressure catmospheri
52
P
ghPP 12
11.4 Pressure Gauges
AB PPP 2
ghPPA 1
ghPP atm pressure gauge
2
absolute pressure
11.5 Pascal’s Principle
PASCAL’S PRINCIPLE
Any change in the pressure applied to a completely enclosed fluid is transmitted undiminished to all parts of the fluid and enclosing walls.
11.5 Pascal’s Principle
m 012 gPP
1
1
2
2
A
F
A
F
1
212 A
AFF
11.6 Archimedes’ Principle
APPAPAPFB 1212
ghPP 12
ghAFB
hAV
gVFB
fluiddisplaced
of mass
11.6 Archimedes’ Principle
ARCHIMEDES’ PRINCIPLE
Any fluid applies a buoyant force to an object that is partiallyor completely immersed in it; the magnitude of the buoyantforce equals the weight of the fluid that the object displaces:
fluid displaced
ofWeight
fluid
forcebuoyant of Magnitude
WFB
11.6 Archimedes’ Principle
If the object is floating then the magnitude of the buoyant forceis equal to the magnitude of itsweight.
11.8 The Equation of Continuity
Incompressible fluid: 2211 vAvA
Volume flow rate Q: AvQ
11.9 Bernoulli’s Equation
The fluid accelerates toward the lower pressure regions.
According to the pressure-depthrelationship, the pressure is lowerat higher levels, provided the areaof the pipe does not change.
11.9 Bernoulli’s Equation
2222
11
212
1nc mgymvmgymvW
VPPAsPsFsFW 12
11.9 Bernoulli’s Equation
2222
11
212
112 mgymvmgymvVPP
2222
11
212
112 gyvgyvPP
BERNOULLI’S EQUATION
In steady flow of a nonviscous, incompressible fluid, the pressure, the fluid speed, and the elevation at two points are related by:
2222
121
212
11 gyvPgyvP
11.10 Applications of Bernoulli’s Equation
Conceptual Example 14 Tarpaulins and Bernoulli’s Equation
When the truck is stationary, the tarpaulin lies flat, but it bulges outwardwhen the truck is speeding downthe highway.
Account for this behavior.
11.10 Applications of Bernoulli’s Equation
11.10 Applications of Bernoulli’s Equation
Example 16 Efflux Speed
The tank is open to the atmosphere atthe top. Find an expression for the speed of the liquid leaving the pipe atthe bottom.
11.10 Applications of Bernoulli’s Equation
2222
121
212
11 gyvPgyvP
atmPPP 2102 v
hyy 12
ghv 212
1
ghv 21
12.1 Common Temperature Scales
Temperatures are reported in degreesCelsius or degrees Fahrenheit.
Temperatures changed, on theother hand, are reported in Celsius degrees or Fahrenheit degrees:
FC 5
9 1
AT SEA LEVEL
12.2 The Kelvin Temperature Scale
15.273 cTT
Kelvin temperature
AT SEA LEVEL
12.2 The Kelvin Temperature Scale
absolute zero point = -273.15oC
12.4 Linear Thermal Expansion
LINEAR THERMAL EXPANSION OF A SOLID
The length of an object changes when its temperature changes:
TLL o
coefficient of linear expansion
Common Unit for the Coefficient of Linear Expansion: 1C
C
1
12.4 Linear Thermal Expansion
12.4 Linear Thermal Expansion
THE BIMETALLIC STRIP
12.4 Linear Thermal Expansion
12.5 Volume Thermal Expansion
VOLUME THERMAL EXPANSION
The volume of an object changes when its temperature changes:
TVV o
coefficient of volume expansion
Common Unit for the Coefficient of Volume Expansion: 1C
C
1
12.5 Volume Thermal Expansion
Expansion of water.
The physics of burstingwater pipes.
12.6 Heat and Internal Energy
DEFINITION OF HEAT
Heat is energy that flows from a higher-temperature object to a lower-temperature object because of a difference in temperatures.
SI Unit of Heat: joule (J)
12.6 Heat and Internal Energy
The heat that flows from hot to cold originates in the internal energy ofthe hot substance.
It is not correct to say that a substancecontains heat.
13.1 Convection
CONVECTION
Convection is the process in which heat is carried from one placeto another by the bulk movement of a fluid.
convection currents
13.2 Conduction
CONDUCTION
Conduction is the process whereby heat is transferred directly througha material, with any bulk motion of the material playing no role in the transfer.
One mechanism for conduction occurs when the atoms or moleculesin a hotter part of the material vibrate or move with greater energy thanthose in a cooler part.
By means of collisions, the more energetic molecules pass on some oftheir energy to their less energetic neighbors.
Materials that conduct heat well are called thermal conductors, and thosethat conduct heat poorly are called thermal insulators.
13.2 Conduction
The amount of heat Q that is conducted through the bar depends on a number of factors:
1. The time during which conduction takes place.2. The temperature difference between the ends of the bar.3. The cross sectional area of the bar.4. The length of the bar.
13.3 Radiation
RADIATION
Radiation is the process in whichenergy is transferred by means ofelectromagnetic waves.
A material that is a good absorber is also a good emitter.
A material that absorbs completelyis called a perfect blackbody.
13.4 Applications
A thermos bottle minimizes heattransfer via conduction, convection,and radiation.
The space between the inner glass walls minimizes heat transfer by conduction and convection.
The silvered surfaces reflect radiatedheat back to the inside.
13.4 Applications
GREENHOUSE EFFECT-Depletion of the ozone layer is harmful to Earth-Harmful effects of technology and urbanization-Most heat transfer is by radiation.
14.1 Molecular Mass, the Mole, and Avogadro’s Number
One mole of a substance contains as manyparticles as there are atoms in 12 grams ofthe isotope cabron-12.
The number of atoms per mole is known asAvogadro’s number, NA.
123 mol10022.6 AN
AN
Nn
number ofmoles
number ofatoms
14.2 The Ideal Gas Law
An ideal gas is an idealized model for real gases that have sufficiently low densities.
The condition of low density means that the molecules are so far apart that they do not interact except during collisions, which are effectively ELASTIC.
TP
At constant volume, the pressure isdirectly proportional to the temperature.
14.2 The Ideal Gas Law
At constant temperature, the pressure is inversely proportional to the volume.
VP 1
The pressure is also proportionalto the amount of gas.
nP
14.2 The Ideal Gas Law
THE IDEAL GAS LAW
The absolute pressure of an ideal gas is directly proportional to the Kelvintemperature and the number of moles of the gas and is inversely proportionalto the volume of the gas.
V
nRTP
nRTPV
KmolJ31.8 R
14.2 The Ideal Gas Law
Consider a sample of an ideal gas that is taken from an initial to a finalstate, with the amount of the gas remaining constant.
nRTPV
i
ii
f
ff
T
VP
T
VP
constant nRT
PV
14.2 The Ideal Gas Law
i
ii
f
ff
T
VP
T
VP
Constant T, constant n:iiff VPVP Boyle’s law
Constant P, constant n:
i
i
f
f
T
V
T
V Charles’ law
Constant V, constant n:
i
i
f
f
T
P
T
P Gay Lussac’s law
14.3 Kinetic Theory of Gases
The particles are in constant, randommotion, colliding with each otherand with the walls of the container.
Each collision changes the particle’s speed.
As a result, the atoms and molecules have different speeds.
14.3 Kinetic Theory of Gases
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THE INTERNAL ENERGY OF A MONATOMIC IDEAL GAS
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15.1 Thermodynamic Systems and Their Surroundings
Thermodynamics is the branch of physics that is built upon the fundamental laws that heat and work obey.
The collection of objects on which attention is being focused is called the system, while everything elsein the environment is called the surroundings.
Walls that permit heat flow are called diathermal walls,while walls that do not permit heat flow are calledadiabatic walls.
To understand thermodynamics, it is necessary to describe the state of a system.
15.2 The Zeroth Law of Thermodynamics
Two systems are said to be in thermal equilibrium if there is no heat flowbetween then when they are brought into contact.
Temperature is the indicator of thermal equilibrium in the sense that there is nonet flow of heat between two systems in thermal contact that have the sametemperature.
15.2 The Zeroth Law of Thermodynamics
THE ZEROTH LAW OF THERMODYNAMICS
Two systems individually in thermal equilibriumwith a third system are in thermal equilibriumwith each other.
15.3 The First Law of Thermodynamics
Suppose that a system gains heat Q and that is the only effect occurring.
Consistent with the law of conservation of energy, the internal energyof the system changes:
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Heat is positive when the system gains heat and negative when the systemloses heat.
15.3 The First Law of Thermodynamics
Thermodynamics is a conservation law; i.e. heat added to a system is usedby the system to increase its internal energy or to do work in expanding.
An increase in internal energy due to heat added to the system (positive) orwork done on the system (positive).
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Work done on a system, according to this convention, would result in adecrease in volume:
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15.3 The First Law of Thermodynamics
THE FIRST LAW OF THERMODYNAMICS
Process Definition Result
Isothermal
Adiabatic
Isochoric or Isovolumetric
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15.3 The First Law of Thermodynamics
Example 1 Positive and Negative Work
In part a, the system gains 1500J of heatand 2200J of work is done BY the system on its surroundings.
In part b, the system also gains 1500J of heat, but2200J of work is done ON the system.
In each case, determine the change in internal energyof the system.
15.4 Thermal Processes
An isobaric process is one that occurs atconstant pressure.
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At constant pressure, if volume decreases,ΔV is negative, and work done is positive.
15.4 Thermal Processes
Example 3 Isobaric Expansion of Water
One gram of water is placed in the cylinder and the pressure is maintained at 2.0x105Pa. Thetemperature of the water is raised by 31oC. Thewater is in the liquid phase and expands by thesmall amount of 1.0x10-8m3.
Find the work done and the change in internal energy.
15.4 Thermal Processes
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15.4 Thermal Processes
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15.4 Thermal Processes
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15.4 Thermal Processes
Example 4 Work and the Area Under a Pressure-Volume Graph
Determine the work for the process in which the pressure, volume, and temp-erature of a gas are changed along thestraight line in the figure.
The area under a pressure-volume graph isthe work for any kind of process.
15.4 Thermal Processes
Since the volume increases, the workis negative.
Estimate that there are 8.9 colored squares in the drawing.
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15.5 Thermal Processes Using an Ideal Gas
ISOTHERMAL EXPANSION OR COMPRESSION
Isothermalexpansion orcompression ofan ideal gas
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15.5 Thermal Processes Using an Ideal Gas
Example 5 Isothermal Expansion of an Ideal Gas
Two moles of the monatomic gas argon expand isothermally at 298Kfrom and initial volume of 0.025m3 to a final volume of 0.050m3. Assumingthat argon is an ideal gas, find (a) the work done by the gas, (b) the change in internal energy of the gas, and (c) the heat supplied to the gas. ??
15.5 Thermal Processes Using an Ideal Gas
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15.3 The First Law of Thermodynamics
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15.3 The First Law of Thermodynamics
Example 2 An Ideal Gas
The temperature of three moles of a monatomic ideal gas is reduced from 540K to 350K as 5500J of heat flows into the gas.
Find (a) the change in internal energy and (b) the work done by the gas. ???
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15.3 The First Law of Thermodynamics
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15.4 Thermal Processes
A quasi-static process is one that occurs slowly enough that a uniformtemperature and pressure exist throughout all regions of the system at alltimes.
isobaric: constant pressure
isochoric: constant volume
isothermal: constant temperature
adiabatic: no transfer of heat
15.7 The Second Law of Thermodynamics
THE SECOND LAW OF THERMODYNAMICS: THE HEAT FLOW STATEMENT
Heat flows spontaneously from a substance at a higher temperature to a substanceat a lower temperature and does not flow spontaneously in the reverse direction.
The second law is a statement about the natural tendency of heat to flow from hot to cold, whereas the first law deals with energy conservationand focuses on both heat and work.
15.8 Heat Engines
A heat engine is any device that uses heat to perform work. It has three essential features.
1. Heat is supplied to the engine at a relatively high temperature from a place called the hot reservoir.
2. Part of the input heat is used to perform work by the working substance of the engine.
3. The remainder of the input heat is rejected to a place called the cold reservoir.
heatinput of magnitude HQ
heat rejected of magnitude CQ
done work theof magnitude W
15.8 Heat Engines
The efficiency of a heat engine is defined asthe ratio of the work done to the input heat:
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If there are no other losses, then
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15.8 Heat Engines
Example 6 An Automobile Engine
An automobile engine has an efficiency of 22.0% and produces 2510 J of work. How much heat is rejected by the engine?
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15.8 Heat Engines
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15.9 Carnot’s Principle and the Carnot Engine
A reversible process is one in which both the system and the environment can be returned to exactly the states they were in before the process occurred.
CARNOT’S PRINCIPLE: AN ALTERNATIVE STATEMENT OF THE SECONDLAW OF THERMODYNAMICS
No irreversible engine operating between two reservoirs at constant temperaturescan have a greater efficiency than a reversible engine operating between the sametemperatures. Furthermore, all reversible engines operating between the sametemperatures have the same efficiency.
15.9 Carnot’s Principle and the Carnot Engine
The Carnot engine is useful as an idealizedmodel.
All of the heat input originates from a singletemperature, and all the rejected heat goesinto a cold reservoir at a single temperature.
Since the efficiency can only depend onthe reservoir temperatures, the ratio of heats can only depend on those temperatures.
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15.11 Entropy
Any irreversible process increases the entropy of the universe. 0universe S
THE SECOND LAW OF THERMODYNAMICS STATEDIN TERMS OF ENTROPY
The total entropy of the universe does not change when a reversible process occurs and increases when an irreversibleprocess occurs.
15.11 Entropy
Example 12 Energy Unavailable for Doing Work
Suppose that 1200 J of heat is used as input for an engine under two different conditions (as shown on the right).
Determine the maximum amount of work that can be obtainedfor each case.
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15.11 Entropy
The maximum amount of work will be achieved when theengine is a Carnot Engine, where
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The irreversible process of heat through the copperrod causes some energy to become unavailable.
15.12 The Third Law of Thermodynamics
THE THIRD LAW OF THERMODYNAMICS
It is not possible to lower the temperature of any system to absolute zero in a finite number of steps.