ThermodynamicsThermal Expansion

Lana Sheridan

De Anza College

April 19, 2018

Last time

• heat, thermal equilibrium, and the 0th law

• temperature

Overview

• thermal expansion

Thermal Expansion

Most substances (solid, liquid, or gas) expand when heated.

This is due to the fact that in substances at higher temperatures,the molecules move around faster and more violently, so theyspread out more.

Different substances expand by different amounts for a giventemperature change.

Thermal Expansion

Thermal expansion has been a common cause of derailments oftrains.

Thermal Expansion

Different rates of thermal expansion can cause glass to shatter.

Thermal ExpansionThis expansion is taken into account by civil engineers whendesigning bridges, pipes, and buildings.

Expansion joints are built into sections of bridges to allow forexpansion without buckling.

19.4 Thermal Expansion of Solids and Liquids 573

Earth. Therefore, if you encounter an equation that calls for a temperature T or that involves a ratio of temperatures, you must convert all temperatures to kelvins. If the equation contains a change in temperature DT, using Celsius temperatures will give you the correct answer, in light of Equation 19.3, but it is always safest to convert temperatures to the Kelvin scale.

Q uick Quiz 19.2 Consider the following pairs of materials. Which pair repre-sents two materials, one of which is twice as hot as the other? (a) boiling water at 1008C, a glass of water at 508C (b) boiling water at 1008C, frozen methane at 2508C (c) an ice cube at 2208C, flames from a circus fire-eater at 2338C (d) none of those pairs

Example 19.1 Converting Temperatures

On a day when the temperature reaches 508F, what is the temperature in degrees Celsius and in kelvins?

Conceptualize In the United States, a temperature of 508F is well understood. In many other parts of the world, how-ever, this temperature might be meaningless because people are familiar with the Celsius temperature scale.

Categorize This example is a simple substitution problem.

S O L U T I O N

Solve Equation 19.2 for the Celsius temperature and sub-stitute numerical values:

TC 5 59 1TF 2 32 2 5 5

9 150 2 32 2 5 108C

Use Equation 19.1 to find the Kelvin temperature: T 5 TC 1 273.15 5 108C 1 273.15 5 283 K

A convenient set of weather-related temperature equivalents to keep in mind is that 08C is (literally) freezing at 328F, 108C is cool at 508F, 208C is room temperature, 308C is warm at 868F, and 408C is a hot day at 1048F.

19.4 Thermal Expansion of Solids and LiquidsOur discussion of the liquid thermometer makes use of one of the best-known changes in a substance: as its temperature increases, its volume increases. This phe-nomenon, known as thermal expansion, plays an important role in numerous engi-neering applications. For example, thermal-expansion joints such as those shown in Figure 19.7 must be included in buildings, concrete highways, railroad tracks,

Figure 19.7 Thermal-expansion joints in (a) bridges and (b) walls.

The long, vertical joint is filled with a soft material that allows the wall to expand and contract as the temperature of the bricks changes.

b

© C

enga

ge L

earn

ing/

Geor

ge S

empl

e

Without these joints to separate sections of roadway on bridges, the surface would buckle due to thermal expansion on very hot days or crack due to contraction on very cold days.

a

© C

enga

ge L

earn

ing/

Geor

ge S

empl

e

0Picture from Serway & Jewett.

Thermal Expansion

A coefficient of linear expansion α for a solid relates how muchit will expand when its temperature changes by an amount ∆T .

∆L = αLi ∆T

Li is the original length of the solid before the temperature change.

α takes different values for different substances, but is almostalways a positive number.

Thermal Expansion: Bimetallic Strip

A bimetallic strip is a strip made of two kinds of metal, very oftenbrass and iron, that have quite different coefficients of linearexpansion.

The strip curves downward when heated and can curl upward whenit is chilled.

Used in thermostats and thermometers, its deformation can makeor break an electrical contact.

Bimetallic Strip Question

Suppose a bimetallic strip is composed of 0.10 m of brass and ironbound together at room temperature (20◦C).

The strip is heated 15◦C. How much longer is the brass part thanthe iron part?

αbrass = 19 × 10−6(◦C)−1

αiron = 12 × 10−6(◦C)−1

1.05 × 10−5 m = 0.0105 mm

Bimetallic Strip Question

Suppose a bimetallic strip is composed of 0.10 m of brass and ironbound together at room temperature (20◦C).

The strip is heated 15◦C. How much longer is the brass part thanthe iron part?

αbrass = 19 × 10−6(◦C)−1

αiron = 12 × 10−6(◦C)−1

1.05 × 10−5 m = 0.0105 mm

Thermal Expansion Question

The pendulum of a certain pendulum clock is made of brass.When the temperature increases, what happens to the period ofthe clock?

(A) It increases.

(B) It decreases.

(C) It remains the same.

1Serway & Jewett, Objective question 4, page 581.

Thermal Expansion Question

The pendulum of a certain pendulum clock is made of brass.When the temperature increases, what happens to the period ofthe clock?

Period of an ideal pendulum: T = 2π√

Lg

Period of a physical pendulumT = 2π√

Imgd

(A) It increases.

(B) It decreases.

(C) It remains the same.

1Serway & Jewett, Objective question 4, page 581.

Thermal Expansion Question

The pendulum of a certain pendulum clock is made of brass.When the temperature increases, what happens to the period ofthe clock?

Period of an ideal pendulum: T = 2π√

Lg

Period of a physical pendulumT = 2π√

Imgd

(A) It increases. ←(B) It decreases.

(C) It remains the same.

1Serway & Jewett, Objective question 4, page 581.

Thermal Expansion: Why does it happen?

As the kinetic energy of the atoms / molecules increase, they canmove further out of their potential wells.

460 Chapter 15 Oscillatory Motion

position, the potential energy curve for this function approximates a parabola, which represents the potential energy function for a simple harmonic oscillator. Therefore, we can model the complex atomic binding forces as being due to tiny springs as depicted in Figure 15.11b. The ideas presented in this chapter apply not only to block–spring systems and atoms, but also to a wide range of situations that include bungee jumping, playing a musical instrument, and viewing the light emitted by a laser. You will see more examples of simple harmonic oscillators as you work through this book.

r

U

a b

Figure 15.11 (a) If the atoms in a molecule do not move too far from their equilibrium positions, a graph of potential energy versus separation distance between atoms is similar to the graph of potential energy versus posi-tion for a simple harmonic oscillator (dashed black curve). (b) The forces between atoms in a solid can be modeled by imagining springs between neighboring atoms.

t x v

t x v

a K U

00 0

0 0

0

0 0

0

!v2AA

0

0

!A

0

A

!vA

0

T4

T

vA

0–A A

Potentialenergy

Totalenergy

Kineticenergy

%

050

100

%

050

100

%

050

100

%

050

100

%

050

100

%

050

100

a

c

e

f

b

d

x

amaxS

amaxS

vmaxS

vmaxS

!v2A

v2A

!v2x

T2

3T4

amaxS

vS

x

kA212

kA212

kA212

kA212

kA212

12mv2 1

2kx2

Figure 15.10 (a) through (e) Several instants in the simple harmonic motion for a block–spring system. Energy bar graphs show the distri-bution of the energy of the system at each instant. The parameters in the table at the right refer to the block–spring system, assuming at t 5 0, x 5 A; hence, x 5 A cos vt. For these five special instants, one of the types of energy is zero. (f) An arbitrary point in the motion of the oscilla-tor. The system possesses both kinetic energy and potential energy at this instant as shown in the bar graph.

Example 15.3 Oscillations on a Horizontal Surface

A 0.500-kg cart connected to a light spring for which the force constant is 20.0 N/m oscillates on a frictionless, hori-zontal air track.

(A) Calculate the maximum speed of the cart if the amplitude of the motion is 3.00 cm.

Conceptualize The system oscillates in exactly the same way as the block in Figure 15.10, so use that figure in your mental image of the motion.

AM

S O L U T I O N

The Lennard-Jones potential bonds modeled as springs

The average inter-atom spacing increases.

1Diagrams from Serway & Jewett, 9th ed, page 460.

Volume Thermal Expansion

We can model volume expansion in a similar way:

∆V = βVi ∆T

β is the average coefficient of volume expansion.

If the material is isotropic (the same in all directions, symmetrywrt rotations of coordinate systems) then:

β = 3α

using the fact that α∆T � 1.

(This entire model is only approximately true over a restrictedrange of temperatures.)

Thermal Expansion QuestionThe figure here shows four rectangular metal plates, with sides ofL, 2L, or 3L. They are all made of the same material, and theirtemperature is to be increased by the same amount. Rank theplates according to the expected increase in

(a) their vertical heights greatest first.

48318-7 TE M PE RATU R E AN D H EATPART 2

HALLIDAY REVISED

This behavior of water is the reason lakes freeze from the top down rather thanfrom the bottom up. As water on the surface is cooled from, say, 10°C toward thefreezing point, it becomes denser (“heavier”) than lower water and sinks to thebottom. Below 4°C, however, further cooling makes the water then on the surfaceless dense (“lighter”) than the lower water, so it stays on the surface until it freezes.Thus the surface freezes while the lower water is still liquid. If lakes froze from thebottom up, the ice so formed would tend not to melt completely during the sum-mer, because it would be insulated by the water above. After a few years, manybodies of open water in the temperate zones of Earth would be frozen solid all yearround—and aquatic life could not exist.

CHECKPOINT 2

The figure here shows four rectangularmetal plates, with sides of L, 2L, or 3L.Theyare all made of the same material, and theirtemperature is to be increased by the sameamount. Rank the plates according to the ex-pected increase in (a) their vertical heightsand (b) their areas,greatest first.

Sample Problem

volume of the fuel did also, as given by Eq. 18-10 (!V "Vb !T).

Calculations: We find!V" (37 000 L)(9.50 # 10$4/C°)($23.0 K) " $808 L.

Thus, the amount delivered was

Vdel " V % !V " 37 000 L $ 808 L" 36 190 L. (Answer)

Note that the thermal expansion of the steel tank has nothing to do with the problem. Question: Who paid for the“missing” diesel fuel?

Thermal expansion of a volume

On a hot day in Las Vegas, an oil trucker loaded 37 000 L ofdiesel fuel. He encountered cold weather on the way toPayson, Utah, where the temperature was 23.0 K lower thanin Las Vegas, and where he delivered his entire load. Howmany liters did he deliver? The coefficient of volume expan-sion for diesel fuel is 9.50 # 10$4/C°, and the coefficient oflinear expansion for his steel truck tank is 11 # 10$6/C°.

The volume of the diesel fuel depends directly on the tem-perature. Thus, because the temperature decreased, the

KEY I DEA

Additional examples, video, and practice available at WileyPLUS

(1) (2) (3) (4)

18-7 Temperature and HeatIf you take a can of cola from the refrigerator and leave it on the kitchen table, itstemperature will rise—rapidly at first but then more slowly—until the tempera-ture of the cola equals that of the room (the two are then in thermal equilibrium).In the same way, the temperature of a cup of hot coffee, left sitting on the table,will fall until it also reaches room temperature.

In generalizing this situation, we describe the cola or the coffee as a system(with temperature TS) and the relevant parts of the kitchen as the environment(with temperature TE) of that system. Our observation is that if TS is not equal toTE, then TS will change (TE can also change some) until the two temperatures areequal and thus thermal equilibrium is reached.

Such a change in temperature is due to a change in the thermal energy of thesystem because of a transfer of energy between the system and the system’senvironment. (Recall that thermal energy is an internal energy that consists of the

halliday_c18_476-506v2.qxd 22-10-2009 12:03 Page 483

(A) 1, 2, 3, 4

(B) (2 and 3), 1, 4

(C) 3, 2, (1 and 4)

(D) all the same1Halliday, Resnick, Walker, page 483.

Thermal Expansion QuestionThe figure here shows four rectangular metal plates, with sides ofL, 2L, or 3L. They are all made of the same material, and theirtemperature is to be increased by the same amount. Rank theplates according to the expected increase in

(a) their vertical heights greatest first.

48318-7 TE M PE RATU R E AN D H EATPART 2

HALLIDAY REVISED

This behavior of water is the reason lakes freeze from the top down rather thanfrom the bottom up. As water on the surface is cooled from, say, 10°C toward thefreezing point, it becomes denser (“heavier”) than lower water and sinks to thebottom. Below 4°C, however, further cooling makes the water then on the surfaceless dense (“lighter”) than the lower water, so it stays on the surface until it freezes.Thus the surface freezes while the lower water is still liquid. If lakes froze from thebottom up, the ice so formed would tend not to melt completely during the sum-mer, because it would be insulated by the water above. After a few years, manybodies of open water in the temperate zones of Earth would be frozen solid all yearround—and aquatic life could not exist.

CHECKPOINT 2

The figure here shows four rectangularmetal plates, with sides of L, 2L, or 3L.Theyare all made of the same material, and theirtemperature is to be increased by the sameamount. Rank the plates according to the ex-pected increase in (a) their vertical heightsand (b) their areas,greatest first.

Sample Problem

volume of the fuel did also, as given by Eq. 18-10 (!V "Vb !T).

Calculations: We find!V" (37 000 L)(9.50 # 10$4/C°)($23.0 K) " $808 L.

Thus, the amount delivered was

Vdel " V % !V " 37 000 L $ 808 L" 36 190 L. (Answer)

Note that the thermal expansion of the steel tank has nothing to do with the problem. Question: Who paid for the“missing” diesel fuel?

Thermal expansion of a volume

On a hot day in Las Vegas, an oil trucker loaded 37 000 L ofdiesel fuel. He encountered cold weather on the way toPayson, Utah, where the temperature was 23.0 K lower thanin Las Vegas, and where he delivered his entire load. Howmany liters did he deliver? The coefficient of volume expan-sion for diesel fuel is 9.50 # 10$4/C°, and the coefficient oflinear expansion for his steel truck tank is 11 # 10$6/C°.

The volume of the diesel fuel depends directly on the tem-perature. Thus, because the temperature decreased, the

KEY I DEA

Additional examples, video, and practice available at WileyPLUS

(1) (2) (3) (4)

18-7 Temperature and HeatIf you take a can of cola from the refrigerator and leave it on the kitchen table, itstemperature will rise—rapidly at first but then more slowly—until the tempera-ture of the cola equals that of the room (the two are then in thermal equilibrium).In the same way, the temperature of a cup of hot coffee, left sitting on the table,will fall until it also reaches room temperature.

In generalizing this situation, we describe the cola or the coffee as a system(with temperature TS) and the relevant parts of the kitchen as the environment(with temperature TE) of that system. Our observation is that if TS is not equal toTE, then TS will change (TE can also change some) until the two temperatures areequal and thus thermal equilibrium is reached.

Such a change in temperature is due to a change in the thermal energy of thesystem because of a transfer of energy between the system and the system’senvironment. (Recall that thermal energy is an internal energy that consists of the

halliday_c18_476-506v2.qxd 22-10-2009 12:03 Page 483

(A) 1, 2, 3, 4

(B) (2 and 3), 1, 4←(C) 3, 2, (1 and 4)

(D) all the same1Halliday, Resnick, Walker, page 483.

Thermal Expansion QuestionThe figure here shows four rectangular metal plates, with sides ofL, 2L, or 3L. They are all made of the same material, and theirtemperature is to be increased by the same amount. Rank theplates according to the expected increase in

(b) their areas greatest first.

48318-7 TE M PE RATU R E AN D H EATPART 2

HALLIDAY REVISED

This behavior of water is the reason lakes freeze from the top down rather thanfrom the bottom up. As water on the surface is cooled from, say, 10°C toward thefreezing point, it becomes denser (“heavier”) than lower water and sinks to thebottom. Below 4°C, however, further cooling makes the water then on the surfaceless dense (“lighter”) than the lower water, so it stays on the surface until it freezes.Thus the surface freezes while the lower water is still liquid. If lakes froze from thebottom up, the ice so formed would tend not to melt completely during the sum-mer, because it would be insulated by the water above. After a few years, manybodies of open water in the temperate zones of Earth would be frozen solid all yearround—and aquatic life could not exist.

CHECKPOINT 2

The figure here shows four rectangularmetal plates, with sides of L, 2L, or 3L.Theyare all made of the same material, and theirtemperature is to be increased by the sameamount. Rank the plates according to the ex-pected increase in (a) their vertical heightsand (b) their areas,greatest first.

Sample Problem

volume of the fuel did also, as given by Eq. 18-10 (!V "Vb !T).

Calculations: We find!V" (37 000 L)(9.50 # 10$4/C°)($23.0 K) " $808 L.

Thus, the amount delivered was

Vdel " V % !V " 37 000 L $ 808 L" 36 190 L. (Answer)

Note that the thermal expansion of the steel tank has nothing to do with the problem. Question: Who paid for the“missing” diesel fuel?

Thermal expansion of a volume

On a hot day in Las Vegas, an oil trucker loaded 37 000 L ofdiesel fuel. He encountered cold weather on the way toPayson, Utah, where the temperature was 23.0 K lower thanin Las Vegas, and where he delivered his entire load. Howmany liters did he deliver? The coefficient of volume expan-sion for diesel fuel is 9.50 # 10$4/C°, and the coefficient oflinear expansion for his steel truck tank is 11 # 10$6/C°.

The volume of the diesel fuel depends directly on the tem-perature. Thus, because the temperature decreased, the

KEY I DEA

Additional examples, video, and practice available at WileyPLUS

(1) (2) (3) (4)

18-7 Temperature and HeatIf you take a can of cola from the refrigerator and leave it on the kitchen table, itstemperature will rise—rapidly at first but then more slowly—until the tempera-ture of the cola equals that of the room (the two are then in thermal equilibrium).In the same way, the temperature of a cup of hot coffee, left sitting on the table,will fall until it also reaches room temperature.

In generalizing this situation, we describe the cola or the coffee as a system(with temperature TS) and the relevant parts of the kitchen as the environment(with temperature TE) of that system. Our observation is that if TS is not equal toTE, then TS will change (TE can also change some) until the two temperatures areequal and thus thermal equilibrium is reached.

Such a change in temperature is due to a change in the thermal energy of thesystem because of a transfer of energy between the system and the system’senvironment. (Recall that thermal energy is an internal energy that consists of the

halliday_c18_476-506v2.qxd 22-10-2009 12:03 Page 483

(A) 1, 2, 3, 4

(B) (2 and 3), 1, 4

(C) 3, 2, (1 and 4)

(D) all the same1Halliday, Resnick, Walker, page 483.

Thermal Expansion QuestionThe figure here shows four rectangular metal plates, with sides ofL, 2L, or 3L. They are all made of the same material, and theirtemperature is to be increased by the same amount. Rank theplates according to the expected increase in

(b) their areas greatest first.

48318-7 TE M PE RATU R E AN D H EATPART 2

HALLIDAY REVISED

This behavior of water is the reason lakes freeze from the top down rather thanfrom the bottom up. As water on the surface is cooled from, say, 10°C toward thefreezing point, it becomes denser (“heavier”) than lower water and sinks to thebottom. Below 4°C, however, further cooling makes the water then on the surfaceless dense (“lighter”) than the lower water, so it stays on the surface until it freezes.Thus the surface freezes while the lower water is still liquid. If lakes froze from thebottom up, the ice so formed would tend not to melt completely during the sum-mer, because it would be insulated by the water above. After a few years, manybodies of open water in the temperate zones of Earth would be frozen solid all yearround—and aquatic life could not exist.

CHECKPOINT 2

The figure here shows four rectangularmetal plates, with sides of L, 2L, or 3L.Theyare all made of the same material, and theirtemperature is to be increased by the sameamount. Rank the plates according to the ex-pected increase in (a) their vertical heightsand (b) their areas,greatest first.

Sample Problem

volume of the fuel did also, as given by Eq. 18-10 (!V "Vb !T).

Calculations: We find!V" (37 000 L)(9.50 # 10$4/C°)($23.0 K) " $808 L.

Thus, the amount delivered was

Vdel " V % !V " 37 000 L $ 808 L" 36 190 L. (Answer)

Note that the thermal expansion of the steel tank has nothing to do with the problem. Question: Who paid for the“missing” diesel fuel?

Thermal expansion of a volume

On a hot day in Las Vegas, an oil trucker loaded 37 000 L ofdiesel fuel. He encountered cold weather on the way toPayson, Utah, where the temperature was 23.0 K lower thanin Las Vegas, and where he delivered his entire load. Howmany liters did he deliver? The coefficient of volume expan-sion for diesel fuel is 9.50 # 10$4/C°, and the coefficient oflinear expansion for his steel truck tank is 11 # 10$6/C°.

The volume of the diesel fuel depends directly on the tem-perature. Thus, because the temperature decreased, the

KEY I DEA

Additional examples, video, and practice available at WileyPLUS

(1) (2) (3) (4)

18-7 Temperature and HeatIf you take a can of cola from the refrigerator and leave it on the kitchen table, itstemperature will rise—rapidly at first but then more slowly—until the tempera-ture of the cola equals that of the room (the two are then in thermal equilibrium).In the same way, the temperature of a cup of hot coffee, left sitting on the table,will fall until it also reaches room temperature.

In generalizing this situation, we describe the cola or the coffee as a system(with temperature TS) and the relevant parts of the kitchen as the environment(with temperature TE) of that system. Our observation is that if TS is not equal toTE, then TS will change (TE can also change some) until the two temperatures areequal and thus thermal equilibrium is reached.

Such a change in temperature is due to a change in the thermal energy of thesystem because of a transfer of energy between the system and the system’senvironment. (Recall that thermal energy is an internal energy that consists of the

halliday_c18_476-506v2.qxd 22-10-2009 12:03 Page 483

(A) 1, 2, 3, 4

(B) (2 and 3), 1, 4

(C) 3, 2, (1 and 4)←(D) all the same

1Halliday, Resnick, Walker, page 483.

Thermal Expansion of Rings 19.4 Thermal Expansion of Solids and Liquids 575

temperature changes to Ti 1 DT, its volume changes to Vi 1 DV, where each dimen-sion changes according to Equation 19.4. Therefore,

Vi 1 DV 5 (, 1 D,)(w 1 Dw)(h 1 Dh)

5 (, 1 a, DT )(w 1 aw DT )(h 1 ah DT )

5 ,wh(1 1 a DT)3

5 Vi[1 1 3a DT 1 3(a DT )2 1 (a DT )3]

Dividing both sides by Vi and isolating the term DV/Vi , we obtain the fractional change in volume:

DVVi

5 3a DT 1 3 1a DT 22 1 1a DT 23

Because a DT ,, 1 for typical values of DT (, , 1008C), we can neglect the terms 3(a DT)2 and (a DT)3. Upon making this approximation, we see that

DVVi

5 3a DT S DV 5 13a 2Vi DT

Comparing this expression to Equation 19.6 shows that

b 5 3a

In a similar way, you can show that the change in area of a rectangular plate is given by DA 5 2aAi DT (see Problem 61). A simple mechanism called a bimetallic strip, found in practical devices such as mechanical thermostats, uses the difference in coefficients of expansion for differ-ent materials. It consists of two thin strips of dissimilar metals bonded together. As the temperature of the strip increases, the two metals expand by different amounts and the strip bends as shown in Figure 19.9.

Q uick Quiz 19.3 If you are asked to make a very sensitive glass thermometer, which of the following working liquids would you choose? (a) mercury (b) alco-hol (c) gasoline (d) glycerin

Q uick Quiz 19.4 Two spheres are made of the same metal and have the same radius, but one is hollow and the other is solid. The spheres are taken through the same temperature increase. Which sphere expands more? (a) The solid sphere expands more. (b) The hollow sphere expands more. (c) They expand by the same amount. (d) There is not enough information to say.

Table 19.1 Average Expansion Coefficients for Some Materials Near Room Temperature Average Linear Average Volume Expansion ExpansionMaterial Coefficient Material Coefficient(Solids) (a)(°C)21 (Liquids and Gases) (b)(°C)21

Aluminum 24 3 1026 Acetone 1.5 3 1024

Brass and bronze 19 3 1026 Alcohol, ethyl 1.12 3 1024

Concrete 12 3 1026 Benzene 1.24 3 1024

Copper 17 3 1026 Gasoline 9.6 3 1024

Glass (ordinary) 9 3 1026 Glycerin 4.85 3 1024

Glass (Pyrex) 3.2 3 1026 Mercury 1.82 3 1024

Invar (Ni–Fe alloy) 0.9 3 1026 Turpentine 9.0 3 1024

Lead 29 3 1026 Aira at 08C 3.67 3 1023

Steel 11 3 1026 Heliuma 3.665 3 1023

aGases do not have a specific value for the volume expansion coefficient because the amount of expansion depends on the type of process through which the gas is taken. The values given here assume the gas undergoes an expansion at constant pressure.

Steel

BrassRoomtemperature

Highertemperature

Bimetallicstrip

Off 30!COn 25!C

a

b

Figure 19.9 (a) A bimetallic strip bends as the temperature changes because the two metals have different expansion coeffi-cients. (b) A bimetallic strip used in a thermostat to break or make electrical contact.

Figure 19.8 Thermal expansion of a homogeneous metal washer. (The expansion is exaggerated in this figure.)

a

b

b " #b

a " #a

Ti " #T

Ti

As the washer is heated, all dimensions increase, including the radius of the hole.

Question

Quick Quiz 19.41 Two spheres are made of the same metal andhave the same radius, but one is hollow and the other is solid. Thespheres are taken through the same temperature increase. Whichsphere expands more?

(A) The solid sphere expands more.

(B) The hollow sphere expands more.

(C) They expand by the same amount.

(D) There is not enough information to say.

1Serway & Jewett, pg575.

Question

Quick Quiz 19.41 Two spheres are made of the same metal andhave the same radius, but one is hollow and the other is solid. Thespheres are taken through the same temperature increase. Whichsphere expands more?

(A) The solid sphere expands more.

(B) The hollow sphere expands more.

(C) They expand by the same amount. ←(D) There is not enough information to say.

1Serway & Jewett, pg575.

Thermal Expansion and Water

Water has a strange behavior with temperature change.

Ice is less dense than water, but even in its liquid phase, waterexpands as it cools between 4◦C and 0◦C.

Water forms crystals as it freezes. Those crystals have a greatervolume than liquid water.

Between 4◦C and 0◦C some small crystals begin to form,expanding the volume of the water.

1Image from its.caltech.edu.

Thermal Expansion and Water

1Figure from Chemwiki ucdavis.edu.

Summary

• thermal expansion

(Uncollected) HomeworkSerway & Jewett:

• Ch 19, onward from page 581. Probs: 11, 13, 17, 21, 23, 51,57, 61, 62, 67