OpenStax University Physics Volume II
Unit 1: Thermodynamics
Chapter 1: Temperature and Heat
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,OpenStax University Physics Volume II
Unit 1: Thermodynamics
Chapter 1: Temperature and Heat
University Physics Volume II
Unit 1: Thermodynamics
Chapter 1: Temperature and Heat
Conceptual Questions
1. What does it mean to say that two systems are in thermal equilibrium?
Solution
They are at the same temperature, and if they are placed in contact, no net heat flows between
them.
2. Give an example in which A has some kind of non-thermal equilibrium relationship with B,
and B has the same relationship with C, but A does not have that relationship with C.
Solution
One possibility is that in some game, A and C are both equally matched with B, but C
consistently beats A, maybe because C’s style is hard for A to cope with or C has some
psychological advantage. Another is that if two people of different weights lean at the same
angle against a wall, they are each in equilibrium with the wall, but they would not be in
equilibrium with each other. Other answers are possible.
3. If a thermometer is allowed to come to equilibrium with the air, and a glass of water is not in
equilibrium with the air, what will happen to the thermometer reading when it is placed in the
water?
Solution
The reading will change.
4. Give an example of a physical property that varies with temperature and describe how it is
used to measure temperature.
Solution
Volume—as the volume of liquid in an ordinary thermometer increases, the liquid’s interface
with air rises along a scale. Electrical resistance—the resistance of a piece of silicon in a
thermistor decreases with increasing temperature and is read electronically. Color—certain
chemical reactions cause color changes at certain temperatures, so a set of spots containing such
chemicals with slightly different color-change temperatures can indicate temperature. Radiated
power and frequency spectrum—a bolometer can be pointed at an object, especially one that is
too hot or too distant to put a thermometer in contact with, and the radiated power or peak
frequency can be measured and converted into a temperature. Other answers are possible.
5. Pouring cold water into hot glass or ceramic cookware can easily break it. What causes the
breaking? Explain why Pyrex®, a glass with a small coefficient of linear expansion, is less
susceptible.
Solution
The cold water cools part of the inner surface, making it contract, while the rest remains
expanded. The strain is too great for the strength of the material. Pyrex contracts less, so it
experiences less strain.
6. One method of getting a tight fit, say of a metal peg in a hole in a metal block, is to
manufacture the peg slightly larger than the hole. The peg is then inserted when at a different
temperature than the block. Should the block be hotter or colder than the peg during insertion?
Explain your answer.
Solution
The block should be hotter so the hole will be bigger.
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Unit 1: Thermodynamics
Chapter 1: Temperature and Heat
7. Does it really help to run hot water over a tight metal lid on a glass jar before trying to open it?
Explain your answer.
Solution
In principle, the lid expands more than the jar because metals have higher coefficients of
expansion than glass. That should make unscrewing the lid easier. (In practice, getting the lid and
jar wet may make gripping them more difficult.)
8. When a cold alcohol thermometer is placed in a hot liquid, the column of alcohol goes down
slightly before going up. Explain why.
Solution
The glass expands before the alcohol does.
9. Calculate the length of a 1-meter rod of a material with thermal expansion coefficient
when the temperature is raised from 300 K to 600 K. Taking your answer as the new initial
length, find the length after the rod is cooled back down to 300 K. Is your answer 1 meter?
Should it be? How can you account for the result you got?
Solution
After being heated, the length is ( )( ). After being cooled, the length is
. That answer is not 1 m, but it should be. The explanation is that
even if is exactly constant, the relation is strictly true only in the limit of small
. Since values are small, the discrepancy is unimportant in practice.
10. Noting the large stresses that can be caused by thermal expansion, an amateur weapon
inventor decides to use it to make a new kind of gun. He plans to jam a bullet against an
aluminum rod inside a closed invar tube. When he heats the tube, the rod will expand more than
the tube and a very strong force will build up. Then, by a method yet to be determined, he will
open the tube in a split second and let the force of the rod launch the bullet at very high speed.
What is he overlooking?
Solution
The force will go to zero over a very short distance as the rod reaches its expanded length, so
very little work will be done. Also, the force is proportional to the area, so on something the size
of a bullet it will not be as great as the inventor thinks.
11. How is heat transfer related to temperature?
Solution
Temperature differences cause heat transfer.
12. Describe a situation in which heat transfer occurs.
Solution
Many answers are possible. The energy transfer should be due to a temperature difference.
13. When heat transfers into a system, is the energy stored as heat? Explain briefly.
Solution
No, it is stored as thermal energy. A thermodynamic system does not have a well-defined
quantity of heat.
14. The brakes in a car increase in temperature by when bringing the car to rest from a
speed v. How much greater would be if the car initially had twice the speed? You may
assume the car stops fast enough that no heat transfers out of the brakes.
Solution
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Unit 1: Thermodynamics
Chapter 1: Temperature and Heat
four times as great, since
15. A pressure cooker contains water and steam in equilibrium at a pressure greater than
atmospheric pressure. How does this greater pressure increase cooking speed?
Solution
It raises the boiling point, so the water, which the food gains heat from, is at a higher
temperature.
16. As shown below, which is the phase diagram for carbon dioxide, what is the vapor pressure
of solid carbon dioxide (dry ice) at (Note that the axes in the figure are nonlinear and
the graph is not to scale.)
Solution
1 atm
17. Can carbon dioxide be liquefied at room temperature ( )? If so, how? If not, why not?
(See the phase diagram in the preceding problem.)
Solution
Yes, by raising the pressure above 56 atm.
18. What is the distinction between gas and vapor?
Solution
Vapor is gas in the presence of the liquid or solid phase of the same substance.
19. Heat transfer can cause temperature and phase changes. What else can cause these changes?
Solution
work
20. How does the latent heat of fusion of water help slow the decrease of air temperatures,
perhaps preventing temperatures from falling significantly below in the vicinity of large
bodies of water?
Solution
As heat is removed, the temperature of the water does not fall till the water is frozen (at least on
the surface), so the air tends to stay in equilibrium with it and remains close to .
21. What is the temperature of ice right after it is formed by freezing water?
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Unit 1: Thermodynamics
Chapter 1: Temperature and Heat
Solution
(at or near atmospheric pressure)
22. If you place 0 °C ice into 0 °C water in an insulated container, what will the net result be?
Will there be less ice and more liquid water, or more ice and less liquid water, or will the
amounts stay the same?
Solution
If the container is perfectly insulated, the amount of ice and the amount of liquid water will stay
the same.
23. 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 melting process or slow it down?
Solution
Condensation releases heat, so it speeds up the melting.
24. In Miami, Florida, which has a very humid climate and numerous bodies of water nearby, it
is unusual for temperatures to rise above about ( ). In the desert climate of
Phoenix, Arizona, however, temperatures rise above that almost every day in July and August.
Explain how the type of heat transfer accounts for this difference and how it helps limit high
temperatures in humid climates.
Solution
Evaporation absorbs heat that would otherwise go into raising the temperature.
25. In winter, it is often warmer in San Francisco than in Sacramento, 150 km inland. In summer,
it is nearly always hotter in Sacramento. Explain how the bodies of water surrounding San
Francisco moderate its extreme temperatures.
Solution
Because of water’s high specific heat, it changes temperature less than land. Also, evaporation
reduces temperature rises. The air tends to stay close to equilibrium with the water, so its
temperature does not change much where there’s a lot of water around, as in San Francisco but
not Sacramento.
26. 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.
Solution
Low pressure reduces the boiling point and increases evaporation, which cools the food it
evaporates from.
27. In a physics classroom demonstration, an instructor inflates a balloon by mouth and then
cools it in liquid nitrogen. When cold, the shrunken balloon 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
crystals sublime, with some crystals lingering for a while and then producing a liquid. Identify
the blue liquid and the two solids in the cold balloon. Justify your identifications using data from
the following table.
Substance Melting Point kJ/kg kcal/kg Boiling Point kJ/kg kcal/kg
(°C) (°C)
Helium[2] 5.23 1.25 20.9 4.99
Hydrogen 58.6 14.0 452 108
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Unit 1: Thermodynamics
Chapter 1: Temperature and Heat
Nitrogen 25.5 6.09 201 48.0
Oxygen 13.8 3.30 213 50.9
Ethanol –114 104 24.9 78.3 854 204
Ammonia –75 332 79.3 –33.4 1370 327
Mercury –38.9 11.8 2.82 357 272 65.0
Water 0.00 334 79.8 100.0 2256[3] 539[4]
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
Solution
The liquid is oxygen, whose boiling point is above that of nitrogen but whose melting point is
below the boiling point of liquid nitrogen. The crystals that sublime are carbon dioxide, which
has no liquid phase at atmospheric pressure. The crystals that melt are water, whose melting
point is above carbon dioxide’s sublimation point. The water came from the instructor’s breath.
28. What are the main methods of heat transfer from the hot core of Earth to its surface? From
Earth’s surface to outer space?
Solution
convection and conduction; radiation
29. When our bodies get too warm, they respond by sweating and increasing blood circulation to
the surface to transfer thermal energy away from the core. What effect will those processes have
on a person in a hot tub?
Solution
Increasing circulation to the surface will warm the person, as the temperature of the water is
warmer than human body temperature. Sweating will cause no evaporative cooling under water
or in the humid air immediately above the tub.
30. Shown below is a cut-away drawing of a thermos bottle (also known as a Dewar flask),
which is a device designed specifically to slow down all forms 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, the rubber support, the air layer, and the stopper.
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Unit 1: Thermodynamics
Chapter 1: Temperature and Heat
Solution
The vacuum prevents conduction and convection. The silvering reduces radiation by reducing
emissivity. The thin walls, which necessarily touch both the hot or cold liquid and the outer
container of the bottle, reduce conduction by having a small A and relatively large L. The
support, which also necessarily connects the inner wall to the outer container, reduces
conduction by being made of a material with low conductivity. The air layer also has low
conductivity. The stopper prevents convection (and contamination of the drink).
31. Some electric stoves have a flat ceramic surface with heating elements hidden beneath. A pot
placed over a heating element will be heated, while the surface only a few centimeters away is
safe to touch. Why is ceramic, with a conductivity less than that of a metal but greater than that
of a good insulator, an ideal choice for the stove top?
Solution
It spread the heat over the area above the heating elements, evening the temperature there, but
does not spread the heat much beyond the heating elements.
32. Loose-fitting white clothing covering most of the body, shown below, is ideal for desert
dwellers, both in the hot Sun and during cold evenings. Explain how such clothing is
advantageous during both day and night.
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Unit 1: Thermodynamics
Chapter 1: Temperature and Heat
Solution
By day, it allows low-speed air circulation and thus evaporative cooling of sweat. Being white, it
reduces absorption of heat radiation. By night, it reduces convective loss, and being white,
reduces emission of heat radiation.
33. One way to make a fireplace more energy-efficient is to have room air circulate around the
outside of the fire box and back into the room. Detail the methods of heat transfer involved.
Solution
Heat is conducted from the fire through the fire box to the circulating air and then convected by
the air into the room (forced convection).
34. On cold, clear nights horses will sleep under the cover of large trees. How does this help
them keep warm?
Solution
The tree blocks radiative loss to space. The mass of the tree may also reduce its temperature
change.
35. When watching a circus during the day in a large, dark-colored tent, you sense significant
heat transfer from the tent. Explain why this occurs.
Solution
The tent is heated by the Sun and transfers heat to you by all three processes, especially
radiation.
36. Satellites designed to observe the radiation from cold (3 K) dark space have sensors that are
shaded from the Sun, Earth, and the Moon and are cooled to very low temperatures. Why must
the sensors be at low temperature?
Solution
If not, their own radiation would overwhelm the radiation from space.
37. Why are thermometers that are used in weather stations shielded from the sunshine? What
does a thermometer measure if it is shielded from the sunshine? What does it measure if it is not?
Solution
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Unit 1: Thermodynamics
Chapter 1: Temperature and Heat
If shielded, it measures the air temperature. If not, it measures the combined effect of air
temperature and net radiative heat gain from the Sun.
38. Putting a lid on a boiling pot greatly reduces the heat transfer necessary to keep it boiling.
Explain why.
Solution
The lid blocks convection. In particular, it blocks the loss of steam, keeping of the latent heat of
the steam in the pot.
39. Your house will be empty for a while in cold weather, and you want to save energy and
money. Should you turn the thermostat down to the lowest level that will protect the house from
damage such as freezing pipes, or leave it at the normal temperature? (If you don’t like coming
back to a cold house, imagine that a timer controls the heating system so the house will be warm
when you get back.) Explain your answer.
Solution
Turn the thermostat down. To have the house at the normal temperature, the heating system must
replace all the heat that was lost. For all three mechanisms of heat transfer, the greater the
temperature difference between inside and outside, the more heat is lost and must be replaced. So
the house should be at the lowest temperature that does not allow freezing damage.
40. You pour coffee into an unlidded cup, intending to drink it 5 minutes later. You can add
cream when you pour the cup or right before you drink it. (The cream is at the same temperature
either way. Assume that the cream and coffee come into thermal equilibrium with each other
very quickly.) Which way will give you hotter coffee? What feature of this question is different
from the previous one?
Solution
Add the cream first to lower the temperature and reduce the heat loss, as in the previous problem.
The different feature is that the cream lightens the color of the coffee and thus reduces its
emissivity, further reducing radiative heat loss.
41. Broiling is a method of cooking by radiation, which produces somewhat different results
from cooking by conduction or convection. A gas flame or electric heating element produces a
very high temperature close to the food and above it. Why is radiation the dominant heat-transfer
method in this situation?
Solution
Air is a good insulator, so there is little conduction, and the heated air rises, so there is little
convection downward.
42. On a cold winter morning, why does the metal of a bike feel colder than the wood of a porch?
Solution
Because metal conducts heat faster than wood, and the feeling of cold is caused by the rate of
heat conduction out of the skin.
Problems
43. While traveling outside the United States, you feel sick. A companion gets you a
thermometer, which says your temperature is 39. What scale is that on? What is your Fahrenheit
temperature? Should you seek medical help?
Solution
That must be Celsius. Your Fahrenheit temperature is 102 °F. Yes, it is time to get treatment.
44. What are the following temperatures on the Kelvin scale?
(a) 68.0 °F, an indoor temperature sometimes recommended for energy conservation in winter
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Unit 1: Thermodynamics
Chapter 1: Temperature and Heat
(b) 134.0 °F, one of the highest atmospheric temperatures ever recorded on Earth (Death
Valley, California, 1913)
(c) 9890 °F, the temperature of the surface of the Sun
Solution
a. To convert from Fahrenheit to Kelvin, first convert to Celsius:
.
Then convert to Kelvin: ; b. 330 K; c. 5750 K
45. (a) Suppose a cold front blows into your locale and drops the temperature by 40.0 Fahrenheit
degrees. How many degrees Celsius does the temperature decrease when it decreases by 40.0 °F?
(b) Show that any change in temperature in Fahrenheit degrees is nine-fifths the change in
Celsius degrees
Solution
a. ; b. We know that . We also know that and
. So, substituting, we have . Partially solving and
rearranging the equation, we have . Therefore, .
46. An Associated Press article on climate change said, “Some of the ice shelf’s disappearance
was probably during times when the planet was 36 degrees Fahrenheit (2 degrees Celsius) to 37
degrees Fahrenheit (3 degrees Celsius) warmer than it is today.” What mistake did the reporter
make?
Solution
The reporter was given temperature differences in Celsius, but treated them as temperatures and
converted them to Fahrenheit. However, he should have used the relationship for temperature
differences derived in the previous problem, without adding 32.
47. (a) At what temperature do the Fahrenheit and Celsius scales have the same numerical value?
(b) At what temperature do the Fahrenheit and Kelvin scales have the same numerical value?
Solution
a. ; b. 575 K
48. A person taking a reading of the temperature in a freezer in Celsius makes two mistakes: first
omitting the negative sign and then thinking the temperature is Fahrenheit. That is, the person
reads as . Oddly enough, the result is the correct Fahrenheit temperature. What is
the original Celsius reading? Round your answer to three significant figures.
Solution
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Unit 1: Thermodynamics
Chapter 1: Temperature and Heat
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,OpenStax University Physics Volume II
Unit 1: Thermodynamics
Chapter 1: Temperature and Heat
University Physics Volume II
Unit 1: Thermodynamics
Chapter 1: Temperature and Heat
Conceptual Questions
1. What does it mean to say that two systems are in thermal equilibrium?
Solution
They are at the same temperature, and if they are placed in contact, no net heat flows between
them.
2. Give an example in which A has some kind of non-thermal equilibrium relationship with B,
and B has the same relationship with C, but A does not have that relationship with C.
Solution
One possibility is that in some game, A and C are both equally matched with B, but C
consistently beats A, maybe because C’s style is hard for A to cope with or C has some
psychological advantage. Another is that if two people of different weights lean at the same
angle against a wall, they are each in equilibrium with the wall, but they would not be in
equilibrium with each other. Other answers are possible.
3. If a thermometer is allowed to come to equilibrium with the air, and a glass of water is not in
equilibrium with the air, what will happen to the thermometer reading when it is placed in the
water?
Solution
The reading will change.
4. Give an example of a physical property that varies with temperature and describe how it is
used to measure temperature.
Solution
Volume—as the volume of liquid in an ordinary thermometer increases, the liquid’s interface
with air rises along a scale. Electrical resistance—the resistance of a piece of silicon in a
thermistor decreases with increasing temperature and is read electronically. Color—certain
chemical reactions cause color changes at certain temperatures, so a set of spots containing such
chemicals with slightly different color-change temperatures can indicate temperature. Radiated
power and frequency spectrum—a bolometer can be pointed at an object, especially one that is
too hot or too distant to put a thermometer in contact with, and the radiated power or peak
frequency can be measured and converted into a temperature. Other answers are possible.
5. Pouring cold water into hot glass or ceramic cookware can easily break it. What causes the
breaking? Explain why Pyrex®, a glass with a small coefficient of linear expansion, is less
susceptible.
Solution
The cold water cools part of the inner surface, making it contract, while the rest remains
expanded. The strain is too great for the strength of the material. Pyrex contracts less, so it
experiences less strain.
6. One method of getting a tight fit, say of a metal peg in a hole in a metal block, is to
manufacture the peg slightly larger than the hole. The peg is then inserted when at a different
temperature than the block. Should the block be hotter or colder than the peg during insertion?
Explain your answer.
Solution
The block should be hotter so the hole will be bigger.
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Unit 1: Thermodynamics
Chapter 1: Temperature and Heat
7. Does it really help to run hot water over a tight metal lid on a glass jar before trying to open it?
Explain your answer.
Solution
In principle, the lid expands more than the jar because metals have higher coefficients of
expansion than glass. That should make unscrewing the lid easier. (In practice, getting the lid and
jar wet may make gripping them more difficult.)
8. When a cold alcohol thermometer is placed in a hot liquid, the column of alcohol goes down
slightly before going up. Explain why.
Solution
The glass expands before the alcohol does.
9. Calculate the length of a 1-meter rod of a material with thermal expansion coefficient
when the temperature is raised from 300 K to 600 K. Taking your answer as the new initial
length, find the length after the rod is cooled back down to 300 K. Is your answer 1 meter?
Should it be? How can you account for the result you got?
Solution
After being heated, the length is ( )( ). After being cooled, the length is
. That answer is not 1 m, but it should be. The explanation is that
even if is exactly constant, the relation is strictly true only in the limit of small
. Since values are small, the discrepancy is unimportant in practice.
10. Noting the large stresses that can be caused by thermal expansion, an amateur weapon
inventor decides to use it to make a new kind of gun. He plans to jam a bullet against an
aluminum rod inside a closed invar tube. When he heats the tube, the rod will expand more than
the tube and a very strong force will build up. Then, by a method yet to be determined, he will
open the tube in a split second and let the force of the rod launch the bullet at very high speed.
What is he overlooking?
Solution
The force will go to zero over a very short distance as the rod reaches its expanded length, so
very little work will be done. Also, the force is proportional to the area, so on something the size
of a bullet it will not be as great as the inventor thinks.
11. How is heat transfer related to temperature?
Solution
Temperature differences cause heat transfer.
12. Describe a situation in which heat transfer occurs.
Solution
Many answers are possible. The energy transfer should be due to a temperature difference.
13. When heat transfers into a system, is the energy stored as heat? Explain briefly.
Solution
No, it is stored as thermal energy. A thermodynamic system does not have a well-defined
quantity of heat.
14. The brakes in a car increase in temperature by when bringing the car to rest from a
speed v. How much greater would be if the car initially had twice the speed? You may
assume the car stops fast enough that no heat transfers out of the brakes.
Solution
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Unit 1: Thermodynamics
Chapter 1: Temperature and Heat
four times as great, since
15. A pressure cooker contains water and steam in equilibrium at a pressure greater than
atmospheric pressure. How does this greater pressure increase cooking speed?
Solution
It raises the boiling point, so the water, which the food gains heat from, is at a higher
temperature.
16. As shown below, which is the phase diagram for carbon dioxide, what is the vapor pressure
of solid carbon dioxide (dry ice) at (Note that the axes in the figure are nonlinear and
the graph is not to scale.)
Solution
1 atm
17. Can carbon dioxide be liquefied at room temperature ( )? If so, how? If not, why not?
(See the phase diagram in the preceding problem.)
Solution
Yes, by raising the pressure above 56 atm.
18. What is the distinction between gas and vapor?
Solution
Vapor is gas in the presence of the liquid or solid phase of the same substance.
19. Heat transfer can cause temperature and phase changes. What else can cause these changes?
Solution
work
20. How does the latent heat of fusion of water help slow the decrease of air temperatures,
perhaps preventing temperatures from falling significantly below in the vicinity of large
bodies of water?
Solution
As heat is removed, the temperature of the water does not fall till the water is frozen (at least on
the surface), so the air tends to stay in equilibrium with it and remains close to .
21. What is the temperature of ice right after it is formed by freezing water?
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Unit 1: Thermodynamics
Chapter 1: Temperature and Heat
Solution
(at or near atmospheric pressure)
22. If you place 0 °C ice into 0 °C water in an insulated container, what will the net result be?
Will there be less ice and more liquid water, or more ice and less liquid water, or will the
amounts stay the same?
Solution
If the container is perfectly insulated, the amount of ice and the amount of liquid water will stay
the same.
23. 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 melting process or slow it down?
Solution
Condensation releases heat, so it speeds up the melting.
24. In Miami, Florida, which has a very humid climate and numerous bodies of water nearby, it
is unusual for temperatures to rise above about ( ). In the desert climate of
Phoenix, Arizona, however, temperatures rise above that almost every day in July and August.
Explain how the type of heat transfer accounts for this difference and how it helps limit high
temperatures in humid climates.
Solution
Evaporation absorbs heat that would otherwise go into raising the temperature.
25. In winter, it is often warmer in San Francisco than in Sacramento, 150 km inland. In summer,
it is nearly always hotter in Sacramento. Explain how the bodies of water surrounding San
Francisco moderate its extreme temperatures.
Solution
Because of water’s high specific heat, it changes temperature less than land. Also, evaporation
reduces temperature rises. The air tends to stay close to equilibrium with the water, so its
temperature does not change much where there’s a lot of water around, as in San Francisco but
not Sacramento.
26. 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.
Solution
Low pressure reduces the boiling point and increases evaporation, which cools the food it
evaporates from.
27. In a physics classroom demonstration, an instructor inflates a balloon by mouth and then
cools it in liquid nitrogen. When cold, the shrunken balloon 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
crystals sublime, with some crystals lingering for a while and then producing a liquid. Identify
the blue liquid and the two solids in the cold balloon. Justify your identifications using data from
the following table.
Substance Melting Point kJ/kg kcal/kg Boiling Point kJ/kg kcal/kg
(°C) (°C)
Helium[2] 5.23 1.25 20.9 4.99
Hydrogen 58.6 14.0 452 108
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Chapter 1: Temperature and Heat
Nitrogen 25.5 6.09 201 48.0
Oxygen 13.8 3.30 213 50.9
Ethanol –114 104 24.9 78.3 854 204
Ammonia –75 332 79.3 –33.4 1370 327
Mercury –38.9 11.8 2.82 357 272 65.0
Water 0.00 334 79.8 100.0 2256[3] 539[4]
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
Solution
The liquid is oxygen, whose boiling point is above that of nitrogen but whose melting point is
below the boiling point of liquid nitrogen. The crystals that sublime are carbon dioxide, which
has no liquid phase at atmospheric pressure. The crystals that melt are water, whose melting
point is above carbon dioxide’s sublimation point. The water came from the instructor’s breath.
28. What are the main methods of heat transfer from the hot core of Earth to its surface? From
Earth’s surface to outer space?
Solution
convection and conduction; radiation
29. When our bodies get too warm, they respond by sweating and increasing blood circulation to
the surface to transfer thermal energy away from the core. What effect will those processes have
on a person in a hot tub?
Solution
Increasing circulation to the surface will warm the person, as the temperature of the water is
warmer than human body temperature. Sweating will cause no evaporative cooling under water
or in the humid air immediately above the tub.
30. Shown below is a cut-away drawing of a thermos bottle (also known as a Dewar flask),
which is a device designed specifically to slow down all forms 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, the rubber support, the air layer, and the stopper.
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Chapter 1: Temperature and Heat
Solution
The vacuum prevents conduction and convection. The silvering reduces radiation by reducing
emissivity. The thin walls, which necessarily touch both the hot or cold liquid and the outer
container of the bottle, reduce conduction by having a small A and relatively large L. The
support, which also necessarily connects the inner wall to the outer container, reduces
conduction by being made of a material with low conductivity. The air layer also has low
conductivity. The stopper prevents convection (and contamination of the drink).
31. Some electric stoves have a flat ceramic surface with heating elements hidden beneath. A pot
placed over a heating element will be heated, while the surface only a few centimeters away is
safe to touch. Why is ceramic, with a conductivity less than that of a metal but greater than that
of a good insulator, an ideal choice for the stove top?
Solution
It spread the heat over the area above the heating elements, evening the temperature there, but
does not spread the heat much beyond the heating elements.
32. Loose-fitting white clothing covering most of the body, shown below, is ideal for desert
dwellers, both in the hot Sun and during cold evenings. Explain how such clothing is
advantageous during both day and night.
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Chapter 1: Temperature and Heat
Solution
By day, it allows low-speed air circulation and thus evaporative cooling of sweat. Being white, it
reduces absorption of heat radiation. By night, it reduces convective loss, and being white,
reduces emission of heat radiation.
33. One way to make a fireplace more energy-efficient is to have room air circulate around the
outside of the fire box and back into the room. Detail the methods of heat transfer involved.
Solution
Heat is conducted from the fire through the fire box to the circulating air and then convected by
the air into the room (forced convection).
34. On cold, clear nights horses will sleep under the cover of large trees. How does this help
them keep warm?
Solution
The tree blocks radiative loss to space. The mass of the tree may also reduce its temperature
change.
35. When watching a circus during the day in a large, dark-colored tent, you sense significant
heat transfer from the tent. Explain why this occurs.
Solution
The tent is heated by the Sun and transfers heat to you by all three processes, especially
radiation.
36. Satellites designed to observe the radiation from cold (3 K) dark space have sensors that are
shaded from the Sun, Earth, and the Moon and are cooled to very low temperatures. Why must
the sensors be at low temperature?
Solution
If not, their own radiation would overwhelm the radiation from space.
37. Why are thermometers that are used in weather stations shielded from the sunshine? What
does a thermometer measure if it is shielded from the sunshine? What does it measure if it is not?
Solution
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Chapter 1: Temperature and Heat
If shielded, it measures the air temperature. If not, it measures the combined effect of air
temperature and net radiative heat gain from the Sun.
38. Putting a lid on a boiling pot greatly reduces the heat transfer necessary to keep it boiling.
Explain why.
Solution
The lid blocks convection. In particular, it blocks the loss of steam, keeping of the latent heat of
the steam in the pot.
39. Your house will be empty for a while in cold weather, and you want to save energy and
money. Should you turn the thermostat down to the lowest level that will protect the house from
damage such as freezing pipes, or leave it at the normal temperature? (If you don’t like coming
back to a cold house, imagine that a timer controls the heating system so the house will be warm
when you get back.) Explain your answer.
Solution
Turn the thermostat down. To have the house at the normal temperature, the heating system must
replace all the heat that was lost. For all three mechanisms of heat transfer, the greater the
temperature difference between inside and outside, the more heat is lost and must be replaced. So
the house should be at the lowest temperature that does not allow freezing damage.
40. You pour coffee into an unlidded cup, intending to drink it 5 minutes later. You can add
cream when you pour the cup or right before you drink it. (The cream is at the same temperature
either way. Assume that the cream and coffee come into thermal equilibrium with each other
very quickly.) Which way will give you hotter coffee? What feature of this question is different
from the previous one?
Solution
Add the cream first to lower the temperature and reduce the heat loss, as in the previous problem.
The different feature is that the cream lightens the color of the coffee and thus reduces its
emissivity, further reducing radiative heat loss.
41. Broiling is a method of cooking by radiation, which produces somewhat different results
from cooking by conduction or convection. A gas flame or electric heating element produces a
very high temperature close to the food and above it. Why is radiation the dominant heat-transfer
method in this situation?
Solution
Air is a good insulator, so there is little conduction, and the heated air rises, so there is little
convection downward.
42. On a cold winter morning, why does the metal of a bike feel colder than the wood of a porch?
Solution
Because metal conducts heat faster than wood, and the feeling of cold is caused by the rate of
heat conduction out of the skin.
Problems
43. While traveling outside the United States, you feel sick. A companion gets you a
thermometer, which says your temperature is 39. What scale is that on? What is your Fahrenheit
temperature? Should you seek medical help?
Solution
That must be Celsius. Your Fahrenheit temperature is 102 °F. Yes, it is time to get treatment.
44. What are the following temperatures on the Kelvin scale?
(a) 68.0 °F, an indoor temperature sometimes recommended for energy conservation in winter
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Chapter 1: Temperature and Heat
(b) 134.0 °F, one of the highest atmospheric temperatures ever recorded on Earth (Death
Valley, California, 1913)
(c) 9890 °F, the temperature of the surface of the Sun
Solution
a. To convert from Fahrenheit to Kelvin, first convert to Celsius:
.
Then convert to Kelvin: ; b. 330 K; c. 5750 K
45. (a) Suppose a cold front blows into your locale and drops the temperature by 40.0 Fahrenheit
degrees. How many degrees Celsius does the temperature decrease when it decreases by 40.0 °F?
(b) Show that any change in temperature in Fahrenheit degrees is nine-fifths the change in
Celsius degrees
Solution
a. ; b. We know that . We also know that and
. So, substituting, we have . Partially solving and
rearranging the equation, we have . Therefore, .
46. An Associated Press article on climate change said, “Some of the ice shelf’s disappearance
was probably during times when the planet was 36 degrees Fahrenheit (2 degrees Celsius) to 37
degrees Fahrenheit (3 degrees Celsius) warmer than it is today.” What mistake did the reporter
make?
Solution
The reporter was given temperature differences in Celsius, but treated them as temperatures and
converted them to Fahrenheit. However, he should have used the relationship for temperature
differences derived in the previous problem, without adding 32.
47. (a) At what temperature do the Fahrenheit and Celsius scales have the same numerical value?
(b) At what temperature do the Fahrenheit and Kelvin scales have the same numerical value?
Solution
a. ; b. 575 K
48. A person taking a reading of the temperature in a freezer in Celsius makes two mistakes: first
omitting the negative sign and then thinking the temperature is Fahrenheit. That is, the person
reads as . Oddly enough, the result is the correct Fahrenheit temperature. What is
the original Celsius reading? Round your answer to three significant figures.
Solution
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