ANSWERS TO QUESTIONS
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
(See Figure 5.2)
The Fahrenheit and Kelvin scales match at T = 574.5875 ºF = 574.5875 K. The Celsius and
Kelvin scales differ by 273.15 degrees at all temperatures.
Absolute zero is the lowest possible temperature. At this temperature atoms and molecules
would be motionless. (Note: This is really an oversimplification. Quantum mechanics tells a
somewhat different story.)
The kinetic energies of atoms and molecules in a substance increase as the temperature rises.
The moon doesn’t have an atmosphere because its gravitational field is too weak—so atoms
and molecules escape. Mercury doesn’t have an atmosphere because its surface temperature
is too high—so the kinetic energies of gas molecules would be high enough for them to
escape.
Increasing temperatures would make the liquid column go down, so the scale would have to
be labeled with higher temperatures at the bottom, backwards from what you are used to.
A bimetallic strip consists of two different metal strips bonded together. As the temperature
of the strip changes, the two metals expand or contract different amounts, causing the strip
to bend. (See Figure 5.9.)
From the photo you can see that the thermometer pointer must rotate clockwise as the
temperature increases, since the labeled numbers get bigger in that direction. To make the
pointer go clockwise the coil will have to unwind slightly, as if trying to straighten out. This
means the inner side of coil must stretch more than the outer side. I predict that the inner
side has the larger coefficient of expansion. One could test this by cutting a piece of the strip
out of an old thermometer, straightening it out and dipping it into some warm water to see
which way it bends.
From Table 5.2 (Transparency #58), aluminum has a coefficient of linear expansion that is
about twice as large as that of iron. Therefore an aluminum part would expand about 2 mm.
Water expands when its temperature decreases within the range of 0 °C to 4 °C, whereas
most substances (including water above 4 °C) contract when the temperature decreases.
a) If the water freezes solid, it would expand and break the glass.
b) The water level would fall as the thermometer cooled, until it reached 4 ℃. As the
water's temperature decreased below 4 ℃, the water would expand so the water level would
rise.
One, expose it to something with a higher temperature, and two, do work on it. Placing a pan
on a hot stove is an example of the former, and rubbing your hands together rapidly is an
example of the latter.
The temperature of the air escaping from a tire is lower than the temperature of the air inside
the tire. As a gas is compressed its temperature increases, so as it expands its temperature
decreases. Another way to look at it: as the air escapes it displaces the outside air and
therefore does work on it. Some of the kinetic energy of the air molecules is used to do this
work so the temperature drops.
Yes. If air is compressed at the same time that heat is allowed to flow out of it at exactly the
same rate that work is done on it, the internal energy will not change.
(See Section 5.4.) There is conduction of heat from your skin to the cooler air in contact
with it, there is convection around hot light bulbs, there is radiation of heat from hot objects
like light bulbs, and so on.
A large iron nail is a much better conductor of heat than the potato so heat will flow to the
interior of the potato faster.
17. The coin will feel warmer because it is a conductor and heat will flow from it into your
finger more rapidly. Since glass is a poor conductor, the spot that is touched will give up
heat and its temperature will drop, so it will feel cooler.
18. The heater should be placed near the bottom of the aquarium so that a natural circulation
will be set up due to convection (similar to Figure 5.22).
19. Air warmed by a campfire expands and the buoyant force exerted by the cooler surrounding
air forces it to rise upward. The breeze is air moving to take the place of the rising air. (More
specifically, the breeze is air moving toward the region of lowered air pressure around the
fire that results when the warmed air rises.)
20. Your palm would feel cool because it would be receiving less infrared from the cold ice than
it was receiving from the walls of the room, which are warmer. Therefore the temperature
of your skin would drop some. Below the ice your palm would feel even cooler because in
addition to the radiation cooling described above, there would be "upside-down" convection:
air in contact with the ice would be cooled by conduction, it's density would decrease, so in
would sink and cool your palm more as it flowed over it.
21. It takes longer to bring a full pan of water to the boiling point than a pan that is half full
(assuming the same burner or heating element is used) because more energy has to be given
to the full pan.
22. Since water has a much larger specific heat capacity than iron, the heat that flows out of the
iron will raise the temperature of the water less than it lowers the temperature of the iron, so
the final temperature will be closer to the water’s initial temperature than the iron’s. So the
final temperature will be closer to 0 °C than 50 or 100 °C. (The actual final temperature
turns out to be 9.9 °C.)
23. The mass of the block does not matter. The temperature change will be the same no matter
what the block’s mass is.
24. The temperature of the iron will increase more than the temperature of the aluminum
because aluminum’s specific heat capacity is higher. The kinetic energy of each object is
converted to heat, but aluminum needs about twice as much heat to change its temperature
one degree as iron does.
25. It would take a bit more water to put out fires, but if the latent heat of vaporization were the
same, the heat taken from the fire as the water boils would still be responsible for most of
the cooling. Water cooled engines would need larger capacity cooling systems so that a
greater volume of water would flow through the engine each second.
26. The average kinetic energy of water molecules stays the same while water is boiling so the
temperature stays the same. The internal energy gained by boiling water goes to increase the
potential energy of the molecules.
27. The boiling temperature of water increases when the air pressure increases, and it decreases
when the air pressure decreases.
28. If you boil the water by heating it you must add heat to both warm the water to the boiling
temperature and then add enough heat to vaporize it. Due to water’s high specific heat
capacity and even larger latent heat of vaporization, the total is a large amount of heat.
29. The saturation density is the highest possible humidity—the point beyond which water
vapor starts to condense out of the air. At higher temperature the saturation density is higher
because the water molecules are moving faster and are less likely to condense into droplets.
(See Table 5.5, Transparency #67.)
30. If no water vapor is added to the air, the relative humidity will decrease as the temperature
of the air is increased because the saturation density increases.
31. It could be used in the trigger mechanism. It would melt when a fire raised its temperature
sufficiently and this could release a spring-loaded valve that starts water flowing through the
sprinkler system to put out the fire.
32. At the dew point, energy lost by the air results in a change of phase from vapor to liquid
droplets, rather than a change in temperature.
33. A heat engine takes in heat at some high temperature, converts some of this energy into
useful mechanical energy or work, and releases the remaining energy as heat at some lower
temperature. A heat mover takes in heat at some lower temperature, has an input of
mechanical energy or work, and releases heat at some higher temperature. (See Section 5.7.)
34. No. There are two energy inputs into a heat pump; heat from some low temperature source
and mechanical energy or work. The sum of these two energy inputs equals the heat energy
output.
ANSWERS TO EVEN NUMBERED PROBLEMS
2.
4.
6.
8.
10.
12.
14.
16.
18.
20.
22.
24.
– 60 °F = – 51 °C (actually – 51.1 °C)
l = 0.0136 m
T = – 47 °C
U = 20 J
Q = 213,000 J
a) Q = 570,000 J
b) 7.74 cups
T = 154 °C
T = 0.22 °C
a) humidity = 0.0305 kg/m3
b) about 30 °C
m = 0.0213 kg
m = 3.16 kg
a) 100%, after some water condenses out.
b)
0.05
Saturation density
Density (kg/m 3)
0.04
breath
0.03
mixture
0.02
0.01
outside air
0
-10
0
10
20
30
40
T (°C)
The above graph shows that the mixture will fall on the other side of the saturation density
curve. This means that there is excess moisture in the mixture, and some will condense out
as fog—you will ―see‖ your breath.
26. Efficiency = 26.8%
28. Efficiency = 6.7%
ANSWERS TO CHALLENGES
1.
2.
3.
Initially the densities of the solid and the liquid are identical. Expansion causes both
densities to decrease but since the liquid expands more, its density will be lower that the
solid’s. Consequently the solid will sink.
One reason why things break during a sudden temperature change is that during the process
different parts of the object have different temperatures. The corresponding expansions or
contractions of the parts are different, so forces arise. For example, the outer part of a rock
that is suddenly thrown into a fire gets hot and expands more quickly than the interior. The
resulting stresses can crack the rock. Pyrex has a very low coefficient of linear expansion so
temperature changes cause relatively small expansions and contractions. The resulting forces
inside the Pyrex are consequently small and are less likely to cause breaks.
Yes, if the air is allowed to expand and do work as heat is added to it.
4. a) The water heated by the heater would
sink to the bottom of the container, as
shown. The circulation is opposite that
shown in Figure 5.22.
5.
6.
7.
b) The heater should be placed initially near the surface of the water. After the water is
warmer than about 4°C, the heater should be placed near the bottom of the container because
the heated water rises and the circulation is reversed.
a) The air pressure is lower at higher altitudes. Therefore, rising air expands as the pressure
on it decreases. But as the rising air expands, it does work on the surrounding air (this is
similar to the situation shown in the right side of Figure 5.19). By the first law of
thermodynamics, as the air does work its internal energy decreases if no heat is added to it.
This decrease in U lowers the temperature of the air.
b) Condensation and cloud formation occur when the temperature of the rising air is so low
that the decreased saturation density is lower than the humidity. In dry climates like deserts,
the humidity is very low so the air must be cooled more, and therefore must rise higher,
before condensation begins.
At 25°C, the saturation density equals 0.0228 kg/m3. From problem 18, the humidity equals
0.0305 kg/m3. Therefore the amount of water that will condense out of each cubic meter of
air is 0.0305 kg – 0.0228 kg = 0.0077 kg. The volume of a room measuring 5 m by 4 m by 3
m is 60 m3. The total amount of water that will condense out is:
m = 60 m3 0.0077 kg/m3
m = 0.46 kg
No. For each joule of heat removed from air inside the refrigerator, more than one joule is
added to the air outside of the refrigerator. The added heat arises from the energy input to
the refrigerator mechanism. With the door open and the air circulating in a closed room, the
refrigerator will actually heat the air in the room.
The way to cool the room is to arrange the refrigerator’s heat ―exhaust‖ to leave the room.
Sticking the refrigerator in a doorway with its door open to the inside of the room and its
rear (where the cooling coils are) to the outside would work.