1. Inanimate things such as tables, chairs, furniture, and so on, have the same temperature as the surrounding air
(assuming they are in thermal equilibrium with the air
—i.e., no sudden gush of different-temperature air or such). People and other mammals, however, generate their own heat and have body temperatures that are normally higher than air temperature.
2. Since Celsius degrees are larger than Fahrenheit degrees, an increase of 1 C° is larger. It’s 9 /
5
as large.
3. Yes, the same average speed, but not the same instantaneous speed. At any moment molecules with the same average speed can have enormously different instantaneous speeds.
4. Gas molecules move haphazardly and move at random speeds. They continually run into one another, sometimes giving kinetic energy to neighbors, sometimes receiving kinetic energy. In this continual interaction, it would be statistically impossible for any large number of molecules to have the same speed. Temperature has to do with average speeds.
5. You cannot establish by your own touch whether or not you are running a fever because there would be no temperature difference between your hand and forehead. If your forehead is a couple of degrees higher in temperature than normal, your hand is also a couple of degrees higher.
6. Molecules in a gram of steam have considerably more energy, as evidenced by the considerable amount of work needed to change phase from solid ice to gaseous steam.
7. The hot coffee has a higher temperature, but not a greater internal energy. Although the iceberg has less internal energy per mass, its enormously greater mass gives it a greater total energy than that in the small cup of coffee. (For a smaller volume of ice, the fewer number of more energetic molecules in the hot cup of coffee may constitute a greater total amount of internal energy
—but not compared to an iceberg.)
8. Mercury must expand more than glass. If the expansion rates were the same there would be no different readings for different temperature. All temperatures would have the same reading.
9. Calorie, which is 1000 calories.
10. The hot rock will cool and the cool water will warm, regardless of the relative amounts of each. The amount of temperature change, however, does depend in great part on the relative masses of the materials. For a hot rock dropped into the Atlantic Ocean, the change in temperature would be too small to measure. Keep increasing the mass of the rock or keep decreasing the mass of the ocean and the change will be evident.
11. The average speed of molecules in both containers is the same. There is greater internal energy in the full glass
(twice the matter at the same temperature). More heat will be required to increase the temperature of the full glass, twice as much, in fact.
12. Other effects aside, the temperature should be slightly higher, because the PE of the water above has been transformed to KE below, which in turn is transformed to heat and internal energy when the falling water is stopped. (On his honeymoon, James Prescott Joule could not be long diverted from his preoccupation with heat, and he attempted to measure the temperature of the water above and below a waterfall in Chamonix. The temperature increase he expected, however, was offset by cooling due to evaporation as the water fell.)
13. Gaseous pressure changes with changes in temperature.
14. Increasing temperature means increasing KE which means increasing momentum of molecules, which means greater impact and greater pressure against the walls of the container. Simply put, as the temperature of a confined gas is increased, the molecules move faster and exert a greater pressure as they rebound from the walls of the container.
15. Different substances have different thermal properties due to differences in the way energy is stored internally in the substances. When the same amount of heat produces different changes in temperatures in two substances of the same mass, we say they have different specific heat capacities. Each substance has its own

characteristic specific heat capacity. Temperature measures the average kinetic energy of random motion, but not other kinds of energy.
16. The substance with the small specific heat capacity, iron, undergoes the greatest change in temperature.
17. The slowly cooling object has the greater specific heat.
18. Less specific heat means shorter time for temperature change, and a shorter hot bath.
19. A high specific heat. The more ways a molecule can move internally, the more energy it can absorb to excite these internal motions. This greater capacity for absorbing energy makes a higher specific heat.
20. Water has a high specific heat capacity, which is to say, it normally takes a long time to heat up, or cool down.
Water’s high specific heat enables the watermelon to resist changes in temperature, so once cooled it will stay cool longer than non-watery substances under the same conditions. Be glad water has a high specific heat capacity the next time you’re enjoying cool watermelon on a hot day!
21. Alcohol, for less specific heat means less thermal inertia and a greater change in temperature.
22. Both the pan and water undergo the same temperature change. But water, with its greater specific heat capacity, absorbs more heat.
23. The climate of Bermuda, like that of all islands, is moderated by the high specific heat of water. What moderates the climates are the large amounts of energy given off and absorbed by water for small changes in temperature.
When the air is cooler than the water, the water warms the air; when the air is warmer than the water, the water cools the air.
24. The climate of Iceland, like that of Bermuda in the previous exercise, is moderated by the surrounding water.
25. In winter months when the water is warmer than the air, the air is warmed by the water to produce a seacoast climate warmer than inland. In summer months when the air is warmer than the water, the air is cooled by the water to produce a seacoast climate cooler than inland. This is why seacoast communities and especially islands do not experience the high and low temperature extremes that characterize inland locations.
26. As the ocean off the coast of San Francisco cools in the winter, the heat it loses warms the atmosphere it comes in contact with. This warmed air blows over the California coastline to produce a relatively warm climate.
If the winds were easterly instead of westerly, the climate of San Francisco would be chilled by winter winds from dry and cold Nevada. The climate would be reversed also in Washington, D.C. because air warmed by the cooling of the Atlantic Ocean would blow over Washington, D.C. and produce a warmer climate in winter there.
27. The brick will cool off too fast and you’ll be cold in the middle of the night. Bring a jug of hot water with its higher specific heat to bed and you’ll make it through the night.
28. Sand has a low specific heat, as evidenced by its relatively large temperature changes for small changes in internal energy. A substance with a high specific heat, on the other hand, must absorb or give off large amounts of internal energy for comparable temperature changes.
29. Water is an exception.
30. No, the different expansions are what bends the strip or coil. Without the different expansions a bimetallic strip would not bend when heated.
31. When the rivets cool they contract. This tightens the plates being attached.
32. When doused, the outer part of the boulders cooled while the insides were still hot. This caused a difference in contraction, which fractured the boulders.
33. The tires heat up, which heat the air within. The molecules in the heated air move faster, which increases air pressure in the tires. (See Exercise 12.)
34. Temperature differences cause differences in expansion and contraction, which produce sounds as structures expand or contract.

35.
Cool the inner glass and heat the outer glass. If it’s done the other way around, the glasses will stick even tighter (if not break).
36. Higher expansion rate would mean greater difference in shape with different temperature, a liability for a telescope mirror.
37.
If both expanded differently, as for different materials, the key and lock wouldn’t match.
38. A chimney undergoes more changes in temperature than any other part of the building, and therefore more changes in expansion and contraction. Such changes should be the same for all parts of the building that bear the building’s weight. Otherwise, sags and worse occur.
39. The photo was likely taken on a warm day. If it were taken on a cold day there would be more space between the segments.
40. Gas is sold by volume. The gas meter that tallies your gas bill operates by measuring the number of volume units (such as cubic feet) that pass through it. Warm gas is expanded gas and occupies more space, and if it passes through your meter, it will be registered as more gas than if it were cooled and more compact. The gas company gains if gas is warm when it goes through your meter because the same amount of warmer gas has a greater volume.
41. Overflow is the result of liquid gasoline expanding more than the solid tank.
42. Every part of a metal ring expands when it is heated —not only the thickness, but the outer and inner circumference as well. Hence the ball that normally passes through the hole when the temperatures are equal will more easily pass through the expanded hole when the ring is heated. (Interestingly enough, the hole will expand as much as a disk of the same metal undergoing the same increase in temperature. Blacksmiths mounted metal rims in wooden wagon wheels by first heating the rims. Upon cooling, the contraction resulted in a snug fit.)
43. The heated balls would have the same diameter.
44. Brass expands and contracts more than iron for the same changes in temperature. Since they are both good conductors and are in contact with each other, one cannot be heated or cooled without also heating or cooling the other. If the iron ring is heated, it expands —but the brass expands even more. Cooling the two will not result in separation either, for even at the lowest temperatures the shrinkage of brass over iron would not produce separation.
45. The gap in the ring will become wider when the ring is heated. Try this: Draw a couple of lines on a ring where you pretend a gap to be. When you heat the ring, the lines will be farther apart
—the same amount as if a real gap were there. Every part of the ring expands proportionally when heated uniformly —thickness, length, gap and all.
46. When a mercury thermometer is warmed, the outside glass is heated before heat gets to the mercury inside. So the glass is the first to expand, momentarily opening (like the ring in Exercise 42) which allows the mercury to drop from the glass tube into the slightly enlarged reservoir. When the mercury warms to the same temperature of the glass, it is then forced up the glass tube because of its greater expansion rate.
47. The U shape takes up the slack of expansion or contraction, without changing the positions at end points.
48. Thin glass is used because of the sudden temperature changes. If the glass were thicker, unequal expansions and contractions would break the glass with sudden temperature changes.
49. In the construction of a light bulb, it is important that the metal leads and the glass have the same rate of heat expansion. If the metal leads expand more than glass, the glass may crack. If the metal expands less than glass upon being heated, air will leak in through the resulting gaps.
50. On a hot day a steel tape will expand more than the ground. You will be measuring land with a “stretched” tape.
So your measurements of a plot of land will be smaller than measurements made on a cold day. Measurements made on a cold day will show the ground to be larger. (If, on the other hand, you’re staking off land not already plotted, then on a hot day you’ll get more land.)
51. 4°C.

52. Water has the greatest density at 4°C; therefore, either cooling or heating at this temperature will result in an expansion of the water. A small rise in water level would be ambiguous and make a water thermometer impractical in this temperature region.
53. The atoms and molecules of most substances are more closely packed in solids than in liquids. So most substances are denser in the solid phase than in the liquid phase. Such is the case for iron and aluminum and most all other metals. But water is different. In the solid phase the structure is open-spaced and ice is less dense than water. Hence ice floats in water.
54. The combined volume of all the billions of “open rooms” in the hexagonal ice crystals of a piece of ice is equal to the volume of the part of the ice that extends above water when ice floats. When the ice melts, the open spaces are filled in by the amount of ice that extends above the water level. This is w hy the water level doesn’t rise when ice in a glass of ice water melts
—the melting ice “caves in” and nicely fills the open spaces.
55. The curve for density versus temperature is:
56. Volume increases.
57. At 0°C it will contract when warmed a little; at 4°C it will expand, and at 6°C it will expand.
58. It is important to keep water in pipes from freezing because when the temperature drops below freezing, the water expands as it freezes whereas the pipe (if metal) will fracture if water in them freezes.
59. If cooling occurred at the bottom of a pond instead of at the surface, ice would still form at the surface, but it would take much longer for ponds to freeze. This is because all the water in the pond would have to be reduced to a temperature of 0

C rather than 4

C before the first ice would form. Ice that forms at the bottom where the cooling process is occurring would be less dense and would float to the surface (except for ice that may form about material anchored to the bottom of the pond).
60. Ponds would be more likely to freeze if water had a lower specific heat. This is because the temperature would decrease more when water gives up energy; water would more readily be cooled to the freezing point.

1. Heat gained by the cooler water = heat lost by the warmer water. Since the masses of water are the same, the final temperature is midway, 30°C. So you’ll end up with 100 g of 30°C water.
2. Each kilogram requires 1 kilocalorie for each degree change, so 100 kg needs 100 kilocalories for each degree change. Twenty degrees means twenty times this, which is 2,000 kcal .
By formula, Q = cm∆T = (1 cal/g°C)(100,000 g)(20°C) = 2,000 kcal. We can convert this to joules knowing that
4.184 J = 1 cal. In joules this quantity of heat is 8370 kJ .
3. Raising the temperature of 10 gm of copper by one degree takes 10

0.092 = 0.92 calories, and raising it through 100 degrees takes 100 times as much, or 92 calories.
By formula, Q = cm∆T = (0.092 cal/g°C)(10 g)(100°C) = 92 cal .
Heating 10 grams of water through the same temperature difference takes 1,000 calories, more than ten times
more than for the copper —another reminder that water has a large specific heat capacity.
4 . Heat gained by cool water = heat lost by warm water
cm
1 ∆
T
1 = cm
2 ∆
T
2 c (100)( T - 25) = c (75)(40 - T )
(Note that common sense dictates that ∆
T
1 is final temperature
T minus 25°, since
T will be greater than 25°, and ∆
T
2 is 40° minus
T , because T will be less than 40°. ∆
T
1 does not equal ∆ the different masses of cool and warm water.) From 100 T - 2500 = 3000
– 75
T
T =
31.4°C
.
T
2 as in Problem 1 because of
5. Heat gained by water = heat lost by nails
( cm
∆
T ) water
= ( cm
∆
T ) nails
(1)(100) ( T - 20) = (0.12)(100)(40 - T ), giving T =
22.1°C
.
6. If a 1-m long bar expands 1 /
2
cm when heated, a bar of the same material that is 100 times as long will expand
100 times as much, 0.5 cm for each meter, or 50 cm . (The heated bar will be 100.5 m long.)
7.
By formula: ∆
L = L o
 ∆
T = (1300 m)(11

10 -6 /°C)(15°C) =
0.21 m .
8. This is similar to the previous problem, with different values.
By formula: ∆ L = L o
 ∆ T = (10.0 m)(11

10 -6 /°C)(20°C) = 0.002 m or 0.2
cm = 2 mm .
9. Aluminum expands more as evidenced by its greater coefficient of linear expansion. The ratio of the increases is equal to the ratios of the coefficients of expansion, i.e., 24

10 -6 /11

10 -6 = 2.2. So the same increase in temperature, the change in length of aluminum will be 2.2 times greater than the change in length of steel.
10. If a snugly fitting steel pipe that girdled the world were heated by 1 Celsius degree, it would stand about 70 meters off the ground! The most straight-forward way to see this is to consider the radius of the 40,000 long kilometer pipe, which is the radius of the Earth, 6370 kilometers. Steel will expands 11 parts in a million for each
C° increase in temperature; the radius as well as the circumference will expand by this fraction. So 11 millionths of 6370 kilometers = 70 meters . Is this not astounding? Or by formula for the Earth’s radius, ∆
L = L o
 ∆
T =
(6370

10 3 m)(11

10 -6 /°C)(1°C) = 70 m.
1. The metal doorknob conducts heat better than wood.
2. Feathers are good insulators and thus conduct body heat very slowly to the surroundings.
3. No, the coat is not a source of heat, but merely keeps the thermal energy of the wearer from leaving rapidly.

4.
Air at 70°F feels comfortable principally because it is a poor conductor. Our warmer skin is slow to transfer heat to the air. Water, however, is a better conductor of heat than air, so our warmer bodies in water more readily transfer heat to the water.
5. When the temperatures of the blocks are the same as the temperature of your hand, then no heat transfer occurs. Heat will flow between your hand and something being touched only if there is a temperature difference between them.
6. Energy “flows” from higher to lower temperature, from your hand to the ice. It is the energy, heat, flowing from your hand that produces the sensation of coolness. There is no flow from cold to hot; only from hot to cold.
7. Copper and aluminum are better conductors than stainless steel, and therefore more quickly transfer heat to the cookware’s interior.
8. The main reason for serving potatoes wrapped in aluminum foil is to increase the time that the potatoes remain hot after being removed from the oven. Heat transfer by radiation is minimized as radiation from the potatoes is internally reflected, and heat transfer by convection is minimized as circulating air cannot make contact with the shielded potatoes. The foil also serves to retain moisture.
9. In touching the tongue to very cold metal, enough heat can be quickly conducted away from the tongue to bring the saliva to sub-zero temperature where it freezes, locking the tongue to the metal. In the case of relatively nonconducting wood, much less heat is conducted from the tongue and freezing does not take place fast enough for sudden sticking to occur.
10. Air is an excellent insulator. The reason that fiberglass is a good insulator is principally because of the vast amount of air spaces trapped in it.
11. Heat from the relatively warm ground is conducted by the gravestone to melt the snow in contact with the gravestone. Likewise for trees or any materials that are better conductors of heat than snow, and that extend into the ground.
12. There is more air space in mittens than in gloves, which makes for warmer hands. Also, the fingers in mittens are next to one another which also keeps hands warmer.
13. The snow and ice of the igloo is a better insulator than wood. You would be warmer in the igloo than the wooden shack.
14. Much of the energy of the flame is readily conducted through the paper to the water. The large amount of water relative to the paper absorbs the energy that would otherwise raise the temperature of the paper. The upper limit of 212°F for the water is well below the ignition temperature of the paper, 451°F (hence the title “451” of
Ray Bradbury’s science fiction novel about book burning).

15. The high conductivity of metal means a lot of heat transfer, hence the ouch. But the low conductivity of air results in less heat transfer and less pain.
16. Wood is a poor conductor whatever the temperature, so you can safely grab a pan by its wooden handle for a short time. As with the hot air in the previous exercise, this is because very little heat will be conducted to your hand. Touching the iron part of the pan is another story, for then heat is readily conducted to your hand. Ouch again!
17. The conductivity of wood is relatively low whatever the temperature —even in the stage of red hot coals. You can safely walk barefoot across red hot wooden coals if you step quickly (like removing the wooden-handled pan with bare hands quickly from the hot oven in the previous exercise) because very little heat is conducted to your feet. Because of the poor conductivity of the coals, energy from within the coals does not readily replace the energy that transfers to your feet. This is evident in the diminished redness of the coal after your foot has left it. Stepping on red-hot iron coals, however, is a different story. Because of the excellent conductivity of iron, very damaging amounts of heat would transfer to your feet. More than simply ouch!
18. Yes in both cases, as long as one has a higher temperature than the other. Differences in temperature , not internal energy, dictates heat flow.
19. The temperature will be midway because one decreases in temperature and the other increases in temperature.
20. It is thermal energy that flows —heat. It is therefore correct to say that thermal energy flows between the objects.
21. It is correct to say that the increase in thermal energy of one object equals the decrease in thermal energy of the other —not temperature. The statement is correct when the hot and warm objects are the same material and same mass.
22. Agree, for your friend is correct. The gases will have the same temperature, which is to say they’ll have the same average kinetic energy per molecule.
23. Disagree, for although the mixture has the same temperature, which is to say, the same KE per molecule, the lighter hydrogen molecules have more speed than heavier nitrogen for the same KE.
24. Air molecules in your room have the same average kinetic energy, but not the same average speed. Air is made up of molecules of different mass —some nitrogen, some oxygen, and a small percentage of other gases. So even though they have the same average kinetic energy, they won’t have the same average speed. The lighter molecules will have average speeds greater than the heavier molecules.
25. Hydrogen molecules will be the faster moving when mixed with oxygen molecules. They will have the same temperature, which means they will have the same average kinetic energy. Recall that KE = 1 /
2 mv 2 . Since the mass of hydrogen is considerably less than oxygen, the speed must correspondingly be greater.
26. As in the explanation of the previous exercise, the molecules of gas with the lesser mass will have the higher average speeds. A look at the periodic table will show that argon (A = 18) has less massive atoms than krypton
(A = 36). The faster atoms are those of argon. This is the case whether or not the gases are in separate containers.

27. Molecules of gas with greater mass have a smaller average speed. So molecules containing heavier U-238 are slower on the average. This favors the diffusion of the faster gas containing U-235 through a porous membrane (which is how U-235 was separated from U-238 by scientists in the 1940s).
28. As with the previous question, the faster molecules with U-235 will diffuse faster than the slower molecules with heavier U-238.
29. More molecules are in the cooler room. The greater number of slower-moving molecules there produce air pressure at the door equal to the fewer number of faster-moving molecules in the warmer room.
30. In winter you want warm air near the floor, so the fan should push warmer ceiling air downward. In summer you want cooler air near the floor, so the fan should pull air upward.
31. The smoke, like hot air, is less dense than the surroundings and is buoyed upward. It cools with contact with the surrounding air and becomes more dense. When its density matches that of the surrounding air, its buoyancy and weight balance and rising ceases.
32. At the same temperature, molecules of helium, nitrogen, and oxygen have the same average kinetic energy.
But helium, because of its smaller mass, has greater average speed. So some helium atoms, high in the atmosphere, will be moving faster than escape speed from the Earth and will be lost to space. Through random collisions, every helium atom will eventually surpass escape speed.
33.
If ice cubes were at the bottom they wouldn’t be in contact with the warmest part of the tea at the surface, so cooling would be less. Ice cubes are preferable at the surface to decrease the temperature of the warmer part of the tea.
34. It is the faster molecules that bumble their way to the higher altitudes. Oxygen molecules are heavier than nitrogen, travel slower at the same temperature, and therefore undergo less upward migration.
35. Both the molecule and the baseball are under the influence of gravity, and both will accelerate downward at g .
When other molecules impede downward fall, then the free-fall acceleration g isn’t maintained.
36. Yes, gravity decreases upward movement of molecules, and increases downward movement. So the effect of gra vity on molecular speed favors a downward migration of molecules. And yes, there is a greater “window” upward due to the smaller density of gas with altitude. The wider density window favors upward migration.
When these two influences are equal, no convection occurs and the air is in thermal equilibrium.
37. Because of the high specific heat of water, sunshine warms water much less than it warms land. As a result, air is warmed over the land and rises. Cooler air from above the cool water takes its place and convection currents are formed. If land and water were heated equally by the Sun, such convection currents (and the winds they produce) wouldn’t be.
38. When we warm a volume of air, we add energy to it. When we expand a volume of air, we normally take energy out of it (because the expanding air does work on its surroundings). So the conditions are quite different and the results will be different. Expanding a volume of air actually lowers its temperature.

39.
40.
The mixture expands when it is ejected from the nozzle, and therefore cools. At the freezing temperature of 0°C, ice forms.
41. Black is the most efficient color for steam radiators. Much of the heat a steam radiator produces, however, is a result of the convection it produces, which has to do with its temperature rather than its radiating ability.
42. Radiation requires no medium for transfer.
43. The heat you received was from radiation.
44. A good emitter, by virtue of molecular-or-whatever design, is also a good absorber. A good absorber appears black because radiation that impinges upon it is absorbed; just the opposite of reflection. The blackness of materials is evidence for their absorption. By the same token the blackness is also evidence for their emission.
The radiation that an object emits at normal temperatures is too low in frequency to be seen by the eye and too feeble to be felt. But it’s there. A warm black pot will emit more energy in a given time than a warm silver pot of the same mass and material.
45. If good absorbers were not also good emitters, then thermal equilibrium would not be possible. If a good absorber only absorbed, then its temperature would climb above that of poorer absorbers in the vicinity. And if poor absorbers were good emitters, their temperatures would fall below that of better absorbers.
46 . A good reflector is a poor radiator of heat, and a poor reflector is a good radiator of heat.
47. Human eyes are insensitive to the infrared radiated by objects at average temperatures.
48. The energy given off by rock at the Earth’s surface transfers to the surroundings practically as fast as it is generated. Hence there isn’t the buildup of energy that occurs in the Earth’s interior.
49. Put the cream in right away for at least three reasons. Since black coffee radiates more heat than white coffee, make it whiter right away so it won’t radiate and cool so quickly while you are waiting. Also, by Newton’s law of cooling, the higher the temperature of the coffee above the surroundings, the greater will be the rate of cooling —so again add cream right away and lower the temperature to that of a reduced cooling rate, rather than allowing it to cool fast and then bring the temperature down still further by adding the cream later. Also
—by adding the cream, you increase the total amount of liquid, which for the same surface area, cools more slowly.
50. Heat radiates into the clear night air and the temperature of the car goes down. Normally, heat is conducted to the car by the relatively warmer ground, but the rubber tires prevent the conduction of heat from the ground. So heat radiated away is not easily replaced and the car cools to temperatures below that of the surroundings. In this way frost can form on a below-freezing car in the above-freezing environment.
51. Under open skies, the ground radiates upward but the sky radiates almost nothing back down. Under the benches, downward radiation of the benches decreases the net radiation from the ground, resulting in warmer ground and, likely, no frost.
52. When it is desirable to reduce the radiation that comes into a greenhouse, whitewash is applied to the glass to simply reflect much of the incoming radiation. Energy reflected is energy not absorbed.
53. For maximum warmth, wear the plastic coat on the outside and utilize the greenhouse effect.

54. If the upper atmosphere permitted the escape of more terrestrial radiation than it does presently, more energy would escape and the Earth’s climate would be cooler.
55. Kelvins and Celsius degrees are the same size, and although ratios of these two scales will produce very different results, differences in kelvins and differences in Celsius d egrees will be the same. Since Newton’s law of cooling involves temperature differences, either scale may be used.
56. Turn your heater off altogether and save fuel. When it is cold outside, your house is constantly losing heat. How much is lost depends on the insulation and the difference in in side and outside temperature (Newton’s law of cooling). Keeping ∆ T high consumes more fuel. To consume less fuel, keep ∆ T low and turn your heater off altogether. Will more fuel be required to reheat the house when you return than would have been required to keep it warm while you were away? Not at all. When you return, you are replacing heat lost by the house at an average temperature below the normal setting, but if you had left the heater on, it would have supplied more heat, enough to make up for heat lost by the house at its normal, higher temperature setting. (Perhaps your instructor will demonstrate this with the analogy of leaking water buckets.)
57. Turn the air conditioner off altogether to keep ∆ T small, as in the preceding answer. Heat leaks at a greater rate into a cold house than into a not-so-cold house. The greater the rate at which heat leaks into the house, the greater the amount of fuel consumed by the air conditioner.
58. Because warm air ris es, there’s a higher temperature at the ceiling than at the walls. With a greater difference in inside and outside temperatures, thicker insulation is needed to slow the transfer of heat.
59.
If the Earth’s temperature increases, its rate of radiating will increase. And if much of this extra terrestrial radiation is blocked, and the temperature of the Earth increases more, then its rate of radiating simply increases further. A new and higher equilibrium temperature is established.
60. Open-ended.

1. (a) The amount of heat absorbed by the water is Q = cm∆T = (1.0 cal/g C°)(50.0 g)(50°C – 22°C) = 1400 cal. At 40% efficiency only 0.4 of the energy from the peanut raises the water temperature, so the calorie content of the peanut is 1400/0.4
= 3500 cal .
(b) The food value of a peanut is 3500 cal/0.6 g = 5.8 kilocalories per gram .
2. From Q = cm ∆ T, Q/m = c ∆ T = (800 J/kg
 C°)(500°C) = 400,000 J/kg. The time required is (400,000J/kg)/(0.03
J/kg
 yr) = 13.3 million years . Small wonder it remains hot down there!
3. Work the hammer does on the nail is given by F

d , and the temperature change of the nail can be found from using Q = cm
∆
T . First, we get everything into more convenient units for calculating: 5 grams = 0.005 kg; 6 cm =
0.06 m. Then F

d = 500 N
 0.06 m = 30 J, and 30 J = (0.005 kg)(450 J/kg°C)(∆
T ) which we can solve to get
∆ T = 30/(0.005

450) = 13.3°C . (You will notice a similar effect when you remove a nail from a piece of wood.
The nail that you pull out is noticeably warm.)
4.
Initially, the container is 60 degrees warmer than its surroundings. According to Newton’s law of cooling, its rate of cooling is proportional to the difference in tem perature between it and its surroundings. That’s 1°C per 15 seconds. When this temperature difference is half, that is when the container is 30 degrees warmer than its surroundings, the water cools at half the initial rate. That’s 1°C per 30 seconds (half the cooling rate means twice the time for the same one degree). So the time to cool from 50°C to 49°C will be 30 seconds. When the container reaches 40°C, it will be 20 degrees warmer than its surroundings and will cool at one-third its initial rate
—45 seconds to cool from 40°C to 39°C.
5.
According to Newton’s law of cooling, its rate of cooling is proportional to the temperature difference, so when the temperature difference is half as great, the rate of cooling will be half as great. After another eight hours, the coffee will lose 12.5 degrees, half as much as in the first eight hours, cooling from 50°C to 37.5°C . (Newton’s law of cooling leads to exponential behavior, in which the fractional change is the same in each equal increment of time.)
6. Because of the 10-percent conversion efficiency, each square meter of collector will supply 20 watts of electric power on the average. So to meet the 3 kW requirement you will need (3000 W)/(20 W/m 2 ) = 150 m 2 of collector area. This is the area of a square about 12 or 40 ft on a side. It would fit in a typical yard, but is a little larger than a typical roof.
1. Alcohol produces more cooling because of its higher rate of evaporation.
2. When a wet finger is held to the wind, evaporation is greater on the windy side, which feels cool. The cool side of your finger is windward.
3. The water evaporates rapidly in the dry air, gaining its energy from your skin, which is cooled.
4. When sweat evaporates it carries energy from the skin, producing cooling.
5. When you blow over the top of a bowl of hot soup, you increase net evaporation and its cooling effect by removing the warm vapor that tends to condense and reduce net evaporation.
6. Hot coffee poured into a saucer cools because (1) the greater surface area of the coffee permits more evaporation to take place, and (2) by the conservation of energy, the internal energy that heats up the saucer comes from the coffee, cooling it.
7. From our macroscopic point of view, it appears that nothing is happening in a covered glass of water, but at the atomic level there is chaotic motion as molecules are continually bumbling about. Molecules are leaving the water surface to the air above while vapor molecules in the air are leaving the air and plunging into the liquid.
Evaporation and condensation are taking place continually, even though the net evaporation or net condensation is zero. Here we distinguish between the processes and the net effect of the processes.
8. When water freezes it leave impurities such as salt behind. Melting the ice then produces desalinized water.

9. In this hypothetical case evaporation would not cool the remaining liquid because the energy of exiting molecules would be no different than the energy of molecules left behind. Although internal energy of the liquid would decrease with evaporation, energy per molecule would not change. No temperature change of the liquid would occur. (The surrounding air, on the other hand, would be cooled in this hypothetical case. Molecules flying away from the liquid surface would be slowed by the attractive force of the liquid acting on them.)
10. The energy that keeps the dunking duck in operation comes from the Sun, lamps, or whatever is heating the lower chamber where evaporation is taking place. To see this, simply direct heat energy to the lower chamber of the duck and you’ll see an increase in the number of times per minute the duck dunks.
11. A fan does not cool the room, but instead promotes evaporation of perspiration, which cools the body.
12. If the perfume doesn’t evaporate it will produce no odor. The odor of a substance is evidence for its evaporation.
13. Water leaks through the porous canvas bag, evaporating from its outer surface and cooling the bag. The motion of the car increases the rate of evaporation and therefore the rate of cooling, just as blowing over a hot bowl of soup increases the rate at which soup cools (Exercise 3).
14. A bottle wrapped in wet cloth will cool by the evaporation of liquid from the cloth. As evaporation progresses, the average temperature of the liquid left behind in the cloth can easily drop below the temperature of the cool water that wet it in the first place. So to cool a bottle of beer, soda, or whatever at a picnic, wet a piece of cloth in a bucket of cool water. Wrap the wet cloth around the bottle to be cooled. As evaporation progresses, the temperature of the water in the cloth drops, and cools the bottle to a temperature below that of the bucket of water.
15.
The body maintains its temperature at a normal 37°C by the process of evaporation. When the body tends to overheat, perspiration occurs, which cools the body if the perspiration is allowed to evaporate. (Interestingly enough, if you’re immersed in hot water, perspiration occurs profusely, but evaporation and cooling do not follow
— that’s why it is inadvisable to stay too long in a hot bath.)
16. Visibility of the windows is impaired if there is any condensation of water between the panes of glass. Hence the gas between the panes should contain no water vapor.
17. Air above the freezing temperature is chilled in the vicinity of an iceberg and condensation of the water vapor in the air results in fog.
18. Aside from the connotation of kissing molecules and parking on a cool night, the warm air generate d in the car’s interior meets the cold glass and a lowering of molecular speed results in condensation of water on the inside of the windows.
19. On a day where the outside of the windows is warmer than the inside, condensation will occur on the outside of the windows. You can also see this on the windshield of your car when you direct the air conditioner against the inside of the glass.
20. A temperature gradient normally exists in a room, with cooler air near the bottom. Hence frost forms on the colder part of the window, the bottom.
21. Air swept upward expands in regions of less atmospheric pressure. The expansion is accompanied by cooling, which means molecules are moving at speeds low enough for coalescing upon collisions; hence the moisture that is the cloud.
22. Clouds tend to form over islands because land has a lower specific heat than water, so the land is warmed faster than the surrounding water. This causes updrafts above the warmed land; the rising air laden with H
2
O expands and cools, allowing the H
2
O molecules to coalesce (Figure 17.7).
23. Enormous thermal energy is released as molecular potential energy is transformed to molecular kinetic energy in condensation. (Freezing of the droplets to form ice adds even more thermal energy.)
24. You can add heat without changing temperature when the substance is undergoing a change of phase.
25. You can withdraw heat without changing temperature when the substance is undergoing a change of phase.

26. When water is boiling, it is being cooled by the boiling process as fast as it is being heated by the stove. Hence its temperature remains the same
— 100°C.
27. As the bubbles rise, less pressure is exerted on them.
28. Increased pressure presses harder on the water, which squeezes more and prevents molecules from separating to form vapor.
29. Decreased pressure lessens the squeezing of molecules, which favors their tendency to separate and form vapor.
30. When the jar reaches the boiling temperature, further heat does not enter it because it is in thermal equilibrium with the surrounding 100°C water. This is the principle of the “double boiler.”
31. The hot water is below the boiling point for the very high pressure there, somewhat like the higher boiling point of water in a pressure cooker.
32. Moisture in the cloth will convert to steam and burn you.
33. You could not cook food in low-temperature water that is boiling by virtue of reduced pressure. Food is cooked by the high temperature it is subjected to, not by the bubbling of the surrounding water. For example, put roomtemperature water in a vacuum and it will boil. But this doesn’t mean the water will transfer more internal energy to an egg than before boiling — an egg in this boiling water won’t cook at all!
34. As in the answer to the previous exercise, high temperature and the resulting internal energy given to the food are responsible for cooking
— if the water boils at a low temperature (presumably under reduced pressure), the food isn’t hot enough to cook.
35. The ice is indeed cold. Why cold? Because rapid evaporation of the water cooled the water to the freezing point.
36. Both heat and pressure are involved in boiling. Reduction of pressure only can produce boiling (see Figure
17.13).
37. The air in the flask is very low in pressure, so that the heat from your hand will produce boiling at this reduced pressure. (Your instructor will want to be sure that the flask is strong enough to resist implosion before handing it to you!)
38. Cooking time will be no different for vigorously boiling water and gently boiling water, for both have the same temperature. The reason spaghetti is cooked in vigorously boiling water is simply to ensure the spaghetti doesn’t stick to itself and the pan. For fuel economy, simply stir your spaghetti in gently boiling water.
39. The lid on the pot traps heat which quickens boiling; the lid also slightly increases pressure on the boiling water which raises its boiling temperature. The hotter water correspondingly cooks food in a shorter time, although the effect is not significant unless the lid is held down as on a pressure cooker.
40. The boiling point of water is higher in a nuclear reactor because of increased pressure. The reactor behaves like a pressure cooker.
41. After a geyser has erupted, it must refill and then undergo the same heating cycle. If the rates of filling and heating don’t change, then the time to boil to the eruption stage will be the same.
42. Water in the pressurized radiator doesn’t boil, even when its temperature exceeds 100°C (like water in a pressure cooker). But when the radiator cap is suddenly removed, pressure drops and the high-temperature water immediately boils. Do not have your head above a hot radiator when removing the cap!

43. Yes, ice can be mu ch colder than 0°C, which is the temperature at which ice will melt when it absorbs energy.
The temperature of an icewater mixture in equilibrium is 0°C. Iced tea, for example, is 0°C.
44.
The moisture on your skin freezes only at a temperature below 0°C because it contains salt. Very cold ice in contact with your hand freezes the moisture on your skin and bonding takes place between your skin and the ice. That’s why it’s sticky.
45.
Regelation would not occur if ice crystals weren’t open structured. The pressure of the wire on the open network of crystals caves them in and the wire follows. With the pressure immediately above the wire relieved, the molecules again settle to their low energy crystalline state. Interestingly, the energy score balances for these changes of state: The energy given up by the water that refreezes above the wire is conducted through the wire thickness to melt the ice being crushed beneath. The more conductive the wire, the faster regelation occurs. For an insulator like string , regelation won’t occur at all. Try it and see!
46. Snowfall certainly is possible on very cold days. But when the snow is forming, the temperature of the air increases because of the change of state of the H
2
O from gas to solid or from liquid to solid. So one’s observation is warmness when snowing, and one’s misinterpretation is therefore that snowfall can’t happen if it is cold. (Similarly, it is a fact that our ears continue to grow all through life. So old people usually have big ears.
Some people who see children with big ears mistakenly say they are destined to have a long life.)
47. The wood, because its greater specific heat capacity means it will release more energy in cooling.
48. The H
2
O absorbs energy in the change of state from ice to water. If this energy is supplied by the surrounding air, then the temperature of the surrounding air is decreased.
49. This is an example that illustrates Figure 17.7. Water vapor in the warm air condenses on the relatively lowtemperature surface of the can. When the can is at room temperature, the speeds of the molecules encountering it are unaffected, and condensation doesn’t occur.
50. Water in the soda expands when it turns to ice, bulging the ends of the soda can.
51.
Sugar doesn’t freeze with the water in the punch, so half-frozen punch has the sugar of the original mixture— twice the original concentration.
52. This is another example that illustrates Figure 17.7. Water vapor in the warm air condenses on the lowtemperature metal surface of the unit.
53. Condensation occurs on the cold coils, which is why the coils drip water.
54. The practice of wrapping newspaper around ice in an icebox is inadvisable, unless one only wants to make the ice last longer at the expense of reducing the cooling effect. The insulating newspaper slows the melting process, which diminishes the extraction of heat from the surroundings. The surroundings are cooled principally because the ice melts. To inhibit this melting is to reduce the desired cooling process.
55. The temperature of nearby air increases due to energy released by the melting ice.
56. Every gram of water that undergoes freezing releases 80 calories of thermal energy to the cellar. This continual releas e of energy by the freezing water keeps the temperature of the cellar from going below 0°C. Sugar and salts in the canned goods prevent them from freezing at 0°C. Only when all the water in the tub freezes will the temperature of the cellar go below 0°C and then freeze the canned goods. The farmer must, therefore, replace the tub before or just as soon as all the water in it has frozen.
57. The answer to this is similar to the previous answer, and also the fact that the coating of ice acts as an insulating blanket. Every gram of water that freezes releases 80 calories, much of it to the fruit; the thin layer of ice then acts as an insulating blanket against further loss of heat.
58. As more freezing takes places and the polar icecaps grow, less water surface is exposed for evaporation. This results in less clouds and consequently, less precipitation. Without the pileup of new snow, melting can more readily occur. The ice age withdraws.
59. Yes, for the device is a heat pump, with the characteristic of being able to operate both ways —heater when the change of phase is from gas to liquid, and cooler when the change of phase is from liquid to gas.

60. Dogs have no sweat glands (except between the toes for most dogs) and therefore cool by the evaporation of moisture from the mouth and the respiratory track. So dogs literally cool from the inside out when they pant.

1.
(a) 1 kg 0°C ice to 0°C water requires
80 kilocalories .
(b) 1 kg 0°C water to 100°C water requires 100 kilocalories .
(c) 1 kg 100°C water to 100°C steam requires
540 kilocalories .
(d) 1 kg 0°C ice to 100°C steam requires (80 + 100 + 540) =
720 kilocalories
or 720,000 calories.
2. From 273°C “ice” to 0°C ice requires (273)(0.5) = 140 calories.
From 0°C ice to 0°C water requires 80 calories.
From 0°C water to 100°C water requires 100 calories. The total is 320 calories.
Boiling this water at 100°C takes 540 calories, considerably more energy than it took to bring the water all the way from absolute zero to the boiling point! (In fact, at very low temperature, the specific heat capacity of ice is less than 0.5 cal/g°C, so the true difference is even greater than calculated here.)
3. First, find the number of calories that 10 g of 100°C steam will give in changing to 10 g of 0°C water.
10 g of steam changing to 10 g of boiling water at 100°C releases 5400 calories.
10 g of 100°C water cooling to 0°C releases 1000 calories.
So 6400 calories are available for melting ice.
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= 80 grams of ice.
4. The final temperature of the water will be the same as that of the ice, 0°C . The quantity of heat given to the ice by the water is
Q = cm∆T = (1 cal/g°C)(50 g)(80°C) = 4000 cal. This heat melts ice. How much? From Q = mL , m = Q/L =
(4000 cal)/(80 cal/g) = 50 grams
. So water at 80°C will melt an equal mass of ice at 0°C.
5. The quantity of heat lost by the iron is Q = cm∆T = (0.11 cal/g°C)(50 g)(80°C) = 440 cal. The iron will lose a quantity of heat to the ice Q = mL . The mass of ice melted will therefore be m = Q/L = (440 cal)/(80 cal/g) = 5.5 grams . (The lower specific of heat of iron shows itself compared with the result of the previous problem.)
6. mgh = mL , so gh = L and h = L / g . h = (334000 J/kg)/(9.8 m/s 2 ) = 34000 m = 34 km .
Note that the mass cancels and that the unit J/kg is the same as the unit m 2 /s 2 . So in the ideal case of no energy losses along the way, any piece of ice that freely falls 34 km will completely melt upon impact.
7. 0.5
mgh = cm∆T
∆
T = 0.5
mgh/cm = 0.5
gh / c = (0.5)(9.8 m/s 2 )(100 m)/450 J/kg°C = 1.1°C
.
Again, note that the mass cancels, so the same temperature would hold for any mass ball, assuming half the heat generated goes into warming the ball. As in the previous problem, the units check because 1 J/kg = 1 m 2 /s 2 .
8. Note that the heat of vaporization of ethyl alcohol (200 cal/g) is 2.5 times more than the heat of fusion of water
(80 cal/g), so in a change of phase for both, 2.5 times as much ice will change phase; 2.5

2 kg = 5 kg.
Or via formula, the refrigerant would draw away Q = mL = (2000 g)(200 cal/g) = 4

10 5 calories. The mass of ice formed is then (4

10 5 cal)/(8
1. In the case of the 500degree oven it makes a lot of difference. 500 kelvins is 227°C, quite a bit different than
500°C. But in the case of the 50,000-degree star, the 273 increments either way makes practically no difference. Give or take 2
73, the star is still 50,000 K or 50,000°C when rounded off.
2. No, for as in the previous exercise, a difference of 273 in 10,000,000 is insignificant.
3. Not ordinarily. They undergo the same change in internal energy , which translates to the same temperature change when both objects are the same mass and composed of the same material.

4. No
—internal energy, unlike temperature, is not an average quantity.
5. Its absolute temperature is 273 +10 = 283 K. Double this and you have 566 K. Expressed in Celsius; 566 - 273
= 293 °C.
6. You do work on the liquid when you vigorously shake it back and forth, which increases its internal energy. This is noted by an increase in temperature. (In the mid-nineteenth century, James Joule, by measuring the tempera ture of a liquid before and after doing known work with a stirring paddle, revealed what he called “the mechanical equivalent of heat,” a discovery that led to the general law of energy conservation.)
7. You do work in compressing the air, which increases its internal energy. This is evidenced by an increase in temperature.
8. The change in internal energy is 100 J
– 80 J = 20 J.
9. The pump becomes hot for two reasons: First, the work done in compressing the air increases its internal energy which is conducted to and shared with the pump. The second reason for the increase in temperature involves friction, for the piston rubs against the inner wall of the pump cylinder.
10. Gas pressure increases in the can when heated, and decreases when cooled. The pressure that a gas exerts depends on the average kinetic energy of its molecules, therefore on its temperature.
11. A given amount of mechanical energy can be easily and commonly converted to thermal energy; any body moving with kinetic energy that is brought to rest by friction transforms all its kinetic energy into thermal energy
(for example, a car skidding to rest on a horizontal road). The converse is not true, however. In accord with the
2 nd law of thermodynamics, only a fraction of a given amount of thermal energy can be converted to mechanical energy. For example, even under ideal conditions, less than half of the heat energy provided by burning fuel in a power plant can go into mechanical energy of electric generators.
12. The high compression of fuel mixture in the cylinders of a diesel engine heats the mixture to the ignition point, so spark plugs are not needed.
13. When a blob of air rises in the atmosphere it does work on the surrounding lower-pressure air as it expands.
This work output is at the expense of its internal energy, which is diminished, which in turn is evidenced by a lower temperature. Hence the temperature of air at the elevation of mountain tops is usually less than down below.

14. Solar energy. The terms renewable and non-renewable really refer to time scales for regeneration
—tens of years for wood versus millions of years for coal and oil.
15. Solar energy.
16. This transfer would not violate the 1 st law because energy has been transferred without loss or gain. It would violate the 2 nd law because internal energy will not freely transfer from a cooler to a warmer object.
17. The term pollution refers to an undesirable by-product of some process. The desirability or undesirability of a particular by-product is relative, and depends on the circumstances. For example, using waste heat from a power plant to heat a swimming pool could be desirable whereas using the same heat to warm a trout stream could be undesirable.
18. The can is crushed by atmospheric pressure when vapor pressure in the can has been significantly reduced.
Reduction of vapor pressure in the can is accomplished by condensation of the vapor on the surface of water entering the opening in the can. If that water is boiling, then it supplies vapor at about the same rate as condensation occurs, resulting in no net condensation and no crunching. But even hot water, if its temperature is less than 100°C, will result in net condensation and a crushed can.
19. It is advantageous to use steam as hot as possible in a steam-driven turbine because the efficiency is higher if there is a greater difference in temperature between the source and the sink (see Sadi Carnot’s equation in the chapter).
20. Motor driven autos are more efficient, for they can supply energy by the generator effect, which internal combustion engines cannot do. Hybrid autos, for example, convert braking energy into internal energy, whereas autos with internal combustion engines dissipate braking energy as heat.
21. As in the preceding exercise, efficiency is higher with greater difference in temperature between the heat source
(combustion chamber in the engine) and sink (air surrounding the exhaust). All other things being equal, and strictly speaking, a car is more efficient on a cold day.
22. Efficiency will increase, because back pressure is reduced. This is similar to reducing the back pressure on turbine blades in a steam generator. Efficiency increases (though not noticeably) on a cold day because of the greater ∆ T in Carnot’s equation.
23. When the temperature is lowered in the reservoir into which thermal energy is rejected, efficiency increases; substitution of a smaller value of T cold
into (T hot
- T cold
)/T hot
will confirm this. (Re-express the equation as 1 -
T cold
/T hot
to better see this.)
24. As in the preceding exercise, inspection will show that decreasing T cold
will contribute to a greater increase in efficiency than by increasing T hot by the same amount. For example, let T hot
be 600K and T cold
be 300K. Then efficiency = (600 - 300)/600 = 1/2. Now let T hot
be increased by 200K. Then efficiency = (800 - 300)/800 = 5/8.
Compare this with T cold
decreased by 200K, in which case efficiency = (600 - 100)/600 = 5/6, which is clearly greater.
25. Only when the sink is at absolute zero (0 K) will a heat engine have an ideal efficiency of 100%.
26. Even if the refrigerator were magically 100% efficient, the room wouldn’t be cooled because the heat sink is also in the room. That’s why the condensation coils are in a region outside the region to be cooled. What actually happens in the case of the refrigerator being operated with its door open in a closed room is that the room temperature increases. This is because the refrigerator motor warms the surrounding air. Net electric energy is coming into the room, heating it.
27. Most certainly! Unlike the cooling wished for in the previous exercise, the energy given to the room by the open oven raises room temperature.
28. You are cooled by the fan, which blows air over you to increase the rate of evaporation from your skin, but you are a small part of the overall system, which warms.

29. Work must be done to establish a temperature difference between the inside of the refrigerator and the surrounding air. The greater the temperature difference to be established, the more work and hence more energy is consumed. So the refrigerator uses more energy when the room is warm rather than cold.
30. It doesn’t violate the second law of thermodynamics because an external agent does work on the system.
31. The gas is more compact
—density increases.
32. You do work in compressing the gas, which increases the internal energy.
33. Most people know that electric lights are inefficient when it comes to converting electrical energy into light energy, so they are surprised to learn there is a 100% conversion of electrical energy to thermal energy. If the building is being heated electrically, the lights do a fine job of heating, and it is not at all wasteful to keep them on when heating is needed. It is a wasteful practice if the air conditioners are on and cooling is desired, for the energy input to the air conditioners must be increased to remove the extra thermal energy given off by the lights.
34. Energy transfers from the bathing suit and its occupant to the surrounding air. No energy is lost, but is simply spread out as molecules evaporating from the suit become more disordered. The disorder associated with the escape of molecules more than offsets the order associated with the cooling of the bathing suit and its occupant —so the second law is “saved.”
35. Some of the electric energy that goes into lighting a lamp is transferred by conduction and convection to the air, some is radiated at invisible wavelengths (“heat radiation”) and converted to internal energy when it is absorbed, and some appears as light. In an incandescent lamp, only about 5% goes into light, and in a fluorescent lamp, about 20% goes to light. But all of the energy that takes the form of light is converted to internal energy when the light is absorbed by materials upon which it is incident. So by the 1 st law, all the electrical energy is ultimately converted to internal energy. By the second law, organized electrical energy degenerates to the more disorganized form, internal energy.
36. As the gas streams out of the nozzle, much of the kinetic energy of its molecules is ordered energy of the flowing gas, and less of the kinetic energy is in random motion, so the temperature drops. Expansion of the gas also contributes to its lower temperature.
37. Energy in the universe is tending toward unavailability with time. Hotter things are cooling as cooler things are warming. If this is true, the universe is tending toward a common temperature, the so-called “heat death,” when energy can no longer do work. (But we don’t know for sure that the laws of thermodynamics apply to the universe as a whole, since we don’t understand the ultimate source of the vast churning energy that is now apparent throughout the universe. Nature may have some surprises for us!)
38. The universe is moving toward a more disordered state.
39. It is fundamental because it governs the general tendency throughout nature to move from order to disorder, yet it is inexact in the sense that it is based on probability, not certainty.
40. More energy would be used to extract the energy than would be available from it. So although extracting ocean energy is possible, it is not practical, and cannot produce net power.
41. There are more ways for molecules in the liquid phase to move, resulting in more chaotic motion.
42. No, the entropy principle has not been violated because the order of the salt crystals is at the expense of a greater disorder of the water in the vapor state after evaporation. Even if we confine the system to the crystals themselves, there would be no violation of entropy because there is work input to the system by sunlight or other means.
43. No, the freezing of water is not an exception to the entropy principle because work has been put into the refrigeration system to prompt this change of state. There is actually a greater net disorder when the environment surrounding the freezer is considered.
44. Entropy of the overall system, of which the chicken is a small part, increases. So when the larger system is taken into account, there is no violation of the principle of entropy.

45. Such machines violate at least the second law of thermodynamics, and perhaps the first law as well. These laws are so richly supported by so many experiments over so long a time that the Patent Office wisely assumes that there is a flaw in the claimed invention.
46. A perpetual motion machine increases energy. This has never been recorded, and if it were, the conservation of energy principle would be challenged. It hasn’t happened, nor is it expected to happen. Molecules, on the other hand, are in continual perpetual motion, but do not do more work on the surroundings than the energy they possess.
47. Remind your friend that perpetual motion is the normal state of the universe, that all substances are composed of perpetually-moving particles. What is impossible is not perpetual motion, but a perpetual motion machine that multiplies energy input.
48. (a) Yes, very likely. Two heads would come up on average one throw out of four. (b) Not likely. The chance for ten coins to come up all heads is only about 1 in 1000. (c) Extremely unlikely, even with a lifetime of trying. The laws of thermodynamics are based on the statistics of large numbers.
49. As in the previous exercise, the smaller the number of random particles, the more the likelihood of them becoming “spontaneously” ordered. But the number of molecules in even the smallest room? Sleep comfortably!
50. Open-ended.

1. Heat added to system = change in system’s internal energy + work done by the system, Q = ∆E + W so W
= Q
– ∆E
= 0J
–(-3000 J) =
3000 J .
2. Ideal efficiency is (2700 - 270)/2700 = 2430/2700 = 0.90 or 90% .
3. Converting to kelvins; 25°C = 298 K; 4°C = 277 K. So Carnot efficiency =
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=
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= 0.07, or
7%.
This is very low, which means that large volumes of water (which there are) must be processed for sufficient power generation.
4. If by “twice as cold” she means one-half the absolute temperature, the temperature would be (1/2)(273 +10) =
141.5 K. To find how many Celsius degrees below 0°C this is, we first subtract 141.5 K from 273 K; this is 273 K
- 141.5 K = 131.5 K below the freezing point of ice, or 131.5°C . (Or simply, 141.5 K - 273 K = 131.5°C.) Quite nippy!
5. Adiabatic compression would heat the confined air by about 10°C for each kilometer decrease in elevation. The
35°C air would be heated 100°C and have a ground temperature of about (-35 + 100) = 65°C . (This is 149°F, roasting hot!)
6. Heating each kg of water through 3 degrees takes 3°C  4,184 J/kg°C = 12,550 J/kg. The number of joules of heat supplied to the water each second is 1.5

10 8 , so the number of kilograms of water heated each second is (1.5

10 8 J)/(12,550 J/kg) = 12,000 kg .
7. (a) For the room, W = 0.044 J .
(b) For the freezer, W = 0.69 J .
(c) For the helium refrigerator, W = 74 J
. The bigger the temperature “hill” relative to the lower temperature, the more work is needed to move the energy.
8. Seven is most likely because there are more combinations that give seven than any other sum. Of the 36 possible combinations, 6 gives seven.