# 15 Heat_ Temperature_ and Expansion by pptfiles

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```									Solutions to Chapter 15 Exercises
2. Since Celsius degrees are larger than Fahrenheit degrees, an increase of 1 C° is larger. It’s /5 as large. 9. Calorie, which is 1000 calories. 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. 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. 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. 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. 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. 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.) 51. 4°C.
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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.

Chapter 15 Problem Solutions
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. 6. If a 1-m long bar expands /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 = Lo∆T = (1300 m)(11  10 /°C)(15°C) = 0.21 m.
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Solutions to Chapter 16 Exercises
7. Copper and aluminum are better conductors than stainless steel, and therefore more quickly transfer heat to the cookware’s interior. 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. 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. 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. 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. 42. Radiation requires no medium for transfer.

47. Human eyes are insensitive to the infrared radiated by objects at average temperatures.

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.
53. For maximum warmth, wear the plastic coat on the outside and utilize the greenhouse effect.

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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 rises, 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.

Chapter 16 Problem Solutions
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 temperature 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 2 electric power on the average. So to meet the 3 kW requirement you will need (3000 W)/(20 W/m ) = 2 150 m 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.

Solutions to Chapter 17 Exercises
4. When sweat evaporates it carries energy from the skin, producing cooling. 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. 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.) 24. You can add heat without changing temperature when the substance is undergoing a change of phase.

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25. You can withdraw heat without changing temperature when the substance is undergoing a change of phase. 29. Decreased pressure lessens the squeezing of molecules, which favors their tendency to separate and form vapor. 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 release 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. 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.

Chapter 17 Problem Solutions
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.)

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