Exercises – Chapter 8 1. Drinking fountains that actively chill the water they serve can’t work without ventilation. They usually have louvers on their sides so that air can flow through them. Why do they need this airflow? E.1 They are heat pumps and transfer heat to the surrounding air. 2. If you open the door of your refrigerator with the hope of cooling your room, you will find that the room’s temperature actually increases somewhat. Why doesn’t the refrigerator remove heat from the room? E.2 The refrigerator doesn't eliminate thermal energy; it merely pumps it from one place to the other and consumes ordered energy in the process. If you open the refrigerator, it will just move heat around the room and produce additional thermal energy in the process. The room will actually become warmer. 3. The outdoor portion of a central air-conditioning unit has a fan that blows air across the condenser coils. If this fan breaks, why won’t the air conditioner cool the house properly? E.3 Without the fan, the air conditioner won’t be able to transfer its waste heat to the surrounding air. It will stop pumping heat. 4. If you block the outlet of a hand bicycle pump and push the handle inward to compress the air inside the pump, the pump will become warmer. Why? E.4 As you push the handle inward to compress the air, you do work on the handle and air. The air receives this work and converts it into thermal energy within the air. The air becomes hotter. 5. When the gas that now makes up the sun was compressed together by gravity, what happened to the temperature of that gas? Why? E.5 Its temperature increased. Gravity did work on the gas, and this work appeared in the gas as thermal energy. The gas became hot. 6. Why is a car more likely to knock on a hot day than on a cold day? E.6 When a car engine compresses air that was already hot, the air's peak temperature is higher than it would have been if it had started cold. Since knocking occurs when the compression process heats the fuel and air mixture until it ignites, the higher the mixture's peak temperature, the more likely it is to knock. 7. A soda siphon carbonates water by injecting carbon dioxide gas into it. The gas comes compressed in a small steel container. As the gas leaves the container and pushes its way into the water, why does the container become cold? E.7 The gas still in the container does work pushing the other gas into the siphon and uses up some of its thermal energy. It cools. 8. A high-flying airplane must compress the cold, rarefied outside air before delivering it to the cabin. Why must this air be air conditioned after the compression? E.8 Compressing the outside air involves work and the air's temperature rises as a result of this work. The temperature becomes high enough that the compressed air must air-conditioned before it can be delivered to the cabin. 9. If you drop a glass vase on the floor, it will become fragments. If you drop those fragments on the floor, however, they will not become a glass vase. Why not? E.9 Though not forbidden by the laws of motion, it’s extraordinarily unlikely for the vase fragments to reassemble themselves. 10. When you throw a hot rock into a cold puddle, what happens to the overall entropy of the system? E.10 The entropy of the system goes up. E.10 By letting heat flow freely from a hot object to a cold object, you lower the entropy of the hot object but raise the entropy of the cold object even more. The total entropy of the system increases. 11. What prevents the bottom half of a glass of water from spontaneously freezing while the top half becomes boiling hot? E.11 This uneven distribution of thermal energies is extraordinarily unlikely. It would violate the second law of thermodynamics. 12. Suppose someone claimed to have a device that could convert heat from the room into electric power continuously. You would know that this device was a fraud because it would violate the second law of thermodynamics. Explain. E.12 Converting thermal energy continuously into electric energy involves an overall decrease in entropy (the disorder thermal energy becomes ordered electric energy) and thus violates the second law of thermodynamics. 13. Why does snow blanket the ground almost uniformly rather than creating tall piles in certain areas and bare spots in others? E.13 Though not forbidden by the laws of motion, such uneven distributions of snow are remarkably unlikely. 14. If you transfer a glass baking dish from a hot oven to a cold basin of water, that dish will probably shatter. What produces the ordered mechanical energy needed to tear the glass apart? E.14 Heat flowing from the hot dish to the cold water provides the necessary entropy to allow some of that heat to become mechanical work. 15. Freezing and thawing cycles tend to damage road pavement during the winter, creating potholes. What provides the mechanical work that breaks up the pavement? E.15 Heat flowing into or out of the pavement during weather changes allows the pavement to do work as it tears itself apart. 16. The air near a woodstove circulates throughout the room. What provides the energy needed to keep the air moving? E.16 Heat flowing from the hot stove to the cold room provides the necessary entropy to allow some of that heat to become mechanical work. 17. Winds are driven by differences in temperature at the earth’s surface. Air rises over hot spots and descends over cold spots, forming giant convection cells of circulating air. Near the ground, winds blow from the cold spots toward the hot spots. Explain how the atmosphere is acting as a heat engine. E.17 As heat flows from the hot spots to the cold spots, by way of huge convection cells, some heat is becoming ordered kinetic energy. 18. Hurricanes are giant heat engines powered by the thermal energy in warm ocean regions and the order in colder surrounding areas. Why are hurricanes most violent when they form over regions of unusually hot water at the end of summer? E.18 The hotter the water, the more thermal energy can be harnessed and the greater the temperature difference between the hot water and the colder surrounding, the more efficient the hurricane is at converting that thermal energy into mechanical work. 19. On a clear sunny day, the ground is heated uniformly and there is very little wind. Use the second law of thermodynamics to explain this absence of wind. E.19 Without temperature differences, heat won’t naturally flow. Such heat flow is what powers a heat engine such as the winds. 20. A plant is a heat engine that operates on sunlight flowing from the hot sun to the cold earth. The plant is a highly ordered system with relatively low entropy. Why doesn’t the plant’s growth violate the second law of thermodynamics? E.20 Heat flowing from the hot sun to the colder earth provides the necessary entropy to allow the plant to harness some of that heat to make it grow. 21. A diesel engine burns its fuel at a higher temperature than a gasoline engine. Why does this difference allow the diesel engine to be more efficient at converting the fuel’s energy into work? E.21 The hotter the burned gas, the larger the fraction of heat that can be converted to work as it flows to the outdoor air. 22. A chemical rocket is a heat engine, propelled forward by its hot exhaust plume. The hotter the fire inside the chemical rocket, the more efficient the rocket can be. Explain this fact in terms of the second law of thermodynamics. E.22 The hotter the hot region and the colder the cold region, the larger the fraction of heat flowing from the hot region to the cold region that can be diverted and converted into useful work. 23. An acquaintance claims to have built a gasoline-burning car that doesn’t release any heat to its surroundings. Use the second law of thermodynamics to show that this claim is impossible. E.23 Converting burned fuel entirely into work would violate the second law of thermodynamics. Problems – Chapter 8 1. You stir 1 kg of water until its temperature rises by 1 °C. How much work did you do on the water? P.1 4190 J. 2. While polishing a 1-kg brass statue, you do 760 J of work against sliding friction. Assuming all of the resulting heat flows into the statue, how much does its temperature rise? P.2 2 K. 3. You drop a lead ball on a cement floor from a height of 10 m. When the ball stops bouncing, how much will its temperature have risen? P.3 0.77 °C. 4. Roughly how high could a 300 K copper ball lift itself if it could transform all of its thermal energy into work? P.4 About 12 kilometers. 5. Drilling a hole in a piece of wood takes 1000 J of work. How much does the total internal energy of the wood and drill increase as a result of this process? P.5 1000 J. 6. An ideally efficient freezer cools food to 260 K. If room temperature is 300 K, how much work does this freezer consume when removing 100 J of heat from the food? P.6 15.4 J when the food is at 260 K. 7. An ideally efficient refrigerator removes 900 J of heat from food at 270 K. How much heat does it then deliver to the 300 K room air? P.7 1000 J. 8. An ideally efficient heat pump delivers 1000 J of heat to room air at 300 K. If it extracted heat from 260 K outdoor air, how much of that delivered heat was originally work consumed in the transfer? P.8 133 J. 9. An ideally efficient air conditioner keeps the room air at 300 K when the outdoor air is at 310 K. How much work does it consume when delivering 1240 J of heat outside? P.9 40 J. 10. An ideally efficient airplane engine provides work as heat flows from 1500 K burned gases to 300 K air. What fraction of the heat leaving the burned gases is converted into work? P.10 0.8 or 80%. 11. An ideally efficient steamboat engine operates on 500 K steam in 300 K weather. How much work can it obtain when 1000 J of heat leaves the steam? P.11 400 J. 12. An offshore breeze at the beach is powered by heat flowing from hot land (310 K) to cool water (290 K). Assuming ideal efficiency, how much work can this breeze provide for each 1000 J of heat it carries away from the land? P.12 65 J. 13. An ideally efficient solar energy system produces work as heat flows from the 6100 K surface of the sun to the 300 K room air. What fraction of the solar heat can it transform into work? P.13 95% of the heat can become work.