Chapter 12 Homework Solutions

Transcription

1 Chapter 12 Homework Solutions Contents Page 319 #3-5; Page 322 # Page 321 #6-9; Page 336 #36-40, Page 325 #19-21; Page 328 # Page 336 #35, 41-44, Chapter 12 Study Guide Page 319 #3-5; Page 322 # When you turn on the hot water to wash dishes, the water pipes have to heat up. How much heat is absorbed by a copper water pipe with a mass of 2.3 kg when its temperature is raised from 20.0 C to 80.0 C? 4. The cooling system of a car engine contains 20.0 L of water (1 L of water has a mass of 1 kg). a. What is the change in the temperature of the water if the engine operates until kj of heat is added? b. Suppose that it is winter, and the car s cooling system is filled with methanol. The density of methanol is 0.80 g/cm 3. What would be the increase in temperature of the methanol if it absorbed kj of heat? c. Which is the better coolant, water or methanol? Explain. For temperature where both methanol and water are liquid, water is the better coolant, because it can absorb more heat without changing its temperature as much as methanol does.

2 5. Electric power companies sell electricity by the kwh, where. Suppose that it costs $0.15 per kwh to run an electric water heater in your neighborhood. How much does it cost to heat 75 kg of water from 15 C to 43 C to fill a bathtub? Converting units: Multiply by the unit cost: 10. Temperature: Make the following conversions. a. 5 C to kelvins b. 34 K to degrees Celsius c. 212 C to kelvins d. 316 K to degrees Celsius 11. Conversions: Convert the following Celsius temperatures to Kelvin temperatures. a. 28 C b. 154 C c. 568 C d. e. 12. Thermal Energy: Could the thermal energy of a bowl of hot water equal that of a bold of cold water? Explain your answer. Yes. Thermal energy is the measure of the total energy of all the molecules in an object. The temperature (hot or cold) measures the average amount of energy per molecule. If the cold water bowl has more mass than the hot water bowl, then the two thermal energies could be equal. 13. Heat Flow: On a dinner plate, a baked potato always stays hot longer than any other food. Why? A potato has a large specific heat capacity and conducts heat poorly, so it loses its heat energy slowly. It is not because of the mass of the potato.

3 Page 321 #6-9; Page 336 #36-40, A sample of water at is mixed with of water at. Assume that there is no heat loss to the surroundings. What is the final temperature of the mixture? Since and, there is cancellation in this particular case so that 7. A sample of water at is mixed with of water at. Assume that there is no heat loss to the surroundings. What is the final temperature of the mixture? Since, there is cancellation in this particular case so that 8. Three lead fishing weights, each with a mass of and at a temperature of, are placed in of water at. The final temperature of the mixture is. What is the specific heat of the lead in the weights?

4 9. A aluminum block at is placed in of water at. The final temperature of the mixture is. What is the specific heat of the aluminum? 36. Explain the differences among the mechanical energy of a ball, its thermal energy, and its temperature. The mechanical energy is the sum of the potential and kinetic energies of the ball considered as one mass. The thermal energy is the sum of the potential and kinetic energies of the individual particles that make up the mass of the ball. The temperature is a measure of the average energy of the individual particles that make up the mass of the ball. 37. Can temperature be assigned to a vacuum? Explain. No, since there are no particles in a vacuum, there is no average energy of particles in a vacuum. 38. Do all molecules or atoms in a liquid have the same speed? No. There is a distribution of velocities of the atoms or molecules. (The center of this distribution corresponds to the temperature of the liquid.) 39. Is your body a good judge of temperature? On a cold winter day, a metal doorknob feels much colder to your hand than a wooden door does. Explain why this is true. Your skin measures heat flow to or from itself, not temperature. The metal doorknob absorbs heat from your skin faster than the wooden door, so it feels colder. However, the temperatures of the doorknob and door are likely the same (or at least very close). 40. When heat flows from a warmer object in contact with a colder object, do the two have the same temperature changes? Generally, no. The two objects will change temperatures depending on their masses and specific heats. 52. How much heat is needed to raise the temperature of of water from to?

5 53. A block of metal absorbs of heat when its temperature changes from to. Calculate the specific heat of the metal. 54. Coffee Cup: A g glass coffee cup is at room temperature. It is then plunged into hot dishwater at a temperature of, as shown in Figure If the temperature of the cup reaches that of the dishwater, how much heat does the cup absorb? Assume that the mass of the dishwater is large enough so that it does not change appreciably. 55. A g mass of tungsten at is placed in g of water at. The mixture reaches equilibrium at. Calculate the specific heat of tungsten. 56. A g sample of water at is mixed with g of water at. Assume that there is no heat loss to the surroundings. What is the final temperature of the mixture? Since, there is cancellation in this particular case so that

6 57. A kg piece of zinc at is placed in a container of water, as shown in Figure The water has a mass of kg and a temperature of before the zinc is added. What is the final temperature of the water and the zinc Since, we can replace both with and solve for : 58. The kinetic energy of a compact car moving at is. To get a feeling for the amount of energy needed to heat water, what volume of water (in liters) would temperature to boiling? of energy warm from room The density of water is, which we can use to find the volume of water. 59. Water Heater: A W electric immersion heater is used to heat a cup of water, as shown in Figure The cup is made of glass, and its mass is g. It contains 250 g of water at. How much time is needed to bring the water to the boiling point? Assume that the temperature of the cup is the same as the temperature of the water at all times and that no heat is lost to the air.

7 60. Car Engine: A kg cast-iron car engine contains water as a coolant. Suppose that the engine s temperature is when it shuts off, and the air temperature is. The heat given off by the engine and water in it as they cool to air temperature is. What mass of water is used to cool the engine? Page 325 #19-21; Page 328 # How much heat is absorbed by g of ice at to become water at? 20. A g sample of water at is heated to steam at. How much heat is absorbed? 21. How much heat is needed to change g of ice at to steam at? ( )

8 22. A gas balloon absorbs 75 J of heat. The balloon expands but stays at the same temperature. How much work did the balloon do in expanding? Since the balloon did not change temperature,. Therefore,. Thus, the balloon did 75 J of work in expanding. 23. A drill bores a small hole in a 0.40 kg block of aluminum and heats the aluminum by. How much work did the drill do in boring the hole? 24. How many times would you have to drop a kg bag of lead shot from a height of 1.5 m to heat the shot by. The energy required to heat the lead is given by Each time the bas is raised, its gravitational potential energy (relative to ground level) is Assuming that each time the bag is dropped, this gravitational potential energy is converted into thermal energy. The number of required drops is then 25. When you stir a cup of tea, you do about J of work each time you circle the spoon in the cup. How many times would you have to stir the spoon to heat a 0.15 kg cup of tea by?

9 26. How can the first law of thermodynamics be used to explain how to reduce the temperature of an object? Since, it is possible to have a negative, and therefore, cool an object if and the object does work (for instance, by expanding). Alternatively, it is possible to have and by having the object transfer heat to its surroundings. Any combination of these will work as well. Page 336 #35, 41-44, Complete the following concept map using the following terms: heat, work, internal energy. 41. Can you add thermal energy to an object without increasing its temperature? Explain. Yes. When you melt a solid or boil a liquid, you add thermal energy without changing the temperature. 42. When wax freezes, does it absorb or release energy? When wax (or anything else) freezes, it releases energy. 43. Explain why water in a canteen that is surrounded by dry air stays cooler if it has a canvas cover that is kept wet. When the water in the cover evaporates into the dry air, it must absorb an amount of energy proportional to its heat of fusion. In doing so, it cools off the canteen. This works only if the air is dry; if the air is humid, then the water will not evaporate. 44. What process occurs at the coils of a running air conditioner inside a house, vaporization or condensation? Explain. Inside the house, the coolant is evaporating in the coils to absorb energy from the rooms. 61. Years ago, a block of ice with a mass of about 20.0 kg was used daily in a home icebox. The temperature of the ice was when it was delivered. As it melted, how much heat did the block of ice absorb?

10 62. A 40.0 g sample of chloroform is condensed from a vapor at to a liquid at. It liberates of heat. What is the heat of vaporization of chloroform? 63. A 750 kg car moving at 23 m/s brakes to a stop. The brakes contain about 15 kg of iron, which absorbs the energy. What is the increase in temperature of the brakes? During braking, the kinetic energy of the car is converted into heat, which is absorbed by the brakes. 64. How much heat is added to 10.0 g of ice at to convert it to steam at? ( )

11 65. A 4.2 g lead bullet moving at 275 m/s strikes a steel plate and comes to a stop. If all its kinetic energy is converted to thermal energy and none leaves the bullet, what is its temperature change. ( ) 66. Soft Drink: A soft drink from Australia is labeled Low-Joule Cola. The label says 100 ml yields 1.7 kj. The can contains 375 ml of cola. Chandra drinks the cola and then wants to offset this input of food energy by climbing stairs. How high would Chandra have to climb if she has a mass of 65.0 kg? The amount of energy Chandra gains from the drink is Chandra would need to climb stairs to change her gravitational potential energy by the same 6375 J. 67. What is the efficiency of an engine that produces while burning enough gasoline to produce? How much waste heat does the engine produce per second? For one second, and

12 68. Stamping Press: A metal stamping machine in a factory does 2100 J of work each time it stamps out a piece of metal. Each stamped piece is then dipped in a 32.0 kg vat of water for cooling. By how many degrees does the vat heat up each time a piece of stamped metal is dipped into it? If we assume the 2100 J of work from the machine is absorbed as thermal energy in the stamped piece, then the vat must absorb 2100 J in the form of heat from each piece. No work is done on the water, only heat is transferred. The change in temperature of the water is given by 69. A 1500 kg automobile comes to a stop from 25 m/s. All of the energy of the automobile is deposited in the brakes. Assuming that the brakes are about 45 kg of aluminum, what would be the change in temperature of the brakes? ( ) 70. Iced Tea: To make iced tea, you start by brewing the tea with hot water. Then you add ice. If you start with 1.0 L of tea, what is the minimum amount of ice needed to cool it to? Would it be better to let the tea cool to room temperature before adding ice? The heat that must be lost by the tea is The same amount of heat must be absorbed by the ice as it melts. This is more ice than tea, which would result it weak tea. It would be better to let the tea cool to room temp.

13 71. A block of copper at comes in contact with a block of aluminum at, as shown in Figure The final temperature of the blocks is. What are the relative masses of the blocks? Dividing both sides by, The mass of the copper block is 2.3 times the mass of the aluminum block. 72. A 0.35 kg block of copper sliding on the floor hits an identical block moving at the same speed from the opposite direction. The two blocks come to a stop together after the collision. Their temperatures increase by as a result of the collision. What was their velocity before the collision? The change in internal energy of each block is Therefore, each block has 27 J of kinetic energy before the collision.

14 73. A 2.2 kg block of ice slides across a rough floor. Its initial velocity is and its final velocity is. How much of the ice melted as a result of the work done by friction? Therefore, 6.6 J is added to the ice. Chapter 12 Study Guide Vocabulary Review 1. Thermal equilibrium 2. Heat 3. Specific heat 4. Heat of fusion 5. First law of thermodynamics 6. Conduction 7. Entropy 8. Heat engine 9. Second law of thermodynamics 10. Convection 11. Heat of vaporization 12. Radiation Section 12.1: Temperature and Thermal Energy 1. average 2. True 3. thermal 4. True 5. or K 7. True

15 8. f. 9. e. 10. d. 11. a. K 12. b. S 13. g. 14. c. 15. In the Kelvin scale, there are no negative temperatures. All temperatures are related to the kinetic energy of the molecules, with 0 K corresponding to zero kinetic energy. 16. a. A vacuum is an area with no matter. If there is no matter, then there are no particles to conduct heat. The only conduction could take place through the cap, but cork is a very poor conductor. b. Convection is a transfer of energy within a fluid. With the bottle tightly closed, thermal energy cannot be lost to the atmosphere, and instead is contained within the inner container. c. The wall of the outer container physically interferes with the direct radiation of energy to or from the inner container holding the liquid Positive 19. Negative 20. They should be the same. 21. If there is no heat transfer with the surroundings, then Section 12.2: Changes of State and the Laws of Thermodynamics 1. c. freezing point 2. a. boiling point 3. d. They are the same 4. b. 5. c. only its potential energy increases (For a pure substance, phase changes occur at a constant temperature. Since temperature is a measure of average kinetic energy of the particles, no temperature change means no change in kinetic energy.) 6. d. It takes more than six times as much energy to boil the water as to melt the ice. 7.

16 8. a. The water must be heating to its boiling point,, vaporized, then the steam must be heated to the final temperature. ( ) b. This is just the reverse of part a, so 9. The change in thermal energy of an object,, is equal to the heat that is added to the object,, minus the work done by the object,. 10. As the refrigerator attempts to remove energy from the air inside the refrigerator, it releases heat out the back of the refrigerator. Since the refrigerator is not 100% efficient, it releases more heat out the back than it removes from the air inside. The net result is heating up the kitchen, not cooling it. 11. Overall, there is an increase in entropy, so the second law holds. The system in which the paint is acting includes the water or other solvent that made the paint a liquid. When the paint dries, the solvent absorbs energy and changes state from a liquid to a gas. The entropy of the gas is greater than the entropy of the liquid A heat engine uses the natural flow of heat to produce work. If there is no heat sink, then there would be no flow of heat, and the engine could do no work. 20. The more efficient a device is, the more work it can do for the amount of energy it uses. Less energy is wasted because that energy does not get converted and released as thermal energy. 21. Efficient products waste less energy and so can use less energy, making them cheaper to operate.