Ch. 10 Review questions
The greatest obstacle to learning anything is thinking you already know everything.
1. A container of gas is at a pressure of 1.7 x 10^5 Pa and a volume of 4.9 m^3. How much work is done by the gas if it expands at constant pressure to twice its initial volume?
Ans: 8.3 x 105 J
2. An ideal gas is maintained at a constant pressure of 9.8 x10^4 Pa while its volume decreases by 0.38 m^3. What work is done by the system on its environment?
Ans: -3.7 x 104 J
3. Gas within a cylinder expands outward against a piston with a radius of 0.15 m so that 6680 J of work is to be done by the gas. If the net pressure exerted on the gas is 3.8 x 10^5 Pa, how far is the piston displaced?
Ans: 0.25 m
4. A total of 198 J of work is done on a gaseous refrigerant as it undergoes compression. If the internal energy of the gas increases by 121 J during the process, what is the total amount of energy transferred as heat?
-77 J
5. The piston and flywheel part of a steam engine takes in 993 J of energy as heat and expels 514 J of energy as heat. The internal energy of the system increases by 372 J during the process. Work is done by steam at a pressure of 2.21 x 10^5 Pa. If the radius of the piston is 4.14 x 10^-2 m, how far is the piston displaced?
Ans: 0.0899m
6. A gas balloon absorbs 75 J of heat. The balloon expands but stays at the same temperature. What kind of process is this? Was work done on the balloon (system) or the environment? How much work was done?
Ans: isothermal, on the environment, 75 J
7. A drill bores a small hole into a 0.40 kg aluminum block, which causes it to increase its temperature by 5.0 C. How much work did the drill do to bore the hole? The specific heat of aluminum is 899 J/kg*C.
Ans: 1.8 x 103 J
8. When you stir a cup of tea, you do about 0.0500 J of work each time you complete a circle around the cup. How many circles would you have to complete to heat 0.15 kg of tea by 2.0 C? Assume no energy is lost to the cup or the environment and the specific heat of tea is 4186 J/kg*C.
Ans: 2.5 x 104 stirs.
9. You do 25 kJ of work on a system that contains 3.0 kg of water by stirring it with a paddle. During this time, 6.3 x 104 J of heat is removed from the system. How much did the system’s internal energy change?
Ans: -37.7 kJ
10. Gas confined by a piston in a heat engine expands against a constant pressure of 100. kPa. When 2.0 x 10^4 J of heat are absorbed by the system, the gas expands from 0.15 m^3 to to 0.25 m^3. What is the work done by the system during the process?
What is the change in the systems internal energy?
Ans: 1.0 x 10^4 J of work, 1.0 x 10^4 J increase of internal energy
11. A heat engine undergoes a process in which its internal energy decreases by 400. J while it is doing 250. J of work. What is the heat transfer by the engine during this process?
Ans: -150 J aka, leaves the system.
12. Suppose you are hired to carry 207 kg of bricks up a ladder 3.65 m and set them on top of a massive balloon. If this work is then used to compress a gas at a constant pressure of 1.8 x 10^6 Pa, what is the change in volume of the balloon?
Ans: -4.1 x 10-3 m3
13. A meteorologist inflates a weather balloon by shear manpower. The final radius of this balloon when fully inflated is 1.22 m. If 642 kJ of work was done to inflate the balloon, what is the net pressure at which the balloon was inflated?
Ans: 8.44 x 104 Pa
14. A world champion bubble gum bubble blower once blew a bubble that was 29.2 cm at a constant pressure of 25.0 kPa. If this work was used to launch a 160.0 g model airplane, what would its velocity be right at take off?
Ans: 181 m/s
15. What is the efficiency of an engine that produces 2200 J of work each second while burning 5300 J of gasoline? How much energy is removed as waste heat?
Ans: 42 %, 3100 J
16. A 2.2 kg block of ice slides across a rough floor. Its initial velocity is 2.5 m/s and its final velocity is 0.50 m/s. If all of the work done by friction goes into increasing the internal energy of the ice, how much ice would melt if it is already at its melting point? The latent heat of fusion for ice 3.33 x 10^5 J/kg.
Ans: 2.0 x 10^-5 kg
17. A heat engine removed 50.0 J of energy from a heat source at 545 K and expels 40.0 J of energy into a heat sink that is at 325 K. How much entropy has been removed from the heat source? How much has entropy increased in the heat sink? What is the overall change in entropy?
Ans: 0.0917 J/K out, 0.123 J/K in, 0.031 J/K net increase.
18. You do 0.50 J of work on the coffee in your cup each time you stir it. What would be the increase in entropy of 125 mL of coffee at 65 C when you stir it 85 times?
Ans: 0.013 J/K
19. An engine takes in 9220 J of energy and does 1750 J of work each cycle. What is its actual efficiency?
Ans: 0.190 or 19.0 %
20. A gas in a piston of a heat engine expands against 2.56 x 10^5 Pa of pressure. When 40.0 kJ oh heat is added to the system, the volume increases from 0.105 m^3 to 0.235 m^3. What is the change in internal energy of the system?
Ans: 6.7 kJ
21. Over several cycles, a refrigerator compressor does work on the refrigerant by causing a net change in volume of –0.164 m^3 under a constant pressure of 3.31 x 10^5 Pa. This causes the refrigerant to remove 6.37 x 10^4 J of energy as heat from the interior of the refrigerator. Because the compartment is not perfectly insulated, 1.1 x 10^3 J of energy leaks into the compartment from outside the refrigerator. Treating the compressor, refrigerant, and refrigerator compartment as a single system, and assuming that the refrigerator requires 355 J of energy to change its interior temperature by 1.00 C, what is the final temperature of the refrigerator? Assume that its temperature at the start of the process is 27.2 C.
Ans: 3.8 C
22. An engine absorbs 2310 J as heat from a hot reservoir and gives off 830 J as heat to a cold reservoir during each cycle. What is the efficiency of the engine?
Ans: 0.64
23. An engine adds 62000 J of energy as heat and removes 17000 J of energy as heat. What is the engine’s efficiency?
Ans: 0.73
24. A heat engine performs 2300.0 J of net work while adding 7100.0 J of heat to the low-temperature reservoir. What is the efficiency of the engine?
Ans: 0.24468
25. The piston of an engine has a radius of 5.5 x 10^-2 m and is displaced a distance of 0.28 m when the pressure within the cylinder is 3.5 x 10^5 Pa. If the efficiency of the engine is 0.44, how much work must the engine give up as heat to the low-temperature reservoir?
Ans: 1.1 x 103 J
26. Calculate the change in entropy of 0.020 kg of ice when it melts at 0.0C. The heat of fusion of ice is 3.36 x 10^5 J/kg.
Ans: 25J/K
27. A heat engine operates between a high-temperature source and a low-temperature sink. It takes 200 J from the source and delivers 120 J to the sink. What is the efficiency of the heat engine?
Ans: 40%
28. A gas is kept in a rigid container and 100 J of heat is supplied to it. What is the work done by the gas and the change in the internal energy of the gas?
Ans: W=0 U= 100J
29. 0.2000 kg of water at 20.00C is contained in a 0.1000-kg copper container. The container is shaken vigorously for 10.00 minutes to cause the temperature to rise to 22.00C. Calculate the work done on the system and the heat supplied to the system. The specific heat of copper is 385.0 J/kgK and of water is 4200.0 J/kgK.
Ans: 1757 J
30. A heat engine absorbs 200 J of heat from the hot reservoir, does work, and exhausts 160 J to a cold reservoir. What is the efficiency of the engine?
Ans: 20%
31. An engine with 20% efficiency does 100 J of work. How much heat does it take in? How much is removed to the heat sink, or wasted heat?
Ans: 500J, 400 J
32. An engine absorbs 400 J of heat and deos 120 J of work. What is its efficiency?
Ans: 30%
33. The heaviest snake ever found had a mass of 227 kg and was 8.45 m long. Suppose a contained gas with an internal energy of 42.0 kJ does enough work to lift the snake to a height equal to its own weight. If 4.00 kJ of energy is transferred to the gas as heat during the lifting process, what is the final internal energy of the gas?
Ans: 27.2 kJ
34. The most massive cannon ever built was, of course, built in Russia. It has a mass of 1.40 x 10^5 kg and could fire cannonballs with masses of 480. Kg. If the gunpowder in the cannon went through adiabatic expansion to form compressed gas in the barrel, how much work would be done by this gas if the initial speed of the cannonball was 200. m/s? If the initial energy of the barrel was 12.0 MJ, when the cannonball leaves the barrel, what was it at the moment that the powder burned?
Ans: 9.60 MJ, 21.6 MJ
35. An average elephant has a mass of 5.00 x 10^3 kg. Elephants can run up to 40.0 km/h. Imagine a gas does work equal to the work required for an elephant to move from rest to its maximum speed. If the initial internal energy of the gas, 2.50 x 10^5 J, is to be doubled, how much energy must be transferred to the gas by heat?
Ans: 5.59 x 10^5 J
36. The rate of nuclear energy production in the USA was about 5.9 x 10^9 J every second. Suppose that one second of this energy is added to an ideal gas. How much work must be done on or by this gas so that the net increase in its internal energy is 2.6 x 10^9 J?
Ans: 3.3 x 10^9 J, done by the gas.
37. In 1989, Brendan Keenoy ran up 1760 steps in the CN Tower in Toronto, reaching a height of 342 m in 7 minutes and 52 seconds. Suppose the amount of work done by Keenoy is done by a heat engine. The engine’s input energy is 1.34 MJ, and its efficiency is 0.18. How much energy is exhausted from and how much work is done by the engine?
Ans: Qc= 1.1 x 106 J Wnet = 2.4 x 105J
38. The oldest working steam engine was designed in 1779 by James Watt. Suppose this engine is 8.0% efficient. How much energy must be transferred by heat to the engine’s surroundings if 2.5 kJ is transferred by heat into the engine? How much work does it accomplish?
Ans: 2.3 kJ, 0.20 J of work
39. In 1894 the first turbine driven ship was designed. If the engine is 16% efficient, how much energy leaves through the exhaust if the input energy is 2.0 x 10^9 J ?
Ans: 1.72 x 10^9 J
40. A steam engine built in 1812 delivers 19 kW of net power at 6.0 % efficiency. How much energy must be transferred to the engine every hour?
Ans: 1.1 x 10^9 J
41. The first motorcycle built in 1885 could reach a top speed of 19 km/h. The output power of the engine is 370 W. If the efficiency is 0.19, how much energy is put into the engine over one minute?
Ans: 120 kJ
42. A steam engine requires 0.80 kg of coal to produce 2.6 MJ of work. What is the efficiency of this engine if 1.0 kg of coal releases 32.6 MJ of energy.
Ans: 0.10
43. A crane lifts 3.00 x 10^4 kg to a height of 1.60 x 10^2 m. What is the efficiency of a heat engine that completes this same task while losing 3.60 x 10^8 J of energy to its surroundings?
Ans: 0.12
44. A volume of air increases 0.227 m^3 at a net pressure of 2.07 x 10^7 Pa, how much work is done on the air?
Ans: 4.70 x 10^6 J
45. The air in a hot-air balloon does 3.29 x 10^6 J of work. Increasing the balloon’s volume by 2190 m^3. What is the net pressure in the balloon?
Ans: 1.50 kPa
46. Filling a fire extinguisher with nitrogen gas at a net pressure of 25.0 kPa requires 472.5 J of work on the gas. Find the change in the gas’s volume.
Ans: 0.189 m3
47. The internal energy of air in a closed car rises 873 J. How much heat energy is transferred to the air?
Ans: 873 J
48. A system’s internal energy increases from 39 J to 163 J. If 144 J of heat are added to the system, how much work is done on the system?
Ans: -10. J
49. A gas does 623 J of work on its surroundings when 867 J are added to the gas as heat. What is the change in internal energy of the gas?
Ans: 244 J
50. An engine with an efficiency of 0.29 takes in 693 J as heat. How much work does the engine do?
Ans: 200. J
51. An engine with an efficiency of 0.19 does 998 J of work. How much energy is taken in as heat?
Ans: 5.3 x 103 J
52. Find the efficiency of an engine that receives 571 J of heat and loses 463 J of heat.
Ans: 0.189
53. A 5.4 x 10^-4 m^3 increase in steam’s volume does 1.3 J of work on a piston. What is the pressure?
Ans: 2.4 kPa
54. A pressure of 655 kPa does 393 J of work inflating a bike tire. Find the change in volume.
Ans: 6.00 x 10-4 m3
55. An engine’s internal energy changes from 8093 J to 2.0920 x 10^4 J. If 6932 J are added as heat, how much work is done on or by the system?
Ans: 5895 J
56. Steam expands from a geyser to do 192 kJ of work. If the system’s internal energy increases by 786 kJ, how much energy is transferred as heat?
Ans: 9.78 x 105 J
57. If 632 kJ are added to a boiler and 102 kJ of work are done as steam escapes from a safety valve, what is the net change in the system’s internal energy?
Ans: 5.30 x 105 J
58. A power plant with an efficiency of 0.35 requires 7.37 x 108 J of energy as heat. How much work is done by the power plant?
Ans: 2.6 x 108 J
59. An engine with an efficiency of 0.11 does 1150 J of work. How much energy is taken in as heat?