Mastering Physics Solutions Chapter 18 The Laws of Thermodynamics
Chapter 18 The Laws of Thermodynamics Q.1CQ
If an engine has a reverse gear. does this make it reversible?
Solution:
If the engine is in reverse gear, is not reversible when it has friction.
Chapter 18 The Laws of Thermodynamics Q.1P
CE Give the change in internal energy of a system if (a) W = 50 J, Q = 50 J; (b) W = −50 J, Q = −50 J; or (c) W = 50 J, Q = −50 J.
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Chapter 18 The Laws of Thermodynamics Q.2CQ
The temperature of a substance is held fixed. Is it possible for heat to flow (a) into or (b) out of this system? For each case, give an explanation if your answer is no. If your answer is yes, give a specific example.
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Chapter 18 The Laws of Thermodynamics Q.2P
CE A gas expands, doing 100 J of work. How much heat must be added to this system for its internal energy to increase by 200 J?
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Chapter 18 The Laws of Thermodynamics Q.3CQ
A substance is thermally insulated, so that no heat can flow between it and its surroundings. Is it possible for the temperature of this substance to (a) increase or (b) decrease? For each case, give an explanation if your answer is no. If your answer is yes, give a specific example.
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Chapter 18 The Laws of Thermodynamics Q.3P
A swimmer does 6.7 × 105 J of work and gives off 4.1 × 105 J of heat duringa workout. Determine ∆U, W,and Q for the swimmer.
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Chapter 18 The Laws of Thermodynamics Q.4CQ
Heat is added to a substance. Is it safe to conclude that the temperature of the substance will rise? Give an explanation if your answer is no. If your answer is yes, give a specific example.
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Chapter 18 The Laws of Thermodynamics Q.4P
When 1210 Jof heat are added to one mole of an ideal monatomic gas, its temperature increases from 272 K to 276 K. Find the work done by the gas during this process.
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Chapter 18 The Laws of Thermodynamics Q.5CQ
The temperature of a substance is increased. Is it safe to conclude that heat was added to the substance? Give an explanation if your answer is no. If your answer is yes, give a specific example.
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Chapter 18 The Laws of Thermodynamics Q.5P
Three different processes act on a system. (a) In process A, 42 J of work are done on the system and 77 J of heat are added to the system. Find the change in the system’s internal energy. (b) In process B, the system does 42 J of work and 77 Jof heat are added to the system. What is the change in the system’s internal energy? (c) In process C, the system’s internal energy decreases by 120 J while the system performs 120 J of work on its surroundings. How much heat was added to the system?
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Chapter 18 The Laws of Thermodynamics Q.6CQ
Are there thermodynamic processes in which all the heat absorbed by an ideal gas goes completely into mechanical work? If so, give an example.
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Chapter 18 The Laws of Thermodynamics Q.6P
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Chapter 18 The Laws of Thermodynamics Q.7CQ
Is it possible to convert a given amount of mechanical work completely into heat? Explain.
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Chapter 18 The Laws of Thermodynamics Q.7P
· · A basketball player does 2.43 × 105 J of work during her time in the game, and evaporates 0.110 kg of water. Assuming a latent heat of 2.26 × 106 J/kg for the perspiration (the same as for water), determine (a) the change in the player’s internal energy and (b) the number of nutritional calories the player has converted to work and heat.
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Chapter 18 The Laws of Thermodynamics Q.8CQ
An ideal gas Is held in an insulated container at the temperature T. All the gas is initially in one-half of the container, with a partition separating the gas from the other half of the container, which is a vacuum. If the partition ruptures, and the gas expands to fill the entire container, what is its final temperature?
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Chapter 18 The Laws of Thermodynamics Q.8P
IP One mole of an ideal monatomic gas is initially at a temperature of 263 K. (a) Find the final temperature of the gas if 3280 J of heat are added to it and it does 722 J of work. (b) Suppose the amount of gas is doubled to two moles. Does the final temperature found in part (a) increase, decrease, or stay the same? Explain.
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Chapter 18 The Laws of Thermodynamics Q.9CQ
Which of the following processes are approximately reversible? (a) Lighting a match. (b) Pushing a block up a frictionless inclined plane. (c) Frying an egg. (d) Swimming from one end of a pool to the other. (e) Stretching a spring by a small amount. (f) Writing a report for class.
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Chapter 18 The Laws of Thermodynamics Q.9P
· · IP Energy from Gasoline Burning a gallon of gasoline releases 1.19 × 108 J of internal energy. If a certain car requires 5.20 × 1.05 J of work to drive one mile, (a) how much heat is given off to the atmosphere each mile, assuming the car gets 25.0 miles to the gallon? (b) If the miles per gallon of the car is increased, does the amount of heat released to the atmosphere increase, decrease, or stay the same? Explain.
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Chapter 18 The Laws of Thermodynamics Q.10CQ
Which law of thermodynamics would be violated if heat were to spontaneously flow between two objects of equal temperature?
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Chapter 18 The Laws of Thermodynamics Q.10P
A cylinder contains 4.0 moles of a monatomic gas at an initial temperature of 27 °C. The gas is compressed by doing 560 J of work on it, and its temperature increases by 130 °C. How much heat flows into or out of the gas?
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Chapter 18 The Laws of Thermodynamics Q.11CQ
Heat engines always give off a certain amount of heat to a low-temperature reservoir. Would it be possible to use this “waste” heat as the heat input to a second heat engine, and then use the “waste” heat of the second engine to run a third engine, and so on?
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Chapter 18 The Laws of Thermodynamics Q.11P
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Chapter 18 The Laws of Thermodynamics Q.12CQ
A heat pump uses 100 J of energy as it operates for a given time. Is it possible for the heat pump to deliver more than 100 J of heat to the inside of the house in this same time? Explain.
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Chapter 18 The Laws of Thermodynamics Q.12P
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Chapter 18 The Laws of Thermodynamics Q.13CQ
If you clean up a messy room, putting things back where they belong, you decrease the room’s entropy. Does this violate the second law of thermodynamics? Explain.
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Chapter 18 The Laws of Thermodynamics Q.13P
A system consisting of an ideal gas at the constant pressure of 110 kPa gains 920 J of heat. Find the change in volume of the system if the internal energy of the gas increases by (a) 920 J or (b) 360 J.
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Chapter 18 The Laws of Thermodynamics Q.14CQ
Which law of thermodynamics is most pertinent to the statement that “all the king’s horses and all the king’s men couldn’t put Humpty Dumpty back together again?”
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Chapter 18 The Laws of Thermodynamics Q.14P
An ideal gas is compressed at constant pressure to one-half its initial volume. If the pressure of the gas is 120 kPa, and 790 J of work is done on it, find the initial volume of the gas.
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Chapter 18 The Laws of Thermodynamics Q.15CQ
Which has more entropy: (a) popcorn kernels, or the resulting popcorn; (b) two eggs in a carton, or an omelet made from the eggs; (c) a pile of bricks, or the resulting house; (d) a piece of paper, or the piece of paper after it has been burned?
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Chapter 18 The Laws of Thermodynamics Q.15P
As an ideal gas expands at constant pressure from a volume of 0.74 m3 to a volume of 2.3 m3 it does 93 J of work. What is the gas pressure during this process?
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Chapter 18 The Laws of Thermodynamics Q.16P
The volume of a monatomic ideal gas doubles in an isother mal expansion. By what factor does its pressure change?
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Chapter 18 The Laws of Thermodynamics Q.17P
IP (a) If the internal energy of a system increases as the result of an adiabatic process, is work done on the system or b the system? (b) Calculate the work done on or by the system in part (a) if its internal energy increases by 670 J.
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Chapter 18 The Laws of Thermodynamics Q.18P
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Chapter 18 The Laws of Thermodynamics Q.19P
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Chapter 18 The Laws of Thermodynamics Q.20P
IP If 8.00 moles of a monatomic ideal gas at a temperature of 245 K are expanded isothennally from a volume of 1.12 L to a volume of 4.33 T, calculate (a) the work done and (b) the heat flow into or out of the gas. (c) If the number of moles is doubled, by what factors do your answers to parts (a) and (b) change? Explain.
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Chapter 18 The Laws of Thermodynamics Q.21P
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Chapter 18 The Laws of Thermodynamics Q.22P
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Chapter 18 The Laws of Thermodynamics Q.23P
IP (a) A monatomic ideal gas expands at constant pressure. Is heat added to the system or taken from the system during this process? (b) Find the heat added to or taken from the gas in part (a) if it expands at a pressure of 130 kPa from a volume of 0.76 m3 to a volume of 0.93 m3.
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Chapter 18 The Laws of Thermodynamics Q.24P
During an adiabatic process, the temperature of 3.92 moles of a monatomic ideal gas drops from 485 °C to 205 °C. For this gas, find (a) the work it does, (b) the heat it exchanges with its surroundings, and (c) the change in its internal energy.
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Chapter 18 The Laws of Thermodynamics Q.25P
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Chapter 18 The Laws of Thermodynamics Q.26P
With the pressure held constant at 210 kPa, 49 mol of a monatomic ideal gas expands from an initial volume of 0.75 m3 to a final volume of 1.9 m3. (a) How much work was done by the gas during the expansion? (b) What were the initial and final temperatures of the gas? (c) What was the change in the internal energy of the gas? (d) How much heat was added to the gas?
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Chapter 18 The Laws of Thermodynamics Q.27P
IP Suppose 67.5 moles of an ideal monatomic gas undergo the series of processes shown in Figure 18–24. (a) Calculate the temperature at the points A, B, and C. (b) For each process, A → B, B →C, and C → A, state whether heat enters or leaves the system. Explain in each case. (c) Calculate the heat exchanged with the gas during each of the three processes.
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Chapter 18 The Laws of Thermodynamics Q.28P
A gas is contained in a cylinder with a pressure of 140 kPa and an initial volume of 0.66 m3. How much work is done by the gas as it (a) expands at constant pressure to twice its initial volume, or (b) is compressed to one-third its initial volume?
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Chapter 18 The Laws of Thermodynamics Q.29P
A system expands by 0.75m3 at a constant pressure of 125 kPa. Find the heat that flows into or out of the system if its internal energy (a) increases by 65 J or (b) decreases by 1850 J. In each case, give the direction of heat flow.
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Chapter 18 The Laws of Thermodynamics Q.30P
IP An ideal monatomic gas is held in a perfectly insulated cylinder fitted with a movable piston. The initial pressure of the gas is 110 kPa, and its initial temperature is 280 K. By pushing down on the piston, you are able to increase the pressure to 140 kPa, (a) During this process, did the temperature of the gas increase, decrease, or stay the same? Explain. (b) Find the final temperature of the gas.
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Chapter 18 The Laws of Thermodynamics Q.31P
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Chapter 18 The Laws of Thermodynamics Q.32P
An ideal gas doubles its volume in one of three different ways: (i) at constant pressure; (ii) at constant temperature; (iii) adiabatically. Explain your answers to each of the following questions: (a) In which expansion does the gas do the most work? (b) In which expansion does the gas do the least work? (c) Which expansion results in the highest final temperature? (d) Which expansion results in the lowest final temperature?
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Chapter 18 The Laws of Thermodynamics Q.33P
CE Predict/Explain You plan to add a certain amount of heat to a gas in order to raise its temperature. (a) If you add the heat at constant volume, is the increase in temperature greater than, less than, or equal to the increase in temperature if you add the heat at constant pressure? (b) Choose the best explanation from among the following:
I. The same amount of heat increases the temperature by the same amount, regardless of whether the volume or the pressure is held constant.
II. All the heat goes into raising the temperature when added at constant volume;none goes into mechanical work.
III. Holding the pressure constant will cause a greater increase in temperature than simply having a fixed volume.
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Chapter 18 The Laws of Thermodynamics Q.34P
Find the amount of heat needed to increase the temperature of 3.5 mol of an ideal monatomic gas by 23 K if (a) the pressure or (b) the volume is held constant.
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Chapter 18 The Laws of Thermodynamics Q.35P
(a) If 535 J of heat are added to 45 moles of a monatomic gas at constant volume, how much does the temperature of the gas increase? (b) Repeat part (a), this time for a constant-pressure process.
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Chapter 18 The Laws of Thermodynamics Q.36P
A system consists of 2.5 mol of an ideal monatomic gas at 325 K. How much heat must be added to the system to double its internal energy at (a) constant pressure or (b) constant volume?
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Chapter 18 The Laws of Thermodynamics Q.37P
Find the change in temperature if 170 J of heat are added to 2.8 mol of an ideal monatomic gas at (a) constant pressure or (b) constant volume.
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Chapter 18 The Laws of Thermodynamics Q.38P
IP A cylinder contains 18 moles of a monatomic ideal gas at a constant pressure of 160 kPa. (a) How much work does the gas do as it expands 3200 cm3, from 5400 cm3 to 8600 cm3? (b) If the gas expands by 3200 cm3 again, this time from 2200 cm3 to 5400 cm3, is the work it does greater than, less than, or equal to the work found in part (a)? Explain. (c) Calculate the work done as the gas expands from 2200 cm3 to 5400 cm3.
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Chapter 18 The Laws of Thermodynamics Q.39P
· · IP The volume of a monatomic ideal gas doubles in an adiabatic expansion. By what factor do (a) the pressure and (b) the temperature of the gas change? (c) Verify your answers to parts (a) and (b) by considering 135 moles of gas with an initial pressure of 330 kPa and an initial volume of 1.2 m3. Find the pressure and temperature of the gas after it expands adiabatically to a volume of 2.4 m3.
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Chapter 18 The Laws of Thermodynamics Q.40P
A monatomic ideal gas is held in a thermally insulated container with a volume of 0.0750 m3. The pressure of the gas is 105 kPa, and its temperature is 317 K. (a) To what volume must the gas be compressed to increase its pressure to 145 kPa? (b) At what volume will the gas have a temperature of 295 K?
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Chapter 18 The Laws of Thermodynamics Q.41P
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Chapter 18 The Laws of Thermodynamics Q.42P
Referring to Problem 41, suppose the gas is expanded along processes 3 and 4 in Figure 18–26. On process 3 the gas expands at constant pressure from an initial volume of 1.00 m3 to a final volume of 3.00 m3. On process 4 the gas is heated at constant volume from an initial pressure of 106 kPa to a final pressure of 212 kPa. (a) How much heat is added to the gas during these two processes? (b) How much work does the gas do during this expansion? (c) What is the change in the internal energy of the gas?
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Chapter 18 The Laws of Thermodynamics Q.43P
CE A Carnot engine operates between a hot reservoir at the Kelvin temperature Th and a cold reservoir at the Kelvin temperature Tc.(a) If both temperatures are doubled, does the efficiency of the engine increase, decrease, or stay the same? Explain. (b) If both temperatures are increased by 50 K, does the efficiency of the engine increase, decrease, or stay the same? Explain.
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Chapter 18 The Laws of Thermodynamics Q.44P
· CE A Carnot engine can be operated with one of the following four sets of reservoir temperatures: A, 400 K and 800 K; B, 400 K and 600 K; C, 800 K and 1200 K; and D, 800 K and 1000 K. Rank these reservoir temperatures in order of increasing efficiency of the Carnot engine. Indicate ties where appropriate.
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Chapter 18 The Laws of Thermodynamics Q.45P
What is the efficiency of an engine that exhausts 870 J of heat in the process of doing 340 J of work?
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Chapter 18 The Laws of Thermodynamics Q.46P
An engine receives 690 J of heat from a hot reservoir and gives off 430 J of heat to a cold reservoir. What arc (a) the work done and (b) the efficiency of this engine?
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Chapter 18 The Laws of Thermodynamics Q.47P
A Carnot engine operates between the temperatures 410 K and 290 K. (a) How much heat must be given to the engine to produce 2500 J of work? (b) How much heat is discarded to the cold reservoir as this work is done?
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Chapter 18 The Laws of Thermodynamics Q.48P
A nuclear power plant has a reactor that produces heat at the rate of 838 MW. This heat is used to produce 253 MW of mechanical power to drive an electrical generator. (a) At what rate is heat discarded to the environment by this power plant? (b) What is the thermal efficiency of the plant?
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Chapter 18 The Laws of Thermodynamics Q.49P
At a coal-burning power plant a steam turbine is operated with a power output of 548 MW. The thermal efficiency of the power plant is 32.0%. (a) At what rate is heat discarded to the environment by this power plant? (b) At what rate must heat be supplied to the power plant by burning coal?
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Chapter 18 The Laws of Thermodynamics Q.50P
IP If a heat engine does 2700 J of work with an efficiency of 0.18, find (a) the heat taken in from the hot reservoir and (b) the heat given off to the cold reservoir. (c) If the efficiency of the engine is increased, do your answers to parts (a) and (b) increase decrease, or stay the same? Explain.
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Chapter 18 The Laws of Thermodynamics Q.51P
IP The efficiency of a particular Carnot engine is 0.300. (a) If the high-temperature reservoir is at a temperature of 545 K, what is the temperature of the low-temperature reservoir? (b) To increase the efficiency of this engine to 40.0%, must the temperature of the low-temperature reservoir be increased or decreased? Explain. (c) Find the temperature of the low-temperature reservoir that gives an efficiency of 0.400.
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Chapter 18 The Laws of Thermodynamics Q.52P
During each cycle a reversible engine absorbs 2500 J of heat from a high-temperature reservoir and performs 2200 J of work. (a) What is the efficiency of this engine? (b) How much heat is exhausted to the low-temperature reservoir during each cycle? (c) What is the ratio, Th/Tc,of the two reservoir temperatures?
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Chapter 18 The Laws of Thermodynamics Q.53P
The operating temperatures for a Carnot engine are Tc and Th = Tc + 55 K. The efficiency of the engine is 11%. Find Tc and Th.
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Chapter 18 The Laws of Thermodynamics Q.54P
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Chapter 18 The Laws of Thermodynamics Q.55P
CE Predict/Explain (a) If the temperature in the kitchen is decreased, is the cost (work needed) to freeze a dozen ice cubes greater than, less than, or equal to what it was before the kitchen was cooled? (b) Choose the best explanation from among the following:
I. The difference intemperature between the inside and the outside of the refrigerator is decreased, and hence less work is required to freeze the ice.
II. The same amount of ice is frozen in either case, which requires the same amount of heat to be removed and hence the same amount of work.
III. Cooling the kitchen means that the refrigerator must do more work, both to freeze the ice cubes and to warm the kitchen.
Solution:
ANSWER:
(a) If the temperature of the kitchen is decreased, then less energy is required to cool the
water. At a lower temperature, the heat extracted from the water can be expelled. Due to this reason, less work done is needed to freeze the a dozen ice cubes.
Therefore, if the temperature in the kitchen is decreased, then the work needed to freeze a dozen ice cubes less than before the kitchen is cooled.
(b) The difference in temperature between the inside and the outside of the refrigerator isdecreased, and hence less work is required to freeze the ice.Using the explanation given in the part (a), this is the correct explanation.
Hence, the best explanation from the given statements is.
Chapter 18 The Laws of Thermodynamics Q.56P
The refrigerator in your kitchen does 480 J of work to remove 110 J of heat from its interior. (a) How much heat does the refrigerator exhaust intothe kitchen? (b) What is the refrigerator’s coefficient of performance?
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Chapter 18 The Laws of Thermodynamics Q.57P
A refrigerator with a coefficient of performance of 1.75 absorbs 3.45 × 104 J of heat from the low-temperature reservoir during each cycle. (a) How much mechanical work is required to operate the refrigerator for a cycle? (b) How much heat does the refrigerator discard to the high-temperature reservoir during each cycle?
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Chapter 18 The Laws of Thermodynamics Q.58P
To keep a room at a comfortable 21.0 °C, a Carnot heat pump does 345 J of work and supplies it with 3240 J of heat. (a) How much heat is removed from the outside air by the heat pump? (b) What is the temperature of the outside air?
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Chapter 18 The Laws of Thermodynamics Q.59P
· · An air conditioner is used to keep the interior of a house at a temperature of 21 °C while the outside temperature is 32 °C. If heat leaks into the house at the rate of 11 kW, and the air conditioner has the efficiency of a Carnot engine, what is the mechanical power required to keep the house cool?
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Chapter 18 The Laws of Thermodynamics Q.60P
A reversible refrigerator has a coefficient of performance equal to 10.0. What is its efficiency?
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Chapter 18 The Laws of Thermodynamics Q.61P
A freezer has a coefficient of performance equal to 4.0. How much electrical energy must this freezer use to produce 1.5 kg of ice at −5.0 °C from water at 15 °C?
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Chapter 18 The Laws of Thermodynamics Q.62P
If a Carnot engine has an efficiency of 0.23, what is its coefficient of performance if it is run backward as a heat pump?
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Chapter 18 The Laws of Thermodynamics Q.63P
CE Predict/Explain (a) If you rub your hands together, does the entropy of the universe increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. Rubbing hands together draws heat from the surroundings, and therefore lowers the entropy.
II. No mechanicalwork is done by the rubbing, and hence the entropydoes not change.
III. The heat produced by rubbing raises the temperature of your hands and the air, which increases the entropy.
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Chapter 18 The Laws of Thermodynamics Q.64P
Predict/Explain (a) An ideal gas is expanded slowly and isothermally. Does its entropy increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. Heat must be added to the gas to maintain a constant temperature, and this increases the entropy of the gas.
II. The temperature of the gas remains constant, which means its entropy also remains constant.
III. As the gas is expanded its temperature and entropy will decrease.
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Chapter 18 The Laws of Thermodynamics Q.65P
Predict/Explain (a) A gas isexpanded reversibly and adiabarically. Does its entropy increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. The process is reversible, and no heat is added to the gas. Therefore, the entropy of the gas remains the same.
II. Expanding the gas gives it more volume to occupy, and this increases its entropy.
III. The gas is expanded with no heat added to it, and hence its temperature will decrease. This, in turn, will lower its entropy.
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Chapter 18 The Laws of Thermodynamics Q.66P
Find the change in entropy when 1.85 kg of water at 100 °C is boiled away to steam at 100 °C.
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Chapter 18 The Laws of Thermodynamics Q.67P
Determine the change in entropy that occurs when 3.1 kg of water freezes at 0 °C.
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Chapter 18 The Laws of Thermodynamics Q.68P
· CEYou heat a pan of water on the stove. Rank the following temperature increases in order of increasing entropy change. Indicate ties where appropriate: A, 25 °C to 35 °C; B, 35 °C to 45 °C; C, 45 °C to 50 °C; and D, 50 °C to 55 °C.
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Chapter 18 The Laws of Thermodynamics Q.69P
On a cold winter’s day heat leaks slowly out of a house at the rate of 20.0 kW. If the inside temperature is 22 °C, and the outside temperature is −14.5 °C, find the rate of entropy increase.
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Chapter 18 The Laws of Thermodynamics Q.70P
· An 88-kg parachutist descends through a vertical height of 380 m with constant speed. Find the increase in entropy produced by the parachutist, assuming the air temperature is 21 °C.
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Chapter 18 The Laws of Thermodynamics Q.71P
IP Consider the air-conditioning system described in Problem 59. (a) Does the entropy of the universe increase, decrease, or stay the same as the air conditioner keeps the imperfectly insulated house cool? Explain. (b) What is the rate at which the entropy of the universe changes during this process?
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Chapter 18 The Laws of Thermodynamics Q.72P
A heat engine operates between a high-temperature reservoir at 610 K and a low-temperaturereservoir at 320 K. In one cycle, the engine absorbs 6400 J of heat from the high-temperature reservoirand does 2200 J of work. What is the net change in entropy as a result of this cycle?
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Chapter 18 The Laws of Thermodynamics Q.73GP
CE An ideal gas is held in an insulated container at the temperature T. All the gas is initially in one-half of the container, with a partition separating the gas from the other half of the container, which is a vacuum. If the partition ruptures, and the gas expands to fill the entire container, is the final temperature greater than, less than, or equal to 77 Explain.
Solution:
The final temperature is unchanged as no work is done by the gas expanding into the vacuum. As the container is insulated, heat does not flow into or out of the system. Therefore, the internal energy and the temperatures of the system remain constant.
Chapter 18 The Laws of Thermodynamics Q.74GP
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Chapter 18 The Laws of Thermodynamics Q.75GP
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Chapter 18 The Laws of Thermodynamics Q.76GP
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Chapter 18 The Laws of Thermodynamics Q.77GP
Heat is added to a 0.14-kg block of ice at 0 °C, increasing its entropy by 87 J/K. How much ice melts?
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Chapter 18 The Laws of Thermodynamics Q.78GP
The heat that goes into a particular Carnot engine is 4.00 times greater than the work it performs. What is the engine’s efficiency?
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Chapter 18 The Laws of Thermodynamics Q.79GP
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Chapter 18 The Laws of Thermodynamics Q.80GP
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Chapter 18 The Laws of Thermodynamics Q.81GP
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Chapter 18 The Laws of Thermodynamics Q.82GP
IP Engine A has an efficiency of 66%. Engine B absorbs the same amount of heat from the hot reservoir and exhausts twice as much heat to the cold reservoir. (a) Which engine has the greater efficiency? Explain. (b) What is the efficiency of engine B?
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Chapter 18 The Laws of Thermodynamics Q.83GP
A freezer with a coefficient of performance of 3.88 is used to convert 1.75 kg of water to ice in one hour. The water starts at a temperature of 20.0 °C, and the ice that is produced is cooled to a temperature of −5.00 °C. (a) How much heat must be removed from the water for this process to occur? (b) How much electrical energy does the freezer use during this hour of operation? (c) How much heat is discarded into the room that houses the freezer?
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Chapter 18 The Laws of Thermodynamics Q.84GP
Suppose 1800 J of heat are added to 3.6 mol of argon gas at a constant pressure of 120 kPa. Find the change in (a) internal energy and (b) temperature for this gas. (c) Calculate the change in volume of the gas. (Assume that the argon can be treated as an ideal monatomic gas.)
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Chapter 18 The Laws of Thermodynamics Q.85GP
Entropy and the Sun The surface of the Sun has a temperature of 5500 °C and the temperature of deep space is 3.0 K. (a) Find the entropy increase produced by the Sun in one day, given that it radiates heat at the rate of 3.80 × 1026 W. (b) How much work could have been done if this heat had been used to run an ideal heat engine?
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Chapter 18 The Laws of Thermodynamics Q.86GP
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Chapter 18 The Laws of Thermodynamics Q.87GP
· · A cylinder with a movable piston holds 2.75 mol of argon at a constant temperature of 295 K. As the gas is compressed isothermally, its pressure increases from 101 kPa to 121 kPa. Find (a) the final volume of the gas, (b) the work done by the gas, and (c) the heat added to the gas.
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Chapter 18 The Laws of Thermodynamics Q.88GP
An inventor claims a new cyclic engine that uses organic grape juice as its working material. According to the claims, the engine absorbs 1250 J of heat from a 1010-K reservoir and performs 1120 J of work each cycle. The waste heat is exhausted to the atmosphere at a temperature of 302 K. (a) What is the efficiency that is implied by these claims? (b) What is the efficiency of a reversible engine operating between the same high and low temperatures used by this engine? (Should you invest in this invention?)
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Chapter 18 The Laws of Thermodynamics Q.89GP
A nonreversible heat engine operates between a high-temperature reservoir at Th = 810 K and a low-temperature reservoir at Tc = 320 K. During each cycle the engine absorbs 660 J of heat from the high-temperature reservoir and performs 250 I of work. (a) Calculate the total entropy change ∆Stot for one cycle. (b) How much work would a reversible heat engine perform in one cycle if it operated between the same two temperatures and absorbed the same amount of heat? (c) Show that the difference in work between the nonreversible engine and the reversible engine is equal to Tc∆Stot.
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Chapter 18 The Laws of Thermodynamics Q.90GP
IP A small dish containing 530 g of water is placed outside for the birds. During the night the outside temperature drops to −5.0 °C and stays at that value for several hours. (a) When the water in the dish freezes at 0 °C, does its entropy increase, decrease, or stay the same? Explain. (b) Calculate the change in entropy that occurs as the water freezes. (c) When the water freezes, is there an entropy change anywhere else in the universe? If so, specify where the change occurs.
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Chapter 18 The Laws of Thermodynamics Q.91GP
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Chapter 18 The Laws of Thermodynamics Q.92GP
Which would make the greater change in the efficiency of a Carnot heat engine: (a) raising the temperature of the high-temperature reservoir by ∆T, or (b) lowering the temperature of the Low-temperature reservoir by ∆T? Justify your answer by calculating the change in efficiency for each of these cases.
Solution:
Chapter 18 The Laws of Thermodynamics Q.93GP
Solution:
Chapter 18 The Laws of Thermodynamics Q.94GP
When a heat Q is added to a monatomic ideal gas at constant pressure, the gas does a work W. Find the ratio, W/Q.
Solution:
Chapter 18 The Laws of Thermodynamics Q.95GP
Solution:
Chapter 18 The Laws of Thermodynamics Q.96GP
A Carnot engine and a Carnot refrigerator operate between the same two temperatures. Show that the coefficient of performance, COP, for the refrigerator is related to the efficiency, e,of the engine by the following expression; COP = (1 – e)/e.
Solution:
Chapter 18 The Laws of Thermodynamics Q.97PP
Suppose an OTEC system operates with surface water at 22 °C and deep water at 4.0 °C. What is the maximum efficiency this system could have?
A. 6.10%
B. 8.20%
C. 9.40%
D. 18.0%
Solution:
Chapter 18 The Laws of Thermodynamics Q.98PP
If 1500 kg of water at 22 °Cis cooled to 4.0 °C, how much energy is released? (For comparison, the energy released in burning a gallon of gasoline is 1.3 × 108 J.)
A. 2.5 × 107 J
B. 1.1 x 108 J
C. 1.4 × 108 J
D. 1.6 × 108 J
Solution:
Chapter 18 The Laws of Thermodynamics Q.99PP
If we go deeper for colder water, where the temperature is only 2.0 °C, what is the maximum efficiency now?
A. 6.78%
B. 9.09%
C. 9.32%
D. 19.0%
Solution:
Chapter 18 The Laws of Thermodynamics Q.100IP
· · IP Referring to Active Example 18–3 Suppose we lower the temperature of the cold reservoir to 295 K; the temperature of the hot reservoir is still 576 K. (a) Is the new efficiency of the engine greater than, less than, or equal to 0.470? Explain. (b) What is the new efficiency? (c) Find the work done by this engine when 1050 J of heat is drawn from the hot reservoir.
Solution:
Chapter 18 The Laws of Thermodynamics Q.101IP
· · IP Referring to Active Example 18–3 Suppose the temperature of the hot reservoir is increased by 16 K, from 576 K to 592 K, and that the temperature of the cold reservoir is also increased by 16 K,from 305 K to 321 K. (a) Is the new efficiency greater than, less than, or equal to 0.470? Explain. (b) What is the new efficiency? (c) What is the change in entropy of the hot reservoir when 1050 J of heat is drawn from it? (d) What is the change in entropy of the cold reservoir?
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