1. D. |Q| is the same for all three paths.
A system can be taken from state a to state b along any of the three paths shown in the p-V diagram. If state b has greater internal energy than state a, along which path is the absolute value |Q| of the heat transfer the greatest?
path 1
path 2
path 3
D. |Q| is the same for all three paths.
E. Not enough information is given to decide.
Answer: A

2. A19.1
A system can be taken from state a to state b along any of the three paths shown in the p-V diagram. If state b has greater internal energy than state a, along which path is the absolute value |Q| of the heat transfer the greatest?
path 1
path 2
path 3
D. |Q| is the same for all three paths.
E. Not enough information is given to decide.

3. Q19.2
A system can be taken from state a to state b along any of the three paths shown in the p-V diagram. If state b has greater internal energy than state a, along which path is there a net flow of heat out of the system?
path 1
path 2
path 3
D. all of paths 1, 2, and 3
E. none of paths 1, 2, or 3
Answer: E

4. A19.2
A system can be taken from state a to state b along any of the three paths shown in the p-V diagram. If state b has greater internal energy than state a, along which path is there a net flow of heat out of the system?
path 1
path 2
path 3
D. all of paths 1, 2, and 3
E. none of paths 1, 2, or 3

5. • via state b (at upper left), or • via state d (at lower right)
Q19.3
This p-V diagram shows two ways to take a system from state a (at lower left) to state c (at upper right):
• via state b (at upper left), or • via state d (at lower right)
For which path is W > 0?
A. path abc only
B. path adc only
C. both path abc and path adc
D. neither path abc nor path adc
E. The answer depends on what the system is made of.
Answer: C

6. A19.3
This p-V diagram shows two ways to take a system from state a (at lower left) to state c (at upper right):
• via state b (at upper left), or • via state d (at lower right)
For which path is W > 0?
A. path abc only
B. path adc only
C. both path abc and path adc
D. neither path abc nor path adc
E. The answer depends on what the system is made of.

7. A. is greater than the amount of work done by the gas.
Q19.4
In an isothermal expansion of an ideal gas, the amount of heat that flows into the gas
A. is greater than the amount of work done by the gas.
B. equals the amount of work done by the gas.
C. is less than the amount of work done by the gas, but greater than zero.
D. is zero.
E. is negative (heat flows out of the gas).
Answer: B

8. A19.4
In an isothermal expansion of an ideal gas, the amount of heat that flows into the gas
A. is greater than the amount of work done by the gas.
B. equals the amount of work done by the gas.
C. is less than the amount of work done by the gas, but greater than zero.
D. is zero.
E. is negative (heat flows out of the gas).

9. Q19.5
You put a flame under a piece of metal, raising the temperature of the metal and making the metal expand. The metal is surrounded by air. What are the signs of ∆U, Q, and W for the metal in this process?
A. ∆U > 0, Q > 0, W > 0
B. ∆U < 0, Q > 0, W > 0
C. ∆U > 0, Q > 0, W < 0
D. ∆U < 0, Q > 0, W < 0
E. None of these
Answer: A

10. A19.5
You put a flame under a piece of metal, raising the temperature of the metal and making the metal expand. The metal is surrounded by air. What are the signs of ∆U, Q, and W for the metal in this process?
A. ∆U > 0, Q > 0, W > 0
B. ∆U < 0, Q > 0, W > 0
C. ∆U > 0, Q > 0, W < 0
D. ∆U < 0, Q > 0, W < 0
E. None of these

11. Q19.6
When you are exercising on a stationary bicycle or rowing machine, what are the signs of ∆U, Q, and W for your body?
A. ∆U > 0, Q = 0, W > 0
B. ∆U < 0, Q = 0, W > 0
C. ∆U < 0, Q > 0, W > 0
D. ∆U < 0, Q < 0, W > 0
E. None of these
Answer: D

12. A19.6
When you are exercising on a stationary bicycle or rowing machine, what are the signs of ∆U, Q, and W for your body?
A. ∆U > 0, Q = 0, W > 0
B. ∆U < 0, Q = 0, W > 0
C. ∆U < 0, Q > 0, W > 0
D. ∆U < 0, Q < 0, W > 0
E. None of these

13. Q19.7
An ideal gas is taken around the cycle shown in this p-V diagram, from a to b to c and back to a. Process b c is isothermal. For this complete cycle,
A. Q > 0, W > 0, U = 0
B. Q < 0, W > 0, U = 0
C. Q = 0, W > 0, U < 0
D. Q = 0, W < 0, U > 0
E. Q > 0, W > 0, U > 0
Answer: A

14. A19.7
An ideal gas is taken around the cycle shown in this p-V diagram, from a to b to c and back to a. Process b c is isothermal. For this complete cycle,
A. Q > 0, W > 0, U = 0
B. Q < 0, W > 0, U = 0
C. Q = 0, W > 0, U < 0
D. Q = 0, W < 0, U > 0
E. Q > 0, W > 0, U > 0

15. Q19.8
An ideal gas is taken around the cycle shown in this p-V diagram, from a to b to c and back to a. Process b c is isothermal. For process a b,
A. Q > 0, ∆U > 0
B. Q > 0, ∆U = 0
C. Q = 0, ∆U > 0
D. Q = 0, ∆U < 0
E. Q < 0, ∆U < 0
Answer: A

16. A19.8
An ideal gas is taken around the cycle shown in this p-V diagram, from a to b to c and back to a. Process b c is isothermal. For process a b,
A. Q > 0, ∆U > 0
B. Q > 0, ∆U = 0
C. Q = 0, ∆U > 0
D. Q = 0, ∆U < 0
E. Q < 0, ∆U < 0

17. Q19.9
An ideal gas is taken around the cycle shown in this p-V diagram, from a to b to c and back to a. Process b c is isothermal. For process b c,
A. Q > 0, ∆U > 0
B. Q > 0, ∆U = 0
C. Q = 0, ∆U > 0
D. Q = 0, ∆U < 0
E. Q < 0, ∆U < 0
Answer: B

18. A19.9
An ideal gas is taken around the cycle shown in this p-V diagram, from a to b to c and back to a. Process b c is isothermal. For process b c,
A. Q > 0, ∆U > 0
B. Q > 0, ∆U = 0
C. Q = 0, ∆U > 0
D. Q = 0, ∆U < 0
E. Q < 0, ∆U < 0

19. Q19.10
An ideal gas is taken around the cycle shown in this p-V diagram, from a to b to c and back to a. Process b c is isothermal. For process c a,
A. Q > 0, ∆U > 0
B. Q > 0, ∆U = 0
C. Q = 0, ∆U > 0
D. Q = 0, ∆U < 0
E. Q < 0, ∆U < 0
Answer: E

20. A19.10
An ideal gas is taken around the cycle shown in this p-V diagram, from a to b to c and back to a. Process b c is isothermal. For process c a,
A. Q > 0, ∆U > 0
B. Q > 0, ∆U = 0
C. Q = 0, ∆U > 0
D. Q = 0, ∆U < 0
E. Q < 0, ∆U < 0

21. C. less than Q12, but greater than zero. D. zero.
An ideal gas begins in a thermodynamic state a. When the temperature of the gas is raised from T1 to a higher temperature T2 at a constant volume, a positive amount of heat Q12 flows into the gas. If the same gas begins in state a and has its temperature raised from T1 to T2 at a constant pressure, the amount of heat that flows into the gas is
A. greater than Q12.
B. equal to Q12.
C. less than Q12, but greater than zero.
D. zero.
E. negative (heat flows out of the system).
Answer: A

22. A19.11
An ideal gas begins in a thermodynamic state a. When the temperature of the gas is raised from T1 to a higher temperature T2 at a constant volume, a positive amount of heat Q12 flows into the gas. If the same gas begins in state a and has its temperature raised from T1 to T2 at a constant pressure, the amount of heat that flows into the gas is
A. greater than Q12.
B. equal to Q12.
C. less than Q12, but greater than zero.
D. zero.
E. negative (heat flows out of the system).

23. Q19.12
An ideal gas is taken around the cycle shown in this p-V diagram, from a to c to b and back to a. Process c b is adiabatic. For process c b,
A. Q > 0, W > 0, ∆U = 0
B. Q > 0, W > 0, ∆U > 0
C. Q = 0, W > 0, ∆U < 0
D. Q = 0, W < 0, ∆U > 0
E. Q < 0, W < 0, ∆U = 0
Answer: D

24. A19.12
An ideal gas is taken around the cycle shown in this p-V diagram, from a to c to b and back to a. Process c b is adiabatic. For process c b,
A. Q > 0, W > 0, ∆U = 0
B. Q > 0, W > 0, ∆U > 0
C. Q = 0, W > 0, ∆U < 0
D. Q = 0, W < 0, ∆U > 0
E. Q < 0, W < 0, ∆U = 0

25. D. either A or B, depending on the ratio of V2 to V1.
Q19.13
When an ideal gas is allowed to expand isothermally from volume V1 to a larger volume V2, the gas does an amount of work equal to W12. If the same ideal gas is allowed to expand adiabatically from volume V1 to a larger volume V2, the gas does an amount of work that is
A. less than W12.
B. greater than W12.
C. equal to W12.
D. either A or B, depending on the ratio of V2 to V1.
E. any of A, B, or C, depending on the ratio of V2 to V1.
Answer: A

26. A19.13
When an ideal gas is allowed to expand isothermally from volume V1 to a larger volume V2, the gas does an amount of work equal to W12. If the same ideal gas is allowed to expand adiabatically from volume V1 to a larger volume V2, the gas does an amount of work that is
A. less than W12.
B. greater than W12.
C. equal to W12.
D. either A or B, depending on the ratio of V2 to V1.
E. any of A, B, or C, depending on the ratio of V2 to V1.

27. Q-RT19.1
An ideal gas is taken around the cycle shown in this p-V diagram, from a to b to c and back to a. Process b c is isothermal. Rank the following processes in order of the value of the internal energy ∆U of the ideal gas in the process, from most positive to most negative.
A. a b
B. b c
C. c a
Answer: ABC

28. A-RT19.1
An ideal gas is taken around the cycle shown in this p-V diagram, from a to b to c and back to a. Process b c is isothermal. Rank the following processes in order of the value of the internal energy ∆U of the ideal gas in the process, from most positive to most negative.
A. a b
B. b c
C. c a
Answer: ABC

29. Q-RT19.2
An ideal gas is taken around the cycle shown in this p-V diagram, from a to b to c and back to a. Process b c is isothermal. Rank the following processes in order of the value of the work W done by the ideal gas in the process, from most positive to most negative.
A. a b
B. b c
C. c a
Answer: BAC

30. A-RT19.2
An ideal gas is taken around the cycle shown in this p-V diagram, from a to b to c and back to a. Process b c is isothermal. Rank the following processes in order of the value of the work W done by the ideal gas in the process, from most positive to most negative.
A. a b
B. b c
C. c a
Answer: BAC

31. Q-RT19.3
An ideal gas is taken around the cycle shown in this p-V diagram, from a to b to c and back to a. Process b c is isothermal. Rank the following processes in order of the value of the heat Q into the ideal gas in the process, from most positive to most negative.
A. a b
B. b c
C. c a
Answer: BAC

32. A-RT19.3
An ideal gas is taken around the cycle shown in this p-V diagram, from a to b to c and back to a. Process b c is isothermal. Rank the following processes in order of the value of the heat Q into the ideal gas in the process, from most positive to most negative.
A. a b
B. b c
C. c a
Answer: BAC