1. $W{}_D>W{}_A=W{}_B>W{}_C\text{.}{W}_{\text{out}}=Q_{\text{H}}-Q_{\text{C}}$.

2. b. Energy conservation requires $Q_{\text{H}}=Q_{\text{C}}+W_{\text{in}}$. The refrigerator will exhaust more heat out the back than it removes from the front. A refrigerator with an open door will heat the room rather than cool it.

3. c. $W_{\text{out}}=\text{a}\text{r}\text{e}\text{a}\text{i}\text{n}\text{s}\text{i}\text{d}\text{e}\text{t}\text{r}\text{i}\text{a}\text{n}\text{g}\text{l}\text{e}=1000\text{J}\text{.}\eta =W_{\text{out}}/Q_{\text{H}}=\left(1000\text{J}\right)/\left(4000\text{J}\right)=\mathrm{0.25.}$

4. To conserve energy, the heat $Q_{\text{H}}$ exhausted to the hot reservoir needs to be $Q_{\text{H}}=Q_{\text{C}}+W_{\text{in}}=40\text{J}+10\text{J}=50\text{J}$, not 30 J.

5. b. The efficiency of this engine would be $\eta =W_{\text{out}}/Q_{\text{H}}=0.6$. That exceeds the Carnot efficiency ${\eta }_{\text{Carnot}}=1-T_{\text{C}}/T_{\text{H}}=0.5$, so it is not possible.

1. 0.33

3. $6.4\text{kg}\text{/}\text{s}$

5.

1. 200 J

2. 250 J

7.

1. 13 kJ/cycle

2. 50 kJ

9.

11. $800{\text{cm}}^3$

13.

1. 30 J, 145 J

2. 21%

15. 285 J

17. 0.24

19.

1. 5.0 kW

2. 1.7

21.

1. 64 J

2. 1.6

23.

1. Engine c violates the first law.

2. Engine b violates the second law.

25.

1. 40%

2. $215\text{°}\text{C}$

27. $135\text{°}\text{C}$

29. 5.0 kJ

31.

1. 6.3

2. 32 W

3. 0.23 kW

33.

1. 0 J/K

2. $-1.3\text{J}\text{/}K$

3. 1.3 J/K

37.

• a.

  

  Full Alternative Text

• b. 10 J

• c. 0.13

39. 83 W

41.

1. $3.6\times {10}^6\text{J}$

2. $3.0\times {10}^5\text{J}$

43. 8.3%

45. 6.4 J

47.

1. 2.5 kW

2. $45

49. 57 g

51.

1. 48 m

2. 32%

53. 37%

55.

1. 	$\text{Δ}E{}_{th}\left(J\right)$	$W{}_s\left(J\right)$	Q (J)
   $1\to 2$	13.93	3.04	16.97
   $2\to 3$	$-10.13$	0	$-10.13$
   $3\to 1$	$-3.80$	$-1.52$	$-5.32$
   $\text{Net}$	0	1.52	1.52

2. 9.0%

3. 13 W

57.

1. 1.10 kW

2. 9.01%

59.

1. $1000{\text{cm}}^3$, 696 kPc, 522 K

2. 	$\text{Δ}E{}_{th}\left(J\right)$	$W{}_s\left(J\right)$	Q (J)
   $1\to 2$	741.1	0	741.1
   $2\to 3$	$-741.1$	741.1	0
   $3\to 1$	0	$-554.5$	$-554.5$
   $\text{Net}$	0	186.6	186.6

3. 25%

61.

1. $4\to 3\text{,\hspace{0.17em}}3\to 2$

2. $Q_{\text{H}}$

3. $Q_{\text{H}}=22.28\times {10}^5\text{J}\text{,}{Q}_{\text{C}}=26.33\times {10}^5\text{J}$

4. $W_{\text{in}}=4.05\times {10}^5\text{J}$

5. No

63.

1. $T_1=1.6\text{ kK, }{T}_2=2.4\text{ kK, }{T}_3=6.5\text{ kK}$

2. 	$\text{Δ}E{}_{th}\left(J\right)$	$W{}_s\left(J\right)$	Q (J)
   $1\to 2$	327	$-327$	0
   $2\to 3$	1692	677	2369
   $3\to 1$	$-2019$	0	$-2019$
   $\text{Net}$	0	350	350

65.

2. $1.1\times {10}^3\text{°}\text{C}$

67.

2. $Q_{\text{C}}=80\text{J}$

69. $5.3\times {10}^4\text{J}$

71.

1. 1.19

2. 227 W

73.

• c.

  

  Full Alternative Text