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Two Carnot engines A and B are operated in series. Engine A receives heat from a reservoir at 600 K and rejects heat to a reservoir at temperature T. Engine B receives heat rejected by engine A and in turn rejects it to a reservoir at 100 K. If the efficiencies of the two engines A and B are represented by ηA and ηB respectively, then what is the value of ηA/ηB

1. 12/7
2. 12/5
3. 5/12
4. 7/12

Correct answer: 7/12

Solution

Assuming the two series Carnot engines deliver equal work, the intermediate temperature is T = (600+100)/2 = 350 K. Then eta_A = 1 - 350/600 = 5/12 and eta_B = 1 - 100/350 = 5/7. So eta_A/eta_B = (5/12)/(5/7) = 7/12.

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