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Two Carnot engines A and B are operated in series. The engine A receives heat from the source at temperature T1 and rejects the heat to the sink at temperature T. The second engine B receives the heat at temperature T and rejects to its sink at temperature T2. For what value of T the efficiencies of the two engines are equal?

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a

T1+T22

b

T1−T22

c

T1T2

d

T1T2

answer is D.

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Detailed Solution

η1=1−TT1&η2=1−T2T⇒1−TT1=1−T2T⇒T=T1T2

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Two Carnot engines A and B are operated in series. The engine A receives heat from the source at temperature T1 and rejects the heat to the sink at temperature T. The second engine B receives the heat at temperature T and rejects to its sink at temperature T2. For what value of T the efficiencies of the two engines are equal?