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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

Efficiency of engine A, η1=1−TT1 & Efficiency of engine B, η2=1−T2T Here, η1=η2 ∴TT1=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?