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Q.

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

T1T2

c

T1T2

d

T1+T22

answer is C.

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Detailed Solution

Efficiency of a Carnot engine  η=1-T2T1  where T1 is the temperature of source and T2 is the temperature of sink respectively  For engine A,  ηA=1-TT1  For engine B,  ηB=1-T2T  As per question, ηA=ηB ∴  1-TT1=1-T2T ⇒TT1=T2T or T2=T1T2   or T=T1T2
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