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