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

Question

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

Infinity Learn · Accepted Answer

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,  η$$A=1-TT1$$  For engine B,  η$$B=1-T2T$$  As per question, η$$A=$$ηB ∴  $$1-TT1=1-T2T$$ ⇒$$TT1=T2T$$ or $$T2=T1T2$$   or $$T=T1T2$$

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