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NEET 2013 · Heat Engines, Refrigerators & Second Law

Heat Engines, Refrigerators & Second Law question from NEET 2013

Q73NEET 2013Medium

Heat Engines, Refrigerators & Second Law

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 values of T the efficiencies of the two engines are equal

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Answer: (c)

$\eta_A = 1 - \frac{T}{T_1}$ , $\eta_B = 1 - \frac{T_2}{T}$ .
Equal efficiencies: $\frac{T}{T_1} = \frac{T_2}{T} \Rightarrow T^2 = T_1T_2$ .
So the answer is (c) $\sqrt{T_1T_2}$ .

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