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Efficiency of Machines

Two Carnot en...

Question

Two Carnot engines $A$ and $B$ are operated in series. The first one, $A$ , receives heat at $T_{1} (= 600 K)$ and rejects to a reservoir at temperature $T_{2}$ . The second engine $B$ receives heat rejected by the first engine and, in turn, rejects to a heat reservoir at $T_{3} (= 400 K)$ . Calculate the temperature $T_{2}$ if the work outputs of the two engines are equal

A

400 K

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B

300 K

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C

500 K

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D

600 K

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Solution

The correct option is C $500 K$
Diagram

As given, work output of both the engines are equal.

$W_{1} = W_{2}$

$Δ T_{1} = Δ T_{2}$

$T_{3} - T_{2} = T_{2} - T_{1}$

$2 T_{2} = T_{1} + T_{3}$

$T_{2} = 500 K$

Final answer: (c)

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