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Heat Engines

Two Carnot en...

Question

Two Carnot engines A and B are operated in succession. The first one, A receives heat from a source at $T_{1}$ = 800 K and rejects to a sink at $T_{2} =$ K. The second engine B receives heat rejected by the first engine and rejects to another sink at $T_{3} =$ 300K. If the efficiencies of two engines are equal, then the value of $T_{2}$ is

A

489.4K

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B

469.4K

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C

449.4K

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D

429.4K

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Solution

The correct option is A 489.4K
Efficiency, $η = 1 - \frac{T_{2}}{T_{1}} = 1 - \frac{T_{3}}{T_{2}}$
where $T_{1} =$ temperature of first source, $T_{2} =$ temperature of first sink $=$ temperature of second source,
$T_{3} =$ temperature of second sink
$\Rightarrow T_{2} = \sqrt{300 \times 800} K = 489.4 K$

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Two Carnot engines A and B are operated in succession. The first one, A receives heat from a source at $T_{1}$ = 800 K and rejects to sink at $T_{2}$ K. The second engine B receives heat rejected by the first engine and rejects to another sink at $T_{3}$ = 300 K. If the work outputs of two engines are equal, then the value of $T_{2}$ is

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