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Applying NLM along 3 Axis

Two carnot en...

Question

Two carnot engines are connected in series with a common intermediate reservoir and output work of both engines is same. If temperature of source of $1^{s t}$ engine is at $600 K$ and temperature of sink of $2^{n d}$ engine is at $400 K$ . The temperature of intermediate reservoir will be

A

300 K

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B

400 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 $500 K$

Work done by first engine
$W = Q_{1} - Q_{2}$

Work done by second engine $W = Q_{2} - Q_{3}$

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

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

$\frac{Q_{1}}{Q_{2}} + \frac{Q_{3}}{Q_{2}} = 2$

As in carnot cycle heat is proportional to temperature.

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

$T_{2} = \frac{T_{1} + T_{3}}{2} = 500 K$

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