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Question

A reversible engine exchanges heat from three thermal reservoirs A, B and C at 1000 K, 800 K and 450 K respectively. If the engine receives 500 kJ from A and 400 kJ from B then what is the heat exchanged from thermal reservoir C?

A

450 kJ rejected to thermal reservoir C

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B

350 kJ rejected to thermal reservoir C

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C

250 kJ rejected to thermal reservoir C

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D

200 kJ rejected to thermal reservoir C

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Solution

The correct option is A 450 kJ rejected to thermal reservoir C
$Σ \frac{d Q}{T} = 0$

$\Rightarrow \frac{Q_{1}}{1000} + \frac{Q_{2}}{800} - \frac{Q_{3}}{450} = 0$

$\Rightarrow \frac{500}{1000} + \frac{400}{800} - \frac{Q_{3}}{450} = 0$
$Q_{3} = 450 k J$

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