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Byju's Answer

Standard XII

Physics

Gas Pressure and Temperature

The figure sh...

Question

The figure shows a heat engine (HE) working between two reserviors. The amount of heat $Q_{2}$ rejected by the heat engine is drawn by a heat pump (HP). The heat pump receives the entire work output (W) of the heat engine. If temperature, $T_{1} > T_{3} > T_{2}$ , then the relation between the efficiency $η$ of the heat engine and the coefficient of performance (COP) of the heat pump is

C O P = η^{- 1}

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C O P = η

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C O P = η^{- 1} - 1

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C O P = 1 + η

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Solution

The correct option is A $C O P = η^{- 1}$

$η = \frac{W}{Q_{1}} = \frac{W}{Q_{2} + W}$
$C O P = \frac{Q_{3}}{W}$
$C O P = \frac{Q_{2} + W}{W}$
$C O P = \frac{1}{η} = η^{- 1}$

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The correct option is A COP=η−1 η=WQ1=WQ2+W COP=Q3W COP=Q2+WW COP=1η=η−1

The correct option is A $C O P = η^{- 1}$

$η = \frac{W}{Q_{1}} = \frac{W}{Q_{2} + W}$
$C O P = \frac{Q_{3}}{W}$
$C O P = \frac{Q_{2} + W}{W}$
$C O P = \frac{1}{η} = η^{- 1}$