First slide

Heat Engine; Carnot Engine and refrigerator

Question

An ideal heat engine has an efficiency $η$ . The coefficient of performance of the engine when driven backward will be

Easy

A

$1 - (1 / η)$
B

$η (1 - η)$
C

$(1 / η) - 1$
D

$1 / (1 - η)$

Solution

$η = 1 - \frac{T_{2}}{T_{1}}$
$β = \frac{T_{2}}{T_{1} - T_{2}} = \frac{T_{2} / T_{1}}{1 - (T_{2} / T_{1})} = \frac{(1 - η)}{η} = \frac{1}{η} - 1$

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