First slide

Heat Engine; Carnot Engine and refrigerator

Question

A refrigerator with coefficient of performance $\frac{1}{3}$ releases 200 J of heat to a hot reservoir. Then the work done on the working substance is

Moderate

A

$\frac{100}{3} J$
B

$100 J$
C

$\frac{200}{3} J$
D

$150 J$

Solution

The coefficient of performance of a refrigerator is given by $β = \frac{Q_{2}}{W} = \frac{Q_{2}}{Q_{1} - Q_{2}}$
Substituting the given values, we get
$\begin{array}{l} \frac{1}{3} = \frac{Q_{2}}{200 - Q_{2}} or 200 - Q_{2} = 3 Q_{2} \\ or 4 Q_{2} = 200 or Q_{2} = \frac{200}{4} J = 50 J \\ ∴ W = Q_{1} - Q_{2} = 200 J - 50 J = 150 J \end{array}$

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