Let for a refrigerator the heat extracted from the cold reservoir is $Q_{2}$ and the work done by the system is $W$ , then the coefficient of performance of refrigerator is :

\frac{Q_{1}}{W}

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\frac{Q_{2}}{W}

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\frac{Q_{2}}{Q_{1} - Q_{2}}

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B

and

C

both

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Solution

The correct option is D $B$ and $C$ both
The coefficient of performance of a refrigerator or heat pump is defined as ratio of heat removed $Q_{2}$ per cycle from inside (reservoir) the refrigerator to the energy $W$ given per cycle for this removal of heat ,
$α = Q_{2} / W$
but $Q_{1} - Q_{2} = W$ from first law of thermodynamics for a cyclic process
where $Q_{1} =$ heat given to the surrounding .
Therefore $α = \frac{Q_{2}}{W} = \frac{Q_{2}}{Q_{1} - Q_{2}}$

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Let for a refrigerator the heat extracted from the cold reservoir is Q2 and the work done by the system is W, then the coefficient of performance of refrigerator is :

Let for a refrigerator the heat extracted from the cold reservoir is $Q_{2}$ and the work done by the system is $W$ , then the coefficient of performance of refrigerator is :