Which of the following can be coefficient of performance of refrigerator?

1

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0.5

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9

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all of these

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Solution

The correct options are
A $1$
B $9$
Refrigerator is a power absorbing device.

$C O P$ is nothing but the efficiency in different words.

$C O P = \frac{I n p u t}{O u t p u t} = \frac{(D e s i r e d e f f e c t)}{W o r k I n p u t}$

for a refrigerator working between two temperature limits, $T_{1}$ (higher) and $T_{2}$ (lower)

Refrigerator will be throwing the heat taking from the $T_{2}$ ( Storage Space) to $T_{1}$ (Room or any exhaust at higher temperature).

$C O P =$ (Heat taken from the Storage Space)/(Work Input) = $\frac{Q_{2}}{W}$ , , where W in work input.

as $Q_{1} = Q_{2} + W$

so, $C O P = \frac{Q_{2}}{(Q_{1} - Q_{2})}$

applying the reversible refrigerator theory, Q can be replaced by temperature (100% Second Law Efficiency).

so, $C O P = \frac{T_{2}}{(T_{1} - T_{2})}$

as, $T_{1} > T_{2}$

so, $C O P > 1$

Hence, A and C are the correct options.

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0.5.

A refrigerator is to maintain eatables kept inside at 9°C. If room temperature is 36° C, calculate the coefficient of performance.

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