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  • A refrigerator operates on a Carnot cycle between two reservoirs at temperatures <img alt="\mathrm{T_{\text {hot }}=300 \mathrm{~K}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%

A refrigerator operates on a Carnot cycle between two reservoirs at temperatures \mathrm{T_{\text {hot }}=300 \mathrm{~K}} and \mathrm{T_{\text {cold }}=200 \mathrm{~K}.}Calculate the coefficient of performance (\mathrm{COP}) of the refrigerator.

Option: 1

3


Option: 2

1


Option: 3

20


Option: 4

80


Answers (1)

best_answer

The coefficient of performance (COP) of a refrigerator is given by the formula:
\mathrm{\mathrm{COP}=\frac{Q_{\text {cold }}}{W} }

where \mathrm{Q_{\text {cold }} } is the heat removed from the cold reservoir and W is the work done by the refrigerator.
In a Carnot cycle, the efficiency \mathrm{(\eta) } is given by:
\mathrm{\eta=1-\frac{T_{\text {cold }}}{T_{\text {hot }}} }
Since the COP is the inverse of the efficiency, we have:
\mathrm{\mathrm{COP}=\frac{1}{\eta}=\frac{T_{\mathrm{hot}}}{T_{\mathrm{hot}}-T_{\mathrm{cold}}} }
Substitute the given values:
\mathrm{ \mathrm{COP}=\frac{300 \mathrm{~K}}{300 \mathrm{~K}-200 \mathrm{~K}}=\frac{300 \mathrm{~K}}{100 \mathrm{~K}}=3 }
Therefore, the coefficient of performance of the refrigerator is COP =3.

Posted by

Ritika Kankaria

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