Discussion
For a refrigerator absorbing heat QL from a cold region and rejecting heat QH to a hot region, the coefficient of performance is written as
Answer: A
The coefficient of performance is \(\frac{Q_{L}}{Q_{H} - Q_{L}}\).
A refrigerator's useful effect is the heat removed from the cold space, \(Q_{L}\), and the cost is the net work input, which by the first law is \(W = Q_{H} - Q_{L}\). So \(COP_{R} = Q_{L}/(Q_{H} - Q_{L})\).
\(Q_{H}/(Q_{H} - Q_{L})\) is the COP of a heat pump, whose useful effect is the heat delivered. \((Q_{H} - Q_{L})/Q_{L}\) inverts the refrigerator COP, and \(Q_{L}/Q_{H}\) does not involve the work at all.
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