Consider a refrigerator and a heat pump working on the reversed Carnot cycle between the same temperature limits. Which of the following is correct?
A
COP of refrigerator = COP of heat pump −1
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B
COP of refrigerator = Inverse of the COP of heat pump
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C
COP of refrigerator = COP of heat pump +1
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D
COP of refrigerator = COP of heat pump
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Solution
The correct option is A COP of refrigerator = COP of heat pump −1 Refrigerator:
Coefficient of performance of refrigerator, (COP)R=Coolingeffect:Q2Workinput:W Q2W
Heat pump: Coefficient of performance of heat pump, (COP)HP=Heatingeffect:Q1Workinput:W=Q1W (COP)HP=Q1−Q2+Q2W (COP)HP=W+Q2W∵W=Q1−Q2 (COP)HP=1+Q2W (COP)HP=1+(COP)R
or (COP)R=(COP)HP−1