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Question

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=Q1Q2+Q2W
(COP)HP=W+Q2W W=Q1Q2
(COP)HP=1+Q2W
(COP)HP=1+(COP)R
or (COP)R=(COP)HP1

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