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Define COP of Heat pump and refrigerator and derive the relationship between the two.
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COP of Pump = Ratio of heat transferred to work done.

= Qh/W … i

COP of refrigerater = Ratio of heat removed to work done.

= Ql/W … ii

By first law, Qh = W + Ql

Put in i

(W + QL)/W = 1+ Cop ref (from ii)

So,

COP pump = 1 + COP ref

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