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 $-1$
• B. COP of refrigerator = Inverse of the COP of heat pump
• C. COP of refrigerator = COP of heat pump $+1$
• D. COP of refrigerator = COP of heat pump

Answer 1

The correct option is A COP of refrigerator = COP of heat pump $-1$

Refrigerator:
Coefficient of performance of refrigerator,
$(COP{)}_R=\frac{Coolingeffect:Q_2}{Workinput:W}$
$\frac{Q_2}{W}$

Heat pump:
Coefficient of performance of heat pump,
$(COP{)}_{HP}=\frac{Heatingeffect:Q_1}{Workinput:W}=\frac{Q_1}{W}$
$(COP{)}_{HP}=\frac{Q_1-Q_2+Q_2}{W}$
$(COP{)}_{HP}=\frac{W+Q_2}{W}$ $\because$ $W=Q_1-Q_2$
$(COP{)}_{HP}=1+\frac{Q_2}{W}$
$(COP{)}_{HP}=1+(COP{)}_R$
or $(COP{)}_R=(COP{)}_{HP}-1$