Question

A refrigerator has a coefficient of performance of $1.6$. How much work must be supplied to this refrigerator for it to reject $1000kJ$ of heat?

• A. $385kJ$
• B. $627kJ$
• C. $836kJ$
• D. $1000kJ$

Answer 1

The correct option is A $385kJ$

The first law for this cyclic device is $Q_{in}+W_{in}=Q_{out}$ and the definition of the refrigerator COP gives $Q_{in}=COP\left(W_{in}\right)$. Combining the two equations produces $W_{in}=Q_{out}/(1+COP)=1000/2.6=385kJ$.