Answer
See the detailed answer below.
Work Step by Step
a) Find the work done in one cycle of a refrigerator if you know that its coefficient of performance is 4 and it exhausts 100 J of heat in each cycle.
b) Solving for $W_{in}$;
$$W_{in}=\dfrac{Q_C}{4}$$
where $Q_C=Q_H-W_{in}$
$$W_{in}=\dfrac{Q_H-W_{in}}{4}$$
$$4W_{in}= Q_H-W_{in} $$
$$5W_{in}= Q_H$$
$$ W_{in}= \dfrac{Q_H}{5}=\dfrac{100}{5}=\color{red}{\bf 20}\;\rm J$$
