Refrigerator And Coefficient Of Performance

The coefficient of performance of a refrigerator rates how much heat it removes from the cold space per unit of work input, defined as $\text{COP}=\frac{Q_C}{W}$. Here $Q_C=360\text{ J}$ is the heat drawn from the food and $W=120\text{ J}$ is the work supplied, so $\text{COP}=360/120=3$. The value 4 would arise from dividing the heat rejected to the room, $Q_H=Q_C+W=480\text{ J}$, by the work, which defines a heat pump's COP rather than a refrigerator's. The value 0.33 inverts the ratio, treating it like engine efficiency. The value 2 has no basis in the given numbers. Unlike efficiency, the COP of a refrigerator can exceed one because the work merely pumps heat rather than creating it. By energy conservation the compressor delivers $Q_H=Q_C+W=480\text{ J}$ to the room each cycle, which is why a working refrigerator warms the kitchen overall even as it cools its interior. The theoretical ceiling on COP is set by the Carnot expression $T_C/(T_H-T_C)$, so smaller temperature differences allow far higher performance. As a magnitude check, a good refrigerator moves several joules of heat per joule of electricity, so a COP of 3 is entirely realistic for household appliances.