Coefficient of performance of the cooling machine

A cooling machine is a machine that takes heat from a low-temperature place, then transfers it to a high-temperature area. For this process to happen, the machine must do the work, because the heat naturally flows from high temperature to low temperature. This is by Clausius’s statement:

It is impossible for a cooling machine to transfer heat from a low-temperature place to a high-temperature place, without work (Second law of thermodynamics – Clausius statement).

The machine works (W) to transfer heat, from low temperature (QL) to high temperature (QH). Based on conservation of energy, QL + W = QH.

If the heat engine uses the term efficiency, then the refrigerant uses the term coefficient of performance (CP). The coefficient of performance (CP) of refrigerant is the ratio between heat transferred from low temperature (QL) to work (W), which is done to transfer heat.

Coefficient of performance cooling machine 1

Ideal cooling machine’s coefficient of performance :

Coefficient of performance cooling machine 2
TL = low temperature, TH = high temperature