Thermal Efficiency - Heat Pumps and Refrigerators

Heat Pumps and Refrigerators

Heat pumps, refrigerators and air conditioners use work to move heat from a colder to a warmer place, so their function is the opposite of a heat engine. The work energy (W_in) that is applied to them is converted into heat, and the sum of this energy and the heat energy that is moved from the cold reservoir (Q_C) is equal to the total heat energy added to the hot reservoir (Q_H)

Their efficiency is measured by a coefficient of performance (COP). Heat pumps are measured by the efficiency with which they add heat to the hot reservoir, COP_heating; refrigerators and air conditioners by the efficiency with which they remove heat from the cold interior, COP_cooling:

The reason for not using the term 'efficiency' is that the coefficient of performance can often be greater than 100%. Since these devices are moving heat, not creating it, the amount of heat they move can be greater than the input work. Therefore, heat pumps can be a more efficient way of heating than simply converting the input work into heat, as in an electric heater or furnace.

Since they are heat engines, these devices are also limited by Carnot's theorem. The limiting value of the Carnot 'efficiency' for these processes, with the equality theoretically achievable only with an ideal 'reversible' cycle, is:

The same device used between the same temperatures is more efficient when considered as a heat pump than when considered as a refrigerator:

This is because when heating, the work used to run the device is converted to heat and adds to the desired effect, whereas if the desired effect is cooling the heat resulting from the input work is just an unwanted byproduct.