Coefficient of Performance

The pragmatic definition of the COP is: COP = (What you Get)/(What you Pay For).
This measure of performance can have a value greater than unity, and it is this fact that makes a heat pump an attractive device. In both the Heat Pump and the Refrigerator the quantity "paid for" is the input work and the "gotten" quantity is heat. For the heat pump, the desired heat is that liberated as the freon working fluid is cooled and condensed in the condensing tank. For the refrigerator, the heat adsorbed in the evaporating tank is the quantity of interest. For the Heat Pump:

COP_HP = m'_C c_p ( T_C - T_S)/ W' = (h₂ - h₃) / (h₂ - h₁)

where c_p is the specific heat of water, m' is the mass flow rate of the water, W' is the power from the electrical source, and the h_i are the enthalies. Also, for the Refrigerator:

COP_REF = m'_Ec_p (T_S - T_E)/ W' = (h₁ - h₄) / (h₂ - h₁)