The COP (coefficient of performance) of a heat pump is always Greater than the COP of a refrigerator.

Coefficient of Performance of a Refrigerator

In the case of refrigeration, the prime objective is cooling and this is possible only at the expense of some work. The performance index in the refrigeration cycle is, therefore, expressed (quantified) by a separate parameter called the coefficient of performance (abbreviated as COP).

COP_r = Useful Refrigeration/Total work

In a household refrigerator, the freezer compartment where heat is absorbed by the refrigerant serves as the evaporator and the coils usually behind the refrigerator where heat is dissipated to the surroundings serve as the condenser.

COP_refrigerator = Q₂/(Q₁ − Q₂)

Similarly, the objective of a heat pump is to pump in heat to a chamber for the purpose of heating and this is also possible only when some work is expended.

COP_{Heat pump} = Heat delivered to Chamber/Total work

COP_{Heat pump} = Q₁/(Q₁ − Q₂)

From the expression of COP of refrigerator and heat pump., it is evident that the two are related by the following expressions.

COP_HP = COP_R + 1

From the above equation

The COP of a heat pump is greater than the COP of a refrigerator by unity.

The coefficient of performance of a heat pump is always greater than unity since COP_R is a positive quantity.