The performance of a heat pump degrades (i. e., its COP decreases) as the temperature of the heat source decreases. This makes using heat pumps at locations with severe weather conditions unattractive. Consider a house that is heated and maintained at 26°C by a heat pump during the winter. What is the maximum COP for the heat pump if heat is extracted the out door air at 10 C?

COP_max = 18.69

Explanation:

We are given;

Heated space temperature; T_H = 26°C = 273K + 26 = 299K

Temperature at which heat is extracted; T_L = 10°C = 273 + 10 = 283K

Now the Coefficient of performance (COP) of a heat pump will be a maximum when the heat pump operates in a reversible manner. The COP of a reversible heat pump depends on the temperature limits in the cycle only and is determined by the formula;

COP_max = 1 / (1 - (T_L/T_H))

Thus,

COP_max = 1 / (1 - (283/299))

COP_max = 1 / (1 - 0.9465)

COP_max = 1/0.0535 = 18.69