Heat Pump COP

This formula gives the maximum possible heating COP of an ideal heat pump operating reversibly between a cold reservoir at temperature Tc and a hot reservoir at temperature Th. It comes from the Carnot limit: the pump must deliver heat to the warm side while also obeying the second law of thermodynamics, so its best possible performance depends only on the two absolute temperatures, not on the refrigerant or compressor design. The closer Tc is to Th, the smaller the temperature lift and the larger the theoretical COP; as the hot and cold temperatures move farther apart, the COP falls.

Use this when estimating the theoretical upper bound for a heat pump in heating mode, especially in thermodynamics, HVAC design comparisons, or exam problems on Carnot heat pumps. It is also useful for judging whether a real system’s COP is reasonable relative to the ideal limit.

• Using temperatures in °C instead of K
• Swapping Th and Tc in the denominator
• Using this ideal formula for a real heat pump without noting it is a theoretical maximum