The Carnot coefficient of performance (CCOP) expression for heat pumps operating between four temperature levels is developed from first principles. The four temperature expressions may be used whenever the components are all at different temperatures. The derived Carnot COP expressions for four discrete temperatures become identical to the published ones representing three discrete temperatures when the two intermediate temperatures coalesce into a single value, thereby validating the result.

A heuristic approach is then adopted to analyze some of the possible consequences of fourtemperature cycles, especially regarding improvements in temperature lift and boost.

Units: SI