For cycle devices, the normal sign conventions (heat in and work out are positive) are ignored. Instead, the signs of heat and work are defined such that , and net work are normally positive. The pictures below show the directions of positive heat fluxes and work rates for a heat engine as compared to a heat pump (or refrigeration cycle).
The first law for a cycle:
The Kelvin-Planck Statement: Any working heat engine must dump some waste heat to a lower temperature than the input heat is provided at.
The Clausius Statement: Any working heat pump must have positive work going in.
Thermal efficiency:
Refrigeration coefficient of performance:
Heating heat pump coefficient of performance
:
Ideal gas Carnot cycle: