Conversely, the useful energy for a [[Refrigeration Cycle|refrigeration cycle]] or [[Heat Pump|heat pump]] is to move [[Heat|heat]], while the input is [[Work|work]]. When refrigerating we use a coefficient of performance, $\beta$. Likewise, when heating a space with a heat pump we use a similar coefficient of performance, $\beta^\prime$. $\beta=\dfrac{\text{Benefit}}{\text{Cost}}​=\dfrac{\dot{Q}_{cooling}}{\dot{W}_{compressor}}$ $\beta^\prime=\dfrac{\text{Benefit}}{\text{Cost}}​=\dfrac{\dot{Q}_{heating}}{\dot{W}_{compressor}}$