The Carnot [[Cycle|cycle]] is a theoretical [[Heat Engine|heat engine]] or [[Heat Pump|heat pump]] which is constructed solely of [[Reversibility|reversible]] processes. As such the Carnot cycle is the cycle with the highest possible [[Efficiency|efficiency]]. The Carnot cycle operates between two thermal reservoirs, a high [[Temperature|temperature]] reservoir of temperature $T_H$, and a low temperature thermal reservoir of temperature $T_L$. Application of the [[First Law of Thermodynamics|first law]] on a Carnot cycle shows that [[Work|work]] is the difference between [[Heat|heat]] flow in and heat flow out of the cycle.
$W=Q_H-Q_L$
Heat Engine:
![[heat_engine.png|center|300]]
Heat Pump:
![[heat_pump.png|center|300]]
The efficiency of a Carnot cycle is solely dependent on the temperature of the relevant thermal reservoirs, $T_L$ and $T_H$. For any real cycle the thermal efficiency or [[Coefficient of Performance|coefficient of performance]] must be less than the Carnot efficiency/coefficient of performace.
$\eta<\eta_{rev}$
$\beta<\beta_{rev}$
$\beta^\prime<\beta^\prime_{rev}$
In a Carnot cycle the heat transferred to/from the thermal reservoirs is directly related to the temperature of the reservoirs, in Kelvin.
$\left(\dfrac{Q_H}{Q_L}\right)_{rev}=\dfrac{T_H}{T_L}$
Therefore the Carnot cycle efficiency/COP can be calculated using the temperatures of the thermal reservoirs.
$\eta=\dfrac{W}{Q_H}=\dfrac{T_H−T_L}{T_H}$
$\beta=\dfrac{Q_L}{W}=\dfrac{T_L}{T_H−T_L}$
$\beta^\prime=\dfrac{Q_H}{W}=\dfrac{T_H}{T_H−T_L}$