Carnot cycle

The Carnot cycle is the most theoretically efficient thermodynamic transformation cycle, made up of two isotherms and two adiabatic transformations.

1. $ab$ is constant temperature $T_{2}$ transformation that absorbs heat $Q_{2}$ from a hot heat reservoir.
2. $bc$ is an adiabatic transformation that lowers temperature from $T_{2}$ to $T_{1}$.
3. $cd$ is another constant temperature $T_{1}$ transformation that emits heat $Q_{1}$ to a cold reservoir.
4. $da$ is another adiabatic transformation that increases temperature from $T_{1}$ to $T_{2}$.

Since $\Delta U=0$ for a cycle, the first law of thermodynamics tells us that $\Delta W=\Delta Q$. The work done by this cycle is $W=\Delta Q=Q_{2}-Q_{1}$. So, in a cycle, heat $Q_{2}$ is taken from the hot reservoir, some work $W$ is done and "waste heat" $Q_{1}$ is ejected into the cold reservoir. The thermal efficiency $\eta$ of this process is

This cycle is reversible, so it can be turned into a refrigerator by inverting it.