Heat Engine

A heat engine is a device that takes in heat and converts part of it into useful work, repeating a cyclic process indefinitely. Every heat engine has three essential parts: a hot reservoir (source) at fixed high temperature $T_H$, supplying heat $Q_H$; a working substance (e.g. water/steam, or a gas) that actually absorbs the heat and does the work; and a cold reservoir (sink) at fixed low temperature $T_L$, absorbing the leftover ejected heat $Q_L$ (a "reservoir" being defined as a system with such large heat capacity that its own temperature does not appreciably change no matter how much heat it gives or takes -- e.g. a lake, or the open atmosphere). By energy conservation over one cycle, $Q_H=W+Q_L$, so $W=Q_H-Q_L$, and the engine's efficiency is $\eta=\dfrac{W}{Q_H}=1-\dfrac{Q_L}{Q_H},$ always strictly less than 1 since some heat is always ejected (Example 8.24: 500 J in, 300 J ejected, gives 40% efficiency). This underlies the Kelvin-Planck statement of the second law: "It is impossible to construct a heat engine that operates in a cycle whose sole effect is to …