Hot air engine

Thermodynamics
The classical Carnot heat engine
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Potentials Free energy Free entropy Internal energy ${\displaystyle U(S,V)}$ Enthalpy ${\displaystyle H(S,p)=U+pV}$ Helmholtz free energy ${\displaystyle A(T,V)=U-TS}$ Gibbs free energy ${\displaystyle G(T,p)=H-TS}$
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A hot air engine^[1] (historically called an air engine or caloric engine^[2]) is any heat engine that uses the expansion and contraction of air under the influence of a temperature change to convert thermal energy into mechanical work. These engines may be based on a number of thermodynamic cycles encompassing both open cycle devices such as those of Sir George Cayley^[3] and John Ericsson^[4] and the closed cycle engine of Robert Stirling.^[5] Hot air engines are distinct from the better known internal combustion based engine and steam engine.

In a typical implementation, air is repeatedly heated and cooled in a cylinder and the resulting expansion and contraction are used to move a piston and produce useful mechanical work.