Clausius-Clapeyron relation

The Clausius-Clapeyron relation, from the names of the German physicist and mathematician Rudolf Clausius and the French engineer and physicist Benoît Paul Émile Clapeyron (1799-1864), is used to calculate the latent heat L for the phase change of a pure substance as a function of the molar volumes of the substance in the two phases in equilibrium concerned. In general, the two phases are gas/ liquid or gas/solid and we then obtain the following law for the variation in pressure P of the gas as a function of temperature T:

where v1 and v2 are the molar volumes of the substances in the two phases considered, and L is the latent heat of phase change.

This formula has important applications in solid-liquid transitions. It explains why an increase in pressure at a given temperature makes ice melt (e.g. when ice skating) and more generally why liquid water and ice can co-exist in different temperature and pressure conditions.

The Clausius-Clapeyron relation only applies to first order phase transitions. For second order phase transitions the Ehrenfest formulae are needed.