Ehrenfest equations — equations which describe changes in specific heat capacity and derivatives of specific volume in second-order phase transitions. Clausius–Clapeyron relation does not make sense for second-order phase transitions, as both specific heat capacity and specific volume do not change in second-order phase transitions.
Ehrenfest equations are the consequence of continuity of specific entropy and specific volume , which are first derivatives of specific Gibbs free energy - in second-order phase transitions. If we consider specific entropy as a function of temperature and pressure, then its differential is: . As , then differential of specific entropy also is:
Where and are the two phases which transit one into other. Due to continuity of specific entropy, the following holds in second-order phase transitions: . So,
Therefore, the first Ehrenfest equation:
The second Ehrenfest equation is got in a like manner, but specific entropy is considered as function of temperature and specific volume:
The third Ehrenfest equation is got in a like manner, but specific entropy is considered as function of и .
Continuity of specific volume as of function of and gives the fourth Ehrenfest equation:
Derivatives of Gibbs free energy are not always finite. Transitions between different magnetic states of metals can't be described by Ehrenfest equations.
- Sivuhin D.V. General physics course. V.2. Thermodynamics and molecular physics. 2005