Ehrenfest classification of phase transitions

Summary

The Ehrenfest classification sorts phase transitions by the lowest derivative of the free energy that is discontinuous at the transition. In a first-order transition the entropy or the volume jumps, so there is a latent heat. In a second-order transition these are continuous, but second derivatives such as the heat capacity jump. The scheme is the origin of the words "first-order" and "second-order", though modern usage distinguishes only first-order and continuous transitions.