Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 35B / a / Solution

At a first-order transition the Gibbs free energy is continuous but a first derivative such as entropy or volume jumps; there is latent heat. At a second-order transition the first derivatives are continuous while a second derivative, such as heat capacity or susceptibility, is discontinuous or divergent, and there is no latent heat.