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.

Solution

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

 Solution (source code)