1. Discontinuous Phase Transition

This type of transition is characterized by a discontinuity in the first derivatives of the thermodynamic potential, here the Gibbs free energy G. The following relations hold for the relevant quantities:

Here Cₚ is the specific heat capacity. A typical characteristic of a discontinuous phase transition is thus the discontinuity in the derivatives of G when the coexistence line is crossed, together with the existence of latent heat ΔQ = TΔS.

In most systems, the discontinuities in entropy ΔS and density Δρ decrease with increasing T₀. This defines a critical temperature T_c at which the first derivatives again become continuous. In the study of critical systems, the reduced temperature t is used to compare different measured quantities relative to the critical temperature:

2. Continuous Phase Transition

The essential properties are:

Furthermore, the second derivatives of the thermodynamic potentials—for example, the specific heat capacity Cᵥ at constant volume and the isothermal compressibility κ_T—exhibit singularities.

A distinctive feature of continuous phase transitions is the universality of the physical properties of different systems near the critical point, including binary fluid systems. These properties are discussed in Section 2.2.