# Latent Heat using thermodynamic arguments

Is there a way to demonstrate using thermodynamics(or statistical mechanics) and the fact that $$\frac{\partial G}{\partial P}$$ is discontinuous(in thermodynamic limit) or has a very sharp change at say phase transition temperature, that there is something called Latent heat.

If no, then what more do we need to assume about the process.

Edit 1: I later discovered that $$\frac{\partial G}{\partial T}$$ being discontinuous leads to a discontinuity in entropies which is equal to latent heat by temperature

• Observation of latent heat leads to the mathematical and thermodynamic framework that describes it. Nobody starts with math and thermodynamic concepts, and then attempts to prove that latent heat exists. Physics is about using mathematical models to describe observations ... it is NOT about using math to prove that an observation exists. – David White Aug 30 '19 at 16:21
• You misunderstand my question. Definitely a phase transition with Latent heat has something that can be characterised mathematically. For instance hamiltonian dynamics explains general motion but phase space constraints would constrain the form of hamiltonian. There being a direct relationship between the constraints on phase space and hamiltonian. Similarly a phase transition with late nt heat must constrain the thermodynamic variables in some manner and my question was what kind of constraints on thermodynamic variables lead to the phenomena of latent heat. – Sudipta Nayak Aug 30 '19 at 20:21
• @SudiptaNayak The edit suggests that you may have already found the answer you wanted. I'm posting this comment to corroborate that it really is possible to calculate latent heat using statistical mechanics, given a suitable model. For example, using an expression for the entropy $S(E,V)$ of a van der Waals fluid, and using an ideal gas as a reservoir that can exchange energy and volume (but not particles) with the fluid, we can derive the existence of a first-order "liquid/gas" phase transition in the vdW fluid, and its latent heat can be calculated. – Chiral Anomaly Sep 1 '19 at 1:01