First-order phase transformation at constant volume: a continuous transition?

TL;DR

This paper investigates a first-order phase transition at constant volume, revealing that unlike at constant pressure, the transition can appear continuous with no divergence in heat capacity, emphasizing the importance of control variables.

Contribution

It demonstrates that first-order transitions at constant volume can be continuous in thermodynamic potentials, challenging traditional views and providing new insights into phase transition behavior.

Findings

Transition extends over a finite temperature range

All thermodynamic potentials and entropy are continuous

Heat capacity shows discrete jumps, not divergence

Abstract

We describe a first-order phase transition of a simple system in a process where the volume is kept constant. We show that, unlike what happens when the pressure is constant, (i) the transformation extends over a finite temperature (and pressure) range, (ii) each and every extensive potential (internal energy $U$, enthalpy $H$, Helmholtz energy $F$ and Gibbs energy $G$), and the entropy $S$, is continuous across the transition, and (iii) the constant-volume heat capacity does not diverge during the transition, only exhibits discrete jumps. These non-intuitive results highlight the importance of controlling the correct variables in order to distinguish between continuous and discontinuous transitions. Additionally, they provide a didactic tool to further discuss the phase transitions phenomena. We apply our results to describe the transition between ice VI and liquid water using thermodynamic information available in the literature.