First-Order Phase Transformation at Constant Volume: A Continuous Transition?

Víctor F Correa,Facundo J Castro

doi:10.3390/e24010031

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 and 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. We apply our results to describe the transition between ice VI and liquid water using thermodynamic information available in the literature and also to show that a first-order phase transition driven in isochoric condition can be used as the operating principle of a mechanical actuator.

Highlights

Phase transitions (PT) are probably one of the most interesting and conceptually rich phenomena approached by Thermodynamics and Statistical Mechanics
A second scenario is constant volume only. We will examine this process in detail and demonstrate that: (i) the transformation extends over a finite range of T, and (ii) each and every extensive potential and the entropy S are continuous across the transition when V is constant
After carefully analyzing the details of this transition two examples will be presented: (1) a possible constant volume transformation between liquid water and ice VI and (2) a process analogous to a mechanocaloric cycle but based on a constant volume phase transformation that could be used as a mechanical actuator that does work on a external system by changing the temperature

Summary

Introduction

Phase transitions (PT) are probably one of the most interesting and conceptually rich phenomena approached by Thermodynamics and Statistical Mechanics. Ehrenfest [1] introduces the concept of transition order: When at least one of the first order derivatives of the Gibbs energy G ( T, p) with respect to its natural variables, temperature T, and pressure p, shows a jump discontinuity, the transition is said to be first order; if all the first-order derivatives are continuous but at least one of the second-order derivatives shows a jump discontinuity, the transition is said to be second order, and so on for higher-than-second-order transitions Since this scheme has become universally accepted due to its simplicity and conceptual content. After carefully analyzing the details of this transition two examples will be presented: (1) a possible constant volume transformation between liquid water and ice VI and (2) a process analogous to a mechanocaloric cycle but based on a constant volume phase transformation that could be used as a mechanical actuator that does work on a external system by changing the temperature

Recapitulation of a Constant Pressure Transformation

General Properties

Calculation of Thermodynamic Quantities

Application 1

Application 2

Conclusions