  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.
