Continuous and discontinuous realizations of first-order phase transitions

Abstract

First-order phase transitions are commonly associated with a discontinuous behavior of some of the thermodynamic variables and the presence of a latent heat. In the present study it is shown that this is not necessarily the case. Using standard thermodynamics, the general characteristics of phase transitions are investigated, considering an arbitrary number of conserved particle species and coexisting phases, and an arbitrary set of state variables. It is found that there exist two different possible types of realizations of a phase transition. In the first type, one has the immediate replacement of a single phase with another one. As a consequence, some of the global extensive variables indeed behave discontinuously. In the second type, one has instead the gradual (dis-) appearance of a single phase over a range of the state variables. This leads to a continuous behavior of the (global) basic thermodynamic variables. Furthermore, in this case it is not possible to define a latent heat in a trivial manner. It is derived that the latter (former) case happens if the number of extensive state variables used is larger or equal (lower) than the number of coexisting phases. The choice of the state variables thus place a crucial role for the qualitative properties of the phase transition.

Figures (3)

• Figure 1: An example phase diagram for a one-component substance, with constant number of particles $N$, and the pressure $P$ and the temperature $T$ as the independent state variables. The red lines correspond to phase coexistence of two phases. The red dot marks a triple point, where all three phases are in equilibrium. If the red lines are crossed in a thermodynamic process of the aforementioned state variables, this results in a discontinuous realization of the phase transition. The blue arrows show two examples of realizations where the state variables of Fig. \ref{['fig_2']} are used, see text.
• Figure 2: The phase diagram for a constant number of particles $N$, and for the volume $V$ and the temperature $T$ as the independent state variables. "s" denotes the solid, "l" the liquid and "g" the gas phase. The red line is the triple line, on which all three phases are in equilibrium. Its crossing results in a discontinuous realization. The blue arrows show examples of a continuous phase disappearance (1) and a discontinuous phase replacement (2).
• Figure 3: The phase diagram for a constant number of particles $N$, and for the volume $V$ and the entropy $S$ as the independent state variables. There are no discontinuous phase replacements for this set of state variables. The blue arrows belong to the realizations shown in Fig. \ref{['fig_2']}.