Liquid Water: A Single Approach to Its Two Continuous Phase Transitions

In this paper, we show that both continuous phase transitions of liquid water, the liquid-gas and the liquid-liquid, can be articulated within a single thermodynamic analytical formalism. This result follows from a combination of the two-liquid model (TLM), recently confirmed for water, with the idea of a thermal-dependent excluded volume, v, concept introduced by van der Waals, in his famous state equation. Starting from the fundamentals of thermodynamics, it will be shown that the TLM naturally leads to the idea of an extensive thermal-dependent v that acts as a parameter of the sample thermodynamic potentials. This procedure effectively separates the thermodynamics of the system into two parts: the first concerns the clusters' thermodynamics, taken as wandering particles, and the second concerns the thermal behavior of its internal structure (geometry and number of particles). From this result, we demonstrate that the condition of mechanical instability leads to not one but two critical points, each happening in one of the above-described parts of the system.