An analytical approach to the anomalous density of water

Abstract

Water, which is essential for the existence of life, has almost a hundred properties that distinguish it from other liquids. In this paper, we will focus on its density, which, unlike the absolute majority of other liquids, increases with increasing temperature in the vicinity of the solid–liquid transition, for a wide range of pressures, including ambient pressure. Our approach will present an analytical thermodynamic formulation for this problem that has, as a novelty, the introduction of a variable exclusion volume. The excluded volume will be considered a thermodynamic variable, that is, it depends on the system's thermal conditions. This approach will be applied to the two-liquid theory of water, which claims that water molecules can be assembled into two different kinds of clusters. At a given state, the relative numbers of these aggregates can be very sensitive to thermal variations, and, as the excluded volume for each of them is different, when their relative number changes, the total excluded volume also changes. We will show how to gather the ideas of a non-constant excluded volume with the two-liquid theory of water into a new, elegant, and non-trivial analytical expression for the density of water. In the end, we compare our expression with experimental data and show that it provides an exact understanding of the anomalous behavior of water density.