Correlation of the critical parameters of the gas-liquid phase transition and the density of the crystal at zero absolute temperature

TL;DR

This paper derives an empirical formula linking crystal density at zero temperature to gas-liquid critical parameters, using Van der Waals theory, providing theoretical insights into phase transition properties.

Contribution

It introduces a theoretical derivation of Timmermanns' empirical formula connecting crystal density and critical parameters from Van der Waals equations.

Findings

Derived approximate and exact formulas from Van der Waals equations.

Established theoretical connection between crystal density and critical parameters.

Enhanced understanding of phase transition characteristics.

Abstract

The empirical formula of Timmermanns connecting the density of the crystal at zero absolute temperature with the parameters of the critical point of the gas-liquid phase transition is derived theoretically from the Van der Waals equation of state using the conditions of phase equilibrium. Two equations of state with three parameters describing the critical point of any pure substance are considered. The formula is derived approximately from the first equation and exactly from the second one.