Van-der-Waals supercritical fluid: Exact formulas for special lines

TL;DR

This paper derives exact formulas for thermodynamic extrema lines in the supercritical region of the van-der-Waals fluid, analyzing their merging behavior and properties like the Widom line and pseudo-Gruneisen parameter.

Contribution

It provides analytical expressions for supercritical thermodynamic ridges and examines their merging and properties within the van-der-Waals model.

Findings

Ridges merge into a single Widom line below certain T and P thresholds.

The pseudo-Gruneisen parameter at the critical point is 8/3.

Behavior of Batschinski lines and ridges analyzed in detail.

Abstract

In the framework of the van-der-Waals model, analytical expressions for the locus of extrema (ridges) for heat capacity, thermal expansion coefficient, compressibility, density fluctuation, and sound velocity in the supercritical region have been obtained. It was found that the ridges for different thermodynamic values virtually merge into single Widom line only at $T<1.07 T_c, P<1.25P_c$ and become smeared at $T<2T_c, P<5P_c$, where $T_c$ and $P_c$ are the critical temperature and pressure. The behavior of the Batschinski lines and the pseudo-Gruneisen parameter $\gamma$ of a van-der-Waals fluid were analyzed. In the critical point, the van-der-Waals fluid has $\gamma=8/3$, corresponding to a soft sphere particle system with exponent $n=14$.