Tait equation revisited from the entropic and fluctuational points of view

TL;DR

This paper revisits the Tait equation by deriving it from entropic and fluctuation perspectives, proposing a new predictor for liquid density near melting points based on thermodynamic properties and excess entropy.

Contribution

It introduces a new expression for predicting liquid density that connects the Tait equation parameters with excess entropy and fluctuation theory, validated against experimental data.

Findings

Derived formula aligns well with experimental data on n-alkanes.

The formula simplifies to the Tait equation with physically meaningful parameters.

Predicts liquid density without extensive data fitting across temperatures.

Abstract

We consider the possibilities for prediction of liquids' density under pressure basing on the inverse reduced fluctuations parameter, which is directly connected with the isothermal compressibility. This quantity can be determined basing on the thermodynamical properties of saturated liquid and it consists of only two constant parameters within a relatively wide region close to the melting points. It is confirmed by the comparison with the experimental data on n-alkanes that the derived expression is a quite reasonable estimator without a necessity to fit data along some parts of isotherms for different temperatures. At the same time the obtained formula: i) can be reduced to the form of the Tait equation and ii) the resulting Tait's parameters in this representation have a clear physical meaning as functions of the excess entropy, which determines the mentioned reduced fluctuations.