Analytical calculation of the critical temperature and estimation of the critical region size for a fluid model

TL;DR

This paper develops an analytical method to calculate the critical temperature and estimate the critical region size for a fluid model, validated by alkali metals sodium and potassium, aligning with experimental data.

Contribution

It introduces an analytical approach for critical temperature calculation and critical region estimation in a cell fluid model, applied to alkali metals.

Findings

Critical temperatures for sodium and potassium match experimental data.

Derived expression for critical region size based on critical regime conditions.

Estimated critical region size is on the order of a few hundredths.

Abstract

An analytical procedure for calculating the critical temperature and estimating the size of critical region for a cell fluid model is developed. Our numerical calculations are illustrated by the case of the Morse potential parameters characterizing the alkali metals (sodium and potassium). The critical temperatures found for liquid sodium and potassium as solutions of the resulting quadratic equation agree with experimental data. The expression for the relative temperature determining the critical region size is obtained proceeding from the condition for the critical regime existence. In the cases of sodium and potassium, the value of this temperature is of the order of a few hundredths.