On the heat capacity of liquids at high temperatures

TL;DR

This paper models the temperature dependence of the heat capacity of argon at high temperatures, showing it approaches a limiting value due to changes in collision diameter rather than vibrational degrees of freedom.

Contribution

It introduces a simple approximation method to calculate how the heat capacity of liquids varies with temperature, emphasizing the role of collision diameter changes.

Findings

Heat capacity decreases with temperature roughly as T^{-1/4}.

C_v approaches 1.7-1.8 R at high temperatures.

The limiting value is due to collision diameter variation, not vibrational loss.

Abstract

Making use of a simple approximation for the evolution of the radial distribution function, we calculate the temperature dependence of the heat capacity $C_v$ of Ar at constant density. $C_v$ decreases with temperature roughly according to the law $\sim T^{-1/4}$, slowly approaching the hard sphere asymptotic value $C_v=\frac{3}{2}R$. However, the asymptotic value of $C_v$ is not reachable at reasonable temperatures , but stays close to 1.7--1.8 $R$ over a wide range of temperatures after passing a " magic " $2R$ value at about 2000 K. Nevertheless these values has nothing to do with loss of vibrational degrees of freedom, but arises as a result of a temperature variation of the collision diameter $\sigma$. \end{abstract}