Heat capacity of liquids: an approach from the solid phase

TL;DR

This paper presents a theoretical approach to calculating the heat capacity of liquids based on their elastic and vibrational properties, linking microscopic dynamics to macroscopic thermal behavior.

Contribution

It introduces a model connecting liquid heat capacity to elastic properties and vibrational states, and relates it to viscosity and experimental data.

Findings

Heat capacity decreases with temperature due to loss of transverse modes.

Transverse phonons cannot be excited at low temperatures.

The approach offers insights into the glass transition problem.

Abstract

We calculate the energy and heat capacity of a liquid on the basis of its elastic properties and vibrational states. The experimental decrease of liquid heat capacity with temperature is attributed to the increasing loss of two transverse modes with frequency $\omega<1/\tau$, where $\tau$ is liquid relaxation time. In a simple model, liquid heat capacity is related to viscosity and is compared with the experimental data of mercury. We also calculate the vibrational energy of a quantum liquid, and show that transverse phonons can not be excited in the low-temperature limit. Finally, we discuss the implications of the proposed approach to liquids for the problem of glass transition.