On the heat capacity of quantum hard sphere fluid

TL;DR

This paper investigates the quantum hard sphere fluid's heat capacity, revealing it remains close to classical values at most temperatures but drops to zero at low temperatures, with a linear temperature contribution observed at very low temperatures.

Contribution

It provides the first detailed analysis of the quantum effects on the heat capacity of hard sphere fluids, highlighting the near-constant classical behavior and quantum deviations at low temperatures.

Findings

Heat capacity remains close to classical value of 1.5 k at most temperatures.

At low temperatures, heat capacity drops to zero.

Linear temperature dependence of heat capacity observed at very low temperatures.

Abstract

The thermodynamic properties of the Boltzmann hard sphere system is discussed. It was found that zero point energy decreases with temperature so slowly that it turned out to be an almost a constant addition to the classical value. In result the heat capacity of the system differs little from the classical value of 1.5 k everywhere except for the narrow region of low temperatures, where heat capacity drops to zero. The predicted linear temperature contribution to the heat capacity like in ideal Fermi gas was clearly detected in the quantum hard sphere system at the lowest temperatures.