Thermodynamic Entropy And The Accessible States of Some Simple Systems

TL;DR

This paper compares thermodynamic entropy with Boltzmann's principle for simple systems, providing a physical interpretation of accessible states and microstates, and discusses implications for distinguishability and probability of states.

Contribution

It offers a detailed analysis linking thermodynamic entropy to the number of accessible microstates in simple systems with temperature-independent heat capacities.

Findings

Total arrangements in systems are TC/k under specified conditions.

T1/2 is a natural measure of accessible states for a single particle.

Particles are shown to be distinguishable for counting microstates.

Abstract

Comparison of the thermodynamic entropy with Boltzmann's principle shows that under conditions of constant volume the total number of arrangements in simple thermodynamic systems with temperature-independent heat capacities is TC/k. A physical interpretation of this function is given for three such systems; an ideal monatomic gas, an ideal gas of diatomic molecules with rotational motion, and a solid in the Dulong-Petit limit of high temperature. T1/2 emerges as a natural measure of the number of accessible states for a single particle in one dimension. Extension to N particles in three dimensions leads to TC/k as the total number of possible arrangements or microstates. The different microstates of the system are thus shown a posteriori to be equally probable, with probability T-C/k, which implies that for the purposes of counting states the particles of the gas are distinguishable. The most probable energy state of the system is determined by the degeneracy of the microstates.