  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.
