Canonical Ensemble

Abstract

A classical gas in a volume V is composed of N independent and indistinguishable particles. The single particle Hamiltonian is $H = \tfrac{{{p^2}}}{{2m}}$, with m the mass of the particle and p the absolute value of the momentum. Moreover, for each particle, we find 2 internal energy levels: a ground state with energy 0 and degeneracy g ₁, and an excited state with energy E>0 and degeneracy g ₂. Determine the canonical partition function and the specific heat C _V as a function of the temperature T. Analyze the limit of low temperatures and comment on the final result.