Specific Heat of a Particle in a Box

Abstract

The specific heat of a free particle in a cubic box with reflecting walls is found to be a function of variable η = 2mL2kT/ℏ2 (m = mass of particle, L length of box, T = temperature, k and 2πℏ Boltzmann's and Planck's constants). For large η the specific heat approaches the classical equipartition value dk/2 (d = dimensionality), for small η it approaches zero as T−2 exp (−const T−1), and in between, at η = 9π, it has a maximum, (9/8) (dk/2).