Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 15.1-2

THE CANONICAL FORMALISM; STATISTICAL MECHANICS IN HELMHOLTZ REPRESENTATION

Physics — Statistical Mechanics · microcanonical-harmonic-oscillators-composite

Problem

A system is composed of two harmonic oscillators of natural frequencies ω0\omega_0 and 2ω02\omega_0, respectively. If the system has total energy E=(n+12)ℏω0E = (n + \frac{1}{2})\hbar\omega_0, where nn is an odd integer, what is the entropy of the system? If a composite system is composed of two non-interacting subsystems of the type just described, having energies E1E_1 and E2E_2, what is the entropy of the composite system?

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