1. The problem statement, all variables and given/known data A system consists of N very weakly interacting particles at temperature T sufficiently high so that classical stat mech is applicable. Each particle has mass M and is free to perform one dimensional oscillations about its equilibrium position. Calculate the heat capacity of this system of particles if the restoring force is proportional to x^3. 2. Relevant equations spring constant = q energy of one oscillator E = p^2 / 2m + qx^4 / 4 partition function: Z = integral ( exp(-BE ) dx dp both integrals from -inf to +inf where B = 1/kT 3. The attempt at a solution Cv = N d/dT (average E) average E = - d / dB [ ln Z ] Z = integral [exp (-Bp^2/2m) dp ] * integral [exp (-Bqx^4/4) dx ] the first integral is simply sqrt(pi * 2m / B ) I have no idea how to find the integral of exp(-x^4), so I can't find this partition function.