Classical thermodynamics of particles in harmonic traps

I develop simple thermodynamic relations for a system of noninteracting classical particles confined in an isotropic harmonic trap. The volume occupied by the particles in such a trap is not well defined, and the pressure varies with position, indicating that the thermodynamic relations should be expressed in terms of more appropriate variables. I use the effective spring constant of the trap as a state variable and show that the conjugate state variable is proportional to the ensemble average of the mean squared displacement of the particles from the center of the trap. Thermodynamic relations are derived in terms of these variables, including the pressure and thermal equations of state, the entropy, and the heat capacities. I also consider cyclic thermodynamic processes in a harmonically confined gas. © 2010 American Association of Physics Teachers. DOI: 10.1119/1.3417868