The ideal gas with a harmonic piston and the constant pressure-to-volume ratio ensemble

We consider an ideal gas enclosed in a vessel with a freely moving piston coupled to an ideal spring. In this model, the gas pressure and volume are proportional to each other, with a constant of proportionality depending on the spring constant. To demonstrate its usefulness at a variety of levels in the physics curriculum, we study this system by employing three approaches of increasing complexity: elementary thermal physics, thermodynamic potentials, and statistical mechanics. In particular, we calculate the system's heat capacity at constant P/V in several ways.