The equipartition theorem revisited

We generalize the equipartition theorem to confined systems of structureless independent molecules by introducing a confining potential, which is usually not done explicitly in most textbooks. We show that if the size of the system is much larger than the range of the confining potential, the generalization is independent of the form of the potential but contains corrections produced by the confinement. We demonstrate the important role played by the walls and show how the boundary terms may be employed to describe their contribution to the pressure exerted on the system.