A mechanical approach to one-dimensional interacting gas

Derivations of the van der Waals equation typically use standard recipes involving ensemble averages of statistical mechanics. In this work, we study a box of weakly interacting gas particles in one-dimension by explicitly incorporating the mechanical point of view. This has the merit that it not only reproduces the van der Waals equation but also tells us some extra interesting physics not immediately clear from a pure statistical mechanical approach. For example, we show that the traditional handwaving argument leading to van der Waals equation requires closer scrutiny if it is to get things right.