  Traditional 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 from a purely
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
find that the traditional handwaving interpretation of the van der Waals
equation adopting mean field approximation is actually incorrect. In this
investigation of one-dimensional interacting gas, we demonstrate the
possibility taking a mechanical point of view and having deeper understanding
for the physics of leading order effect of particle-particle interaction, for
weakly interacting N-body systems that are usually studied in the framework of
statistical mechanics or kinetic theory.
