Past exam of the mathematics course of the University of Cambridge / 2009 / ii / Paper 2 / 35D / i / Solution

The Van der Waals equation modifies the ideal-gas pressure in two ways. Short-range repulsion reduces the volume accessible to the particles from $V$ to $V-bN$, while attractive interactions reduce the pressure by $a{N}^2/V^2$. The parameters $b$ and $a$ therefore encode excluded volume and mean attraction respectively. The equation is a phenomenological approximation, not an exact microscopic equation of state.