Van der Waals Gas — 2D Isotherms (2D)

This 2D companion runs the same Lennard-Jones-like pair-potential molecular dynamics as the 3D lab, flattened from a cubic box to a square one so the condensation transition is easy to read at a glance: a few hundred disks move under short-range repulsion (the excluded volume b) and longer-range attraction (the constant a), integrated with velocity-Verlet and held at a target temperature by a velocity-rescaling thermostat. Drop the temperature below T_c or push the attraction and density up, and the disks cluster into a visible liquid droplet surrounded by vapour — the same van der Waals phase transition, drawn directly on a flat canvas instead of an orbiting 3D scene. A side isotherm plot shows the reduced van der Waals P-V curve at the critical temperature and at the current one, with a marker tracking the live virial-pressure state as you tune the controls.