Van der Waals: Condensation and the Maxwell Construction

A van der Waals fluid, shown as a piston and cylinder in reduced units. Compressing an isotherm below the critical temperature drives condensation: gas molecules join a growing liquid pool in the proportion set by the lever rule, a meniscus rises, and the measured pressure stays pinned on a flat plateau, the level fixed by Maxwell's equal-area construction, until the nearly incompressible liquid finally resists. Above the critical temperature the gas passes to liquid continuously and no meniscus ever forms. The side panel shows the p-V isotherm with its thermodynamically unstable S-curve, the Maxwell coexistence line, and the binodal and spinodal envelope with a live operating point, so the link between the loop, the equal-area rule and real condensation is explicit.