Coexistence curve

A coexistence curve is the set of pressure–temperature states at which two phases of a substance exist together in stable equilibrium. Almost everywhere on the P–T plane a substance has one answer — solid, liquid, or vapour — and only on these curves does the answer become two. The physical condition defining them is the equality of the two phases' molar Gibbs free energies: if one phase were cheaper, matter would flow into it until the other disappeared.

A simple substance has three such curves, and they are not independent. The sublimation curve separates solid from vapour, the fusion (melting) curve separates solid from liquid, and the vaporisation curve separates liquid from vapour; all three meet at the triple point. Crossing a coexistence curve requires the absorption or release of a latent heat at constant temperature, which is what produces the flat plateaus of a heating curve.

The vaporisation curve alone does something the others do not: it terminates, at the critical point, ending in the middle of the plane rather than running to infinity. Because the line simply stops, a liquid can be carried around its endpoint and returned as a gas without ever crossing a boundary — which is why liquid and vapour are not fundamentally distinct states of matter, while solid and liquid, whose melting line has no known end, are.

The modern P–T diagram with its three intersecting curves emerged from the work of Clapeyron, Clausius, Andrews and Gibbs during the nineteenth century, with Gibbs's phase rule (1876) explaining why a two-phase equilibrium in a one-component system must be a line rather than an area.