Critical Points

Definition

The point in phase space where the distinction between liquid and vapor disappears.

Elaboration

If you heat water in a closed volume, the temperature and pressure are initially fixed by equilibrium between a liquid and vapor. Beyond a certain temperature and pressure, however, the meniscus that separates the two phases disappears, and they become indistinguishable. If one draws a curve in P-V space that identifies the region where both a liquid and vapor coexist, the critical point lies at the maximum where the slope is zero:

$$ {\left(\frac{\partial P}{\partial V}\right)}_{T={T}_c}=0 \mathrm{and} {\left(\frac{\partial^2 P}{\partial {V}^2}\right)}_{T={T}_c}=0 $$

(1)

As this point is approached, the two phases, gas and liquid, begin to closely resemble one another on a molecular scale. The critical point for pure water is at 374.2 °C and 218.3 atm.

Near the critical point, the structure of these phases is very sensitive to small changes in temperature and pressure, and these...