Corresponding States

Substances are said to be in corresponding states when their reduced state variables—such as their reduced temperature, pressure, and density—have the same values. The reduced state variables are the ratios of the state variables to, most often, the values of the state variables corresponding to the critical state; these values are the critical temperature T_c, pressure p_c, and density p_c (or specific volume v_c).

According to the law of corresponding states, the reduced equation of state is the same for different substances. For example, to identical values of the reduced temperature (τ = T/T_c) and reduced pressure (τ = p/p_c) there corresponds the same value of the reduced specific volume (ø = v/v_c). On the gas-liquid phase diagram, to the same values of the reduced temperature there corresponds the same value of, for example, the reduced pressure, surface tension, or heat of vaporization.

The law of corresponding states is valid only at sufficiently high temperatures, where quantum effects are insignificant, and for those substances for which the dependence of the energy of molecular interaction on distance is identical in character. In practice, the behavior of all substances deviates from the law of corresponding states. Within individual groups of substances with an intermolecular interaction potential of similar form, however, these deviations are often relatively small and are systematic in character. As a result, the properties of little-studied substances can be calculated on the basis of the law of corresponding states.