The Noro–Frenkel law of corresponding states is an equation in thermodynamics that describes the critical temperature of the liquid-gas transition T as a function of the range of the attractive potential R. It states that all short-ranged spherically symmetric pair-wise additive attractive potentials are characterised by the same thermodynamics properties, if compared at the same reduced density and second virial coefficient[1] Johannes Diderik van der Waals's law of corresponding states expresses the fact that there are basic similarities in the thermodynamic properties of all simple gases.
Its essential feature is that if we scale the thermodynamic variables that describe an equation of state (temperature, pressure, and volume) with respect to their values at the liquid-gas critical point, all simple fluids obey the same reduced equation of state.
The Noro–Frenkel law suggests to condensate the three quantities which are expected to play a role in the thermodynamics behavior of a system (hard-core size, interaction energy and range) into a combination of only two quantities: an effective hard core diameter and the reduced second virial coefficient.
Noro and Frenkel suggested to determine the effective hard core diameter following the expression suggested by Barker[2] based on the separation of the potential into attractive Vatt and repulsive Vrep parts used in the Weeks–Chandler– Andersen method.
B2 is defined as The Noro–Frenkel law is particularly useful for the description of colloidal and globular protein solutions,[4] for which the range of the potential is indeed significantly smaller than the particle size.