Theorem of corresponding states

According to van der Waals, the theorem of corresponding states (or principle/law of corresponding states) indicates that all fluids, when compared at the same reduced temperature and reduced pressure, have approximately the same compressibility factor and all deviate from ideal gas behavior to about the same degree.

Material constants that vary for each type of material are eliminated, in a recast reduced form of a constitutive equation. The reduced variables are defined in terms of critical variables.

The principle originated with the work of Johannes Diderik van der Waals in about 1873  when he used the critical temperature and critical pressure to characterize a fluid.

The most prominent example is the van der Waals equation of state, the reduced form of which applies to all fluids.

Compressibility factor at the critical point

Substance	{\displaystyle P_{c}} [Pa]	{\displaystyle T_{c}} [K]	{\displaystyle v_{c}} [m3/K]	{\displaystyle Z_{c}}
H2O	21.817×106	647.3	3.154×10−3	0.23
4He	0.226×106	5.2	14.43×10−3	0.31
He	0.226×106	5.2	14.43×10−3	0.30
H2	1.279×106	33.2	32.3×10−3	0.30
Ne	2.73×106	44.5	2.066×10−3	0.29
N2	3.354×106	126.2	3.2154×10−3	0.29
Ar	4.861×106	150.7	1.883×10−3	0.29
Xe	5.87×106	289.7	0.9049×10−3	0.29
O2	5.014×106	154.8	2.33×10−3	0.291
CO2	7.290×106	304.2	2.17×10−3	0.275
SO2	7.88×106	430.0	1.900×10−3	0.275
CH4	4.58×106	190.7	6.17×10−3	0.285
C3H8	4.21×106	370.0	4.425×10−3	0.267