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theorem of corresponding states : ウィキペディア英語版
theorem of corresponding states

According to van der Waals, the theorem of corresponding states (or principle 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.〔 page 141〕
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.
It originated with the work of Johannes Diderik van der Waals in about 1873〔(''A Four-Parameter Corresponding States Correlation for Fluid Compressibility Factors'' ) by Walter M. Kalback and Kenneth E. Starling, Chemical Engineering Department, University of Oklahoma.〕 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==

The compressibility factor at the critical point, which is defined as Z_c=\frac, where the subscript c indicates the critical point is predicted to be a constant independent of substance by many equations of state; the Van der Waals equation e.g. predicts a value of 3/8 = 0.375.

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