According to van der Waals, the theorem of corresponding states (or principle/law of corresponding states) indicates that all

fluid In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear ...

s, when compared at the same

reduced temperature In thermodynamics, the reduced properties of a fluid are a set of state variables scaled by the fluid's state properties at its critical point. These dimensionless thermodynamic coordinates, taken together with a substance's compressibility facto ...

and

reduced pressure In thermodynamics, the reduced properties of a fluid are a set of state variables scaled by the fluid's state properties at its critical point. These dimensionless thermodynamic coordinates, taken together with a substance's compressibility facto ...

, have approximately the same

compressibility factor In thermodynamics, the compressibility factor (Z), also known as the compression factor or the gas deviation factor, describes the deviation of a real gas from ideal gas behaviour. It is simply defined as the ratio of the molar volume of a gas to ...

and all deviate from ideal gas behavior to about the same degree.

Material constant A materials property is an intensive property of a material, i.e., a physical property that does not depend on the amount of the material. These quantitative properties may be used as a metric by which the benefits of one material versus another ca ...

s that vary for each type of material are eliminated, in a recast reduced form of a

constitutive equation In physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance, and approx ...

. 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''A Four-Parameter Corresponding States Correlation for Fluid Compressibility Factors''
by Walter M. Kalback and Kenneth E. Starling, Chemical Engineering Department,

University of Oklahoma The University of Oklahoma (OU) is a Public university, public research university in Norman, Oklahoma. Founded in 1890, it had existed in Oklahoma Territory near Indian Territory for 17 years before the two Territories became the state of Oklahom ...

. when he used the

critical temperature Critical or Critically may refer to: *Critical, or critical but stable, medical states **Critical, or intensive care medicine *Critical juncture, a discontinuous change studied in the social sciences. *Critical Software, a company specializing in ...

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