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 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 fact ...

, 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 constants 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 app ...

. The reduced variables are defined in terms of critical variables. The principle originated with the work of

Johannes Diderik van der Waals Johannes Diderik van der Waals (; 23 November 1837 – 8 March 1923) was a Dutch theoretical physicist and thermodynamicist famous for his pioneering work on the equation of state for gases and liquids. Van der Waals started his career as a sch ...

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 , mottoeng = "For the benefit of the Citizen and the State" , type = Public research university , established = , academic_affiliations = , endowment = $2.7billion (2021) , pr ...

. when he used the critical temperature and

critical pressure In thermodynamics, a critical point (or critical state) is the end point of a phase equilibrium curve. The most prominent example is the liquid–vapor critical point, the end point of the pressure–temperature curve that designates conditions ...

to characterize a fluid. The most prominent example is the

van der Waals equation In chemistry and thermodynamics, the Van der Waals equation (or Van der Waals equation of state) is an equation of state which extends the ideal gas law to include the effects of interaction between molecules of a gas, as well as accounting for ...

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 In chemistry and thermodynamics, the Van der Waals equation (or Van der Waals equation of state) is an equation of state which extends the ideal gas law to include the effects of interaction between molecules of a gas, as well as accounting for ...

e.g. predicts a value of

3/8 = 0.375

. Where: *

T_c

: critical temperature *

P_c

v_c

: critical specific volume ³⋅kg⁻¹*

R

gas constant The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per ...

(8.314 J⋅ K⁻¹⋅ mol⁻¹) *

\mu

Molar mass In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in moles. The molar mass is a bulk, not molecular, ...

g⋅mol⁻¹ For example:

References

External links

Properties of Natural Gases
Includes a chart of compressibility factors versus reduced pressure and reduced temperature (on last page of the PDF document)
Theorem of corresponding states
o
SklogWiki

Laws of thermodynamics Engineering thermodynamics Continuum mechanics Johannes Diderik van der Waals {{thermodynamics-stub

Compressibility factor at the critical point

See also

References

External links