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 may continuously motion, move and Deformation (physics), deform (''flow'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are M ...

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 fact ...

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 ...

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

Material constant A material property is an intensive property of a material, i.e., a physical property or chemical 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 mat ...

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 or more physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance o ...

. 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 who received the Nobel Prize in Physics in 1910 "for his work on the equation of state for gases and liquids". Van der Waals started his car ...

in about 1873 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 In thermodynamics, a critical point (or critical state) is the end point of a phase equilibrium curve. One example is the liquid–vapor critical point, the end point of the pressure–temperature curve that designates conditions under which a l ...

to derive a universal property of all fluids that follow the

van der Waals equation The van der Waals equation is a mathematical formula that describes the behavior of real gases. It is an equation of state that relates the pressure, volume, Avogadro's law, number of molecules, and temperature in a fluid. The equation modifies ...

of state. It predicts a value of

3/8 = 0.375

that is found to be an overestimate when compared to real gases. Edward A. Guggenheim used the phrase "Principle of Corresponding States" in an oft-cited paper to describe the phenomenon where different systems have very similar behaviors when near a critical point. There are many examples of non-ideal gas models which satisfy this theorem, such as the van der Waals model, the Dieterici model, and so on, that can be found on the page on real gases.

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 physical quantities measured at the critical point, is predicted to be a constant independent of substance by many equations of state. The table below for a selection of gases uses the following conventions: *

T_c

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 p ...

(8.314 J⋅ K⁻¹⋅ mol⁻¹) *

\mu

Molar mass In chemistry, the molar mass () (sometimes called molecular weight or formula weight, but see related quantities for usage) of a chemical substance ( element or compound) is defined as the ratio between the mass () and the amount of substance ...

g⋅mol⁻¹

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