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Real gas effects refers to an assumption base where the following are taken into account:## Modelisation

### Van der Waals modelisation

### Redlich-Kwong modelisation

### Berthelot and modified Berthelot modelisation

### Dieterici modelisation

### Clausius modelisation

### Virial Modelisation

### Peng-Robinson Modelisation

### Wohl modelisation

### Beatte-Bridgeman Modelisation

### Benedict-Webb-Rubin Modelisation

## See also

## References

http://www.ccl.net/cca/documents/dyoung/topics-orig/eq_state.html

- Compressibility effects
- Variable heat capacity
- Van der Waals forces
- Non-equilibrium thermodynamic effects
- Issues with molecular dissociation and elementary reactions with variable composition.

For most applications, such a detailed analysis is "over-kill" and the ideal gas approximation is used. Real-gas models have to be used near condensation point of gases, near critical point, at very high pressures, and in several other less usual cases.

Real gases are often modelized by taking into account their molar weight and molar volume

$RT=(P+frac\{a\}\{V\_m^2\})(V\_m-b)$

Where P is the pressure, T is the temperature, R the ideal gas constant, and V_{m} the molar mass. a and b are parameters that are determined empirically for each gas, but are sometimes estimated from their critical temperature (T_{c}) and critical pressure (P_{c}) using these relations:

$a=frac\{27R^2T\_c\}\{64P\_c\}$

$b=frac\{RT\_c\}\{8P\_c\}$

The Redlich-Kwong equation is another two-parameters equation that is used to modelize real gases. It is almost always more accurate than the Van der Waals equation, and ofter more accurate than some equation with more than two parameters. The equation is

$RT=P+frac\{a\}\{V\_m(V\_m+b)T^frac\{1\}\{2\}\}(V\_m-b)$

where a and b two empirical parameters that are not the same parameters as in the Van der Waals equation.

The Berthelot Equation is very rarely used,

$P=frac\{RT\}\{V-b\}-frac\{a\}\{TV^2\}$

but the modified version is somewhat more accurate

$P=frac\{RT\}\{V\}left(1+frac\{9PT\_c\}\{128P\_cT\}frac\{(1-6T\_c^2)\}\{T^2\}right)$

This modelisation fell out of usage in recent years

$P=RTfrac\{exp\{(frac\{-a\}\{V\_mRT\})\}\}\{V\_m-b\}$

The Clausius equation is a very simply three-parameter equation used to modelize gases.

$RT=left(P+frac\{a\}\{T(V\_m+c)^2\}right)(V\_m-b)$

where

$a=frac\{V\_c-RT\_c\}\{4P\_c\}$

$b=frac\{3RT\_c\}\{8P\_c\}-V\_c$

$c=frac\{27R^2T\_c^3\}\{64P\_c\}$

The Virial equation derives from a perturbative treatment of statistical mechanics.

$PV\_m=RTleft(1+frac\{B(T)\}\{V\_m\}+frac\{C(T)\}\{V\_m^2\}+frac\{D(T)\}\{V\_m^3\}+...right)$

or alternatively

$PV\_m=RTleft(1+frac\{B^prime(T)\}\{P\}+frac\{C^prime(T)\}\{P^2\}+frac\{D^prime(T)\}\{P^3\}+...right)$

where A, B, C, A′, B′, and C′ are temperature dependent constants.

This two parameter equation has the interesting property being useful in modelizing some liquids as well as real gases.

$P=frac\{RT\}\{V\_m-b\}-frac\{a(T)\}\{V\_m(V\_m+b)+b(Vm-b)\}$

The Wohl equation is formulated in terms of critial values, making it useful when real gas constants are not available.

$RT=left(P+frac\{a\}\{TV\_m(V\_m-b)\}-frac\{c\}\{T^2V\_m^3\}right)(V\_m-b)$

where

$a=6P\_cT\_cV\_c^2$

$b=frac\{V\_c\}\{4\}$

$c=4P\_cT\_c^2V\_c^3$

The Beattie-Bridgeman equation

$P=RTd+(BRT-A-frac\{Rc\}\{T^2\})d^2+(-BbRT+Aa-frac\{RBc\}\{T^2\})d^3+frac\{RBbcd^4\}\{T^2\}$

where d is the molal density and a, b, c, A, and B are empirical parameters.

The BWR equation, sometimes referred to as the BWRS equation

$P=RTd+d^2left(RT(B+bd)-(A+ad-a\{alpha\}d^4)-frac\{1\}\{T^2\}[C-cd(1+\{gamma\}d^2)exp(-\{gamma\}d^2)]right)$

Where d is the molal density and where a, b, c, A, B, C, α, and γ are empirical constants.

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Last updated on Saturday October 04, 2008 at 13:33:42 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Saturday October 04, 2008 at 13:33:42 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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