Real gas are non hypothetical gas whose molecules occupy space and also've interaction, and consequently obeys the gas law exactly . To understand the behaviour of real gases, the following must be taken into account:
For most applications, such a detailed analysis is unnecessary, and the ideal gas approximation can be used with reasonable accuracy. On the other hand, realgas models have to be used near the condensation point of gases, near critical points, at very high pressures, to explain the Joule–Thomson effect and in other less usual cases.
Contents

Models 1

van der Waals model 1.1

Redlich–Kwong model 1.2

Berthelot and modified Berthelot model 1.3

Dieterici model 1.4

Clausius model 1.5

Virial model 1.6

Peng–Robinson model 1.7

Wohl model 1.8

Beattie–Bridgeman model 1.9

Benedict–Webb–Rubin model 1.10

See also 2

References 3

External links 4
Models
van der Waals model
Real gases are often modeled by taking into account their molar weight and molar volume

RT=\left(P+\frac{a}{V_\text{m}^2}\right)(V_\text{m}b)
Where P is the pressure, T is the temperature, R the ideal gas constant, and V_{m} the molar volume. 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_\text{c}^2}{64P_\text{c}}

b=\frac{RT_\text{c}}{8P_\text{c}}
Redlich–Kwong model
The Redlich–Kwong equation is another twoparameter equation that is used to model real gases. It is almost always more accurate than the van der Waals equation, and often more accurate than some equations with more than two parameters. The equation is
RT=P(V_\text{m}b)+\frac{a}{V_\text{m}(V_\text{m}+b)T^\frac{1}{2}}(V_\text{m}b)
where a and b two empirical parameters that are not the same parameters as in the van der Waals equation. These parameters can be determined:
a=0.4275\frac{R^2T_\text{c}^{2.5}}{P_\text{c}}
b=0.0867\frac{RT_\text{c}}{P_\text{c}}
Berthelot and modified Berthelot model
The Berthelot equation (named after D. Berthelot^{[1]} is very rarely used,
P=\frac{RT}{V_\text{m}b}\frac{a}{TV_\text{m}^2}
but the modified version is somewhat more accurate
P=\frac{RT}{V_\text{m}}\left[1+\frac{9P/P_\text{c}}{128T/T_\text{c}}\left(1\frac{6}{(T/T_\text{c})^2}\right)\right]
Dieterici model
This model (named after C. Dieterici^{[2]}) fell out of usage in recent years
P=RT\frac{\exp{(\frac{a}{V_\text{m}RT})}}{V_\text{m}b}.
Clausius model
The Clausius equation (named after Rudolf Clausius) is a very simple threeparameter equation used to model gases.
RT=\left(P+\frac{a}{T(V_\text{m}+c)^2}\right)(V_\text{m}b)
where
a=\frac{27R^2T_\text{c}^3}{64P_\text{c}}
b=V_\text{c}\frac{RT_\text{c}}{4P_\text{c}}
c=\frac{3RT_\text{c}}{8P_\text{c}}V_\text{c}
where V_{c} is critical volume.
Virial model
The Virial equation derives from a perturbative treatment of statistical mechanics.
PV_\text{m}=RT\left(1+\frac{B(T)}{V_\text{m}}+\frac{C(T)}{V_\text{m}^2}+\frac{D(T)}{V_\text{m}^3}+...\right)
or alternatively
PV_\text{m}=RT\left(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.
Peng–Robinson model
Peng–Robinson equation of state (named after D.Y. Peng and D. B. Robinson^{[3]}) has the interesting property being useful in modeling some liquids as well as real gases.
P=\frac{RT}{V_\text{m}b}\frac{a(T)}{V_\text{m}(V_\text{m}+b)+b(V_\text{m}b)}
Wohl model
The Wohl equation (named after A. Wohl^{[4]}) is formulated in terms of critical values, making it useful when real gas constants are not available.
RT=\left(P+\frac{a}{TV_\text{m}(V_\text{m}b)}\frac{c}{T^2V_\text{m}^3}\right)(V_\text{m}b)
where
a=6P_\text{c}T_\text{c}V_\text{c}^2
b=\frac{V_\text{c}}{4}
c=4P_\text{c}T_\text{c}^2V_\text{c}^3.
Beattie–Bridgeman model
^{[5]}
This equation is based on five experimentally determined constants. It is expressed as
P=\frac{RT}{v^2}\left(1\frac{c}{vT^3}\right)(v+B)\frac{A}{v^2}
where

A = A_0 \left(1  \frac{a}{v} \right)

B = B_0 \left(1  \frac{b}{v} \right)
This equation is known to be reasonably accurate for densities up to about 0.8 ρ_{cr}, where ρ_{cr} is the density of the substance at its critical point. The constants appearing in the above equation are available in following table
when P is in KPa, v is in \frac{\text{m}^3}{\text{K}\,\text{mol}}, T is in K and R=8.314\frac{\text{kPa}\cdot\text{m}^3}{\text{K}\,\text{mol}\cdot\text{K}}^{[6]}
Gas

A_{0}

a

B_{0}

b

c

Air

131.8441

0.01931

0.04611

0.001101

4.34×10^4

Argon, Ar

130.7802

0.02328

0.03931

0.0

5.99×10^4

Carbon Dioxide, CO_{2}

507.2836

0.07132

0.10476

0.07235

6.60×10^5

Helium, He

2.1886

0.05984

0.01400

0.0

40

Hydrogen, H_{2}

20.0117

0.00506

0.02096

0.04359

504

Nitrogen, N_{2}

136.2315

0.02617

0.05046

0.00691

4.20×10^4

Oxygen, O_{2}

151.0857

0.02562

0.04624

0.004208

4.80×10^4

Benedict–Webb–Rubin model
The BWR equation, sometimes referred to as the BWRS equation,
P=RTd+d^2\left(RT(B+bd)(A+ada{\alpha}d^4)\frac{1}{T^2}[Ccd(1+{\gamma}d^2)\exp({\gamma}d^2)]\right)
where d is the molar density and where a, b, c, A, B, C, α, and γ are empirical constants. Note that the γ constant is a derivative of constant α and therefore almost identical to 1.
See also
References

^ D. Berthelot in Travaux et Mémoires du Bureau international des Poids et Mesures – Tome XIII (Paris: GauthierVillars, 1907)

^ C. Dieterici, Ann. Phys. Chem. Wiedemanns Ann. 69, 685 (1899)

^ Peng, D. Y., and Robinson, D. B. (1976). "A New TwoConstant Equation of State". Industrial and Engineering Chemistry: Fundamentals 15: 59–64.

^ A. Wohl "Investigation of the condition equation", Zeitschrift für Physikalische Chemie (Leipzig) 87 pp. 1–39 (1914)

^ Yunus A. Cengel and Michael A. Boles, Thermodynamics: An Engineering Approach 7th Edition, McGrawHill, 2010, ISBN 007352932X

^ Gordan J. Van Wylen and Richard E. Sonntage, Fundamental of Classical Thermodynamics, 3rd ed, New York, John Wiley & Sons, 1986 P46 table 3.3

Dilip Kondepudi, Ilya Prigogine, Modern Thermodynamics, John Wiley & Sons, 1998, ISBN 0471973939

Hsieh, Jui Sheng, Engineering Thermodynamics, PrenticeHall Inc., Englewood Cliffs, New Jersey 07632, 1993. ISBN 0132757028

Stanley M. Walas, Phase Equilibria in Chemical Engineering, Butterworth Publishers, 1985. ISBN 0409951625

M. Aznar, and A. Silva Telles, A Data Bank of Parameters for the Attractive Coefficient of the Peng–Robinson Equation of State, Braz. J. Chem. Eng. vol. 14 no. 1 São Paulo Mar. 1997, ISSN 01046632

An introduction to thermodynamics by Y. V. C. Rao

The correspondingstates principle and its practice: thermodynamic, transport and surface properties of fluids by Hong Wei Xiang
External links

http://www.ccl.net/cca/documents/dyoung/topicsorig/eq_state.html
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