Real gas

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Real gases - as opposed to a Perfect or Ideal Gas - cannot be explained entirely using the Ideal gas law. To understand real gases, the following must be considered:

For most applications, such a detailed analysis is unnecessary, and the ideal gas approximation can be used with reasonable accuracy. 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.

Contents

[edit] Modelisation

Main article: Equation of state

[edit] van der Waals modelisation

Main article: van der Waals equation

Real gases are often modeled 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 Vm the molar volume. a and b are parameters that are determined empirically for each gas, but are sometimes estimated from their critical temperature (Tc) and critical pressure (Pc) using these relations:

a=\frac{27R^2T_c^2}{64P_c}

b=\frac{RT_c}{8P_c}

[edit] Redlich–Kwong modelisation

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 often 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.

[edit] Berthelot and modified Berthelot modelisation

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)

[edit] Dieterici modelisation

This modelisation fell out of usage in recent years

P=RT\frac{\exp{(\frac{-a}{V_mRT})}}{V_m-b}

[edit] Clausius modelisation

The Clausius equation is a very simple three-parameter equation used to model 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}

[edit] Virial Modelisation

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

PV_m=RT\left(1+\frac{B(T)}{V_m}+\frac{C(T)}{V_m^2}+\frac{D(T)}{V_m^3}+...\right)

or alternatively

PV_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.

[edit] Peng-Robinson Modelisation

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

P=\frac{RT}{V_m-b}-\frac{a(T)}{V_m(V_m+b)+b(Vm-b)}

[edit] Wohl modelisation

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

[edit] Beatte-Bridgeman Modelisation

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.

[edit] Benedict-Webb-Rubin Modelisation

The BWR equation, sometimes referred to as the BWRS equation

P=RTd+d^2\left(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.

[edit] See also

[edit] References

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

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