Real gas
Real gas effects refers to an assumption base where the following are taken into account:
- 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". An example where "Real Gas effects" would have a significant impact would be on the Space Shuttle re-entry where extremely high temperatures and pressures are present.

# Van der Waals modelisation
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 Vm the molar mass. 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}{64P_c}
b=\frac{RT_c}{8P_c}
See Van der Waals equation

# 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 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.
See Redlich-Kwong equation of state

# 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)

# Dieterici modelisation
This modelisation fell out of usage in recent years
P=RT\frac{\exp{(\frac{-a}{V_mRT})}}{V_m-b}

# Clausius modelisation
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}

# 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)
-r 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 and A,B,C are temperature dependent constants.

# Peng-Robinson Modelisation
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)}

# 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

# 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.

# 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}\right)
Where d is the molal density and where a,b,c,A,B,C,, are empirical constants.