One of the cubic equations of real gas state defining the Compressibility factor as a function of Gas pressure and Gas temperature :

Z^3 - Z^2 +(A-B-B^2) \, Z - AB = 0

A=\frac{a \, \alpha \, p}{ R^2 \, T^2}

B=\frac{b \, p}{ R \, T}

a = 0.45747 \cdot \frac{R^2 \, T_c^2}{p_c}

b = 0.08664 \cdot \frac{R \, T_c}{p_c}

\alpha = \left( 1 + \kappa \, (1-T_r^{0.5}) \right)^2

\kappa = 0.48508 + 1.55171 \, \omega -0.15613 \, \omega^2

where

Once compressibility Z-factor is known the gas density can be calculated as:

\rho(p, T) = \frac{1}{Z(p,T)} \cdot \frac{M}{R} \cdot \frac{p}{T}

where

See also