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


Z^3 - (1-B) \, Z^2 +(A-2B-3B^2) \, Z -(AB-B^2-B^3) = 0



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




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




a = 0.45724 \cdot \frac{R^2 \, T_c^2}{p_c}




b = 0.07780 \cdot \frac{R \, T_c}{p_c}




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




\kappa = 0.37464 + 1.54226 \, \omega -0.26992 \, \omega^2


where

Compressibility factor

critical pressure

Gas pressure

critical temperature

Gas temperature

reduced temperature

Gas constant

accentric factor



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

Gas molar mass


See also

Natural Science / Physics / Thermodynamics / Real Gas / Real Gas EOS @model