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



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



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



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



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



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



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


where

LaTeX Math Inline
bodyZ

Compressibility factor

LaTeX Math Inline
bodyp_c

Gas 

critical pressure

LaTeX Math Inline
body

T

p

Gas 
temperature
pressure

LaTeX Math Inline
body

RGas constant

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T_c

critical temperature

LaTeX Math Inline
body

\rho

T

Gas 
density
temperature

LaTeX Math Inline
body

p

T_r = T/T_c

reduced temperature
Gas pressure

LaTeX Math Inline
body

M

R

Gas
 molar mass
constant

LaTeX Math Inline
body\omega

ZCompressibility
accentric factor


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Once compressibility Z-factor

LaTeX Math Inline
bodyZ(p, T

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)
 is known the gas density 

LaTeX Math Inline
body\rho
can be calculated as:

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

where

LaTeX Math Inline

Gas constant

bodyM

Gas molar mass


See also

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

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