Redlich-Kwong equation of state

The Redlich-Kwong equation of state is :

$\left[p+{\frac {a}{T^{1/2}v(v+b)}}\right](v-b)=RT$.

The Redlich-Kwong equation of state has a critical point compressibility factor of :

$Z_{c}={\frac {p_{c}v_{c}}{RT_{c}}}={\frac {1}{3}}$

leading to

$a={\frac {1}{9(2^{1/3}-1)}}{\frac {R^{2}T_{c}^{5/2}}{p_{c}}}\approx 0.4274802336{\frac {R^{2}T_{c}^{5/2}}{p_{c}}}$

and

$b={\frac {(2^{1/3}-1)}{3}}{\frac {RT_{c}}{p_{c}}}\approx 0.08664034995{\frac {RT_{c}}{p_{c}}}$

where $p$ is the pressure, $T$ is the temperature and $R$ is the molar gas constant. $T_{c}$ is the critical temperature and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P_c} is the pressure at the critical point.

Soave Modification

A modification of the the Redlich-Kwong equation of state was presented by Giorgio Soave in order to allow better representation of non-spherical molecules. In order to do this, the square root temperature dependence was replaced with a temperature dependent acentricity factor:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha(T)=\left(1+\left(0.48508+1.55171\omega-0.15613\omega^2\right)\left(1-\sqrt\frac{T}{T_c}\right)\right)^2 }

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T_c} is the critical temperature and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \omega} is the acentric factor for the gas. This leads to an equation of state of the form:

$\left[p+{\frac {a\alpha (T)}{v(v+b)}}\right]\left(v-b\right)=RT$

or equivalently:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p=\frac{RT}{v-b}-\frac{a\alpha(T)}{v(v+b)}}