Question

help me find the derivation of Vm=

(i want to find the Vm)

Soave-Redlich-Kwong (SRK) EOS RT aa Vm - b Vm (Vm + b)

Answer 1

$p=\frac{RT}{V_m-b}-\frac{a\alpha}{V_m(V_m+b)}$

$\Rightarrow p=\frac{RT}{V_m-b}\frac{V_m+b}{V_m+b}-\frac{a\alpha}{V_m(V_m+b)}\frac{V_m-b}{V_m-b}$

$\Rightarrow p=\frac{RT(V_m+b)}{V_m^2-b^2}-\frac{a\alpha(V_m-b)}{V_m(V_m^2-b^2)}$

$\Rightarrow p=\frac{V_mRT(V_m+b)-a\alpha(V_m-b)}{V_m^2-b^2}$

$\Rightarrow p(V_m^2-b^2)=V_mRT(V_m+b)-a\alpha(V_m-b)$

$\Rightarrow pV_m^2-pb^2=RTV_m^2+bRTV_m-a\alpha V_m+a\alpha b$

$\Rightarrow V_m^2(p-RT)+V_m(a\alpha -bRT)+(-pb^2-a\alpha b)=0$

Which is quadratic in $V_m$, Hence

$V_m=\frac{-(a\alpha -bRT)\pm \sqrt{(a\alpha-bRT)^2-4(p-RT)(-pb^2-a\alpha b)})}{2(p-RT)}$