Redlich$-$Kwong Equation of State given by

$z^3-z^2+z(A-B-B^2)-AB=0$ where

$A=0\mathrm{.}42748\frac{P_r}{T_r}F$

$F=\frac{1}{\sqrt[\phantom{2}]{T_r^3}}$

$B=0\mathrm{.}08664\frac{P_r}{T_r}$ and

$z=\frac{Pv}{RT}$;$,T_r=\frac{T}{T_c}$;$,P_r=\frac{P}{P_c}$

Use Matlab function $f$ solve to solve the above equation for the molar volume $v$ of $n-$butane for different pressures at a given temperature. For n$-$butane, $T_c=425\mathrm{.}2K,$ and $P_c=37\mathrm{.}5$atm.

$($a$)$ Provide the necessary Matlab live script, or program files.

$($b$)$ Generate and plot the $P-v$ isotherm for $n-$butane at $510\mathrm{.}24K$ for pressures: $1,5,10,15,20,25$ and $36$atm.

$($c$)$ Report the $v$ of $n-$butane at $510\mathrm{.}24K$ and $37\mathrm{.}4$atm.