The Van der Waals equation of state is for real gases that do not behave as ideal gases. This equation

is a cubic equation of state, meaning that it gives $3$ volume roots. One root will be close to the value of

the constant $b$ liquid root$)$ and the other $($vapor root$)$ can best be estimated using the ideal gas value of

RT$/$P$.$ A third root is meaningless.

$P=\frac{RT}{V-b}-\frac{a}{V^2}$ where $b=\frac{R{T}_C}{8P_C}$ and $a=\frac{27R^2{T}_C^2}{64P_C^2}$

For methane at $50C$ and $15$ bar, determine the gas root of Volume using the Van der Waals EOS. You

will need to use goalseek function to determine the root. For convenience, the $T_C$ of methane is $190\mathrm{.}6K$

and $P_C=46\mathrm{.}1$ bar. Calculate the volume value in liters.