Exercise$-1$: Nonlinear Equations $-$ van der Waals Equation of State

Using GAMS $($as a programming language$)$ solve for $V$ the following van der Waals equation of state for

ammonia at $10$ atm and $250C$ by using Secant Method where two initial guesses for $V$ are $2\mathrm{.}50$ and $2\mathrm{.}51.$

$(P+\frac{a}{V^2})(V-b)=RT$

$a=(\frac{27}{64})(R^2\frac{T_c^2}{P_c})$

$b=R\frac{T_c}{8P_c}$

Given: $R=0\mathrm{.}08206$atm$1K^{-1}mo{l}^{-1},P=10$atm,$T=523K,T_c=407\mathrm{.}5K,P_c=111\mathrm{.}3$atm,$a=4\mathrm{.}238448,b=$

$0\mathrm{.}037556.$

Provide the formulation of the problem, the GAMS $(.$gms$)$ code and progress of the iterations in the report.

Resolve the problem from different initial guesses. Analyse and discuss the effect of initial guesses on the final

solution and on the convergence to the final solution. These values of initial guesses have to be chosen by you.

GAMS codes for this part are not required to be submitted.