Please use microsoft excel to complete I will thumbs up$,$ thank you!

In thermodynamics, an equation of state $($EOS$)$ is a thermodynamic equation relating state variables which describe the state of matter under a given set of physical conditions, such as pressure, volume and temperature. Some examples of EOS: ideal gas, Van der Walls and Peng$-$Robinson. The equation shown below is also one of the EOS.

$p=\frac{RT}{V_m-b}-\frac{a}{\sqrt[\phantom{2}]{T}{V}_m(V_m+b)}$

a and $b$ values can be calculated from $T_c($critical temperature$)$ and $P_c($critical pressure$).$

$R=0\mathrm{.}082Latm{K}^{-1}mo{l}^{-1}$

For Ammonia, $a=84\mathrm{.}6$ and $b=0\mathrm{.}025.$ In a piston cylinder, ammonia at $300K$ and $1\frac{L}{m}ol$ is expanded to $3\frac{L}{m}ol.$ Calculate the work with two different methods and compare your results $($remember that work can be calculated by the equation below$).$

$W={\displaystyle \underset{V_1}{\overset{V_2}{}}}pdV$

a$.$ Trapezoidal rule. Use different increments and $0\mathrm{.}01).$

$.$ Gauss quadrature. Use $2-$point formula.