Problem $5\mathrm{.}60$: Gas A expands through an adiabatic turbine. The inlet stream is at $100$ bar and

$600K$ while the outlet stream is at $20$ bar and $445K.$ Calculate the work produced by the

turbine. The following data are given for gas $A$ : the ideal gas heat capacity for this process is

$c_p=30\mathrm{.}0+0\mathrm{.}02T$ where $c_p$ is in $\frac{J}{m}ol*K$ and $T$ is in $K.PvT$ data is fitted to the following

equation: $P(v-b)=RT+\frac{a{P}^2}{T}$ where $a=0\mathrm{.}001\frac{m^3(K)}{\text{b}\text{a}\text{r}\text{m}\text{o}\text{l}}$ and $b=8{10}^{-5}\frac{m^3}{(mol)}.$ Note: gas $A$

is not ideal in this problem. As a part of your solution, please draw the hypothetical path of your

choice that will help you solve this problem. $(50$ pts$.)$