ONLY DO PART B: Gas A expands through an adiabatic turbine. The inlet stream flows in at $100$ bar and $600$ K while the outlet is at $20$ bar and $445$ K$.$

$($Part A$)$ Calculate the work produced by the turbine. The following data are available for gas A: The ideal gas heat capacity for this process: Cp$=30\mathrm{.}0+0\mathrm{.}02$T where Cp is in J$/$mol$*$K and T is in K$.$ PvT data have been fit to the following equation P$($v$-$b$)=$RT$+($a$*$P$^\{2\})/$T Where a$=0\mathrm{.}001($m$^\{3\}*$K$)/($bar$*$mol$)$and b$=8*10^\{-5\}($m$^\{3\}/$mol$)$

$($Part B$)$ Gas A is NOT ideal: Redo part A with a different EOS $($eg$.$ NOT the given Redlich$-$Kwong equation of state $($EOS$)).$ Please draw the hypothetical path of your choice that will help you solve this problem.