We have a strearo on $n-$butane and carbon dioxide at $15$MPa and $393\mathrm{.}2K$ flowing from

a well. The composition is $50$ mole $\%$ carbon dioxide. We would like to make a separation

of this stream to end with one stream of $2$ mole $\%C{O}_2$ and one with $90\%C{O}_2-$both

streams still at $15$MPa and $393\mathrm{.}2K.$

$($a$)$ What is the minimum work required per mole of inlet feed? Use the Peng$-$Robinson

equation of state.

$($b$)$ How does this value compare if all streams were assumed to be ideal$-$gas mixtures?