$4.[18$ Pts$]$ A mixture of dry air and water vapor is entering an ideal steam turbine $600$ K and

leaves at $400$ K$.$ The partial pressures of both air and water entering the turbine are $100$ kPa. Use

the standard values from $($A$\mathrm{.}8/9)$ for this question.

$($a$)$ What are the mass fractions? $[2$ Pts$]$

$($b$)$ Draw this process in a T$-$s diagram $[2$ Pts$]$

$($c$)$ Assuming the heat capacities and the specific gas constants do not change, what is the specific work produced

by the turbine calculated by the ideal gas law? $[5$ Pts$]($Note: this part aligns with approach $1$ in the class example$)$

$($d$)$ Use the steady state continuity equation to get the specific work produced by the turbine. Comment on the

validity of assumptions in $($c$)[5$ Pts$].($Note: this part aligns with approach $2$ in the class example$)$

$($e$)$ What are the exiting partial pressures of air and water in $($d$)?$ Use constant R$.[4$ Pts$]$ solve equations