$5.(25$ points$)$ An equimolar mixture of helium and argon gases is to be used as the working fluid in a closed$-$loop gas$-$turbine cycle. The mixture enters the turbine at $1$ MPa and $1200$ K and expands isentropically to a pressure of $200$ kPa $.$

$($a$)$ If the mixture is equimolar, determine the percent composition by mass of each gas. $(10$ points$)$

$($b$)$ Determine the mass$-$averaged specific heats and gas constant of the mixture. $(\backslash (\backslash$mathbf$\{5\}\backslash )$ points$)$

$($c$)$ If the mixture's mass flow rate is measured as $\backslash (0\mathrm{.}7\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ),$ determine the power output of this turbine. $(10$ points$)$