Argon$(Ar),$ at $T_1=350K,1$ bar with a mass flow rate of $m_1^{}=1k\frac{g}{s}$ enters the insulated mixing chamber shown in the figure below and mixes with carbon dioxide $(C{O}_2)$ entering as a separate stream at $575K,1$ bar with a mass flow rate of $0\mathrm{.}5k\frac{g}{s}.$ The mixture exits at $1$ bar. Assume ideal gas behavior with $k=1\mathrm{.}67$ for Ar and $k=1\mathrm{.}25$ for $C{O}_2.$

For steady$-$state operation, determine:

$($a$)$ the molar analysis of the exiting mixture.

$($b$)$ the temperature of the exiting mixture, in K $.$

$($c$)$ the rate of entropy production, in $k\frac{W}{K}.$