PROBLEM $2[50$ points$]$

A flow of $n_1^{}=2\mathrm{.}0$kmo$\frac{l}{s}$ of a dry exhaust at $T_1=200C$ and $P_1=100$ kPa mixes with a stream of pure nitrogen at $T_2=25C$ and $P_2=100$ kPa in an adiabatic mixing chamber. The molar composition of the dry exhast is $60\%$ nitrogen and $40\%$ carbon dioxide. If the product stream exits the chamber at $T_3=50C$ and $P_3=100$kPa, determine

$($a$)$ the molar flow rate of the coolant $N_2$ stream, $n_2^{},$ in kmo$\frac{l}{s}$ and

$($b$)$ the rate of entropy generation inside the mixing chamber, in $k\frac{W}{K}.$

Assume all gase behave as ideal gases with variable specific heats.