A constant area duct $)=(0\mathrm{.}25m^2$ with subsonic air flow rate of $215k\frac{g}{s}$ passes through a combustor, which adds heat into the airflow at a rate of $129$ MW $.$ Before entering the duct, the air stagnation temperature and pressure are $800$ kPa and $400$ K $,$ respectively. Find $($a$)$ the Mach number of the flow before enter the combustor, $($b$)$ the stagnation temperature of the flow leaving the combustor, $($c$)$ the Mach number of the flow leaving the combustor, $($d$)$ sketch the process on a T$-$s diagram.

$m^{}=215k\frac{g}{s}$