A rocket motor is fitted with a converging$-$diverging nozzle which has a ratio of exit to throat area of $4\mathrm{.}0.$ The exhaust gases are generated in a combustion chamber with a stagnation pressure of $1750$ kPa, and a stagnation temperature of $2600$ K$.$ Assuming that the flow inside the nozzle is isentropic$,$ and that the flow at the exit is supersonic,

a$)$ determine the mass flow rate out of the rocket in kg$/$s$,$ if the throat area is $0\mathrm{.}32$ m$2.$

$($Assume atmospheric pressure $=101\mathrm{.}325$ kPa, $\backslash$gamma $=1\mathrm{.}4$ and R $=287\mathrm{.}1$ J$/($kgK$).)$