$($Show work and steps. Circle$/$box final answers$)$ Problem $3$

A supersonic air stream enters a constant$-$area duct at M$\_(1)=2,$p$\_(1),=1\mathrm{.}0$atm, and T$\_(1)=288$K$.$

Inside the duct, the heat added per unit mass is q$=120$k$($J$)/($k$)$g$.$

aM$\_(2),$p$\_(2)$T$\_(2),\backslash$rho $\_(2),$T$\_($O$\_(2)),$ and p$\_($O$\_(2))$ at the exit of the duct.

bc$\_($p$)=1\mathrm{.}005$k$($J$)/($kg$*$K$),$c$\_($v$)=0\mathrm{.}718$k$($J$)/($kg$*$K$),$R$=287($J$)/($kg$*$K$),$ and $\backslash$gamma $=1\mathrm{.}4$