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

Air enters a constant$-$area duct at $M_1=2,p_1,=1\mathrm{.}0$atm, and $T_1=15C.$ Inside the duct, the

heat added per unit mass is $q=120k\frac{J}{k}g.$

a$)$ Calculate the flow properties $M_2,p_2{T}_2,{}_2,T_{0_3},$ and $p_{0_2}$ at the exit of the duct.

b$)$ Calculate the amount of heat per unit mass necessary to choke the flow at the exit of the duct.

$($You may use $C_p=1\mathrm{.}005k\frac{J}{kg*K},C_v=0\mathrm{.}718k\frac{J}{kg*K},R=287\frac{J}{kg*K},$ and $=1\mathrm{.}4)$