Answer
a) $T_2=775.1\ K$
b) $\dot{m}_g=14.9\ kg/s$
Work Step by Step
Enthalpies:
Air: Inlet ($T_1=550\ K$): $h_1= 555.74\ kJ/kg$
Gases: Inlet ($T_3=800\ K$): $h_3= 821.95\ kJ/kg$, Outlet ($T_4=600\ K$): $h_4= 607.02\ kJ/kg$
For air:
$\dot{Q}+\dot{m}_ah_1=\dot{m}_ah_2$
$\dot{Q}=3200\ kJ/s,\ \dot{m}_a=800\ kg/min$
$h_2=794.71\ kJ/kg \rightarrow T_2=775.1\ K$
For the gases:
$\dot{m}_gh_3=\dot{m}_gh_4+\dot{Q}$
$\dot{m}_g=14.9\ kg/s$
