Consider air entering a heated duct at \(p_{1}=1 \mathrm{~atm}\) and \(T_{1}=288 \mathrm{~K}\). Ignore the effect of friction. Calculate the amount of heat per unit mass (in joules per kilogram) necessary to choke the flow at the exit of the duct, as well as the pressure and temperature at the duct exit, for an inlet Mach number of

(a) \(M_{1}=2.0\)

(b) \(M_{1}=0.2\).