Consider a rocket engine burning hydrogen and oxygen; the combustion chamber temperature and pressure are \(3517 \mathrm{~K}\) and \(25 \mathrm{~atm}\), respectively. The molecular weight of the chemically reacting gas in the combustion chamber is 16 , and \(\gamma=1.22\). The pressure at the exit of the convergent-divergent rocket nozzle is \(1.174 \times 10^{-2}\). The area of the throat is \(0.4 \mathrm{~m}^{2}\). Assuming a calorically perfect gas and isentropic flow, calculate:

(a) the exit Mach number,

(b) the exit velocity,

(c) the mass flow through the nozzle, and

(d) the area of the exit.