Air flows at the rate of \(39.0 \mathrm{lbm} / \mathrm{sec}\) with a Mach number of 0.30 , a pressure of 50 psia, and a temperature of \(650^{\circ} \mathrm{R}\). The duct has a \(0.5-\mathrm{ft}^{2}\) cross-sectional area. Find the final Mach number, the stagnation temperature ratio \(T_{t 2} / T_{t 1}\), and the density ratio \(ho_{2} / ho_{1}\), if heat is added at the rate of \(290 \mathrm{Btu} / \mathrm{lbm}\) of air.