Air enters a frictionless, constant area duct with \(\mathrm{Ma}=2.5\), \(T_{0}=20^{\circ} \mathrm{C}\), and \(p_{0}=101 \mathrm{kPa}(\mathrm{abs})\). The gas is decelerated by heating until a normal shock occurs where the local Mach number is 1.3. Downstream of the shock, the subsonic flow is accelerated with heating until it exits with a Mach number of 0.9. Determine the static temperature and pressure, the stagnation temperature and pressure, and the fluid velocity at the duct entrance, just upstream and downstream of the normal shock, and at the duct exit. Sketch the temperature-entropy diagram for this flow.