Air passes through a normal shock in a supersonic wind tunnel. Upstream conditions are \(M_{1}=1.8, T_{1}=270 \mathrm{~K}\), and \(p_{1}=\)

\(10.0 \mathrm{kPa}\) absolute. Downstream conditions are \(M_{2}=0.6165, T_{2}=\) \(413.6 \mathrm{~K}\), and \(p_{2}=36.13 \mathrm{kPa}\) absolute. (Four significant figures are given to minimize roundoff errors.) Evaluate local isentropic stagnation conditions

(a) upstream from,

(b) downstream from, the normal shock. Calculate the change in specific entropy across the shock. Plot static and stagnation state points on a Ts diagram.