Consider the normal shock wave properties calculated in Example 3.5. Show that these properties satisfy the Hugoniot equation for a calorically perfect gas.

Data From Example 3.5:

A normal shock wave is standing in the test section of a supersonic wind tunnel. Upstream of the wave, \(M_{1}=3, p_{1}=0.5 \mathrm{~atm}\), and \(T_{1}=200 \mathrm{~K}\). Find \(M_{2}, p_{2}, T_{2}\), and \(u_{2}\) downstream of the wave.