The pressure and temperature upstream from a normal shock in air is $1$atm and $300K$ respectively. The

total pressure $p_0$ is $7\mathrm{.}824$atm.

$($a$)$ Calculate the Mach number upstream of the shock.

$($b$)$

Calculate the pressure and temperature downstream of the shock.

$($c$)$

Calculate the change in entropy across the shock.