$($Show work and steps. Show final answers$)$Problem $4$

The pressure measured by a Pitdt tube located downstream of a normal Shock is $3$ atm and the

total$-$to$-$static temperature ratio downstrean of the shock is $($T$\_($O$\_(2)))/($T$\_(2))=1\mathrm{.}035.$ Calculate:

ac$\_($p$)=1\mathrm{.}005$k$($J$)/($kg$*$K$),$c$\_($v$)=0\mathrm{.}718$k$($J$)/($kg$*$K$),$R$=287($J$)/($kg$*$K$),$ and $\backslash$gamma $=1\mathrm{.}4$