which is flying at 800 km/hour through still air having a pressure 8.0 N/cm2 (abs) and temperature -100 C. Take R=287 L/g K and k =1.4

Given :

$$ \begin{array} \text{V} =800 {Km}/{P h} &=\frac{800 \times 1000}{60 \times 60} \\ &= 222.22 {m} / {s} \\ \text {Pressure of a air }\left(P_{1}\right) &=8 {N} /{cm}^{2} \\&=8 \times 10^{4} {N} / {m}^{2} \\ T =100^{\circ}{C} &=100+273=373 {K} \\ K &=1.4\\ \end{array} $$

Now for Adiabatic process,

The velocity of sound

$$ \begin {aligned} C &=\sqrt{K R T} \\ &=\sqrt{1.4 \times 287 \times 373} \\ &=387.13 {m} / {s} \\ \end{aligned} $$

Mach number(M)

$$ \begin {aligned} M &= \frac{V}{C}=\frac{222.22}{387.13} \\ M &=0.574 \\ \end{aligned} $$

Stagnation Pressure (Ps)

$$ \begin {array} \text{Ps} &=P \left(1+\frac{k-1}{2} \times M^{2}\right)^{\frac{K}{K-1}} \\ &=8\times10^{4}\left(1+\frac{1.4-1}{2} \times 0.574^{2}\right)^{\frac{1.4}{1.4-1}} \\ &= 10 \times 10^{4} N/ m^{2} \\ \end{array} $$

Stagnation Temperature (Ts) $$ \begin {aligned} T_{S} &=T\left(1+\frac{k-1}{2} \times M^{2}\right) \\ &=373\left(1+\frac{1.4-1}{2} \times 0.574^{2}\right) \\ &=397.58 \mathrm{K} \\ T_{S} &=124.58^{\circ} \mathrm{C} \end{aligned} $$

Stagnation density $\left(\rho_{s}\right)$ $$ \begin{aligned} \rho_{s} &=\frac{P_{s}}{R T_{s}}=\frac{10.00 \times 10^{4}}{287 \times 397.58} \\ &=0.8763 \mathrm{~kg} / \mathrm{m}^{3} \end{aligned} $$