Answer
See solution
Work Step by Step
The conservation of mass relation across the shock is $\rho_1 V_1=\rho_2 V_2$ and it can be expressed as $$
\frac{V_2}{V_1}=\frac{\rho_1}{\rho_2}=\frac{P_1 / R T_1}{P_2 / R T_2}=\left(\frac{P_1}{P_2}\right)\left(\frac{T_2}{T_1}\right)
$$ From Eqs. 12-35 and 12-38 from book, $$
\frac{V_2}{V_1}=\left(\frac{1+k \mathrm{Ma}_2^2}{1+k \mathrm{Ma}_1^2}\right)\left(\frac{1+\mathrm{Ma}_1^2(k-1) / 2}{1+\mathrm{Ma}_2^2(k-1) / 2}\right)
$$
