Air $\text{(assumed as an ideal gas)}$ with a mass flow rate of $2.5 \mathrm{~kg} / \mathrm{s}$ enters a horizontal nozzle at $350 \mathrm{~K}, 350 \mathrm{kPa}$ with a velocity of $3 \mathrm{~m} / \mathrm{s}$. The air exits the nozzle at a pressure of $101.5$ kPa and temperature $305$ K with a Mach number of $\frac{9}{7}$. Assuming steady state operation and constant properties given in the data, the ratio of inlet area to exit area required to satisfy the exit condition is ________ $\text{(rounded off to one decimal place)}$.
Use the following data: $\gamma=1.4, c_{p}=1.011 \mathrm{~kJ} / \mathrm{kg} . \mathrm{K}, \quad R=0.287 \mathrm{~kJ} / \mathrm{kg} . \mathrm{K}$
