$9\mathrm{.}7$ Diffuser

A supersonic jet flies at an altitude of $5$ km $,$ where the pressure is $0\mathrm{.}54$ bar $,$ and the temperature is $-17\mathrm{.}5C.$ The jet flies with a velocity of $2000k\frac{m}{h},$ and its diffuser has an inlet cross section of $2m^2.$ Assume negligible diffuser exit velocity, adiabatic reversible flow, and consider air as ideal gas with constant specific heats, $R=0\mathrm{.}287\frac{(kJ)}{kgK},c_p=\frac{7}{2}R.$ Determine the mass flow into the engine, and the pressure increase across the diffuser.