$3.$ A plane is flying $\backslash (220\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ through still air where the ambient air pressure is $\backslash (50\backslash$mathrm$\{$kPa$\}\mathrm{.}10\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash )$ of air enters its turbojet engines at $\backslash (0^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The exhaust exits at $\backslash (340^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ traveling $\backslash (1250\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ relative to the ground. Assume the speed of the air while flowing through the engine is approximately zero relative to the plane, from the time it exits the diffuser until the time it enters the nozzle. Assume cold air standard assumptions and ideal turbojet engine.

a$)$ Determine the temperature of the air at the outlet of the diffuser.

b$)$ Determine the temperature of the air just after passing through the turbine.

c$)$ Determine the rate of energy input $($in MW$)$ provided by burning fuel.