$1.(35$ pts$)$ Consider the Brayton cycle for an ideal turbojet engine. There is no fan and there is no afterburner. Assume, as we did in class, that gas velocities are small at stations $2-5,$ where $2$ is the compressor entrance and $5$ is the turbine exit and e is the nozzle exit. The conditions at the entrance to the compressor $($station $2)$ are: p$2=0\mathrm{.}8$ atm, T$2=268$ K The compressor pressure ratio CPR is $($P$3/$p$2)=20$ The maximum temperature in the engine is T$4=$ unknown At the nozzle exit, the exit velocity is Ue $=966$ m$/$s The pressure at the nozzle exit equals ambient pressure which is Pe $=$ Pa $=0\mathrm{.}7$ atm. Heat capacity is Cp $=1003\mathrm{.}5$ J$/($kg$-$K$)$ Ratio of specific heats $($y$)$ is Y $=1\mathrm{.}4$ Write down a set of all the necessary equation to compute the maximum temperature $($T$4)$ from the given quantities. a$)$ Reduce these equations to three equations with three unknowns; the unknows are $($I$4,$ Is and Te$).$ b$)$ Extra credit: Insert the values listed above so that you get three equations that only contain $($T$4,$ Ts and Te$)$ and the values listed above. c$)$ Extra credit: Solve your three equations for T$42.$