Problem $2$: You are designing a turbojet engine with an afterburner. The inlet and compressor

have ${}_{0-3}=1\mathrm{.}4,c_{p,0-3}=1000\frac{(J)}{(kg)*(K)},$ and the turbine, afterburner and nozzle have ${}_{4-9}=$

$1\mathrm{.}3,c_{p,4-9}=1150\frac{(J)}{(kg)*(K)}.$ The engine is travelling at $V_0=550\frac{m}{s},$ with the ambient conditions

being $p_0=1$atm,$T_0=290K.T_{t4}=1850K$ and $T_{t7}=2200K.$ The inlet and compressor

adiabatic thermal efficiencies are ${}_d=0\mathrm{.}92$ and ${}_c=0\mathrm{.}88.$ The burner pressure ratio and

efficiency are ${}_b=0\mathrm{.}98$ and ${}_b=0\mathrm{.}99.$ The fuel's heating value in both the burner and

afterburner is $Q_R=Q_{R,AB}=41000k\frac{J}{k}g.$ The turbine has a polytropic efficiency $e_t=0\mathrm{.}93$ and

a mechanical efficiency ${}_m=0\mathrm{.}92.$ The afterburner has a pressure ratio ${}_{AB}=0\mathrm{.}97$ and thermal

efficiency ${}_{AB}=0\mathrm{.}95.$ The nozzle is perfectly expanded and has thermal efficiency ${}_n=0\mathrm{.}94.$

a$)$ Using the ideal jet with afterburner result, find the compressor pressure ratio which

maximizes specific thrust. Be careful with the thermal limit parameters.

b$)$ Using the compressor pressure ratio from problem $1($p$3/$p$2)=25,$ drop the ideal jet assumption and

calculate the specific thrust and thermal efficiency of the actual jet.