A jet engine on a plane flying at $277\mathrm{.}8$ m$/$s requires $60\mathrm{.}2$ kg$/$s of air into its

compressor to burn fuel with calorific value $42$ MJ$/$ kg$.$

$($a$)$ With the help of a sketch show all the processes on a T$-$s diagram given that

the exhaust leaves through a nozzle with a loss of in kinetic energy due to

friction as it flows. $[4$ marks$]$

$($b$)$ Calculate the thrust developed if the fuel to air ratio is $1$:$70,$ the isentropic

enthalpy drop is $230$ kJ$/$kg across the nozzle and the loss in kinetic energy is

$16\%.[9$ marks$]$

$($c$)$ Differentiate briefly between the combustion efficiency, the thermal efficiency

and the overall efficiency for the above system, indicating clearly which one

should be highest and why. $[4$ marks$]$

$($d$)$ Calculate the thermal efficiency and the overall efficiency for the above given

that the combustion efficiency is $92\%.$