An aircraft engine has design parameter as shown in table $1$

$\backslash$table$[[$Parameters$,$Value$],[$M$\_(0),0],[$Pa$\_($a$),101$ Kpa$],[$T$\_($a$),15\backslash$deg C$],[$Compressor Pressure Ratio,$25],[$Turbine Entry Temperature $,$ TET,$1500$ K$],[$Compressor Efficiency,$0\mathrm{.}9],[$Turbine Efficiency,$0\mathrm{.}85],[$Low Heating Value, LHV of Jet A$,42800$kJ$/$Kg$],[$Combustor Pressure Loss $(\%$ of Cdp$),5],[$Air Mass Flow,$150$kJ$/$s$],[$C$\_($p$,$ cold $),1000$J$/$kg$/$K$],[\backslash$gamma $\_($cold $),1\mathrm{.}4],[$C$\_($p$,$ Hot $),1150$J$/$Kg$/$K$],[\backslash$gamma $\_($hot $),1\mathrm{.}333]]$

Unless otherwise specified, the turbomachinery efficiency is isentropic$.$

a$)$ Analyze the engine type by sketching a schematic diagram as well as T$-$ s diagram of the engine.

b$)$ determine the thrust and Specific Fuel consumption $($SFC$)$ of the engine if the engine uses convergent nozzle.