Problem $1$:A gas turbine engine is operating at a surrounding temperature of $298$ K$.$ The pressure ratio in the compressor is $25$ and the Combustor exit temperature is $1100$ oC$.$ The performance of different parts of the engine is as follows:$-$ Compressor : c $=75\%,$ Cp $=1\mathrm{.}075$ kJ$/$kg $.$K$,=1\mathrm{.}39-$ Combustor: b $=98\%,$ rp $=0\mathrm{.}93,$ Cp $=1\mathrm{.}12$ kJ$/$kgK$,$ QR $=42,600$ kJ$/$kg$,-$ Turbine : t $=87\%,$ Cp $=1\mathrm{.}12$ kJ$/$kg$.$K$,=1\mathrm{.}34.$ a$-$ Determine the specific power output of the engine, efficiency of engine and SFC$.$ b$-$ Repeat part $($a$)$ if the compressor efficiency is increased to $85\%.$c$-$ Repeat part $($b$)$ if the combustion temperature is also increased to $1320$ oC$.$