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 $1100C.$ The performance of different parts of

the engine is as follows:

Compressor: ${}_c=75\%,Cp=1\mathrm{.}075k\frac{J}{k}g.K,=1\mathrm{.}39$

Combustor: ${}_b=98\%,rp=0\mathrm{.}93,Cp=1\mathrm{.}12k\frac{J}{k}gK,Q_R=42,600k\frac{J}{k}g,$

Turbine : ${}_t=87\%,Cp=1\mathrm{.}12k\frac{J}{k}g.K,=1\mathrm{.}34.$

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 $1320C.$