Problem #$2$: $(16$ Points$)q,$

A stationary Gas Turbine has two ideal Turbine sections, as shown in Figure, the first of which drives the ideal compressor and the second is used for power generation with a compressor inlet Air condition of $290K,100$kPa and exit conditions of $450$ kPa $.$ A fraction of flow x bypasses the burner and the rest goes through the burner where $1200k\frac{J}{k}g$ heat is added by combustion. The two flows then mix before entering the first turbine and continue to the second turbine with exhaust ptessure of $100$ kPa $.$ If the temperature afer mixing is $1000K$;

a$)$ Determine the power required to drive the compressor. $(3$ Points$)$

b$)$ Calculate the air mass fow fraction $x.(7$ Points$)$

c$)$ Calculate the specific power generated by the second Turbine. $(3$ Points$)$

d$)$ Determine the thermal efficiency of this G$.$T$.(3$ Points$)$