The temperature of air entering the compressor of a jet airc

The temperature of air entering the compressor of a jet aircraft is 50oC. The jet’s turbine is producing 200 kJ of energy for every kg of air flowing through it. What is the pressure ratio of the compressor, assuming constant fluid properties, no auxiliary power needs from the turbine, and ideal operation? (Use variable specific heats (IG).

Solution

We know that Gas engines follows the Brayton cycle.Therefore,

P1=P4 and P2= P3,we need to find P2=P1,

Q1 = mCp(T3-T2)

200 = 1(500-x)

X=300°C

Therefore,500/300 =( P2/P1)^y-1/y

1.66=P2/P1^(.285)