The compressor stage of the engine is designed to raise the pressure of the air

Question

The compressor stage of the engine is designed to raise the pressure of the air coming into the engine by performing work on it. The power necessary to drive the compressor, Wcomp, is supplied by the turbine, as discussed in Question 4. Air enters the compressor at p2 = 1.5 atm and T2 = 350 K. Assuming that the compressor is well insulated (adiabatic), what is the power, Wcomp, required to raise the pressure by a factor of 10 (so that p3 / p1 = 15), if the process is an ideal adiabatic compression (pv^y = constant)? You may neglect changes in the kinetic energy of the air during this process

Explanation / Answer

For adiabatic compression, T2/T1 = (P2/P1)^(1-1/n) where n is sp. heat ratio = 1.4 for air. So, T2/350 = 10^(1-1/1.4) T2 = 675.8 K W = Cp(T2 - T1) = 1.005*(675.8-350) = 327.4 kJ/kg where Cp = 1.005 is the sp. heat for air.

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