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A two-stage compressor having an interstage cooler takes in air, 300 K, 100 kPa, and compresses it to 2 MPa, The cooler then cools the air to 340 K, after which it enters the second stage, which has an exit pressure of 15.74 MPa. Both stages are adiabatic, and reversible. Find q in the cooler, total specific work, and compare this to the work required with no intercooler.

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Same flow rate through both stages so the total work is the sum of the two

wcomp = wC1 + wC2 = –408.3 – 274.5 = –682.8 kJ/kg

For no intercooler (P2 = 15.74 MPa) same analysis as stage 1. So

T2 = 300(15740/100) 0.286 = 1274.9 K

wcomp = 1.004(300 – 1274.9) = –978.8 kJ/kg

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