Air is compressed from 15 psia and 70 Air is compressed from 15 psia and 70 degr

Question

Air is compressed from 15 psia and 70

Air is compressed from 15 psia and 70 degree F to 250 psia at a rate of 2 lbm/s. It is accomplished using 2 reversible, adiabatic compressors in series with a heat exchanger in between. There is no pressure drop in the heat exchanger. Clearly state any assumptions. What is the pressure inside the heat exchanger that will minimize the total compressor work? What is the inlet temperature to the heat exchanger, in degreeF? What is the rate of heat removal in the heat exchanger if the inlet to the second compressor is also 70degreeF? What is the total work requirement of the compressors, in Btu/s? What would be the total work requirement of the compressors if they operated polytropically with n=1.1 instead of adiabatically?

Explanation / Answer

a) for minimum work done on compressor, (P2 / P1) = (P4 / P3)

also we know that P2 = P3

P1 * P4 = P2 * P3

P2 = P3 = sqrt( 15*250) = 61.24 psia

b) T2 = T1 * (P2/P1) ^ [(y-1)/y] = ( 273 + 21.11) * (61.24 / 15) ^ [(1.4 - 1)/1.4]

= 294.11*(4.083)^0.286 = 439.794 K

= 166.794 oC = 331.22 F

c) rate of heat removal = 0.907185 * 1.005 * ( 439.794 - 294.11) = 132.823 kW = 126.8923 Btu/s

d) Total Work reqd = 0.907185*1.005*(439.794 - 294.11) + 0.907185*1.005*(439.794 - 294.11)

= 132.823 kW + 132.823 kW = 265.646 kW = 251.785 Btu/s

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