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14-7 14-20 Humid air is compressed in an isentropic compressor. The relative humidity of the air at the compressor outlet is to be determined. Assumptions The air and the water vapor are ideal gases. Properties The specific heat ratio of air at room temperature is k = 1.4 (Table A-2a). The saturation properties of water are to be obtained from water tables. Analysis At the inlet, Pv ,1 1 Pg ,1 1 Psat @ 20C (0.90)(2.3392 kPa) = 2.105 kPa 0.622 Pv,1 2 1 P Pv ,1 (0.622)(2.105 kPa) 0.0134 kg H 2 O/kg dry air (100 2.105) kPa 800 kPa Humid air Since the mole fraction of the water vapor in this mixture is very small, P T2 T1 2 P1 ( k 1) / k 800 kPa (293 K ) 100 kPa 0.4/1.4 531 K The saturation pressure at this temperature is 100 kPa 20C 90% RH Pg , 2 Psat @ 258C 4542 kPa (from EES) The vapor pressure at the exit is Pv , 2 2 P2 (0.0134)(800) 16.87 kPa 2 0.622 0.0134 0.622 The relative humidity at the exit is then 2 Pv , 2 Pg , 2 16.87 0.0037 0.37% 4542 PROPRIETARY MATERIAL. © 2011 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.