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 @ 20C  (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
20C
90% RH
Pg , 2  Psat @ 258C  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
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