# 5.35: Untitled Page 97

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## Chapter 5

In order to determine the absolute humidity, we use Eq. 5‐35 in the more precise form given by Eq. 5‐36

mass of water

mass of water/volume

humidity =

(3)

mass of dry air

mass of dry air/volume

and this leads to an expression for the humidity given by

*MW*

*y*

*MW*

*y*

H2O

H O

H O

H O

H O

2

2

2

2

humidity

*MW*

*y*

*MW *(1 *y*

)

*air*

*air*

*air*

*air*

H O

2

(4)

18.05 g water/mol 0.095

0 066

*. *

g water */ * g dry air

28.85 g dry air/mol (1 0.095)

Once again we have used the subscript “air” as a convenient substitute for dry air and we will continue to make use of this simplification throughout our study of humidification processes. Assuming that water vapor and air behave as ideal gases at atmospheric pressure, we use the ideal gas law given by Eq. 5‐3 to compute the total concentration of the mixture. The concentration of the gas mixture is the total number of moles of air and water per unit volume of the mixture. This can be expressed as *n*

*p*

101 *, * 300 Pa

3

*c *

35 mol/m

(5)

3

*V*

*RT*

m Pa

8 314

*. *

348 16

*. *

K

mol K

This result gives the total number of moles of gas per unit volume of mixture. In order to determine the molar flow rates of water and dry air, we carry out the following calculations to obtain

*M*

*c*

*Q * *y*

*c Q*

H O

H O

H O

2

2

2

(6a)

3

3

0 *. * 095 35 mol/m 100 m /min 332.5 mol water/min *M*

*c Q * *y c Q*

*air*

*air*

*air*

(6b)

(1 *y*

) *c Q * 3 *, * 167 *. * 5 mol dry air /min

H2O

*Two‐Phase Systems* & *Equilibrium Stages* 175

Table 5‐2. Vapor Pressure of Water as a Function of Temperature *T*, C

Vapor Pressure, mm Hg

*T*, F

Vapor Pressure, in Hg

0

4.579

32

0.180

5

6.543

40

0.248

10

9.209

50

0.363

15

12.788

60

0.522

20

17.535

70

0.739

25

23.756

80

1.032

30

31.824

90

1.422

35

42.175

100

1.932

40

55.324

110

2.596

45

71.88

120

3.446

50

92.51

130

4.525

55

118.04

140

5.881

60

149.38

150

7.569

65

187.54

160

9.652

70

233.7

170

12.199

75

289.1

180

15.291

80

355.1

190

19.014

85

433.6

200

23.467

90

525.76

212

29.922

95

633.90

220

34.992

100

760.00

230

42.308

105

906.07

240

50.837

110

1,074.56

250

60.725

115

1,267.98

260

72.134

120

1,489.14

270

85.225

125

1,740.93

280

100.18

130

2,026.16

290

117.19

135

2,347.26

300

136.44

5.4.2 *Modified mole fraction*

In general, the most useful measures of concentration are the molar concentration *c * and the species mass density . Associated with these *A*

*A*

concentrations are the mole fraction defined by Eq. 5‐1f and the mass fraction defined by Eq. 5‐1c. Sometimes it is convenient to use a modified mole fraction or *mole ratio* which is based on all the species *except one*. If we identify that one species as species *N*, we express the modified mole fraction as