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5.35: Untitled Page 97

  • Page ID
    18230
  • 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

    176