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5.34: Untitled Page 96

  • Page ID
    18229
  • Chapter 5

    example we will accept the boiling point of the mixture as T  86 . 85  0 . 05 C .

    Table 5.5. Computational determination of the boiling point of a water-ethanol mixture

    Computation of dew point of ethanol and water mixture

    Temp

    p

    H

    p

    2O

    Et

    Residue

    Degrees C

    mmHg

    mmHg

    mmHg

    60

    74.7483588

    175.7127

    509.539

    70

    116.9527

    270.8179

    372.229

    80

    177.72766

    405.8736

    176.399

    86

    225.542371

    511.0501

    23.4076

    86.8

    232.662087

    526.6464

    0.6915

    86.9

    233.565109

    528.6235

    2.188576

    87

    234.471058

    530.6067

    5.077746

    90

    263.047594

    593.0441

    96.09172

    5.4.1 Humidity

    In air‐water mixtures the humidity is often used as a measure of concentration that is vaguely described according to

    mass of water

    humidity =

    (5‐35)

    mass of dry air

    In Sec. 4.5.1 we have been more precise in terms of measures of concentration and there we have identified point concentrations, area‐average concentrations, and volume‐average concentrations. An analogous set of definitions exists for the humidity. For example, the point version of the humidity is given explicitly by

    H O

    H O

    2

    2

    point humidity =

    (5‐36)

     

    air

    O2

    N2

    Here we note that “air” or “dry air” in terms of humidity calculations means oxygen and nitrogen and this is not to be confused with “standard dry air” that is used in combustion computations (see Example 5.2). The two are quite similar; however, the density of “air” for humidity calculations is given explicitly by

    Two‐Phase Systems & Equilibrium Stages 173

      and thus does not include the water that is present in humid air. It O2

    N2

    will be left as an exercise for the student to show that

    MW

    p

    H O

    H O

    point humidity =

    (5‐37)

    MW

    p p

    air 2

    2

    H2O 

    in which p is the total pressure and p

    is the partial pressure of the water vapor.

    H2O

    This result can be derived from the definition given by Eq. 5‐36 only if the air-water mixture is treated as an ideal gas. The percent relative humidity is often used as a measure of concentration since our personal comfort may be closely connected to this quantity. It is defined by

    p H O

    2

    % relative humidity =

    100

    (5‐38)

    p H O, vap

    2

    where p H O,

    is the vapor pressure of water at the temperature of the system.

    vap

    2

    When the percent relative humidity is 100%, the air is completely saturated and the addition of further water will result in condensation. Values of the vapor pressure of water are listed in Table 5‐2 as a function of the temperature.

    EXAMPLE 5.6. Humid air flow

    Humid air exits a dryer at atmospheric pressure, 75 C, 25% relative humidity, and at a volumetric flow rate of 100 m3/min. In this example we wish to determine:

    a) Absolute humidity of the air in kg water/kg air.

    b) Molar flow rates of water and dry air.

    The vapor pressure of water at 75 C is found in Table 5‐2 to be p

     289 . 1 mm Hg . The density of mercury is found in Table A2 of H

    vap

    2O ,

    Appendix A. We convert all parameters into SI units according to 289 . 1mmHg

    2

    3

    p

     0 2

    . 5

    9 . 81m/s

    13 , 546 kg/m

     9 , 605Pa

    (1)

    H O

    2

    

    1000 mm/m

    and we use Eq. 5‐25 to compute the mole fraction of water in the air as p H O

    9 , 605 Pa

    2

    y

     0 . 095

    (2)

    H2O

    p

    101 , 300 Pa

    174