Document 82b11OvM4ekXeobryNrxONwgB
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CHAPTER 3
1952 Guide
gas is heated or cooled at constant pressure, the volume V varies as the
absolute temperature T. Stated mathematically,
. --p = constant
(volume constant)
(10)
" V-- = constant (pressure constant)
(11)
Boyle's Law and Charles' Law may be combined to form' the equation
of state for the ideal or perfect gas,
-
PV > RT
(12)
where
R is a constant whose value depends on the units selected for P, V, and T.
Dalton's Rule. Dalton stated that each gas in a mixture occupies the total volume of the mixture just as though the other gases were not present. Gibbs later expanded this statement for perfect gases into the
following principles:
1. The pressure of a mixture of gases is the sum of the partial pressures of the in dividual gases when they exist at the total volume and temperature of the mixture-
2. The internal energy, enthalpy, and entropy of a mixture of gases are respec tively equal to the Bums of the individual internal energies, enthalpies, and entropies of the components when they exist at the total volume and temperature of the mix
ture.
While these relationships do not hold exactly for all systems of real
gases, they may be used with a good degree of precision for many engineer ing applications at low pressures. - Moreover, since water vapor very closely follows the perfect gas relationships in, the range usually encountered
in air conditioning, the Gibbs-Dalton Rule may frequently be applied to
mixtures of dry air and water vapor. ;
Thus,
Vm = F. = F,, Tm = To -- T-m .
'.
(13) (14)'
Pm -- Pi + P mmA - mA + mA
(15) (16)
where
Subscript m denotes mixture; subscript a denotes dry air; subscript w denotes
water vapor. Symbol m = weight of dry air crossing any duct section, pounds per minute. .
Using Equations 12, 13, 14, and 15, the relation is obtained as follows:
,, = n,RT _ n,RT _ (n, + nm)RT
9r p.
V-
V
where
. Vt = total volume, cubic feet. n = number of mols of dry air.
Thermodynamics
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n* = number of.mols of water vapor.
,
R = universal gas constant, 1545 foot-pounds per (Fahrenheit degree) (mol).. ; p = partial pressure of dry air.
p = partial pressure of water vapor. .
T = absolute temperature, Fahrenheit degrees.
The partial pressure of water vapor in the mixture is then
------------------ -- n
+
(18)
_or, the partial pressure of the water vapor in moist air is equal to the product *of the mol fraction of the water vapor and the observed pressure of the mixture. A similar expression is obtained for the diy air.
Assuming- that the perfect gas laws can be applied to water vapor at saturation at low pressures, the partial pressure of. water vapor in a satu rated mixture may be written as
where
n. P. = n, + n.
(19)
n " number of mols of .water vapor at saturation.
The relative humidity may be obtained by combining Equations 18 and 19 and solving for the ratio of mol fractions. Thus,-using perfect gas relationships,
(20)
The humidity ratio W may be obtained from.Equation 17:
IF
18.016 pw _
Pw
251966 ^ = 0 622 p - p,,
(21)
where 18.016 and 28.966 are the 'molecular weights of water and dry air, respectively.
Equation 16 may be rewritten as
where
^ = A* + IFAw
(22)
h = enthalpy, Btu per pound of dry air.
In relating the. enthalpy to the state of the moist air, the fact that in all applications only differences in enthalpy are involved, allows the arbitrary selection of a datum or zero enthalpy point. Accordingly, from perfect gas relationships, it is possible to write for any temperature of t, Fahrenheit greater than OF
A. = 0.241
(23)
where it is assumed that the same arbitrary datum of 0 F is Used as in determining the properties of moist air in Table 2.
Tables of Thermodynamic Properties of Moist Air
Research work conducted at the University of Pennsylvania and at other institutions has shown that the Gibbs-Dalton Rule is inaccurate in varying degrees, depending on temperature, pressure and the amount of water