Handbook of air conditioning and refrigeration / Shan K

Moist Volume
where h a and H w are, respectively, enthalpy of dry air and total enthalpy of water vapor, in Btu/lb
(kJ/kg). The following assumptions are made for the enthalpy calculations of moist air:
1. The ideal gas equation and the Gibbs-Dalton law are valid.
2. The enthalpy of dry air is equal to zero at 0°F (�17.8°C).
3. All water vapor contained in the moist air is vaporized at 0°F (�17.8°C).
4. The enthalpy of saturated water vapor at 0°F (�17.8°C) is 1061 Btu/lb (2468 kJ/kg).
5. For convenience in calculation, the enthalpy of moist air is taken to be equal to the enthalpy of a mixture
of dry air and water vapor in which the amount of dry air is exactly equal to 1 lb (0.454 kg).
Based on the preceeding assumptions, the enthalpy h of moist air can be calculated as
h � ha � whw (2.26)
where hw � specific enthalpy of water vapor, Btu/lb (kJ/kg). In a temperature range of 0 to 100°F
(�17.8 to 37.8°C), the mean value for the specific heat of dry air can be taken as 0.240 Btu/lb�°F
(1.005 kJ/kg�K). Then the specific enthalpy of dry air ha is given by
h a � c pd T � 0.240 T (2.27)
where c pd � specific heat of dry air at constant pressure, Btu/lb�°F (kJ/kg�K)
T � temperature of dry air, °F (°C)
The specific enthalpy of water vapor h w at constant pressure can be approximated as
h w � h g0 � c psT (2.28)
where h g0 � specific enthalpy of saturated water vapor at 0°F (�17.8°C)—its value can be taken
as 1061 Btu/lb (2468 kJ/kg)
c ps � specific heat of water vapor at constant pressure, Btu/lb�°F (kJ/kg�K)
In a temperature range of 0 to 100°F (�17.8 to 37.8°C), its value can be taken as 0.444 Btu/lb�°F
(1.859 kJ/kg�K). Then the enthalpy of moist air can be evaluated as
h � c pdT � w(h g0 � c psT) � 0.240 T � w(1061 � 0.444 T) (2.29)
Here, the unit of h is Btu/lb of dry air (kJ/kg of dry air). For simplicity, it is often expressed as
Btu/lb (kJ/kg).
The moist volume of moist air v, ft 3 /lb (m 3 /kg), is defined as the volume of the mixture of the dry
air and water vapor when the mass of the dry air is exactly equal to 1 lb (1 kg), that is,
where V � total volume of mixture, ft 3 (m 3 )
m a � mass of dry air, lb (kg)
(2.30)
In a moist air sample, the dry air, water vapor, and moist air occupy the same volume. If we apply
the ideal gas equation, then
v � V
m a
v � V
m a
� R aT R
p at � p w
PSYCHROMETRICS 2.9
(2.31)