Handbook of air conditioning and refrigeration / Shan K

2.8 CHAPTER TWO
Degree of Saturation
where n a � number of moles of dry air, mol
n w � number of moles of water vapor in moist air sample, mol
n ws � number of moles of water vapor in saturated moist air sample, mol
Moist air is a binary mixture of dry air and water vapor; therefore, we find that the sum of the mole
fractions of dry air x a and water vapor x w is equal to 1, that is,
x a � x w � 1 (2.20)
If we apply ideal gas equations p wV � n wR oT R and p aV � n aR oT R, by substituting them into
Eq. (2.19), then the relative humidity can also be expressed as
(2.21)
The water vapor pressure of saturated moist air p ws is a function of temperature T and pressure p,
which is slightly different from the saturation pressure of water vapor p s. Here p s is a function of
temperature T only. Since the difference between p ws and p s is small, it is usually ignored.
The degree of saturation � is defined as the ratio of the humidity ratio of moist air w to the humidity
ratio of the saturated moist air w s at the same temperature and pressure. This relationship can be
expressed as
(2.22)
Since from Eqs. (2.15), (2.20), and (2.21) w � 0.62198 x w/x a and w s � 0.62198 x ws/x a, Eqs. (2.20),
(2.21), and (2.22) can be combined, so that
�
(2.23)
1 � (1 � �)x ws 1 � (1 � �)( pws /pat) In Eq. (2.23), pws�� pat; therefore, the difference between � and � is small. Usually, the maximum
difference is less than 2 percent.
2.5 PROPERTIES OF MOIST AIR
Enthalpy
� �
The difference in specific enthalpy �h for an ideal gas, in Btu/lb (kJ/kg), at a constant pressure can
be defined as
where c p � specific heat at constant pressure, Btu/lb�°F (kJ/kg�K)
T 1, T 2 � temperature of ideal gas at points 1 and 2, °F (°C)
�
� � p w
� � w
�T,p pws �h � c p (T 2 � T 1) (2.24)
As moist air is approximately a binary mixture of dry air and water vapor, the enthalpy of the moist
air can be evaluated as
w s
h � h a � H w
� T,p
�
(2.25)