Page 106 - Industrial Ventilation Design Guidebook

4,2 STATE VALUES OF HUMID AIR; MOLLIER DIAGRAMS AND THEIR APPLICATIONS 7 S

5
The difference between vapor pressures is /?/,(50 °C, p i = 1C) Pa) -/?/,{SO °t\
/?,- = 0) = 8 Pa.
This shows that the presence of air in the gas phase has a very small influence
on the vapor pressure of water. Repeating the same calculation procedure tor
other temperatures, we can show that the vapor pressure of water can with good
accuracy be taken from the vapor pressure tables for saturated water (water has
the same pressure as water vapor when they are in equilibrium), as though there
were no air in the gas phase. So the vapor pressure of water is with good accuracy
also in this case just a function of temperature, and Eq. (4.97) is valid. New vapor
pressure tables will not be needed for calculations with humid air,

4.2.4 Vapor Pressure of Water and Ice and Calculation of Humid Air State Values

The partial pressure of water vapor in air cannot be higher than the vapor
pressure of saturated water ph(T) corresponding to air temperature T. If it
were higher, condensation of water vapor would occur until the equilibrium
state corresponding to the saturated vapor pressure was achieved.
Saturated water vapor pressure is most accurately found from vapor
tables or can be approximated with the following equation:

The logarithm in Eq. (4.106) is Briggsian (a logarithm with 10 as the base),
pressure is in units of bar, and the temperature is in Celsius.
A simpler approximation for the pressure of saturated water vapor is

s
where the constant p 0 = 10 Pa and the temperature 7' is in degrees Kelvin.
When the temperature is under 0 °C, the saturation pressure p h, is calcu-
lated using the vapor pressure of ice (ice turns into vapor directly, i.e., subli-
mates) and we can use the following empirical formula:

The logarithm in Eq. (4.108) is Briggsian, pressure has units of mbar, and the
temperature is in Celsius.
For the vapor pressure of ice, the equation of Clapeyron can be obtained
in the same wav as for water:

where bj is the enthalpy of ice and v^ is the specific volume of ice.
The relative vapor pressure of air or the relative humidity is defined by the equation