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The Ideal Gas Law relates pressure, temperature, and volume of an ideal or perfect gas.
The Ideal Gas Law can be expressed with the Individual Gas Constant:
p V = m R T (1)
where
p = absolute pressure (N/m2, lb/ft2)
V = volume of gas (m3, ft3)
m = mass of gas (kg, lb)
R = individual gas constant (J/kg oK, ft lb/slugs oR)
T = absolute temperature (oK, oR)
Since density can be expressed as:
ρ = m / V (1b)
where
ρ = density (kg/m3)
equation (1) can be modified to:
p = ρ R T (1c)
The individual gas constant can be expressed with the universal gas constant and the molecular weight of the air as:
R = Ru / Mgas (2)
where
Mgas = molecular weight of the gas
Ru = 8314.47 = universal gas constant (J/(kmol K))
The Molecular weight and the Individual Gas Constants for air and water vapor are listed below:
| Gas | Individual Gas Constant - R | Molecular
Weight (kg/kmole) |
|
| Imperial Units (ft lb/slug oR) |
SI Units (J/kg K) |
||
| Air | 1716 | 286.9 | 28.97 |
| Water vapor | 2760 | 461.5 | 18.02 |
According Daltons Law
The total pressure in moist air can therefore be expressed as
pt = pa + pw (3)
where
pt = total pressure (kPa)
pa = partial pressure dry air (kPa)
pw = partial pressure water vapor (kPa)
Using (1) and (2) the dry air partial pressure expressed in SI units:
pa = ρa (286.9 J/kg K) T (4)
The partial water vapor partial pressure expressed in SI units:
pw = ρw (461.5 J/kg K) T (4b)
Compared to the other gases in the air water may condensate. The boiling point of water at normal atmosphere - 101.3 kPa - is 100oC but the vapor pressure is in general very low compared to the air pressure in moist air mixture. Common values for the vapor pressure range 0.5 to 3.0 kPa.
The maximum vapor pressure possible before the vapor start to condensate at an actual temperature - is called the saturation pressure - pws.
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