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Engineering ToolBox > Density of Dry Air, Water Vapor and Moist Humid Air
Density of air will vary as the temperature and moisture content in the air varies. When the temperature increases, the higher molecular motion results in an expansion of volume and thus a decrease in density.
The density of a gas, either it is dry air, water vapor or a mixture of dry air and water vapor - moist or humid air, can be calculated on basis of the Ideal Gas Law.
The density of dry air can be expressed as:
ρa = 0.0035 pa / T (1)
where
ρa = density dry air (kg/m3)
pa = partial pressure of air (Pa, N/m2)
T = absolute dry bulb temperature (K)
The density of water vapor can be expressed as:
ρw = 0.0022 pw / T (2)
where
pw = partial pressure water vapor (Pa, N/m2)
ρw = density water vapor (kg/m3)
T = absolute dry bulb temperature (K)
The amount of water vapor in the air effects the density. Water vapor is a relatively light gas when compared to diatomic Oxygen and diatomic Nitrogen - the dominant components in air.
When water vapor content increases, the amount of Oxygen and Nitrogen decreases per unit volume and the density will decrease because the mass is decreasing. Dry air is more dense that humid air!
Based on specific volume of moist air the density can be expressed as:
ρ = 1 / v = (p / Ra T) (1 + x) / (1 + x Rw / Ra) (3)
where
v = specific volume of moist air per mass unit of dry air and water vapor (m3/kg)
Ra = 286.9 - the individual gas constant air (J/kg.K)
Rw = 461.5 - the individual gas constant water vapor (J/kg.K)
x = specific humidity or humidity ratio (kg/kg)
p = pressure in the humid air (Pa)
Density of dry air can be expressed as:
ρda = p / Ra T (4)
where
ρda = density dry air (kg/m3)
Combining (4) and (3):
ρ = ρda (1 + x) / (1 + x Rw / Ra) (5)
The gas constant ratio between water vapor and air is 461.5 / 286.9 = 1.609. Inserting the ratio in (5):
ρ = ρda (1 + x) / (1 + 1.609 x ) (6)
Note! As we can see from (6) increased moisture content reduces the density of the moist air - Dry air is more dense than moist air.