Density of Dry Air, Water Vapor and Moist Humid Air

Calculating the density of dry air, water vapor or the mixture of air and water vapor - moist or 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.

Density of Dry Air

The density of dry air can be expressed as:

ρ_a = 0.0035 p_a / T (1)

where

ρ_a = density dry air (kg/m³)

p_a = partial pressure of air (Pa, N/m²)

T = absolute dry bulb temperature (K)

Density of Water Vapor

The density of water vapor can be expressed as:

ρ_w = 0.0022 p_w / T (2)

where

p_w = partial pressure water vapor (Pa, N/m²)

ρ_w = density water vapor (kg/m³)

T = absolute dry bulb temperature (K)

Density of Moist Air - an Air Vapor Mixture

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 / R_a T) (1 + x) / (1 + x R_w / R_a) (3)

where

v = specific volume of moist air per mass unit of dry air and water vapor (m³/kg)

R_a = 286.9 - the individual gas constant air (J/kg.K)

R_w = 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:

ρ_da = p / R_a T (4)

where

ρ_da = density dry air (kg/m³)

Combining (4) and (3):

ρ = ρ_da (1 + x) / (1 + x R_w / R_a) (5)

The gas constant ratio between water vapor and air is 461.5 / 286.9 = 1.609. Inserting the ratio in (5):

ρ = ρ_da (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.

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