Humid Air and the Ideal Gas Law

The Ideal Gas Law relating pressure, temperature, and volume of an ideal or perfect gas can also be used for air with water vapor - moist air

The Ideal Gas Law relates pressure, temperature, and volume of an ideal or perfect gas.

The Ideal Gas Law

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 (m^3, 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 and Universal Gas Constant

The individual gas constant can be expressed with the universal gas constant and the molecular weight of the air as:

R = R_u / M_gas (2)

where

M_gas = molecular weight of the gas

R_u = 8314.47 = universal gas constant (J/(kmol K))

The Molecular weight and the Individual Gas Constants for air and water vapor are listed below:

Dry Air Partial Pressure

Using (1) and (2) the dry air partial pressure can be expressed in SI units as:

p_a = ρ_a 286.9 T (3)

Water Vapor Partial Pressure

The partial water vapor partial pressure can be expressed in SI units as:

p_w = ρ_w 461.5 T (3b)

Compared to the other gases in the air, water may easy condensate. The boiling point of water at normal atmosphere - 101.3 kPa - is 100^oC. The vapor pressure is in general very low compared to the air pressure in a mixture. Common values for the vapor pressure are between 0.5 to 3.0 kPa.

The maximum pressure possible before vapor start to condensate at an actual temperature is called the saturation pressure - p_ws.

The total pressure in the mixture of dry air and water vapor can be expressed with the Daltons Law.

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