Humid Air and the Ideal Gas Law

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

Air Pressure

According Daltons Law

• the total pressure exerted by a mixture of gases is the sum of the partial pressures of the individual gases

The total pressure in moist air can therefore be expressed as

p_t = p_a + p_w         (3)

where

p_t = total pressure (kPa)

p_a = partial pressure dry air (kPa)

p_w = partial pressure water vapor (kPa)

Dry Air Partial Pressure

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

p_a = ρ_a (286.9 J/kg K) T         (4)

Water Vapor Partial Pressure

The partial water vapor partial pressure expressed in SI units:

p_w = ρ_w (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 100^oC 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 - p_ws.

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