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

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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 (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 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 = 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

Dry Air Partial Pressure

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

pa = ρa 286.9 T (3)

Water Vapor Partial Pressure

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

pw = ρw 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 100oC. 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 - pws.

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

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Related Topics

  • Air Psychrometrics Air psychrometrics are the study of moist and humid air and the change of air condition - psychrometric charts, Mollier diagrams, air temperature and absolute and relative humidity, moisture content ..

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