# 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

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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/m^{2}, lb/ft^{2})

V= volume of gas (m^{3,}ft^{3})

m= mass of gas (kg, lb)

R= individual gas constant (J/kg^{o}K, ft lb/slugs^{o}R)

T= absolute temperature (^{o}K,^{o}R)

Since density can be expressed as:

ρ = m / V(1b)

where

ρ= density (kg/m^{3})

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:

Gas | Individual Gas Constant - R | Molecular Weight ( kg/kmole) | |

Imperial Units ( ft lb/slug)^{ o}R | SI Units ( J/kg K) | ||

Air | 1716 | 286.9 | 28.97 |

Water vapor | 2760 | 461.5 | 18.02 |

### 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}(286.9J/kg K)T(4)

#### Water Vapor Partial Pressure

The partial water vapor partial pressure expressed in SI units:

p_{w}= ρ_{w}(461.5J/kg K)T(4b)

Compared to the other gases in the air water may condense. The boiling point of water at normal atmosphere - *101.3 kPa* - is *100 ^{o}C* 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 condense at an actual temperature - is called the saturation pressure - *p*_{ws}.

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