# Humid Air and the Ideal Gas Law

## Pressure, temperature and volume for an ideal or perfect gas like air with water vapor - or moist air

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The Ideal Gas Law express the relation between pressure, temperature and volume in 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)

Density can be expressed as

ρ = m / V(1b)

where

ρ= density (kg/m^{3})

and 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 a gas like

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

Daltons Law states that

*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

By using *(1)* and *(2)*, the dry air partial pressure can be expressed as

p_{a}=ρ_{a}(286.9J/kg K)T(4)

#### Water Vapor Partial Pressure

The water vapor partial pressure can be expressed as

p_{w}= ρ_{w}(461.5J/kg K)T(4b)

Unlike other gases in air, water vapor may condense under common conditions. Since the boiling point of water at normal atmospheric pressure (*101.3 kPa)* is *100 ^{o}C,* the vapor partial pressure of water is low compared to dry air partial pressure in moist air. Common values for vapor pressure in moist air is in the range

*0.5*to

*3.0 kPa*.

Maximum vapor pressure before water vapor start to condense at an actual temperature is called saturation pressure - *p*_{ws}.

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