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Humid Air vs. the Ideal Gas Law

Pressure, temperature and volume in a perfect ideal gas like moist air (air with water vapor).

In a perfect or ideal gas the correlations between pressure, volume, temperature and quantity of gas can be expressed by the Ideal Gas Law.

The Universal Gas Constant, Ru is independent of the particular gas and is the same for all "perfect" gases, and is included in of The Ideal Gas Law:

p V = n R u T (1)

where

p = absolute pressure (N/m2, lb/ft2)

V = volume (m 3, ft3 )

n = is the number of moles of the gas present

R u = universal gas constant (J/mol o K, lbf ft/(lb mol o R) = 8.3145 J/mol K = 0.08206 L atm/mol K  = 62.37 torr /mol K

T = absolute temperature ( o K, o R)

For a given quantity of gas, both n and R u are constant, and Equation (1) can be modified to

p1 V1 / T1 = p2V2/ T2(2)

expressing the relationship between different states for the given quantity of the gas.

Equation (1)  can also be expressed as

p V = N k T                         (3)

N =number of molecules

k = Boltzmann constant = 1.38066 10 -23 J/K = 8.617385 10 -5 eV/K

• One mole of an ideal gas at STP occupies 22.4 liters.

The Ideal Gas Law express the relation between pressure, temperature and volume in an ideal or perfect gas.

The Ideal Gas Law expessed by the Induvidual Gas Constant

The Ideal Gas Law can be expressed with the Individual Gas Constant as

p V = m R T                                       (4)

where

p = absolute pressure (N/m2, lb/ft2)

V = volume of gas (m 3, ft3 )

m = mass of gas (kg, slugs )

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                                     (4b)

where

ρ = density (kg/m3, slugs/ft3 )

and equation (4) can be modified to

p = ρ R T                                   (4c)

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 = universal gas constant ( 8314.47 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 461.4 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 (286.9 J/kg K) T (4)

Water Vapor Partial Pressure

The water vapor partial pressure can be expressed as

p w = ρ w ( 461.5 J/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 oC, 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 are 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 .

Related Topics

• Air Psychrometrics

Moist and humid air calculations. Psychrometric charts and Mollier diagrams. Air-condition systems temperatures, absolute and relative humidities and moisture content in air.
• Basics

Basic engineering data. SI-system, unit converters, physical constants, drawing scales and more.

Related Documents

• Air - Composition and Molecular Weight

Dry air is a mechanical mixture of nitrogen, oxygen, argon and several other gases in minor amounts.
• Air - Humidity Measurement from Dry and Wet Bulb Temperature

Relative humidity in moist air can estimated by measuring the dry and wet bulb temperature.
• Air - Maximum Moisture Carrying Capacity

Maximum water content in humid air vs. temperature.
• Air - Moisture Holding Capacity vs. Temperature

The moisture holding capacity of air increases with temperature.
• Air - Molecular Weight and Composition

Dry air is a mixture of gases where the average molecular weight (or molar mass) can be calculated by adding the weight of each component.
• Dry Air - Thermodynamic and Physical Properties

Thermodynamic properties of dry air - specific heat, ratio of specific heats, dynamic viscosity, thermal conductivity, Prandtl number, density and kinematic viscosity at temperatures ranging 175 - 1900 K.
• Dry Air and Water Vapor - Density and Specific Volume vs. Temperature - Imperial Units

Density and specific volume of dry air and water vapor at temperatures ranging 225 to 900 degF (107 to 482 degC).
• Moist Air - Daltons Law of Partial Pressure

The pressure in a mixture of dry air and water vapor - humid or moist air - can be estimated by using Daltons Law of partial pressures.
• Moist Air - Degree of Saturation

Humidity ratio of moist air to humidity ratio of saturated moist air.
• Moist Air - Density vs. Pressure

Density of moist air vs. pressure ranging 75 - 1000 mmHg.
• Moist Air - Density vs. Water Content and Temperature

Density of the mix of dry air and water vapor - moist humid air.
• Moist Air - Specific Volume

Specific volume of moist air is defined as the total volume of humid air per mass unit of dry air
• Moist Air - Specific vs. Relative Humidity

Specific humidity of moist air vs. relative humidity, water vapor and air density.
• Moist Air - Water Vapor and Saturation Pressure

Saturation pressure of water vapor in moist air vs. temperature.
• Nitrogen - Enthalpy, Internal Energy and Entropy vs. Temperature

Enthalpy, internal energy and entropy of Nitrogen as an ideal gas.
• Non-ideal gas - Van der Waal's Equation and Constants

The van der Waals constants for more than 200 gases used to correct for non-ideal behavior of gases caused by intermolecular forces and the volume occupied by the gas particles.
• The Ideal Gas Law

The relationship between volume, pressure, temperature and quantity of a gas, including definition of gas density.
• Total and Partial Pressure - Dalton's Law of Partial Pressures

How to calculate total pressure and partial pressures for gas mixtures from Ideal Gas Law.
• Universal and Individual Gas Constants

The Universal and Individual Gas Constants in fluid mechanics and thermodynamics. Individual gas constants for the most common gases.

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Citation

• The Engineering ToolBox (2004). Humid Air vs. the Ideal Gas Law. [online] Available at: https://www.engineeringtoolbox.com/humid-air-ideal-gas-d_677.html [Accessed Day Month Year].

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4.10.13

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