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The density of air, ? (Greek: rho) (air density), is the mass per unit volume of Earth's atmosphere
Earth's atmosphere

The Earth's atmosphere is a layer of gases surrounding the planet Earth that is retained by the Earth's gravity. Dry air contains roughly 78.08% nitrogen, 20.95% oxygen, 0.93% argon, 0.038% Carbon dioxide in the Earth's atmosphere, and trace amounts of other gases....
, and is a useful value in aeronautics
Aeronautics

File:An-225 Mriya.jpgFile:Atlantis on Shuttle Carrier Aircraft.jpgFile:Typhoon f2 zj910 arp.jpgAeronautics is the science involved with the study, design, and manufacture of flight-capable machines, or the techniques of operating aircraft....
 and other sciences. Air density decreases with increasing altitude, as does air pressure. It also decreases with increasing temperature or humidity
Humidity

Humidity is the amount of water vapor in the air. In daily language the term "humidity" is normally taken to mean relative humidity. Relative humidity is defined as the ratio of the partial pressure of water vapor in a Air parcel of air to the saturated vapor pressure of water vapor at a prescribed temperature....
. At sea level
Sea level

Mean sea level is the average height of the sea, with reference to a suitable reference surface. Defining the reference level , however, involves complex measurement, and accurately determining MSL can prove difficult....
 and 20 °C, air has a density of approximately 1.2 kg/m3.

e ? is the air density in kilograms per cubic meter, p is pressure in pascals, R is the specific gas constant, and T is temperature in kelvins.

The specific gas constants for dry air are as follows:

Therefore:

addition of water vapor
Water vapor

Water vapor or water vapour , also aqueous vapor, is the gas phase of water . Water vapor is one Phase of the water cycle within the hydrosphere....
 to air (making the air humid) reduces the density of the air, which may at first appear contrary to logic.

This occurs because the molecular mass of water (18) is less than the molecular mass of air (around 29).






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The density of air, ? (Greek: rho) (air density), is the mass per unit volume of Earth's atmosphere
Earth's atmosphere

The Earth's atmosphere is a layer of gases surrounding the planet Earth that is retained by the Earth's gravity. Dry air contains roughly 78.08% nitrogen, 20.95% oxygen, 0.93% argon, 0.038% Carbon dioxide in the Earth's atmosphere, and trace amounts of other gases....
, and is a useful value in aeronautics
Aeronautics

File:An-225 Mriya.jpgFile:Atlantis on Shuttle Carrier Aircraft.jpgFile:Typhoon f2 zj910 arp.jpgAeronautics is the science involved with the study, design, and manufacture of flight-capable machines, or the techniques of operating aircraft....
 and other sciences. Air density decreases with increasing altitude, as does air pressure. It also decreases with increasing temperature or humidity
Humidity

Humidity is the amount of water vapor in the air. In daily language the term "humidity" is normally taken to mean relative humidity. Relative humidity is defined as the ratio of the partial pressure of water vapor in a Air parcel of air to the saturated vapor pressure of water vapor at a prescribed temperature....
. At sea level
Sea level

Mean sea level is the average height of the sea, with reference to a suitable reference surface. Defining the reference level , however, involves complex measurement, and accurately determining MSL can prove difficult....
 and 20 °C, air has a density of approximately 1.2 kg/m3.

Effects of temperature and pressure


The formula for the density of dry air is given by:

where ? is the air density in kilograms per cubic meter, p is pressure in pascals, R is the specific gas constant, and T is temperature in kelvins.

The specific gas constants for dry air are as follows:

Therefore:
  • At IUPAC
    International Union of Pure and Applied Chemistry

    The International Union of Pure and Applied Chemistry is a non-governmental organization established in 1919 for the advancing of chemistry. Its members are national chemistry societies....
     standard temperature and pressure (0 °C
    Celsius

    Celsius is a temperature scale that is named after the Swedish astronomer Anders Celsius , who developed a similar temperature scale two years before his death....
     and 100 kPa
    Pascal (unit)

    The pascal is the SI derived unit of pressure, stress , Young's modulus and tensile strength. It is a measure of force per unit area i.e. equivalent to one newton per square meter or one joule per cubic meter....
    ), dry air has a density of 1.2754 kg
    Kilogram

    The kilogram or kilogrammeThe spelling kilogram is used by the International Committee for Weights and Measures and the U.S....
    /m3.
  • At 20 °C and 101.325 kPa, dry air has a density of 1.2041 kg/m3.
  • At 70 °F
    Fahrenheit

    Fahrenheit is a temperature scale named after the physicist Daniel Gabriel Fahrenheit , who proposed it in 1724. Today, the scale has largely been replaced by the Celsius scale; it is still in use for non-scientific purposes in the United States and a few other countries such as Belize....
     and 14.696 psia
    Pounds per square inch

    The pound per square inch or, more accurately, pound-force per square inch is a unit of pressure or of stress based on avoirdupois units....
    , dry air has a density of 0.074887 lbm
    Pound (mass)

    The pound or pound-mass is a Units of measurement of massused in the Imperial unit, United States customary units and other systems of measurement....
    /ft3
    Cubic foot

    The cubic foot is an Imperial unit and United States customary units unit of volume, used in the United States, Canada and the United Kingdom. It is defined as the volume of a cube with sides of one foot in length.|-...
    .


Effect of water vapor

The addition of water vapor
Water vapor

Water vapor or water vapour , also aqueous vapor, is the gas phase of water . Water vapor is one Phase of the water cycle within the hydrosphere....
 to air (making the air humid) reduces the density of the air, which may at first appear contrary to logic.

This occurs because the molecular mass of water (18) is less than the molecular mass of air (around 29). For any gas, at a given temperature and pressure, the number of molecules present is constant for a particular volume. So when water molecules (vapor) are introduced to the air, the number of air molecules must reduce by the same number in a given volume, without the pressure or temperature increasing. Hence the mass per unit volume of the gas (its density) decreases.

The density of humid air may be calculated as a mixture of ideal gas
Ideal gas

The ideal gas model is a model of matter in which the molecules are treated as non-interacting point particles which are engaged in a random motion that obeys conservation of energy....
es. In this case, the partial pressure
Partial pressure

In a mixture of ideal gases, each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume. The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture....
 of water vapor
Water vapor

Water vapor or water vapour , also aqueous vapor, is the gas phase of water . Water vapor is one Phase of the water cycle within the hydrosphere....
 is known as the vapor pressure
Vapor pressure

Vapor pressure , is the pressure of a vapor in Thermodynamic equilibrium with its non-vapor Phase s. All liquids and solids have a tendency to evaporate to a gaseous form, and all gases have a tendency to Condensation back into their original form ....
. Using this method, error in the density calculation is less than 0.2% in the range of -10 °C to 50 °C. The density of humid air is found by:

Where: Density of the humid air (kg/m³) Partial pressure of dry air (Pa) Specific gas constant for dry air, 287.05 J/(kg·K) Temperature (K) Pressure of water vapor (Pa) Specific gas constant for water vapor, 461.495 J/(kg·K)

The vapor pressure of water may be calculated from the saturation vapor pressure and relative humidity
Relative humidity

Relative humidity is a term used to describe the amount of water vapor that exists in a gaseous mixture of air and water....
. It is found by:

Where: Vapor pressure of water Relative humidity Saturation vapor pressure

The saturation vapor pressure of water at any given temperature is the vapor pressure when relative humidity is 100%. A simplification of the regression used to find this, can be formulated as:

IMPORTANT:
  • This will give a result in mb (millibar), 1 mb=100 Pa


  • is found considering partial pressure
    Partial pressure

    In a mixture of ideal gases, each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume. The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture....
    , resulting in:


Where p simply notes the absolute pressure in the observed system.

Effects of altitude


To calculate the density of air as a function of altitude, one requires additional parameters. They are listed below, along with their values according to the International Standard Atmosphere
International Standard Atmosphere

The International Standard Atmosphere is an atmospheric models of how the pressure, temperature, density, and viscosity of the Earth's atmosphere change over a wide range of altitudes....
, using the universal gas constant
Gas constant

The gas constant is a physical constant which is featured in a large number of fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation....
 instead of the specific one:
  • sea level standard atmospheric pressure p0 = 101325 Pa
    Pascal (unit)

    The pascal is the SI derived unit of pressure, stress , Young's modulus and tensile strength. It is a measure of force per unit area i.e. equivalent to one newton per square meter or one joule per cubic meter....
  • sea level standard temperature T0 = 288.15 K
    Kelvin

    The kelvin is a Units of measurement of temperature and is one of the seven SI base units. The Kelvin scale is a Thermodynamic temperature scale where absolute zero, the theoretical absence of all thermal energy, is zero ....
  • Earth-surface gravitational acceleration g = 9.80665 m/s2.
  • temperature lapse rate L = −0.0065 K
    Kelvin

    The kelvin is a Units of measurement of temperature and is one of the seven SI base units. The Kelvin scale is a Thermodynamic temperature scale where absolute zero, the theoretical absence of all thermal energy, is zero ....
    /m
  • universal gas constant R = 8.31447 J/(mol
    Mole (unit)

    The mole is a Units of measurement of amount of substance: it is an SI base unit, and one of the few units used to measure this physical quantity....
    ·K)
  • molar mass
    Molar mass

    Molar mass, symbol M, is the mass of one mole of a substance . It is a physical property which is characteristic of each pure substance. The base SI unit for mass is the kilogram but, for both practical and historical reasons, molar masses are almost always quoted in grams per mole , especially in chemistry....
     of dry air M = 0.0289644 kg/mol


Temperature at altitude h meters above sea level is given by the following formula (only valid inside the troposphere
Troposphere

The troposphere is the lowest portion of Earth's atmosphere. It contains approximately 75% of the atmosphere's mass and almost all of its water vapor and particulate....
):

The pressure at altitude h is given by:

Density can then be calculated according to a molar form of the original formula:

Importance of temperature


The below table demonstrates that the properties of air change significantly with temperature.

Table — speed of sound
Speed of sound

Sound is a vibration that travels through an elasticity medium as a wave. The speed of sound describes how much distance such a wave travels in a certain amount of time....
 in air c, density of air ?, acoustic impedance
Acoustic impedance

The acoustic impedance Z is a frequency f dependent parameter and is very useful, for example, for describing the behaviour of musical wind instruments....
 Z vs. temperature
Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
 °C
Effect of temperature
°C
Celsius

Celsius is a temperature scale that is named after the Swedish astronomer Anders Celsius , who developed a similar temperature scale two years before his death....
 		 c in m/s
Second

The second , sometimes abbreviated sec., is the name of a units of measurement of time, and is the International System of Units SI base unit of time....
 		 ? in kg
Kilogram

The kilogram or kilogrammeThe spelling kilogram is used by the International Committee for Weights and Measures and the U.S....
/m³ 		Z in Pa
Pascal (unit)

The pascal is the SI derived unit of pressure, stress , Young's modulus and tensile strength. It is a measure of force per unit area i.e. equivalent to one newton per square meter or one joule per cubic meter....
·s/m
-25 1.423  
-20 1.395  
-15 1.368  
-10 325.2 1.342 436.1
-5 328.3 1.317 432.0
0 331.3 1.292 428.4
+5 334.3 1.269 424.3
+10 337.3 1.247 420.6
+15 340.3 1.225 416.8
+20 343.2 1.204 413.2
+25 346.1 1.184 409.8
+30 349.0 1.165 406.3


See also

  • International Standard Atmosphere
    International Standard Atmosphere

    The International Standard Atmosphere is an atmospheric models of how the pressure, temperature, density, and viscosity of the Earth's atmosphere change over a wide range of altitudes....
  • U.S. Standard Atmosphere
  • NRLMSISE-00
    NRLMSISE-00

    NRLMSISE-00 is an empirical, global Mathematical model of the Earth's atmosphere from ground to space. It models the temperatures and density of the atmosphere's components....


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