Density of air

src: geogrify.net

The density of air ? (Greek: rho) (air density) is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variation in temperature and humidity. At sea level and at 15 °C air has a density of approximately 1.225 kg/m³ (1.225 x10^-3 g/cm³, 0.0023769 slug/(cu ft), 0.0765 lb/(cu ft)) according to ISA (International Standard Atmosphere).

Air density is a property used in many branches of science, engineering, and industry, including aeronautics; gravimetric analysis; the air-conditioning industry; atmospheric research and meteorology; agricultural engineering (modeling and tracking of Soil-Vegetation-Atmosphere-Transfer (SVAT) models); and the engineering community that deals with compressed air.

Video Density of air

Density of air calculations

Depending on the measuring instruments used, different sets of equations for the calculation of the density of air can be applied. Air is a mixture of gases and the calculations always simplify, to a greater or lesser extent, the properties of the mixture.

Density of air variables

Temperature and pressure

The density of dry air can be calculated using the ideal gas law, expressed as a function of temperature and pressure:

${\displaystyle \rho ={\frac {p}{R_{\rm {specific}}T}}}$

where:

${\displaystyle \rho =}$ air density (kg/m³)

${\displaystyle p=}$ absolute pressure (Pa)

${\displaystyle T=}$ absolute temperature (K)

${\displaystyle R_{\rm {specific}}=}$ specific gas constant for dry air (J/(kg·K))

The specific gas constant for dry air is 287.058 J/(kg·K) in SI units, and 53.35 (ft·lbf)/(lb·°R) in United States customary and Imperial units. This quantity may vary slightly depending on the molecular composition of air at a particular location.

Therefore:

• At IUPAC standard temperature and pressure (0 °C and 100 kPa), dry air has a density of 1.2754 kg/m³.
• At 20 °C and 101.325 kPa, dry air has a density of 1.2041 kg/m³.
• At 70 °F and 14.696 psi, dry air has a density of 0.074887 lb/ft³.

The following table illustrates the air density-temperature relationship at 1 atm or 101.325 kPa:

Humidity (water vapor)

The addition of water vapor to air (making the air humid) reduces the density of the air, which may at first appear counter-intuitive. This occurs because the molar mass of water (18 g/mol) is less than the molar mass of dry air (around 29 g/mol). For any ideal gas, at a given temperature and pressure, the number of molecules present is constant for a particular volume (see Avogadro's Law). So when water molecules (water vapor) are added to a given volume of air, the dry air molecules must decrease by the same number, to keep the pressure or temperature from increasing. Hence the mass per unit volume of the gas (its density) decreases.

The density of humid air may be calculated by treating it as a mixture of ideal gases. In this case, the partial pressure of water vapor is known as the vapor pressure. 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:

${\displaystyle \rho _{\,\mathrm {humid~air} }={\frac {p_{d}}{R_{d}T}}+{\frac {p_{v}}{R_{v}T}}={\frac {p_{d}M_{d}+p_{v}M_{v}}{RT}}\,}$  

where:

${\displaystyle \rho _{\,\mathrm {humid~air} }=}$ Density of the humid air (kg/m³)

${\displaystyle p_{d}=}$ Partial pressure of dry air (Pa)

${\displaystyle R_{d}=}$ Specific gas constant for dry air, 287.058 J/(kg·K)

${\displaystyle T=}$ Temperature (K)

${\displaystyle p_{v}=}$ Pressure of water vapor (Pa)

${\displaystyle R_{v}=}$ Specific gas constant for water vapor, 461.495 J/(kg·K)

${\displaystyle M_{d}=}$ Molar mass of dry air, 0.028964 kg/mol

${\displaystyle M_{v}=}$ Molar mass of water vapor, 0.018016 kg/mol

${\displaystyle R=}$ Universal gas constant, 8.314 J/(K·mol)

The vapor pressure of water may be calculated from the saturation vapor pressure and relative humidity. It is found by:

${\displaystyle p_{v}=\phi p_{\mathrm {sat} }\,}$

where:

${\displaystyle p_{v}=}$ Vapor pressure of water

${\displaystyle \phi =}$ Relative humidity

${\displaystyle p_{\mathrm {sat} }=}$ Saturation vapor pressure

The saturation vapor pressure of water at any given temperature is the vapor pressure when relative humidity is 100%. One formula used to find the saturation vapor pressure is:

${\displaystyle p_{\mathrm {sat} }=6.1078\times 10^{\frac {7.5T}{T+237.3}}}$

where ${\displaystyle T=}$ is in degrees C.

note:

• This equation will give the result of pressure in hPa (100 Pa, equivalent to the older unit millibar, 1 mbar = 0.001 bar = 0.1 kPa)

The partial pressure of dry air ${\displaystyle p_{d}}$ is found considering partial pressure, resulting in:

${\displaystyle p_{d}=p-p_{v}\,}$

Where ${\displaystyle p}$ simply denotes the observed absolute pressure.

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, using for calculation the universal gas constant instead of the air specific constant:

${\displaystyle p_{0}=}$ sea level standard atmospheric pressure, 101.325 kPa

${\displaystyle T_{0}=}$ sea level standard temperature, 288.15 K

${\displaystyle g=}$ earth-surface gravitational acceleration, 9.80665 m/s²

${\displaystyle L=}$ temperature lapse rate, 0.0065 K/m

${\displaystyle R=}$ ideal (universal) gas constant, 8.31447 J/(mol·K)

${\displaystyle M=}$ molar mass of dry air, 0.0289644 kg/mol

Temperature at altitude ${\displaystyle h}$ meters above sea level is approximated by the following formula (only valid inside the troposphere):

${\displaystyle T=T_{0}-Lh\,}$

The pressure at altitude ${\displaystyle h}$ is given by:

${\displaystyle p=p_{0}\left(1-{\frac {Lh}{T_{0}}}\right)^{\frac {gM}{RL}}}$

Density can then be calculated according to a molar form of the ideal gas law:

${\displaystyle \rho ={\frac {pM}{RT}}\,}$

where:

${\displaystyle M=}$ molar mass

${\displaystyle R=}$ ideal gas constant

${\displaystyle T=}$ absolute temperature

${\displaystyle p=}$ absolute pressure

Composition

Maps Density of air

See also

• Air
• Density
• Atmosphere of Earth
• International Standard Atmosphere
• U.S. Standard Atmosphere
• NRLMSISE-00

src: www.boldmethod.com

Notes

src: s-media-cache-ak0.pinimg.com

References

src: www.boldmethod.com

External links

• Conversions of density units ? by Sengpielaudio
• Air density and density altitude calculations and by Richard Shelquist
• Air density calculations by Sengpielaudio (section under Speed of sound in humid air)
• Air density calculator by Engineering design encyclopedia
• Atmospheric pressure calculator by wolfdynamics
• Air iTools - Air density calculator for mobile by JSyA

Source of the article : Wikipedia