The density of air, ρ (Greek: rho) (air density), is the mass per unit volume of Earth's atmosphere, and is a useful value in aeronautics and other sciences. Air density decreases with increasing altitude, as does air pressure. It also changes with variation in temperature or humidity. At sea level and at 15 °C, air has a density of approximately 1.225 kg/m^{3} (0.0023769 slugs/ft^{3}) according to ISA (International Standard Atmosphere).
Temperature and pressure
The density of dry air can be calculated using the ideal gas law, expressed as a function of temperature and pressure:
 $$
\rho = \frac{p}{R_{\rm specific} T}
where ρ is the air density, p is absolute pressure, R_{specific} is the specific gas constant for dry air, and T is absolute temperature.
The specific gas constant for dry air is 287.058 J/(kg·K) in SI units, and 53.35 (ft·lb_{f})/(lb_{m}·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:
The following table illustrates the air density–temperature relationship at 1 atm or 101.325 kPa:
Effect of temperature on properties of air
Temperature T in °C

Speed of sound c in m·s^{−1}

Density of air ρ in kg·m^{−3}

Acoustic impedance Z in N·s·m^{−3}

+35 
351.88 
1.1455 
403.2

+30 
349.02 
1.1644 
406.5

+25 
346.13 
1.1839 
409.4

+20 
343.21 
1.2041 
413.3

+15 
340.27 
1.2250 
416.9

+10 
337.31 
1.2466 
420.5

+5 
334.32 
1.2690 
424.3

0 
331.30 
1.2922 
428.0

−5 
328.25 
1.3163 
432.1

−10 
325.18 
1.3413 
436.1

−15 
322.07 
1.3673 
440.3

−20 
318.94 
1.3943 
444.6

−25 
315.77 
1.4224 
449.1

Water vapor
The addition of water vapor to air (making the air humid) reduces the density of the air, which may at first appear counterintuitive.
This occurs because the molecular mass of water (18 g/mol) is less than the molecular mass of dry air (around 29 g/mol). For any 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 (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 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:
 $$
\rho_{\,\mathrm{humid~air}} = \frac{p_{d}}{R_{d} T} + \frac{p_{v}}{R_{v} T} = \frac{p_{d}M_{d}+p_{v}M_{v}}{R T} \,
^{[1]}
where:
 $\backslash rho\_\{\backslash ,\backslash mathrm\{humid~air\}\}\; =$ Density of the humid air (kg/m³)
 $p\_\{d\}\; =$ Partial pressure of dry air (Pa)
 $R\_\{d\}\; =$ Specific gas constant for dry air, 287.058 J/(kg·K)
 $T\; =$ Temperature (K)
 $p\_\{v\}\; =$ Pressure of water vapor (Pa)
 $R\_\{v\}\; =$ Specific gas constant for water vapor, 461.495 J/(kg·K)
 $M\_\{d\}\; =$ Molar mass of dry air, 0.028964 (kg/mol)
 $M\_\{v\}\; =$ Molar mass of water vapor, 0.018016 (kg/mol)
 $R\; =$ Universal gas constant, 8.314 J/(K·mol)
The vapor pressure of water may be calculated from the saturation vapor pressure and relative humidity. It is found by:
 $$
p_{v} = \phi p_{\mathrm{sat}} \,
Where:
 $p\_\{v\}\; =$ Vapor pressure of water
 $\backslash phi\; =$ Relative humidity
 $p\_\{\backslash mathrm\{sat\}\}\; =$ Saturation vapor pressure
The saturation vapor pressure of water at any given temperature is the vapor pressure when relative humidity is 100%. One formula ^{[1]} used to find the saturation vapor pressure is:
 $p\_\{\backslash mathrm\{sat\}\}\; =\; 6.1078\; \backslash times\; 10^\{\backslash frac\{7.5\; T\}\{T+237.3\}\}$
where T is in degrees C.
Note:
 This will give a result in hPa (100 Pa, equivalent to the older unit millibar, 1 mbar = 0.001 bar = 0.1 kPa)
 $p\_\{d\}$ is found considering partial pressure, resulting in:
 $$
p_{d} = pp_{v} \,
Where p simply denotes the observed absolute pressure.
Altitude
To calculate the density of air as a function of altitude, one requires additional parameters. They are listed below, along with their values according to the International Standard Atmosphere, using the universal gas constant instead of the specific one:
 sea level standard atmospheric pressure p_{0} = 101.325 kPa
 sea level standard temperature T_{0} = 288.15 K
 Earthsurface gravitational acceleration g = 9.80665 m/s^{2}.
 temperature lapse rate L = 0.0065 K/m
 ideal (universal) gas constant R = 8.31447 J/(mol·K)
 molar mass of dry air M = 0.0289644 kg/mol
Temperature at altitude h meters above sea level is approximated by the following formula (only valid inside the troposphere):
 $$
T = T_0  L h \,
The pressure at altitude h is given by:
 $p\; =\; p\_0\; \backslash left(1\; \; \backslash frac\{L\; h\}\{T\_0\}\; \backslash right)^\backslash frac\{g\; M\}\{R\; L\}$
Density can then be calculated according to a molar form of the ideal gas law:
 $$
\rho = \frac{p M}{R T} \,
where M is molar mass, R is the ideal gas constant, and T is absolute temperature.
See also
References
External links
 Conversions of density units ρ
 Air density and density altitude calculations
 Air Density Calculator
This article was sourced from Creative Commons AttributionShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, EGovernment Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a nonprofit organization.