Density of air

The density of air or atmospheric density, denoted ρ,[1] is the mass per unit volume of Earth's atmosphere.

It also changes with variations in atmospheric pressure, temperature and humidity.

At 101.325 kPa (abs) and 20 °C (68 °F), air has a density of approximately 1.204 kg/m3 (0.0752 lb/cu ft), according to the International Standard Atmosphere (ISA).

At 101.325 kPa (abs) and 15 °C (59 °F), air has a density of approximately 1.225 kg/m3 (0.0765 lb/cu ft), which is about 1⁄800 that of water, according to the International Standard Atmosphere (ISA).

[citation needed] Pure liquid water is 1,000 kg/m3 (62 lb/cu ft).

Air density is a property used in many branches of science, engineering, and industry, including aeronautics;[2][3][4] gravimetric analysis;[5] the air-conditioning industry;[6] atmospheric research and meteorology;[7][8][9] agricultural engineering (modeling and tracking of Soil-Vegetation-Atmosphere-Transfer (SVAT) models);[10][11][12] and the engineering community that deals with compressed air.

[13] Depending on the measuring instruments used, different sets of equations for the calculation of the density of air can be applied.

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

This occurs because the molar mass of water vapor (18 g/mol) is less than the molar mass of dry air[note 2] (around 29 g/mol).

For any ideal gas, at a given temperature and pressure, the number of molecules 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 from increasing or temperature from decreasing.

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.

Using this method, error in the density calculation is less than 0.2% in the range of −10 °C to 50 °C.

One formula is Tetens' equation from[15] used to find the saturation vapor pressure is:

simply denotes the observed absolute pressure.

To calculate the density of air as a function of altitude, one requires additional parameters.

For the troposphere, the lowest part (~10 km) of the atmosphere, 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: Temperature at altitude

meters above sea level is approximated by the following formula (only valid inside the troposphere, no more than ~18 km above Earth's surface (and lower away from Equator)):

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

It can be easily verified that the hydrostatic equation holds:

As the temperature varies with height inside the troposphere by less than 25%,

Which is identical to the isothermal solution, except that Hn, the height scale of the exponential fall for density (as well as for number density n), is not equal to RT0/gM as one would expect for an isothermal atmosphere, but rather:

Note that for different gasses, the value of Hn differs, according to the molar mass M: It is 10.9 for nitrogen, 9.2 for oxygen and 6.3 for carbon dioxide.

Which is identical to the isothermal solution, with the same height scale Hp = RT0/gM.

Note that the hydrostatic equation no longer holds for the exponential approximation (unless L is neglected).

Hp is 8.4 km, but for different gasses (measuring their partial pressure), it is again different and depends upon molar mass, giving 8.7 for nitrogen, 7.6 for oxygen and 5.6 for carbon dioxide.

Further note that since g, Earth's gravitational acceleration, is approximately constant with altitude in the atmosphere, the pressure at height h is proportional to the integral of the density in the column above h, and therefore to the mass in the atmosphere above height h. Therefore, the mass fraction of the troposphere out of all the atmosphere is given using the approximated formula for p:

Higher than the troposphere, at the tropopause, the temperature is approximately constant with altitude (up to ~20 km) and is 220 K. This means that at this layer L = 0 and T = 220 K, so that the exponential drop is faster, with HTP = 6.3 km for air (6.5 for nitrogen, 5.7 for oxygen and 4.2 for carbon dioxide).

Both the pressure and density obey this law, so, denoting the height of the border between the troposphere and the tropopause as U: