# Density of air

## What is the density?

Density is a physical quantity specific to each matter, whether it is solid, liquid or gas. Represented by the Greek letter ρ and expressed in kilogram per cubic meter [kg / m3], it is defined by the mass of a material for a unit of volume.

Its general formula is equal to mass over volume.

## What is the density of air?

Regarding the density of air, it is not generalized because it is variable depending on atmospheric pressure and temperature at a given altitude. It will therefore be necessary to integrate the atmospheric pressure and the temperature in the calculation formula.

As a general rule, this density is equal to 1.29 kg / m3 at an altitude of zero meters (0 m) from mean sea level, at a temperature of 0 ° Celsius and it decreases as l altitude increases.

ρ= P . M / R . t°

P: Atmospheric pressure at the given altitude [Pa]

M: The molar mass of dry air is a constant value which is equal to 28.9644 [kg / kmol]

R: The ideal gas constant which is equal to 8314.32 [J / ° K.kmol]

t°: The temperature at the given altitude expressed in degrees Kelvin [° K]

## Humid air density

A more precise value of the air density can be obtained by taking into account the humidity of the air, since the latter changes the specific air constant R

The density of humid air is written:ρ=p/R_{h}.t°

The specific constant of humid air is written:

R_{h} = R_{s} / (1 - (φ . P_{sat}/ P).(1 - R_{s}/R_{v}))

R_{s}=287.06 J kg^{−1} K^{−1} is the specific constant of dry air;

R_{v}=461 J kg^{−1} K ^{−1} is the specific constant of water vapor;

φ is the relative humidity (0.76 corresponds to 76%);

and P is the air pressure.

P_{sat} is the saturated vapor pressure of water in the air

P_{sat} =611,213 exp(17,5043 . ϑ/241,2 °C-ϑ)

where ϑ is the temperature in degrees Celsius.

To minimize measurement errors, it is recommended to use a suction psychrometer to determine the humidity of the air, and a mercury barometer to determine the ambient pressure (the measurement given by the barometer should be corrected for deviations due to capillarity, to the height of the convex meniscus, to the density of mercury (which depends on the temperature) and to the acceleration of local gravity).