# Airtightness

The air density  ρ (also density of air or density of air ) indicates the mass of air contained in a certain volume . At sea ​​level , the air, at around 1.2041  kg / at 20  ° C, is more compressed by the air mass above than at higher altitudes: The air is therefore relatively denser.

## Altitude dependence

Average air density and air pressure
depending on the altitude

The air on the ground always has the highest density and the highest air pressure and - except for inversions - also the highest temperature; at higher altitudes the air becomes thinner and thinner.

If the temperature were the same at all altitudes, the air pressure and air density would also decrease together with increasing altitude according to the gas law (see barometric altitude formula ). However, the temperature at different altitudes varies greatly.

It is not exactly true that the pressure and density of the air should theoretically decrease by half for every 5000 meters:

90% of the atmosphere is below 20 km.
70% of the atmosphere is below 10 km.
55% of the atmosphere is below 5 km.

## calculation

If air is considered the ideal gas , the air density ρ in kg / m³ is calculated  as:

${\ displaystyle \ rho = {\ frac {p \ cdot M} {R \ cdot T}}}$

With

• the air pressure  p in pascals ; Atmospheric air pressure p 0 = 101325 Pa = 1013.25 hPa = 1013.25 mbar = 1.01325  bar .
• the molar mass  M (in SI units )${\ displaystyle \ mathrm {\ frac {kg} {mol}}}$
• the universal gas constant  R  = 8.3145 J / (mol · K) with the energy in  J (=  N · m )
• the temperature  T in Kelvin ; { T in Kelvin} = {temperature in ° C} + 273.15.

By inserting the specific gas constant for dry air one obtains: ${\ displaystyle R_ {S} = {\ frac {R} {M}} = 287 {,} 058 \ \ mathrm {\ frac {J} {kg \ cdot K}}}$

${\ displaystyle \ rho = {\ frac {p} {R_ {S} \ cdot T}}}$.

## Temperature dependence

Air density as a function of temperature at a pressure of 1  atm
Air density depending on the air temperature at sea level under standard pressure of 1013 mbar
Temperature in ° C
${\ displaystyle \ vartheta}$
Temperature
T in K
Air density in kg / m³
${\ displaystyle \ rho}$
annotation
+35 308.15 1.1455
+30 303.15 1.1644
+25 298.15 1.1839
+20 293.15 1.2041 Laboratory conditions
+15 288.15 1.2250 Aviation standard atmosphere
+10 283.15 1.2466
+5 278.15 1.2690
0 273.15 1.2920 physical standard conditions
−5 268.15 1.3163
−10 263.15 1.3413
−15 258.15 1.3673
−20 253.15 1.3943
−25 248.15 1.4224

## Humidity dependence

An exact determination of the density of the air requires the air humidity to be taken into account , as this changes the gas constant of the air:

${\ displaystyle R _ {\ mathrm {f}} = {\ frac {R _ {\ mathrm {S}}} {1- \ varphi \ cdot {\ frac {p _ {\ mathrm {d}}} {p}} \ cdot (1 - {\ frac {R _ {\ mathrm {S}}} {R _ {\ mathrm {d}}}})}}}$

With

• the gas constant of dry air${\ displaystyle R _ {\ mathrm {S}} = 287 {,} 058 \, \ mathrm {\ frac {J} {kg \ cdot K}}}$
• the gas constant of water vapor${\ displaystyle R _ {\ mathrm {d}} = 461 {,} 523 \, \ mathrm {\ frac {J} {kg \ cdot K}}}$
• the relative humidity (e.g. 0.76 = 76%)${\ displaystyle \ varphi}$
• the saturation vapor pressure of water in air, which in${\ displaystyle p _ {\ mathrm {d}}}$
Wikibooks: data table with more precise formulas  - learning and teaching materials
is tabulated. There are also empirical formulas of varying accuracy such as the Magnus formula or Antoine equation .
• the ambient pressure in Pascal.${\ displaystyle p}$

After adjusting the gas constant, the equation

${\ displaystyle \ rho = {\ frac {p} {R _ {\ mathrm {f}} \ cdot T}}}$

be used.

### Exact determination

In order to minimize measurement errors , we recommend an aspiration psychrometer to determine the air humidity and a mercury barometer to determine the ambient pressure . The barometer reading still has to be corrected for capillarity , the summit height of the mercury level, temperature-dependent density of the mercury and local acceleration due to gravity .

## Reciprocal

The reciprocal value of the density, the specific volume , has the symbol  α in meteorology and the symbol  v air in thermodynamics :

${\ displaystyle \ alpha = v _ {\ text {Air}} = {\ frac {1} {\ rho}}}$.