# Atmospheric pressure

illustration 3: Average air pressure and atmospheric pressure in dependingness on the height.

The atmospheric pressure ρ (also: Density of air or density of air) indicates, like much measure (weight) at air in kg in a cubic meter is contained (kg/m 3). On sea level height is air with approximately 1.2 kg/m 3 with 20 °C by air mass more strongly squeezed together than in larger height, resting over it: air is thus very close.

It has always highest density and highest air pressure at the soil - and except with inversions also the highestTemperature. In larger heights air becomes ever thinner. If the temperature would be alike in all heights, then air pressure and atmospheric pressure would decrease also together with increasing height after the gas law (see barometric elevator formula). The temperature in different heights varies however strongly.

The theoretical acceptanceof pressure and density of air per 5000 meter - whereby it would have to fall on half - is not correct exactly; the deviations are however small.

90% of the atmosphere are below 20 km height,
75% of the atmosphere are below 10 km height,
50% of the atmosphere are below 5 km height.

The atmospheric pressure ρ is:

[itex]

\ rho = \ frac {p} {R \ cdot T} [/itex] in kg/m 3; Air pressure = p, gas constant of R, temperature in Kelvin = T

the individual gas constant of R for dry air is:

[itex]

R= 287 {,} 05 \ \ mathrm {\ frac {J} {kg \ K cdot}} [/itex] with energy joule (J) = Newton · Meter = N m; T in Kelvin = temperature in °C + 273,15.

Atmospheric air pressure p 0 = 101325 Pa = 1013.25 mbar = 1013.25 hPa and R = 287.05 J/kg ·K.

With T 0 = 273.15 K (0 °C) (standard conditions) is the atmospheric pressure:
ρ 0 = 101325/(287,05 · 273,15) = 1.293 kg/m 3.

With T 25 = 298.15 K (25 °C) (standard conditions) is the atmospheric pressure:
ρ25 = 101325/(287,05 · 298,15) = 1.184 kg/m 3.

As one recognizes, these sizes are strongly temperature-dependent.

Table - atmospheric pressure, speed of sound and
sound radiation impedance as a function of the temperature

 effect of the temperature °C C in m/s ρ in kg/m 3 Z in N·s/m 3 - 10 325.4 1.341 436.5 - 5 328.5 1.316 432,4 0 331.5 1.293 428.3 + 5 334.5 1.269 424.5 + 10 337.5 1.247 420.7 + 15 340.5 1.225 417.0 + 20 343.4 1.204 413.5 + 25 346.3 1.184 410.0 + 30 349,2 1,164 406.6

p = sound pressure in Pa = Pascal: p = F/A = N/m 2
A = surface in m 2
F = Kraft in N = Newton: F = kg·m/s 2
ρ = rho = atmospheric pressure in kg/m 3
C = speed of sound in m/s
Z = sound radiation impedance in N · s/m 3

in the meteorology one uses frequently also the reciprocal value of the density and calls the size specific volume α.

[itex]

\ alpha = \ frac {1} {\ rho} [/itex].