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Subsection on the Density of Air page

Relationships

Temperature and pressure

Variation in atmospheric pressure with altitude, computed for 15^oC and 0% relative humidity.

As altitude increases, air density decreases. One can calculate the air density at a given altitude. Atmospheoric pressure is necessary to compute an accurate figure. The graph at right was developed for a temperature of 15^oC and a relative humidity of 0%.

This plastic bottle was sealed at approximately 14,000 feet altitude, and was crushed by the increase in atmospheric pressure (at 9,000 feet and 1,000 feet) as it was brought down towards sea levelThe density of dry air can be calculated using the ideal gas law, expressed as a function of temperature and pressure:.

$\rho ={\frac {p}{R_{\rm {specific}}\cdot T}}$

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.

Therefore:

• At IUPAC standard temperature and pressure (0 °C and 100 kPa), dry air has a density of 1.2754 kg/m³.
• At 20 °C and 101.325 kPa, dry air has a density of 1.2041 kg/m³.
• At 70 °F and 14.696 psia, dry air has a density of 0.074887 lb_m/ft³.

The following table illustrates the air density - temperature relationship at 1 atm or 101.325 kPa:

Effect of temperature on properties of air

Celsius tempe­rature θ [°C]	Speed of sound c [m/s]	Density of air ρ [kg/m3]	Characteristic specific acoustic impedance z0 [Pa⋅s/m]
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

The equation relating atmospheric pressure p in kPa to altitude h in meters and other parameters is

$p=p_{0}\cdot \left(1-{\frac {L\cdot h}{T_{0}}}\right)^{\frac {g\cdot M}{R\cdot L}},$

where the constant parameters are as described below:

Parameter	Description	Value
p0	sea level standard atmospheric pressure	101325 Pa
L	temperature lapse rate	0.0065 K/m
T0	sea level standard temperature	288.15oC
g	Earth-surface gravitational acceleration	9.80665 m/s2
M	molar mass of dry air	0.0289644 kg/mol
R	universal gas constant	8.31447 J/(mol•K)

External Links

Air Pressure at Altitude calculator at altitude.org This site also contains information about altitude sickness and the effects of altitude on oxygen in the blood.