Density of air
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The density of air, ρ (Greek: rho) (air density), is the mass per volume of Earth's atmosphere, and is a useful value in aeronautics. In the SI system it is measured as the number of kilograms of air in a cubic meter (kg/m3). At sea level and at 20 °C dry air has a density of approximately 1.2 kg/m3. varying with pressure and temperature. Air density and air pressure decrease with increasing altitude.
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Effects of temperature and pressure
The formula for the density of air is given by:
- <math>\rho = \frac{p}{R \cdot T}<math>
where ρ is the air density, p is pressure, R is the gas constant, and T is temperature.
The individual gas constant R for dry air is:
- <math>R_{dry air} = 287.05 \frac{\mbox{J}}{\mbox{kg} \cdot \mbox{K}}<math>
Therefore:
- At standard temperature and pressure (0 °C and 101.325 kPa), dry air has a density of ρSTP = 1.293 kg/m3.
- At standard ambient temperature and pressure (25 °C and 100 kPa) dry air has a density of ρSATP = 1.168 kg/m3.
Effect of water vapor
For moist air, the partial pressure of the water vapor must be considered as well. In this case, the density of the air is the sum of the density of the dry air and the density of the water vapor:
- <math>\rho = \frac{p_{dry air}}{R_{dry air} \cdot T} + \frac{p_{water vapor}}{R_{water vapor} \cdot T}<math>
The gas constant for water vapor is:
- <math>R_{water vapor} = 461.495 \frac{\mbox{J}}{\mbox{kg} \cdot \mbox{K}}<math>
Effects of altitude
To calculate the density of air as a function of altitude, one requires additional parameters. They are listed below, along with their values according to the International Standard Atmosphere, using the universal gas constant instead of the specific one:
- sea level atmospheric pressure p0 = 101325 Pa = 1013.25 mbar or hPa = 101.325 kPa (= 101325 kg/m·s2)
- sea level standard temperature T0 = 288.15 K
- Earth-surface gravitational acceleration g = 9.80665 m/s2.
- dry adiabatic lapse rate L = −0.0065 K/m
- universal gas constant R = 8.31447 J/(mol·K)
- molecular weight of dry air M = 0.0289644 kg/mol
Temperature at altitude h metres above sea level is given by the following formula (only valid below the tropopause):
- <math>T = T_0 + L \cdot h<math>
The pressure at altitude h is given by:
- <math>p = p_0 \cdot (1 + \frac{L \cdot h}{T_0})^\frac{g \cdot M}{R \cdot -L}<math>
Density can then be calculated according to a molar form of the original formula:
- <math>\rho = \frac{p \cdot M}{R \cdot T}<math>
Importance of temperature
The below table demonstrates that the properties of air change significantly with temperature.
Table - speed of sound in air c, density of air ρ,
acoustic impedance Z vs. temperature °C
| Impact of temperature | |||
| °C | c in m/s | ρ in kg/m³ | Z in Pa·s/m |
| - 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 |
See also
External links
- Conversions of density units ρ (http://www.sengpielaudio.com/ConvDensi.htm)
- Air density and density altitude calculations (http://wahiduddin.net/calc/density_altitude.htm)