How is air density determined? (FAQ - Mass & Density)
The methods used to determine values of air density fall into two broad categories – indirect (that is calculation from measurement of other parameters and known as the parametric method) and direct measurement. The parametric method is used more commonly.
Parametric method for determining air density
This method calculates air density from measurements of air pressure, temperature, humidity and (when high accuracy is required) carbon dioxide concentration using an equation recommended by the Comité International des Poids et Mesures (CIPM) derived by Giacomo[1] and modified by Davis[2].
'Routine' and 'best achievable' measurement uncertainties using the parametric method.
| Routine measurement | Best capability | |||
| Parameter | Uncertainty in parameter |
Corresponding air density uncertainty ppm |
Uncertainty in parameter |
Corresponding air density uncertainty ppm |
| Temperature (ºC) | 0.1 | 360 | 0.01 | 36 |
| Pressure (hPa) | 0.5 | 500 | 0.05 | 50 |
| Humidity | 5% RH | 350 | 0.25 ºC dew point |
58 |
| CO2 content (ppm) | - | - | 50 | 21 |
| CIPM Equation | 100 | 100 | ||
| Total (x 10-3 kg/m3) | 0.86 | 720 | 0.16 | 133 |
Note that the temperature uncertainties listed here are only achievable inside the small enclosures surrounding modern balances, and when the balances themselves are mounted in closely temperature controlled rooms. Outside such small enclosures, even in state-of-the-art temperature controlled rooms, short-term local temperature changes make it virtually impossible to determine air temperature with an uncertainty approaching about ±0.1 ºC. Thermometers mounted in sheaths, the fabric of the balance, a steel block, or anything else with substantial thermal inertia (compared with air) may indicate a stability better than this figure but such thermometers are measuring the temperature of their mounts, not the surrounding air.
Direct methods for determining air density
Other methods for the measurement of air density have been investigated, principally by national measurement institutes (such as NPL), but also balance and weight manufacturers. The most common method involves comparing artefacts that have comparable masses but (very) different volumes; apparent differences in masses give a direct measure of the density of the air in which they are compared.
Whichever way air density is measured, the conventions for the application of buoyancy corrections remain the same.
References
- Equation for the determination of the density of moist air (1981) Giacomo, P. Metrologia 1982, 15, 33-40
- Equation for the determination of the density of moist air (1981/91) Davis, R.S.P. Metrologia, 1992, 29, 67-70.