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# How is air density determined?

## Measuring the density of air

The air density is the mass per unit volume and like air pressure, it decreases with increasing altitude. It also changes with variation in atmospheric pressure, temperature and humidity. Air density is used in many branches of science, engineering and industry.

Air density can be measured in two broad categories:

1. Indirect measurement or parametric method - the density is determined from measurement of other parameters and is the most commonly used method
2. Direct measurement

### 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 NPL and other national measurement institutes, 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.

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References

1. Equation for the determination of the density of moist air (1981) Giacomo, P. Metrologia 1982, 15, 33-40
2. Equation for the determination of the density of moist air (1981/91) Davis, R.S.P. Metrologia, 1992, 29, 67-70.

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