# Increased accuracy of air density determination for buoyancy correction in precision mass determinations

25.08.2008

The use of buoyancy artefacts and more accurate calculation bases for air density determination made it possible to significantly reduce the uncertainty of the air buoyancy correction in precision mass determinations.

The air buoyancy correction results from the buoyancy difference between the reference weight and the weight to be calibrated so that, depending on the requirements on accuracy of the mass determination, a sufficiently accurate air density determination is necessary. Especially in the case where large density differences occur between the reference weight and the weight to be calibrated, the value of the buoyancy correction can exceed the required uncertainty of the mass determination by far. For example, for the link-up of a 1 kg mass standard made of non-corrosive, non-magnetic steel (density 8000 kg/m³) with a prototype of a kilogram made of platinum-iridium (density 21500 kg/m³), one obtains a volume difference of approx. 80 cm³ and thus, under normal ambient conditions and at an air density of around 1.2 kg/m³, a buoyancy difference of 96 mg.
For the air buoyancy correction, the air density is usually determined on the basis of the parameters pressure, temperature, humidity and, if necessary, CO2 content. Air density is calculated with high requirements according to the so-called "CIPM-81/91 equation" [1] which was recommended by the Comité International des Poids et Mesures (CIPM) in 1981 and revised with regard to certain constants and calculation bases by the Consultative Committee for Mass (CCM) in 1991. At national metrology institutes air density can usually be determined according to the CIPM-81/91 equation in the course of a weighing with a relative standard uncertainty of an order of magnitude of 1 × 10-4. Thus, the air density determination for the prototype link-up of a steel standard alone leads to an uncertainty contribution of approx. 10 µg.
By using buoyancy artefacts for the gravimetric determination of the air density, the uncertainty of the buoyancy correction could be significantly reduced. For air density determination with buoyancy artefacts, relative standard measurement uncertainties in the range of 2 × 10-5 can currently be achieved. Comparison measurements amongst national metrology institutes, however, showed a mean systematic deviation of 6.4 × 10-5 between the air density determination by means of buoyancy artefacts and the CIPM equation of 1981/91. More recent measurements for the determination of the molar fraction of argon in air confirmed the assumption that the argon fraction used for the calculation of the molar mass of dry air needs to be corrected in the CIPM equation of 1981/91. The correction of the CIPM equation with the results of these measurements and the current value of the molar gas constant corresponds to the hitherto systematic deviations from the results of air density determination by means of buoyancy artefacts. In addition, it was possible to reduce the uncertainty of the CIPM equation from 6.5 × 10-5 to 2.2 × 10-5 (relative standard uncertainty of the equation without taking into consideration the air density parameters to be measured) [2]. For the link-up of PTB's primary standards to the national prototype of the kilogram, the improved air density determination led to a reduction of measurement uncertainty by more than 40% down to u(m)/m < 1 × 10-8.

[1] Davis, R. S.: Equation for the determination of the density of moist air (1981/91). Metrologia 29 (1992) 67–70

[2] Picard, A.; Davis, R. S.; Gläser, M.; Fujii, K.: Revised formula for the density of moist air (CIPM-2007). Metrologia 45 (2008) 149–155

### Contact person:

Michael Borys, FB 1.1, AG 1.11, E-Mail: michael.borys@ptb.de