14.11.2018
The volume of silicon spheres with a mass of 1 kg could previously be measured by means of hydrostatic weighing with an uncertainty of 0.8 mm³ (k = 2). Using new and more stable thermistors to determine the temperature distribution in the measuring liquid of the fundamental weighing apparatus, a hydrostatic volume determination with an uncertainty of 0.35 mm³ (k = 2) will be possible in the future.
The volume of silicon spheres with a mass of 1 kg could previously be measured by means of hydrostatic weighing with an uncertainty of 0.8 mm³ (k = 2). Using new and more stable thermistors to determine the temperature distribution in the measuring liquid of the fundamental weighing apparatus, a hydrostatic volume determination with an uncertainty of 0.35 mm³ (k = 2) will be possible in the future.
The previous uncertainties of the hydrostatic volume determination were confirmed by an international CMC comparison with 0.8 mm³ (k = 2) for density standards with a mass of 1 kg [1]. A decisive factor, the temperature, has limited the uncertainties of the measuring liquid density gradient and thus the determination of volume.
In the fundamental weighing apparatus, the volume is determined by means of comparison measurements of two standards and the sample in a vertical arrangement so that the temperature-dependent density gradient of the measuring liquid must be considered. The two standards and the sample are symmetrically arranged for 1 kg of silicon spheres. At the same height of the standards and the sample, the temperatures are measured with thermistors at a maximum vertical distance of 220 mm [2].
Using new and more stable thermistors, the temperature distribution of the measuring liquid – and thus the density of the liquid – can now be determined and controlled more accurately. This exhibits a non-linear temperature distribution in the measuring liquid (Figure 1 [a]), which now enters into the calculations more precisely due to more stable temperature measurements. This innovation enables a hydrostatic volume determination for 1 kg of silicon spheres with an uncertainty of 0.35 mm³ (k = 2), as shown in Figure 1 (b). The volume determination obtained from current results from the interferometric length measurements of the sphere interferometer and from density comparison measurements against the pressure-of-flotation apparatus from the year 2010 confirm the measurement results of the hydrostatic volume determination.
Regarding standards consisting of 1 kg silicon spheres, relative uncertainties of less than 1 ppm can be achieved with these findings by means of hydrostatic volume determination.
Fig. 1: (a) Temperature distribution in the measuring liquid measured at the level of the higher standard 1, the sample and the lower standard 2. (b) Results of the volume determination for the 1 kg silicon sphere “Si9” measured by means of fundamental weighing apparatus (in blue), interferometric length measurement with the sphere interferometer (in red) and density comparison measurements against the pressure-of-flotation apparatus (in green).
Literature:
[1] EURAMET Project 1031: Solid density comparison, Report in progress, Draft A
[2] F. Spieweck, A. Kozdon, H. Wagenbreth, H. Toth, D. Hoburg: “A Computer-controlled Solid-density Measuring Apparatus,” PTB-Mitteilungen 100 (1990) S. 169-173, 
Link
[3] H. Bettin, F. Spieweck, H. Toth: “Verbesserung der hydrostatischen Fundamentalapparatur durch Automatisierung der Substitutionswägungen in Pentadekan”, PTB-Jahresbericht 1995 (1996) S. 206
Contact:
Daniela Eppers, FB 1.8, AG 1.82, E-Mail: 
daniela.eppers(at)ptb.de