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PTB obtains first value for Boltzmann constant

Especially interesting for
  • primary thermometry
  • the fundamentals of metrology
  • the International System of Units (SI)

Initial measurements performed with PTB's dielectric-constant gas thermometer have yielded, a value of 1.380655 • 10–23 J/K with an uncertainty of approx. 8 ppm for the Boltzmann constant. The ultimate step towards an uncertainty of 2 ppm is expected within the next two years, which will pave the way for the redefinition of the unit “kelvin” via the definition of k.

Thermostat probe of the dielectric-constant gas thermometer with gas handling system ensuring gas delivery to the various measuring capacitors.

Within the scope of the redefinition of the base units of the International System of Units (SI) via fundamental constants, research groups from all over the world have been dealing with determining the value of the Boltzmann constant with uncertainties of a few ppm. If they are successful, the unit “kelvin” could be redefined. Many groups apply acoustic gas thermometry, a method which has provided the most accurate value to date (approx. 2 ppm). PTB has chosen a different – and completely independent – path to rule out systematic sources of errors and, thus, to put the redefinition on solid ground.

PTB employs dielectric-constant gas thermometry (DCGT) which is based on the in-situ determination of the density of the measuring gas helium. This approach consists in measuring how much the gas changes the capacitance of a capacitor. From measurements at a constant temperature (at the triple point of water) and at different pressures in the measuring capacitor, k can be determined by means of fundamental relations. This method makes high demands on the measuring technique used and was realised by several departments of PTB in cooperation with external partners. The measurement of the pressure at 7 MPa with piston gauges aimed at uncertainties of 1 ppm was just as demanding as all other sub-projects. In order to measure changes in the capacitance of around 1 billionth, a new capacitance bridge was designed. The required temperature stability of the measuring system is provided by a large bath thermostat which was manufactured and optimised in cooperation with the national metrology institute of Italy (INRiM). This took place within the scope of an EU project coordinated by PTB, which has just been successfully completed.

The experimental set-up developed now allows DCGT measurements to be carried out at the triple point of water and furnishes a value for k of 1.380655 • 10–23 J/K. This value lies approx. 3 ppm above the CODATA value and is, with a relative uncertainty of approx. 8 ppm, the first proof that DCGT is able to determine k with greatest accuracy.

However, until the uncertainty of 2 ppm aimed at is reached, some difficulties will have to be overcome. Thus, besides improving pressure measurement within the next 2 years, especially the design and the materials used for the capacitors will have to be optimised in order to reduce the – currently – dominating uncertainty component which is due to the deformation of the capacitors' electrodes under the effects of the gas pressure. This would pave the way for a reliable redefinition of the unit “kelvin”.

Scientific publication

Fellmuth, B.; Fischer, J.; Gaiser, C.; Jusko, O.; Priruenrom, T.; Sabuga, W.; Zandt, T.: Determination of the Boltzmann constant by dielectric-constant gas thermometry. Metrologia 48 (2011) 382-390