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Boltzmann constant determined

All obstacles to the redefinition of the unit of temperature, the kelvin, have been removed

PTB-News 2.2017
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metrological fundamental research

redefinitions of the units

PTB has succeeded in measuring the Boltzmann constant k independently. A fundamental condition laid down by the Consultative Committee for Thermometry (CCT) has thereby been met, so that all obstacles to the redefinition of the kelvin have been removed by fixing the value of the Boltzmann constant. The final measurements of k with a dielectric-constant gas thermometer were conducted with a relative uncertainty of 1.9 ppm (parts per million). Compared to the uncertainty of 15 ppm obtained at the beginning of the project back in 2007, this represents a reduction by a factor of 8.

PTB scientist Christof Gaiser with the core of the dielectric-constant gasthermometer. The different silver-colored pressure vessels have specialcapacitors which are filled with helium to carry out the measurement thattakes place inside them.

For a unit to be based on a fundamental constant, the latter should, as a matter of principle, be measured by means of two methods which are independent of each other and have a comparable uncertainty. As early as 30 years ago, the Boltzmann constant k had already been determined with a relative uncertainty of 1.8 ppm by means of the acoustic gas thermometer. Over the past decade, this method was further refined by various metrology institutes, with the most Three times a year, PTB News provides topical information from the varied spectrum of activities of the Physikalisch- Technische Bundesanstalt (PTB) consisting of fundamental research, legal metrology and PTB's various activities in the service of the economy. accurate result exhibiting an uncertainty reduced by a factor of 2. These results allow the first condition of the CCT for the new definition to be met, namely obtaining an averaged value for the Boltzmann constant with an uncertainty of less than 1 ppm.

An independent method of doing this is dielectric-constant gas thermometry, which PTB has been using for many years. This method consists in determining the pressure of the measuring gas, helium, in a gas-filled capacitor. This approach is based on the fact that helium, as a dielectric, changes the capacitance of the capacitor. At pressures up to 7 MPa, the uncertainty of the pressure measurement had to be reduced by a factor of 4. This has now been achieved with a worldwide unequalled relative uncertainty of 1 ppm. In order to measure the capacity changes, relative uncertainties of a few parts per billion may not be exceeded. Moreover, the material parameters for the capacitors – at these high pressures – had to be determined at the metrological limit, and a gas purity of better than 99.99999 % had to be ensured. This could only be achieved thanks to various cooperation projects within PTB (with the two working groups “Pressure” and “Geometrical Standards”) and thanks to large-scale international cooperation.

Now that the Boltzmann constant has been determined with sufficient precision by means of both methods, CODATA will compute the final value of k in September 2017. This will pave the way for the redefinition of the kelvin based on a fundamental constant. Presumably in the fall of 2018, the whole International System of Units (SI) will rest upon a new basis.


Christof Gaiser
Department 7.4
Phone: +49 (0)30 3481-7349
Opens window for sending emailchristof.gaiser(at)ptb.de

Scientific publication

C. Gaiser, B. Fellmuth, N. Haft, A. Kuhn, B. Thiele-Krivoi, T. Zandt, J. Fischer, O. Jusko, W. Sabuga: Final determination of the Boltzmann constant by dielectricconstant gas thermometry. Metrologia 54, 280−289 (2017)