Logo of the Physikalisch-Technische Bundesanstalt

Determination of the Boltzmann constant completed


PTB has succeeded in measuring the Boltzmann constant k independently. An essential condition laid down by the Consultative Committee of Thermometry (CCT) has thereby been met, thus paving the way for the new definition of the kelvin by fixing the value of the Boltzmann constant. The final measurements of k with the dielectric-constant gas thermometer were conducted with a relative uncertainty of 1.9 ppm. Compared to the uncertainty of 15 ppm obtained at the beginning of the project back in 2007, this represents a significant reduction by a factor of 8.

As far back as thirty years ago, k was determined with a relative uncertainty of 1.8 ppm by means of the alternative measurement method, the acoustic gas thermometer. Over the past decade, this method was further refined by various metrology institutes; the most accurate result it provided exhibited 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 below 1 ppm.

As early as the beginning of the project, some 10 years ago, PTB had already committed itself to metrologically validating the results obtained by means of acoustic gas thermometry via an independent method with a similar uncertainty. PTB employs dielectric-constant gas thermometry which is based on the in situ determination of the density of the measuring gas helium. This approach is based on the fact that the gas changes the capacitance of a capacitor. This implied a certain number of obstacles to be overcome. The uncertainty of the pressure measurement at pressures up to 7 MPa had to be reduced by a factor of 4, down to a worldwide unequalled relative uncertainty of 1 ppm. The measurement of the capacity changes even requires relative uncertainties of a few parts in a billion. Moreover, the material parameters for the capacitors must – at these high pressures – be determined at the limit of the metrologically feasible, and a gas purity of better than 99.99999 % must be ensured. This was only possible by having different departments within PTB cooperating with each other and thanks to wide international cooperation.