Final determination of the Boltzmann constant by dielectric-constant gas thermometry

Abstract

Gaiser et al published in 2013 (Metrologia 50 L7–11) a second, improved value of the Boltzmann constant k determined by dielectric-constant gas thermometry at the triple point of water (k = 1.380 6509 × 10−23 J K−1, relative standard uncertainty 4.3 parts per million (4.3 ppm)). Subsequently, the uncertainty was able to be reduced to 4.0 ppm by reanalysing the pressure measurement. Since 2013, further progress regarding this primary-thermometry method has been achieved in terms of the design and the assembly of the measuring capacitors, the determination of their effective compressibility, the sensitivity of the capacitance bridge, and the scattering and the evaluation of the data. Based on a huge amount of data, two new k values have been obtained by applying two different capacitors. The combination of these two values with the 2013 result, fully taking into account the correlations, has yielded a final result of k = 1.380 6482 × 10−23 J K−1 with a relative standard uncertainty of 1.9 ppm. This value is about 0.2 ppm smaller than the CODATA 2014 one, which has a relative standard uncertainty of 0.57 ppm.