Improved determination of the Boltzmann constant using a single, fixed-length cylindrical cavity

Abstract

We report improvements to our previous (Zhang et al 2011 Int. J. Thermophys. 32 1297) determination of the Boltzmann constant kB using a single 80 mm long cylindrical cavity. In this work, the shape of the gas-filled resonant cavity is closer to that of a perfect cylinder and the thermometry has been improved. We used two different grades of argon, each with measured relative isotopic abundances, and we used two different methods of supporting the resonator. The measurements with each gas and with each configuration were repeated several times for a total of 14 runs. We improved the analysis of the acoustic data by accounting for certain second-order perturbations to the frequencies from the thermo-viscous boundary layer. The weighted average of the data yielded kB = 1.380 6476 × 10−23 J K−1 with a relative standard uncertainty ur(kB) = 3.7 × 10−6. This result differs, fractionally, by (−0.9 ± 3.7) × 10−6 from the value recommended by CODATA in 2010. In this work, the largest component of the relative uncertainty resulted from inconsistent values of kB determined with the various acoustic modes; it is 2.9 × 10−6. In our previous work, this component was 7.6 × 10−6.