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We report improvements to our previous (Zhang et al 2011 Int. J. Thermophys. 32 1297) determination of the Boltzmann constant k B 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 k B = 1.380 6476 × 10 −23 J K −1 with a relative standard uncertainty u r (k B) = 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 k B determined with the various acoustic modes; it is 2.9 × 10 −6. In our previous work, this component was 7.6 × 10 −6 .

A single, fixed-path-length cylindrical-cavity resonator was used to measure c 0 = (307.825 2 ± 0.001 2) m · s −1 , the zero-density limit of the speed of sound in pure argon at the temperature of the triple point of water. Three even and three odd longitudinal modes were used in this measurement. Based on the ratio M/γ 0 = (23.968 644 ± 0.000 033) g · mol −1 , determined from an impurity and isotopic analysis of the argon used in this measurement and the measured c 0 , the value k B = 1.380 650 6 × 10 −23 J · K −1 was obtained for the Boltzmann constant. This value of k B has a relative uncertainty u r (k B ) = 7.9 × 10 −6 and is fractionally, (0.12 ± 8.1) × 10 −6 larger than the value recommended by CODATA in 2006. (The uncertainty is one standard uncertainty.) Several, comparatively large imperfections of our prototype cavity affect the even longitudinal modes more than the odd modes. The models for these imperfections are approximate, but they suggest that an improved cavity will significantly reduce the uncertainty of c 0 .

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