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 .

We report a new determination of the Boltzmann constant kB using a cylindrical acoustic gas thermometer. We determined the length of the copper cavity from measurements of its microwave resonance frequencies. This contrasts with our previous work (Zhang et al 2011 Int. J. Thermophys. 32 1297, Lin et al 2013 Metrologia 50 417, Feng et al 2015 Metrologia 52 S343) that determined the length of a different cavity using two-color optical interferometry. In this new study, the half-widths of the acoustic resonances are closer to their theoretical values than in our previous work. Despite significant changes in resonator design and the way in which the cylinder length is determined, the value of kB is substantially unchanged. We combined this result with our four previous results to calculate a global weighted mean of our kB determinations. The calculation follows CODATA’s method (Mohr and Taylor 2000 Rev. Mod. Phys. 72 351) for obtaining the weighted mean value of kB that accounts for the correlations among the measured quantities in this work and in our four previous determinations of kB. The weighted mean k̂B is 1.380 6484(28) × 10−23 J K−1 with the relative standard uncertainty of 2.0 × 10−6. The corresponding value of the universal gas constant is 8.314 459(17) J K−1 mol−1 with the relative standard uncertainty of 2.0 × 10−6.

In the application of acoustic gas thermometry to determine the Boltzmann constant and thermodynamic temperatures using resonant cavities, the internal dimensions or the thermal expansion of the cavity have to be known accurately. For this purpose, measurement of the microwave resonances has proved to be an accurate and convenient experimental technique for dimensional measurement of acoustic resonators. We report measurements of the length and longitudinal thermal expansion of a prototype cylindrical cavity made of oxygen-free copper. We studied four non-degenerate transverse magnetic modes for three isotherms at 243, 258 and 273 K. Two procedures were investigated for calculating the length and longitudinal thermal expansion of the cavity at the temperatures examined. The results from both methods agree well. The relative standard uncertainties for the measurements of length and longitudinal thermal expansion are less than 0.47  ×  10−6 and 0.04  ×  10−6, respectively, from 243 to 273 K. The low uncertainty achieved here provides confidence to pursue a determination of the Boltzmann constant and thermodynamic temperature with a cylindrical cavity and microwave techniques.