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Improved Determination of the Boltzmann Constant using a Single, Fixed-Length Cylindrical Cavity

Published

Author(s)

Hong Lin, Keith A. Gillis, XiaoJuan Feng, Michael R. Moldover, J.P. Sun, J.T. Zhang, Y.Y. Duan

Abstract

We report improvements to our previous [Zhang et al., Intl. J. Thermophysics, 32, 1297 (2011)] 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 2nd–order perturbations to the frequencies from the thermo-viscous boundary layer. The weighted average of the data yielded kB=1.380 647 6x10–23 J K-1 with the relative standard uncertainty ur(kB)=3.7x10–6. This result differs by, fractionally, (-0.9+/-3.7)x10-6 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 2.9x10–6. In our previous work, this component was 7.6x10–6.
Citation
Metrologia
Volume
50

Keywords

acoustic thermometry, acoustic resonator, Boltzmann constant, speed of sound, thermometry
Created August 27, 2013, Updated February 19, 2017