Test of a virtual cylindrical acoustic resonator for determining the Boltzmann constant

Published

August 19, 2015

Author(s)

XiaoJuan Feng, Hong Lin, Keith A. Gillis, Michael R. Moldover, Jintao Zhang

Abstract

We report progress in determining the Boltzmann constant k_B using a virtual acoustic resonator derived by combining the measured frequencies of the longitudinal acoustic modes of two argon-filled, cylindrical, cavity resonators in such a way as to minimize the effects of the cavities' ends including transducers and ducts attached to the ends. The cavities had lengths of 80 mm and 160 mm and were operated in their longitudinal (ℓ,0,0) modes. We explored virtual resonators that combine modes of the two resonators that have the nearly the same frequencies. The virtual resonator formed from the (2,0,0) mode of the 80 mm resonator combined with the (4,0,0) mode of the 160 mm resonator yielded a value for k_B that is, fractionally, (0.2 plus or minus} 1.5)×10^-6 larger than the 2010 CODATA-recommended value of k_B. (The estimated uncertainty is one standard uncertainty corresponding to 68 % confidence level.) The same virtual resonator yielded values of the pressure derivatives of the speed of sound c in argon, (dc²/dp)_T and (dc²/dp²)_T that are nearly consistent with literature values even though the values of k_B, (dc²/dp)_T and (dc²/dp²)_T from each cavity, considered separately, were not. However, combining the results from the (3,0,0) or (4,0,0) modes of shorter resonator with the results from the (6,0,0) or (8,0,0) modes of the longer resonator yielded incorrect values of k_B that varied from run-to-run. We speculate that these puzzling results originated in an un-modeled coupling, either between the two cavities (that resonated at nearly identical resonance frequencies in the same pressure vessel) or between the cavities and modes of the pressure vessel.

Citation

Metrologia

Volume

52

Pub Type

Journals

Download Paper

https://doi.org/10.1088/0026-1394/52/5/S343

Local Download

Keywords

Boltzmann constant, acoustic gas thermometer, acoustic resonator, speed of sound, virtual resonator

Citation

Feng, X. , Lin, H. , Gillis, K. , Moldover, M. and Zhang, J. (2015), Test of a virtual cylindrical acoustic resonator for determining the Boltzmann constant, Metrologia, [online], https://doi.org/10.1088/0026-1394/52/5/S343, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=918094 (Accessed April 18, 2024)