Cylindrical Acoustic Resonator for the Re-determination of the Boltzmann Constant

Published

June 1, 2010

Author(s)

J.T. Zhang, H. Lin, X.J. Feng, Keith A. Gillis, Michael R. Moldover

Abstract

We describe progress towards re-determining the Boltzmann constant k_B using two fixed-path, gas-filled, cylindrical, acoustic cavity resonators. The longitudinal acoustic resonance modes of a cylindrical cavity have lower quality factors Q than the radial modes of gas-filled, spherical cavities, of equal volume. The lower Q\I}s result in lower signal-to-noise ratios and wider, asymmetric resonances. We replaced conventional capacitance microphones with 6.3 mm diameter piezoelectric transducers (PZTs) installed on the outer surfaces of each resonator and coupled to the cavity by diaphragms. This arrangement preserved the shape of the cylindrical cavity, prevented contamination of the gas inside the cavity, and enabled us to measure the longitudinal resonance frequencies with a relative standard uncertainty of 0.2×10 -6^. We are using a two-color laser interferometer to measure the interior length of each cavity and its thermal expansion. The lengths of the cavities and the modes studied will be chosen to achieve approximate cancellation of the acoustic perturbations due to nonzero boundary admittances at the endplates, e. g. from endplate bending and ducts and/or transducers installed in the endplates. Alternatively, the acoustic perturbations generated by the viscous and thermal boundary layers at the gas-solid boundary can be approximately cancelled. Using the techniques outlined here, we estimate that /k/_B can be re-determined with a relative standard uncertainty of 1.5¿×10 -6^^ ^.

Citation

International Journal of Thermophysics

Volume

31

Pub Type

Journals

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Keywords

Boltzmann constant, Cylindrical acoustic resonator, two-color interferometry

Citation

Zhang, J. , Lin, H. , Feng, X. , Gillis, K. and Moldover, M. (2010), Cylindrical Acoustic Resonator for the Re-determination of the Boltzmann Constant, International Journal of Thermophysics, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=905511 (Accessed October 8, 2025)