Advertisement

International Journal of Thermophysics

, Volume 31, Issue 7, pp 1273–1293 | Cite as

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

  • J. T. Zhang
  • H. Lin
  • J. P. Sun
  • X. J. Feng
  • K. A. Gillis
  • M. R. Moldover
Article

Abstract

The progress towards re-determining the Boltzmann constant k B using two fixed-path, gas-filled, cylindrical, acoustic cavity resonators is described. The difference in the lengths of the cavities is measured using optical interferometry. Thus, a literature value for the density of mercury is not used, in contrast with the presently accepted determination of k B. 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 Qs result in lower signal-to-noise ratios and wider, asymmetric resonances. To improve signal-to-noise ratios, conventional capacitance microphones were replaced 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. The lengths of the cavities and the modes studied will be chosen to reduce the acoustic perturbations due to non-zero 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 reduced. Using the techniques outlined here, k B can be re-determined with an estimated relative standard uncertainty of 1.5 × 10−6.

Keywords

Boltzmann constant Cylindrical acoustic resonator Two-color interferometry 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Gillis K.A., Moldover M.R.: Int. J. Thermophys. 17, 1305 (1996)CrossRefGoogle Scholar
  2. 2.
    Hurly J.J., Gillis K.A., Mehl J.B., Moldover M.R.: Int. J. Thermophys. 24, 1441 (2003)CrossRefGoogle Scholar
  3. 3.
    Gillis K.A.: Int. J. Thermophys. 15, 821 (1994)CrossRefGoogle Scholar
  4. 4.
    Estela-Uribe J.F., Trusler J.P.M.: Int. J. Thermophys. 21, 1033 (2000)CrossRefGoogle Scholar
  5. 5.
    Trusler J.P.M.: Int. J. Thermophys. 18, 635 (1997)CrossRefGoogle Scholar
  6. 6.
    Moldover M.R., Boyes S.J., Meyer C.W., Goodwin A.R.H.: J. Res. Natl. Inst. Stand. Technol. 104, 11 (1999)Google Scholar
  7. 7.
    Ewing M.B., Trusler J.P.M.: J. Chem. Thermodyn. 32, 1229 (2000)CrossRefGoogle Scholar
  8. 8.
    Benedetto G., Gavioso R.M., Spagnolo R., Marcarino P., Merlone A.: Metrologia 41, 74 (2004)CrossRefADSGoogle Scholar
  9. 9.
    Pitre L., Moldover M., Tew W.L.: Metrologia 43, 142 (2006)CrossRefADSGoogle Scholar
  10. 10.
    Ripple D.C., Strouse G.F., Moldover M.R.: Int. J. Thermophys. 28, 1789 (2007)CrossRefGoogle Scholar
  11. 11.
    Colclough A.R., Quinn T.J., Chandler T.R.D.: Proc. R. Soc. Lond. A 368, 125 (1979)CrossRefADSGoogle Scholar
  12. 12.
    Moldover M.R., Trusler J.P.M., Edwards T.J., Mehl J.B., Davis R.S.: J. Res. Natl. Bur. Stand. 93, 85 (1988)Google Scholar
  13. 13.
    Fischer J., Gerasimov S., Hill K.D., Machin G., Moldover M., Pitre L., Steur P., Stock M., Tamura O., Ugar H., White R., Yang I., Zhang J.: Int. J. Thermophys. 28, 1753 (2007)CrossRefGoogle Scholar
  14. 14.
    Quinn T.J., Colclough A.R., Chandler T.R.D.: Phil. Trans. R. Soc. Lond. A 283, 367 (1976)CrossRefADSGoogle Scholar
  15. 15.
    Morse P.M., Ingard K.U.: Theoretical Acoustics, vol. 606. McGraw-Hill Book Co, New York, pp. 554–557 (1968)Google Scholar
  16. 16.
    Trusler J.P.M.: Physical Acoustics and Metrology of Fluids. Adam Hilger, IOP Publishing Ltd, Bristol (1991)Google Scholar
  17. 17.
    Junger M.C., Feit D.: Sound, Structures, and Their Interaction, pp. 195–234. MIT Press, Cambridge (1986)Google Scholar
  18. 18.
    H. Lin, K.A. Gillis, J.T. Zhang, Int. J. Thermophys. (in press, 2010)Google Scholar
  19. 19.
    Gillis K.A., Lin H., Moldover M.R.: J. Res. Natl. Inst. Stand. Technol. 114, 263 (2009)Google Scholar
  20. 20.
    Moldover M.R.: C.R. Phys. 10, 815 (2009)CrossRefADSGoogle Scholar
  21. 21.
    May E.F., Moldover M.R., Berg R.F.: Int. J. Thermophys. 28, 1085 (2007)CrossRefGoogle Scholar
  22. 22.
    Gillis K.A., Shinder I.I., Moldover M.R.: Phys. Rev. E 70, 021201 (2004)CrossRefADSGoogle Scholar
  23. 23.
    Trusler J.P.M.: Physical Acoustics and Metrology of Fluids, pp. 44–47. Adam Hilger, IOP Publishing Ltd, Bristol (1991)Google Scholar
  24. 24.
    Moldover M.R., Mehl J.B., Greenspan M.: J. Acoust. Soc. Am. 79, 253 (1986)CrossRefADSGoogle Scholar
  25. 25.
    Tilford C.R.: Appl. Opt. 16, 1857 (1977)CrossRefADSGoogle Scholar
  26. 26.
    E.D. Palik (ed.), Handbook of Optical Constants of Solids (Academic Press New York 1985), pp. 275–804Google Scholar
  27. 27.
    Barakat N., Mokhtar S., el Haadi K.A.: J. Opt. Soc. Am. 54, 213 (1964)CrossRefADSGoogle Scholar
  28. 28.
    Thalmann R.: Metrologia 39, 165 (2002)CrossRefADSGoogle Scholar
  29. 29.
    Mohr P.J., Taylor B.N., Newell D.B.: Rev. Mod. Phys. 80, 633 (2008)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • J. T. Zhang
    • 1
  • H. Lin
    • 1
  • J. P. Sun
    • 1
  • X. J. Feng
    • 2
  • K. A. Gillis
    • 3
  • M. R. Moldover
    • 3
  1. 1.National Institute of MetrologyBeijingChina
  2. 2.Tsinghua UniversityBeijingChina
  3. 3.National Institute of Standards and TechnologyGaithersburgUSA

Personalised recommendations