Skip to main content
SpringerLink
Log in

Progress Toward Redetermining the Boltzmann Constant with a Fixed-Path-Length Cylindrical Resonator

  • Published:
International Journal of Thermophysics Aims and scope Submit manuscript

Abstract

A single, fixed-path-length cylindrical-cavity resonator was used to measure c 0 = (307.825 2 ± 0.001 2) m · s−1, the zero-density limit of the speed of sound in pure argon at the temperature of the triple point of water. Three even and three odd longitudinal modes were used in this measurement. Based on the ratio M/γ 0 = (23.968 644 ± 0.000 033) g · mol−1, determined from an impurity and isotopic analysis of the argon used in this measurement and the measured c 0, the value k B = 1.380 650 6 × 10−23J · K−1 was obtained for the Boltzmann constant. This value of k B has a relative uncertainty u r(k B) = 7.9 × 10−6 and is fractionally, (0.12 ± 8.1) × 10−6 larger than the value recommended by CODATA in 2006. (The uncertainty is one standard uncertainty.) Several, comparatively large imperfections of our prototype cavity affect the even longitudinal modes more than the odd modes. The models for these imperfections are approximate, but they suggest that an improved cavity will significantly reduce the uncertainty of c 0.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Mills I.M., Mohr P.J., Quinn T.J., Taylor B.N., Williams E.R.: Metrologia 43, 227 (2006)

    Article  ADS  Google Scholar 

  2. Colclough A.R., Quinn T.J., Chandler T.R.D.: Proc. R. Soc. Lond. A 368, 125 (1979)

    Article  ADS  Google Scholar 

  3. 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 

  4. Pitre L., Gruianvarch C., Sparasci F., Guillou A., Truong D., Hermier Y., Himbert M.E.: C.R. Phys. 10, 835 (2009)

    Article  ADS  Google Scholar 

  5. Gavioso R.M., Benedetto G., Albo P.A.G., Ripa D.M., Merlone A., Guianvarc’h C., Moro F., Cuccaro R.: Metrologia 47, 387 (2010)

    Article  ADS  Google Scholar 

  6. L. Pitre, F. Sparasci, A. Guillou, D. Truong, Y. Hermier, M.E. Himbert, New determination of the Boltzmann constant with an acoustic method, in Conference on Precision Electromagnetic Measurements (Daejeon, Korea, 2010)

  7. Sutton G., Underwood R., Pitre L., de Podesta M., Valkiers S.: Int. J. Thermophys. 31, 1310 (2010)

    Article  ADS  Google Scholar 

  8. Segovia J.J., Maza D.V., Martin M.C., Gomez E., Tabacaru C., del Campo D.: Int. J. Thermophys. 31, 1294 (2010)

    Article  ADS  Google Scholar 

  9. Zhang J.T., Lin H., Sun J.P., Feng X.J., Gillis K.A., Moldover M.R.: Int. J. Thermophys. 31, 1273 (2010)

    Article  ADS  MATH  Google Scholar 

  10. Moldover M.R., Boyes S.J., Meyer C.W., Goodwin A.R.H.: J. Res. Natl. Inst. Stand. Technol. 104, 11 (1999)

    Article  Google Scholar 

  11. Ewing M.B., Trusler J.P.M.: J. Chem. Thermodyn. 321, 229 (2000)

    Google Scholar 

  12. Benedetto G., Gavioso R.M., Spagnolo R., Marcarino P., Merlone A.: Metrologia 41, 74 (2004)

    Article  ADS  Google Scholar 

  13. Pitre L., Moldover M.R., Tew W.L.: Metrologia 43, 142 (2006)

    Article  ADS  Google Scholar 

  14. Ripple D.C., Strouse G.F., Moldover M.R.: Int. J. Thermophys. 28, 1789 (2007)

    Article  ADS  Google Scholar 

  15. Gillis K.A., Lin H., Moldover M.R.: J. Res. Natl. Inst. Stand. Technol. 114, 263 (2009)

    Article  Google Scholar 

  16. Lin H., Gillis K.A., Zhang J.T.: Int. J. Thermophys. 31, 1234 (2010)

    Article  ADS  Google Scholar 

  17. J.T. Zhang, H. Lin, J.P. Sun, X.J. Feng, K.A. Gillis, M.R. Moldover, Re-determination of the Boltzmann constant with fixed path cylinders. Presented at TEMPMEKO & ISHM 2010 (Portorož, Slovenia, 2010)

  18. Mohr P.J., Taylor B.N., Newell D.B.: Rev. Mod. Phys. 80, 633 (2008)

    Article  ADS  Google Scholar 

  19. Ewing M.B., McGlashan M.L., Trusler J.P.M.: Metrologia 22, 93 (1986)

    Article  ADS  Google Scholar 

  20. Moldover M.R., Trusler J.P.M.: Metrologia 25, 165 (1988)

    Article  ADS  Google Scholar 

  21. Ewing M.B., Owusu A.A., Trusler J.P.M: Physica A 156, 899 (1989)

    Article  ADS  Google Scholar 

  22. Ewing M.B., Goodwin A.R.H.: J. Chem. Thermodyn. 24, 531 (1992)

    Article  Google Scholar 

  23. Dittman S., Lindenau B.E., Tilford C.R.: J. Vac. Sci. Technol. A 7, 3356 (1989)

    Article  ADS  Google Scholar 

  24. Berg R.F.: Metrologia 42, 11 (2005)

    Article  ADS  Google Scholar 

  25. Mehl J.B., Moldover M.R., Pitre L.: Metrologia 41, 295 (2004)

    Article  ADS  Google Scholar 

  26. Palik, E.D. (ed.): Handbook of Optical Constants of Solids. Academic Press, New York (1985)

    Google Scholar 

  27. Barakat N., Mokhtar S., Haadi K.A.: J. Opt. Soc. Am. 54, 213 (1964)

    Article  ADS  Google Scholar 

  28. Peck E.R., Fisher D.J.: J. Opt. Soc. Am. 54, 1362 (1964)

    Article  ADS  Google Scholar 

  29. Tilford C.F.: Appl. Opt. 16, 1857 (1977)

    Article  ADS  Google Scholar 

  30. Valkiers S., Vendelbo D., Berglund M., de Podesta M.: Int. J. Mass Spectrom 291, 41 (2010)

    Article  Google Scholar 

  31. L. Pitre, A. Guillou, D. Truong, F. Sparasci, C. Guianvarc’h, An acoustic/microwave determination of the Boltzmann Constant at LNE-INM/CNAM, presented at The IV International Workshop on Progress in Determining the Boltzmann Constant (Torino, Italy, 2009)

  32. Nier A.O.: Phys. Rev. 77, 789 (1950)

    Article  ADS  Google Scholar 

  33. Lee J.Y., Marti K., Severinghaus J.P., Kawamur K., Yoo H.S., Lee J.B., Kim J.S.: Geochim. Cosmochim. Acta 70, 4507 (2006)

    Article  ADS  Google Scholar 

  34. Gillis K.A., Shinder I.I., Moldover M.R.: Phys. Rev. E 70, 021201 (2004)

    Article  ADS  Google Scholar 

  35. Moldover M.R.: C.R. Phys. 10, 815 (2009)

    Article  ADS  Google Scholar 

  36. A.R.H. Goodwin, Thermophysical Properties from the Speed of Sound, Ph.D. Thesis, University of London, 1988

  37. Wieser M.E., Berglund M.: Pure Appl. Chem. 81, 2131 (2009)

    Article  Google Scholar 

  38. Laeter J.R, Bohlke J.K., De Bievre P., Hidaka H., Peiser H.S., Rosman K.J.R., Taylor P.D.P.: Pure Appl. Chem. 75, 683 (2003)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Institute of Metrology, Beijing, 100013, China

    J. T. Zhang, H. Lin, X. J. Feng & J. P. Sun

  2. National Institute of Standards and Technology, Gaithersburg, MD, 20899-8360, USA

    K. A. Gillis & M. R. Moldover

  3. Tsinghua University, Beijing, 100084, China

    Y. Y. Duan

Authors
  1. J. T. Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. X. J. Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. P. Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. K. A. Gillis
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. M. R. Moldover
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Y. Y. Duan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. T. Zhang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, J.T., Lin, H., Feng, X.J. et al. Progress Toward Redetermining the Boltzmann Constant with a Fixed-Path-Length Cylindrical Resonator. Int J Thermophys 32, 1297–1329 (2011). https://doi.org/10.1007/s10765-011-1001-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10765-011-1001-3

Keywords

Search

Navigation