Skip to main content
SpringerLink
Log in

Determination of the Boltzmann Constant by Laser Spectroscopy as a Basis for Future Measurements of the Thermodynamic Temperature

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

Abstract

In this paper, the latest results on the measurement of the Boltzmann constant k B, by laser spectroscopy of ammonia at 10μm are presented. The Doppler absorption profile of a rovibrational line of an NH3 gas sample at thermal and pressure equilibrium is measured as accurately as possible. The absorption cell is placed inside a large 1 m3 thermostat filled with an ice–water mixture, which sets the temperature very close to 273.15 K. Analyzing this profile, which is related to the Maxwell–Boltzmann molecular speed distribution, leads to a determination of the Boltzmann constant via a measurement of the Doppler width (proportional to \({\sqrt{k_{\rm B} T})}\). A spectroscopic determination of the Boltzmann constant with an uncertainty as low as 37 ppm is obtained. Recent improvements with a new passive thermostat lead to a temperature accuracy, stability, and homogeneity of the absorption cell of 1 ppm over a day.

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. 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 

  2. Moldover M.R., Trusler J.P., Edwards T.J., Mehl J.B., Davis R.S.: Phys. Rev. Lett. 60, 249 (1988)

    Article  ADS  Google Scholar 

  3. Mohr P.J., Taylor B.N., Newell D.B.: Rev. Mod. Phys. 80, 633 (2007)

    Article  ADS  Google Scholar 

  4. R. Rusby, M. de Podesta, J. Williams, NPL Report DEPC TH006 (2005)

  5. Fellmuth B., Gaiser C., Fisher J.: Meas. Sci. Technol. 17, R145 (2006)

    Article  ADS  Google Scholar 

  6. Schmidt J.W., Gavioso R.M., May E.F., Moldover M.R.: Phys. Rev. Lett. 98, 254504 (2007)

    Article  ADS  Google Scholar 

  7. Pitre L., Guianvarc’h C., Sparasci F., Richard A., Truong D.: Int. J. Thermophys. 29, 1730 (2008)

    Article  Google Scholar 

  8. Bordé C.J.: Phil. Trans. Roy. Soc. A 363, 2177 (2005)

    Article  ADS  Google Scholar 

  9. Wignall J.W.G.: Metrologia 44, 19 (2007)

    Article  ADS  Google Scholar 

  10. Taylor B.N., Mohr P.J.: Metrologia 36, 63 (1999)

    Article  ADS  Google Scholar 

  11. Fischer J., Gerasimov S., Hill K., Machin G., Moldover M., Pitre L., Steur P., Stock M., Tamura O., Ugur H., White D., Yang I., Zhang J.: Int. J. Thermophys. 28, 1753 (2007)

    Article  Google Scholar 

  12. Petley B.W.: Metrologia 44, 69 (2007)

    Article  ADS  Google Scholar 

  13. Mills I.M., Mohr P.J., Quinn T.J., Taylor B.N., Williams E.R.: Metrologia 42, 71 (2005)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. Stock M., Witt T.J.: Metrologia 43, 583 (2006)

    Article  ADS  Google Scholar 

  16. Becker P.: Metrologia 40, 366 (2003)

    Article  ADS  Google Scholar 

  17. C.J. Bordé, Conference given at the Symposium to Celebrate the 125th Anniversary of the Meter Convention, Paris (2000)

  18. Bordé C.J.: Metrologia 39, 435 (2002)

    Article  ADS  Google Scholar 

  19. C. Daussy, S. Briaudeau, M. Guinet, A. Amy-Klein, Y. Hermier, C.J. Bordé, C. Chardonnet, Spectroscopic Determination of the Boltzmann Constant: First Results, in Laser Spectroscopy, ed. by E. Hinds, A. Ferguson, E. Riis (World Scientific, Cairngorms National Park, Scotland, 2005)

  20. Daussy C., Guinet M., Amy-Klein A., Djerroud K., Hermier Y., Briaudeau S., Bordé C.J., Chardonnet C.: Phys. Rev. Lett. 98, 250801 (2007)

    Article  ADS  Google Scholar 

  21. Daussy C., Bordé C.J., Chardonnet C.: Images de la Physique 2006, 80 (2007)

    Google Scholar 

  22. Casa G., Castrillo A., Galzerano G., Wehr R., Merlone A., Di Serafino D., Laporta P., Gianfrani L.: Phys. Rev. Lett 100, 200801 (2008)

    Article  ADS  Google Scholar 

  23. Yamada K.M.T., Onae A., Hong F.-L., Inaba H., Matsumoto H., Nakajima Y., Ito F., Shimizu T.: J. Mol. Spectrosc 249, 95 (2008)

    Article  ADS  Google Scholar 

  24. Castrillo A., Casa G., Merlone A., Galzerano G., Laporta P., Gianfrani L.: C.R. Physique 10, 894 (2009)

    Article  ADS  Google Scholar 

  25. G.-W. Truong, presented at the IV Int. Workshop on Progress in Determining the Boltzmann Constant, Torino, Italy (2009)

  26. Djerroud K., Daussy C., Lopez O., Amy-Klein A., Briaudeau S., Hermier Y., Chardonnet C.: Ann. Phys. Fr. 32, 175 (2007)

    Article  Google Scholar 

  27. Bernard V., Daussy C., Nogues G., Constantin L., Durand P.E., Amy-Klein A., van Lerberghe A., Chardonnet C.: IEEE J. Quant. Elec. QE-33, 1282 (1997)

    Article  ADS  Google Scholar 

  28. Siegel R., Howell J.: Thermal Radiation Heat Transfer, p. 187. McGraw-Hill, New York (1981)

    Google Scholar 

  29. P. Bouguer, Essai d’optique sur la gradation de la lumière (Claude Jombert, l’Image Notre-Dame, 1729)

  30. Bordé C.J.: C. R. Physique 10, 866 (2009)

    Article  ADS  Google Scholar 

  31. Dicke R.H.: Phys. Rev. 89, 472 (1953)

    Article  ADS  Google Scholar 

  32. Galatry L.: Phys. Rev 122, 1218 (1961)

    Article  MATH  ADS  Google Scholar 

  33. Nelkin M., Ghatak A.: Phys. Rev A 135, 4 (1964)

    Article  MathSciNet  ADS  Google Scholar 

  34. Rautian S.G., Sobel’man I.I.: Sov. Phy. Usp 9, 701 (1967)

    Article  ADS  Google Scholar 

  35. Hartmann J.-M., Boulet C., Robert D.: Collisional Effects on Molecular Spectra: Laboratory Experiments and Models, Consequences for Applications. Elsevier Science, Amsterdam (2008)

    Google Scholar 

  36. C.E. Beker, NASA Tech. Note, TN D-5574 (1969)

  37. Djerroud K., Lemarchand C., Gauguet A., Daussy C., Briaudeau S., Darquié B., Lopez O., Amy-Klein A., Chardonnet C., Bordé C.J.: C. R. Physique 10, 883 (2009)

    Article  ADS  Google Scholar 

  38. Preston-Thomas H.: Metrologia 27, 3 (1990)

    Article  ADS  Google Scholar 

  39. Working Groups of the Consultative Committee for Thermometry, Techniques for Approximating the International Temperature Scale of 1990 (BIPM, 1990)

  40. H. Preston-Thomas, P. Bloembergen, T.J. Quinn, Supplementary Information for the International Temperature Scale of 1990 (CCT, BIPM, 1990)

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Physique des Lasers, UMR 7538 CNRS, Université Paris 13, 99 av. J.-B. Clément, 93430, Villetaneuse, France

    C. Lemarchand, K. Djerroud, B. Darquié, O. Lopez, A. Amy-Klein, C. Chardonnet, Ch. J. Bordé & C. Daussy

  2. Laboratoire Commun de Métrologie LNE-CNAM, 62 rue du Landy, 93210, La Plaine Saint-Denis, France

    S. Briaudeau

Authors
  1. C. Lemarchand
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Djerroud
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. B. Darquié
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. O. Lopez
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. Amy-Klein
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. C. Chardonnet
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Ch. J. Bordé
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. S. Briaudeau
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. C. Daussy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. Daussy.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lemarchand, C., Djerroud, K., Darquié, B. et al. Determination of the Boltzmann Constant by Laser Spectroscopy as a Basis for Future Measurements of the Thermodynamic Temperature. Int J Thermophys 31, 1347–1359 (2010). https://doi.org/10.1007/s10765-010-0755-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10765-010-0755-3

Keywords

Search

Navigation