Measurement of the Boltzmann constant by the Doppler broadening technique at a $ 3.8\times {10}^{-5}$ accuracy level

Khelifa Djerroud; Cyril Lemarchand; Alexandre Gauguet; Christophe Daussy; Stephan Briaudeau; Benoît Darquié; Olivier Lopez; Anne Amy-Klein; Christian Chardonnet; Christian J. Bordé

doi:10.1016/j.crhy.2009.10.020

Measurement of the Boltzmann constant by the Doppler broadening technique at a

3.8 \times 10^{- 5}

accuracy level
[Mesure de la constante de Boltzmann utilisant l'élargissement Doppler avec une incertitude relative de

3, 8 \times 10^{- 5}

]

Khelifa Djerroud ¹ ; Cyril Lemarchand ¹ ; Alexandre Gauguet ¹ ; Christophe Daussy ¹ ; Stephan Briaudeau ² ; Benoît Darquié ¹ ; Olivier Lopez ¹ ; Anne Amy-Klein ¹ ; Christian Chardonnet ¹ ; Christian J. Bordé ¹

¹ Laboratoire de physique des lasers, UMR 7538 CNRS, Université Paris 13, 99, avenue J.-B. Clément, 93430 Villetaneuse, France
² Institut national de métrologie LNE-INM – CNAM, 62, rue du Landy, 93210 La Plaine Saint-Denis, France

Comptes Rendus. Physique, Experimental determination of Boltzmann's constant, Volume 10 (2009) no. 9, pp. 883-893.

Résumé
Abstract

Dans cet article, nous présentons l'expérience développée au Laboratoire de physique des lasers pour la mesure optique de la constante de Boltzmann $k_{B}$ . Cette nouvelle approche ramène la détermination de $k_{B}$ à une mesure de fréquence. L'expérience consiste à mesurer le plus exactement possible le profil d'absorption Doppler d'une raie de vibration–rotation de l'ammoniac à l'équilibre thermodynamique. Ce profil reflète la distribution de Maxwell–Boltzmann des vitesses moléculaires le long du faisceau laser. Une analyse de la forme de la raie d'absorption conduit à une détermination de l'élargissement Doppler, proportionnel à $\sqrt{k_{B} T}$ , et donc à une mesure de la constante de Boltzmann. La mesure spectroscopique est réalisée à l'aide d'un laser à CO₂ ultra-stable de longueur d'onde $λ \approx 10 μm$ . La cellule d'absorption est placée dans un thermostat qui permet de contrôler la température autour de 273,15 K avec une incertitude de 1,4 mK. Ces mesures nous ont conduit récemment à une détermination de $k_{B}$ avec une incertitude relative de $3, 8 \times 10^{- 5}$ . Cela représente, pour des temps de mesure comparables, un gain d'un ordre de grandeur par rapport à notre précédente mesure publiée en Daussy et al. (2007).

In this article, we describe an experiment performed at the Laboratoire de physique des lasers and dedicated to an optical measurement of the Boltzmann constant $k_{B}$ . With the proposed innovative technique, determining $k_{B}$ comes down to an ordinary frequency measurement. The method consists in measuring as accurately as possible the Doppler absorption profile of a rovibrational line of ammonia in thermal equilibrium. This profile is related to the Maxwell–Boltzmann molecular velocity distribution along the laser beam. A fit of the absorption line shape leads to a determination of the Doppler width proportional to $\sqrt{k_{B} T}$ and thus to a determination of the Boltzmann constant. The laser source is an ultra-stable CO₂ laser with a wavelength $λ \approx 10 μm$ . The absorption cell is placed in a thermostat, keeping the temperature at 273.15 K within 1.4 mK. We were able to measure $k_{B}$ with a relative uncertainty as small as $3.8 \times 10^{- 5}$ , which represents an improvement of an order of magnitude for an integration time comparable to our previous measurement published in 2007.

Publié le : 2009-11-01

DOI : 10.1016/j.crhy.2009.10.020

Keywords: Fundamental constants, Laser spectroscopy, Absorption line shape
Mots-clés : Constantes fondamentales, Spectroscopie laser, Forme de raie d'absorption

Affiliations des auteurs :

Khelifa Djerroud ¹ ; Cyril Lemarchand ¹ ; Alexandre Gauguet ¹ ; Christophe Daussy ¹ ; Stephan Briaudeau ² ; Benoît Darquié ¹ ; Olivier Lopez ¹ ; Anne Amy-Klein ¹ ; Christian Chardonnet ¹ ; Christian J. Bordé ¹

¹ Laboratoire de physique des lasers, UMR 7538 CNRS, Université Paris 13, 99, avenue J.-B. Clément, 93430 Villetaneuse, France
² Institut national de métrologie LNE-INM – CNAM, 62, rue du Landy, 93210 La Plaine Saint-Denis, France

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     title = {Measurement of the {Boltzmann} constant by the {Doppler} broadening technique at a $ 3.8\times {10}^{-5}$ accuracy level},
     journal = {Comptes Rendus. Physique},
     pages = {883--893},
     publisher = {Elsevier},
     volume = {10},
     number = {9},
     year = {2009},
     doi = {10.1016/j.crhy.2009.10.020},
     language = {en},
}

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Khelifa Djerroud; Cyril Lemarchand; Alexandre Gauguet; Christophe Daussy; Stephan Briaudeau; Benoît Darquié; Olivier Lopez; Anne Amy-Klein; Christian Chardonnet; Christian J. Bordé. Measurement of the Boltzmann constant by the Doppler broadening technique at a $ 3.8\times {10}^{-5}$ accuracy level. Comptes Rendus. Physique, Experimental determination of Boltzmann's constant, Volume 10 (2009) no. 9, pp. 883-893. doi : 10.1016/j.crhy.2009.10.020. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2009.10.020/

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