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Détermination de la constante de Boltzmann au plus haut niveau d’exactitude par spectroscopie acoustique dans un résonateur quasi sphérique : Vers une nouvelle définition de l’unité internationale de température.

Abstract : Since 2005, there is an important interest in the international metrology community fornew accurate determinations of the Boltzmann constant kB ; the purpose is to redefine in2015 the unit of thermodynamic temperature, the kelvin. Currently, five techniques areimplemented for determining kB with the objective to achieve a relative uncertainty below1 × 10−6. The method used in the present work is based on acoustic measurements.The Boltzmann constant is linked to the speed of sound u in a noble gas by the virial acousticalequation. The method described here consists in measuring u inside a quasi-sphericalacoustic resonator of inner volume of 0.5 L filled with argon. Measurements are performedduring an isotherm process at the temperature of the triple point of water, T = 273.16 K,at static pressures P from 0.05 MPa to 0.7 MPa. The Boltzmann constant is then determinedby estimating u at zero pressure limit with a polynomial regression.In the present work an acoustic wave propagation model within a quasi-spherical resonatoris defined. Also, the technical means used to carefully control the parameters of theexperiment with an effect on the measurement of u (like temperature, static pressure, gascomposition, etc.) are presented. New exprimental methods and data analyses are described,like the measurement of the radius of the resonator by electromagnetic spectroscopy,as well as the use of the Allan deviation as an efficient tool to study the gas impuritypresence during a long-term experience. Systematic effects are analyzed and corrected. Insome cases the corrections are based on analytical models like the thermal layer boundaryeffect. In other cases, empirical correction functions are proposed, as for the case of changesin the measurements of u related to the continuous gas flow, which was experimentally characterizedin the present work.Finally, the analysis of the data acquiered in 2009 at LCM/LNE-CNAM during two isothermprocesses using argon is presented. This leads to the value kB = 1.3806475 (16) ×10−23 J · K−1, i.e. with a relative uncertainty of 1.14 × 10−6.
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Arnaud Guillou. Détermination de la constante de Boltzmann au plus haut niveau d’exactitude par spectroscopie acoustique dans un résonateur quasi sphérique : Vers une nouvelle définition de l’unité internationale de température.. Autre. Conservatoire national des arts et metiers - CNAM, 2012. Français. ⟨NNT : 2012CNAM0843⟩. ⟨tel-00795225⟩

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