There is currently great interest in the international metrological community for new accurate determinations of the Boltzmann constant k B , with the prospect of a new definition of the unit of thermodynamic temperature, the kelvin. In fact, k B relates the unit of energy (the joule) to the unit of the thermodynamic temperature (the kelvin). One of the most accurate ways to access the value of the Boltzmann constant is from measurements of the velocity of the sound in a noble gas. In the method described here, the experimental determination has been performed in a closed quasi-spherical cavity. To improve the accuracy, all the parameters in the experiment (purity of the gas, static pressure, temperature, exact shape of the cavity monitored by EM microwaves, etc.) have to be carefully controlled. Correction terms have been computed using carefully validated theoretical models, and applied to the acoustic and microwave signals. We report on two sets of isothermal acoustic measurements yielding the value k B = 1.380 647 74(171) × 10 −23 J · K −1 with a relative standard uncertainty of 1.24 parts in 10 6 . This value lies 1.9 parts in 10 6 below the 2006 CODATA value (Mohr et al., Rev. Mod. Phys. 80, 633 (2008)), but, according to the uncertainties, remains consistent with it.

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des modifications et des améliorations apportées par le présent dispositif, les premiers éléments de caractérisation obtenus, et les bénéfices attendus en termes d'incertitude, font l'objet du présent article.

The SI unit of temperature will soon be redefined in terms of a fixed value of the Boltzmann constant k derived from an ensemble of measurements worldwide. We report on a new determination of k using acoustic thermometry of helium-4 gas in a 3 l volume quasi-spherical resonator. The method is based on the accurate determination of acoustic and microwave resonances to measure the speed of sound at different pressures. We find for the universal gas constant R=8.3144614 (50) J•mol -1 •K -1 . Using the current best available value of the Avogadro constant, we obtain k=1.38064878(83)×10 -23 J•K -1 with u(k) /k = 0.60x10 -6 , where the uncertainty u is one standard uncertainty corresponding to a 68 % confidence level. This value is consistent with our previous determinations and with that of the 2014 CODATA adjustment of the fundamental constants (Mohr et al., Rev. Mod. Phys. 88, 035009 (2016)), within the standard uncertainties. We combined the present values of k and u(k) with earlier values that were measured at LNE. Assuming the maximum possible correlations between the measurements, (kpresent/〈k〉 − 1) = 0.07 × 10 −6 and the combined ur(k) is reduced to 0.56 × 10 −6 . Assuming minimum correlations, (kpresent/〈k〉 − 1) = 0.10 × 10 −6 and the combined ur(k) is reduced to 0.48 × 10 −6 .