A determination of the molar gas constant R by acoustic thermometry in helium

We have determined the acoustic and microwave frequencies of a misaligned spherical resonator maintained near the temperature of the triple point of water and filled with helium with carefully characterized molar mass M = (4.002 6032 ± 0.000 0015) g mol-1, with a relative standard uncertainty ur(M) = 0.37×10-6. From these data and traceable thermometry we estimate the speed of sound in our sample of helium at TTPW = 273.16 K and zero pressure to be u0 2 = (945 710.45 ± 0.85) m2 s-2 and correspondingly deduce the value R = (8.314 4743 ± 0.000 0088) J mol-1 K-1 for the molar gas constant. We estimate the value k = R/NA = (1.380 6508 ± 0.000 0015) × 10-23 J K-1 for the Boltzmann constant using the currently accepted value of the Avogadro constant NA. These estimates of R and k, with a relative standard uncertainty of 1.06 × 10-6, are 1.47 parts in 106 above the values recommended by CODATA in 2010

Champs acoustiques en melanges gaz-vapeurs saturees : diffusion moleculaire et precondensation aux parois

Un nouveau mod`ele pour d´ecrire le mouvement acoustique dans des m´elanges gazeux est pr´esent´e ici en partant des ´equations fondamentales de l’hydrodynamique et de la thermodynamique, et en y associant des conditions aux fronti`eres adapt´ees pour d´ecrire les ph´enom`enes d’´evaporation et de condensation sur les parois quand un des composants du m´elange se trouve au voisinage de son point de saturation. Les solutions analytiques g´en´erales de ces ´equations orent `a pr´esent une description unifi´ee de la propagation acoustique en espaces infinis, semi infinis et confin´es, loin de et dans les couches limites. Ces solutions tiennent compte des couplages forts entre le mouvement acoustique et les processus de diusion de chaleur et de concentration, incluant les ph´enom`enes de pr´econdensation sur les parois. Les r´esultats th´eoriques ainsi obtenus sont compar´es `a ceux issus de mod`eles propos´es et d’exp´eriences eectu´ees par le pass´e, mais ne susent toujours pas `a expliquer tous les r´esultats exp´erimentaux disponibles dans la litt´erature. Des exp´eriences sont en cours de pr´eparation, qui ont pour but de valider et compl´eter cette approche analytique par une caract´erisation empirique de certains param`etres li´es aux propri´et´es physiques des gaz utilis´es et `a l’´etat de surface des parois

Progress in INRiM Experiment for the Determination of the Boltzmann Constant with a Quasi-spherical Resonator

Current progress in the INRiM experiment for the determination of the Boltzmann constant k (B) by means of acoustic thermometry is reported. Particularly, the microwave determination of the volume of a triaxial ellipsoidal resonator with an inner radius of 5 cm which was designed at LNE-CNAM is discussed. For the same cavity, acoustic measurements in helium at T (w) over the extended pressure range between 50 kPa and 1.4 MPa are reported and these results are compared with the predictions of a model which accounts for several perturbing effects. The procedures, methods, and results obtained in the calibration of several capsule-type SPRTs used in the experiment are briefly illustrated, together with the estimate of the temperature uniformity of the experiment

New measurement of the Boltzmann constant k by acoustic thermometry of helium-4 gas

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 = 8.314 4614(50) J.mol(-1).K-1. Using the current best available value of the Avogadro constant, we obtain k = 1.380 648 78(83) x 10(-23) J.K-1 with u(k)/k = 0.60 x 10(-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 2016 Rev. Mod. Phys. 88 035009), 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, (k(present)/ -1) = 0.07 x 10(-6) and the combined u(r)(k) is reduced to 0.56 x 10(-6). Assuming minimum correlations, (k(present)/ -1) = 0.10 x 10(-6) and the combined u(r)(k) is reduced to 0.48 x 10(-6)

THE IMERAPLUS JOINT RESEARCH PROJECT FOR DETERMINATIONS OF THE BOLTZMANN CONSTANT

To provide new determinations of the Boltzmann constant, k, which has been asked for by the International Committee for Weights and Measures concerning preparative steps towards new definitions of the kilogram, the ampere, the kelvin and the mole, an iMERAPlus joint research project has coordinated the European activities in this field. In this major European research project the Boltzmann constant has been determined by various methods to support the new definition of the kelvin. The final results of the project are reviewed in this paper. Determinations of the Boltzmann constant k were achieved within the project by all three methods acoustic gas thermometry, Doppler broadening thermometry, and dielectric constant gas thermometry. All of these results are consistent with the currently accepted value of k. Remarkably, the standard uncertainty associated to the most recent acoustic result by LNE-INM/CNAM is a factor of 1.5 smaller than the best previous determination. These results were exploited by the interdisciplinary Committee on Data for Science and Technology (CODATA) in their recent adjustment of recommended values for fundamental constants. As a result, the CODATA group recommended a new value for k with a relative standard uncertainty about a factor of two smaller than the previous ur of 1.7×10−6