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Boltzmann Constant
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M E Himbert – 1st expert on this subject based on the ideXlab platform

determinations of the Boltzmann Constant
Comptes Rendus Physique, 2018CoAuthors: L Pitre, F Sparasci, M D Plimmer, M E HimbertAbstract:Abstract We review measurements of the Boltzmann Constant, k, the value of which is soon to be fixed at exactly 1.380 649 × 10 − 23 J⋅K−1 for the future revised Systeme international of units. In addition to a description of the theoretical background and of diverse experimental techniques (acoustic thermometry, Johnson noise thermometry, dielectric Constant gas thermometry, and Doppler broadened molecular spectroscopy), the article highlights the decisive role of ab initio calculations of the thermophysical properties of gases, especially helium4. Perspectives for improvements in thermometry are outlined in the wake of the new definition.

new measurement of the Boltzmann Constant k by acoustic thermometry of helium 4 gas
Metrologia, 2017CoAuthors: L Pitre, F Sparasci, M E Himbert, M D Plimmer, C Guianvarch, L. Risegari, C Martin, A Allard, B Marty, P Giuliano A AlboAbstract: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 helium4 gas in a 3litre volume quasispherical resonator. The method is based on the accurate determine of acoustic and microwave resonances to measure the speed of sound at different pressures. We find for the universal gas Constant R = 8.31 44614 (50) Jmol1K1. Using the current best available value of the Avogadro Constant, we obtain k = 1.38 064 878(83) ×10^(23) JK1 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 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, (klsubgpresentl/subg/〈k〉1) = 0.071×10lsupg6l/supg and the combined ur(k) is reduced to 0.56×10lsupg6l/supg. Assuming minimum correlations, (klsubgpresentl/subg/〈k〉1) = 0.10×10lsupg6l/supg and the combined ur(k) is reduced to 0.49×10lsupg6l/supg.

determination of the Boltzmann Constant k from the speed of sound in helium gas at the triple point of water
Metrologia, 2015CoAuthors: L Pitre, F Sparasci, M E Himbert, M D Plimmer, L. Risegari, P Giuliano A AlboAbstract:The Boltzmann Constant k has been determined from a measurement of the speed of sound in helium gas in a quasispherical resonator (volume 0.5 l) maintained at a temperature close to the triple point of water (273.16 K). The acoustic velocity c is deduced from measured acoustic resonance frequencies and the dimensions of the quasisphere, the latter being obtained via simultaneous microwave resonance. Values of c are extrapolated to the zero pressure limit of ideal gas behaviour. We find J⋅K−1, a result consistent with previous measurements in our group and elsewhere. The value for k, which has a relative standard uncertainty of 1.02 ppm, lies 0.02 ppm below that of the CODATA 2010 adjustment.
L Pitre – 2nd expert on this subject based on the ideXlab platform

determinations of the Boltzmann Constant
Comptes Rendus Physique, 2018CoAuthors: L Pitre, F Sparasci, M D Plimmer, M E HimbertAbstract:Abstract We review measurements of the Boltzmann Constant, k, the value of which is soon to be fixed at exactly 1.380 649 × 10 − 23 J⋅K−1 for the future revised Systeme international of units. In addition to a description of the theoretical background and of diverse experimental techniques (acoustic thermometry, Johnson noise thermometry, dielectric Constant gas thermometry, and Doppler broadened molecular spectroscopy), the article highlights the decisive role of ab initio calculations of the thermophysical properties of gases, especially helium4. Perspectives for improvements in thermometry are outlined in the wake of the new definition.

determinations of the Boltzmann Constant
Conference on Precision Electromagnetic Measurements, 2018CoAuthors: L PitreAbstract:In the last decade, more than 25 publications have reported a determination of the Boltzmann Constant. Consequently, the International Committee for Weights and Measures (CIPM), at its meeting in October 2017 followed the recommendation of the Consultative Committee for Units (CCU) on the redefinition of the kilogram, ampere, kelvin and mole. For the redefinition of the kelvin the Boltzmann Constant will be fixed with the numerical value 1.380 649 10−23J·K−1.

new measurement of the Boltzmann Constant k by acoustic thermometry of helium 4 gas
Metrologia, 2017CoAuthors: L Pitre, F Sparasci, M E Himbert, M D Plimmer, C Guianvarch, L. Risegari, C Martin, A Allard, B Marty, P Giuliano A AlboAbstract: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 helium4 gas in a 3litre volume quasispherical resonator. The method is based on the accurate determine of acoustic and microwave resonances to measure the speed of sound at different pressures. We find for the universal gas Constant R = 8.31 44614 (50) Jmol1K1. Using the current best available value of the Avogadro Constant, we obtain k = 1.38 064 878(83) ×10^(23) JK1 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 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, (klsubgpresentl/subg/〈k〉1) = 0.071×10lsupg6l/supg and the combined ur(k) is reduced to 0.56×10lsupg6l/supg. Assuming minimum correlations, (klsubgpresentl/subg/〈k〉1) = 0.10×10lsupg6l/supg and the combined ur(k) is reduced to 0.49×10lsupg6l/supg.
Michael R Moldover – 3rd expert on this subject based on the ideXlab platform

determination of the Boltzmann Constant with cylindrical acoustic gas thermometry new and previous results combined
Metrologia, 2017CoAuthors: Xiaojuan Feng, Michael R Moldover, Keith A Gillis, J Zhang, James B Mehl, K Zhang, Y N DuanAbstract:We report a new determination of the Boltzmann Constant k B using a cylindrical acoustic gas thermometer. We determined the length of the copper cavity from measurements of its microwave resonance frequencies. This contrasts with our previous work (Zhang et al 2011 Int. J. Thermophys. 32 1297, Lin et al 2013 Metrologia 50 417, Feng et al 2015 Metrologia 52 S343) that determined the length of a different cavity using twocolor optical interferometry. In this new study, the halfwidths of the acoustic resonances are closer to their theoretical values than in our previous work. Despite significant changes in resonator design and the way in which the cylinder length is determined, the value of k B is substantially unchanged. We combined this result with our four previous results to calculate a global weighted mean of our k B determinations. The calculation follows CODATA’s method (Mohr and Taylor 2000 Rev. Mod. Phys. 72 351) for obtaining the weighted mean value of k B that accounts for the correlations among the measured quantities in this work and in our four previous determinations of k B. The weighted mean is 1.380 6484(28) × 10−23 J K−1 with the relative standard uncertainty of 2.0 × 10−6. The corresponding value of the universal gas Constant is 8.314 459(17) J K−1 mol−1 with the relative standard uncertainty of 2.0 × 10−6.

improving acoustic determinations of the Boltzmann Constant with mass spectrometer measurements of the molar mass of argon
Metrologia, 2015CoAuthors: Inseok Yang, L Pitre, Jintao Zhang, Michael R Moldover, Xiaojuan FengAbstract:We determined accurate values of ratios among the average molar masses MAr of 9 argon samples using two completelyindependent techniques: (1) mass spectrometry and (2) measured ratios of acoustic resonance frequencies. The two techniques yielded mutually consistent ratios (RMS deviation of 0.16 × 10−6 MAr from the expected correlation) for the 9 samples of highlypurified, commerciallypurchased argon with values of MAr spanning a range of 2 × 10−6 MAr. Among the 9 argon samples, two were traceable to recent, accurate, argonbased measurements of the Boltzmann Constant kB using primary acoustic gas thermometers (AGT). Additionally we determined our absolute values of MAr traceable to two, completelyindependent, isotopicreference standards; one standard was prepared gravimetrically at KRISS in 2006; the other standard was isotopicallyenriched 40Ar that was used during NIST’s 1988 measurement of kB and was sent to NIM for this research. The absolute values of MAr determined using the KRISS standard have the relative standard uncertainty ur(MAr) = 0.70 × 10−6 (Uncertainties here are one standard uncertainty.); they agree with values of MAr determined at NIM using an AGT within the uncertainty of the comparison ur(MAr) = 0.93 × 10−6. If our measurements of MAr are accepted, the difference between two, recent, argonbased, AGT measurements of kB decreases from (2.77 ± 1.43) × 10−6 kB to (0.16 ± 1.28) × 10−6 kB. This decrease enables the calculation of a meaningful, weighted average value of kB with a uncertainty ur(kB) ≈ 0.6 × 10−6.

correlations among acoustic measurements of the Boltzmann Constant
Metrologia, 2015CoAuthors: Michael R Moldover, R M Gavioso, David B NewellAbstract:We review correlated uncertainties among the accurate determinations of the Boltzmann Constant that used the techniques of primary acoustic gas thermometry (AGT). We find correlated uncertainty contributions from four sources: (1) the uncertain chemical and isotopic compositions of the test gases that lead to an uncertain average molar mass, (2) measurements of the temperature, (3) measurements of the shape and dimensions of the cavity resonators, and (4) fitting acoustic resonance frequencies as a function of the pressure. Molarmassdependent uncertainties are correlated among those measurements that used argon with isotopic abundances determined using an isotopic standard prepared at the Korea Research Institute of Standards and Science in 2006. Correlated, cavitydependent uncertainties result from using the same cavity for more than one measurement. Small, correlated uncertainties propagate into all the AGT determinations of when acoustic resonance frequencies are fit for using uncertain literature data for the Avogadro Constant and for the thermal conductivity and the higher acoustic virial coefficients of helium or argon.