New measurement of the Boltzmann constantkby acoustic thermometry of helium-4 gas

Abstract

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 .

Realization of ppm level pressure stability for primary thermometry using a primary piston gauge

“…The gas source is a bottle of high purity (>99.99999%) 4 He at high pressure (20 MPa). Using the pressure regulator, the gas pressure at the entrance to the 1 L ballast volume is reduced to 1.5 bars (0.15 MPa).…”

“…The 1990 international practical temperature scale (ITS-90, T90) [1] is used worldwide to approximate thermodynamic temperature T. The scale is based on the best thermodynamic temperature measurements that were available in 1990. To measure the temperature in the range 5 K to 24.5561 K (the neon triple point), three primary thermometry techniques are traditionally employed: constant volume gas thermometry (CVGT) [2,3], dielectric constant gas thermometry (DCGT) [2] and acoustic gas thermometry (AGT) [2,4,5]. The core principle of CVGT is to measure the absolute pressure in a constant volume.…”

The Boltzmann Constant for the Definition and Realization of the Kelvin

“…As there was a close cooperation between the research groups pursuing acoustic gas thermometry correlations of uncertainty contributions had to be considered very carefully . The lowest uncertainty in the determination of the Boltzmann constant ever achieved was accomplished by acoustic gas thermometry in a large 3.1 liter quasi‐sphere (90 mm radius) operated with helium at LNE‐Cnam who claimed a relative standard uncertainty of k of 6 × 10 −7 . The two largest uncertainty contributions come from the temperature measurement of the sphere and the determination of the speed of sound.…”

“…have been combined to a mean value according to ref. []. Open circles: The CODATA adjusted values of 2014 and 2017.…”

The Optical Frequency Standards for the Realization of the Meter

“…To this end, the Kibble balance must operate in a moving mode where the velocity of a coil must be precisely measured. The relative uncertainty should not exceed . ‐Absolute primary acoustic gas thermometry played an important role in the determination of the Boltzmann constant k , the defining constant of the kelvin . The dimensional characteristic of hollow resonators (e.g., triaxial ellipsoid) must be determined.…”