We report on acoustic and microwave measurements made with a purified helium sample maintained close to a single thermodynamic state (Texp ∼ 273.16 K, pexp ∼ 410 kPa) within a 2.1 L volume stainless steel spherical cavity. From these measurements and ab initio calculations of the non-ideality and the refractive index of helium, we determine a value for the Boltzmann constant kB which is consistent with the recommended 2006 CODATA value: (kB − k2006)/k2006 = (−7.5 ± 7.5) × 10−6. We discuss the current limits of the experiment and the prospects of a further reduction in the uncertainty associated with the determination of kB.

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 .

The Boltzmann constant k has been determined from a measurement of the speed of sound in helium gas in a quasi-spherical 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 quasi-sphere, the latter being obtained via simultaneous microwave resonance. Values of c are extrapolated to the zero pressure limit of ideal gas behaviour. We find k = 1.380 648 7(14)×10 −23 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.

A newly designed experimental apparatus has been used to measure the speed of sound u in high-purity water on nine isotherms between 274 and 394 K and at pressures up to 90 MPa. The measurement technique is based on a traditional double-reflector pulse-echo method with a single piezoceramic transducer placed at unequal distances from two stainless steel reflectors. The transit times of an acoustic pulse are measured at a high sampling rate by a digital oscilloscope. The distances between the transducer and the reflectors were obtained at ambient temperature and pressure by direct measurements with a coordinate measuring machine. The speeds of sound are subject to an overall estimated uncertainty of 0.05 %. The acoustic data were combined with available values of density ρ and isobaric heat capacity c p along one isobar at atmospheric pressure to calculate the same quantities over the whole temperature and pressure range by means of a numerical integration technique. These results were compared with those calculated from the IAPWS-95 formulation with corresponding relative deviations which are within 0.1%.KEY WORDS: pulse-echo technique; pure water; speed of sound.