A low-uncertainty measurement of the Boltzmann constant

Abstract

The Comité international des poids et mesures (CIPM) has projected a major revision of the International System of Units (SI) in which all of the base units will be defined by fixing the values of fundamental constants of nature. In preparation for this we have carried out a new, low-uncertainty determination of the Boltzmann constant, k B , in terms of which the SI unit of temperature, the kelvin, can be re-defined. We have evaluated k B from exceptionally accurate measurements of the speed of sound in argon gas which can be related directly to the mean molecular kinetic energy, 3 2 k B T . Our new estimate is k B = 1.380 651 56 (98) × 10 −23 J K −1 with a relative standard uncertainty u R = 0.71 × 10 −6 .

Progress towards the determination of thermodynamic temperature with ultra-low uncertainty

“…Also, the overall uncertainty was reduced owing to significant improvements of the methods used to determine the compressibility of the capacitors as a function of temperature, leading to a correction of previous results in the temperature range between 2.5 K and 36 K [26]. -The AGT apparatus used at NPL is based on the resonator previously characterized for an extremely accurate determination of the Boltzmann constant k [46] with multiple modifications to the thermostatting system to cover the overall temperature range between 118 K and 303 K. The AGT was operated in relative mode, with measurements of the speed of sound in Ar recorded as a function of pressure along several (20) closely spaced isotherms, including T TPW . For this experiment, a detailed description of the separate uncertainty contributions to the determinations of T and T 90 , and a critical discussion of the results, may be found elsewhere [47].…”

A determination of the molar gas constantRby acoustic thermometry in helium

“…These have been performed by (i) the measurement of a thermodynamic or electromagnetic intensive property of a macroscopic sample of gas, or (ii) the measurement of the electrical noise in a sense resistor, or (iii) the optical measurement of the absorption spectra of simple molecules. Remarkably, developments in all these methods has achieved a significant reduction of uncertainties: acoustic gas thermometry (AGT) now stands at the relative uncertainty level of 1 ppm or below [2,3,4,5,6], while dielectric constant gas thermometry (DCGT), refractive index gas thermometry (RIGT), Johnson noise thermometry (JNT) demonstrated overall uncertainties at the level of a few ppm [7,8,9], and Doppler broadening thermometry (DBT), shows a potential accuracy at the level of a few ppm or below [10,11]. This outstanding progress in several different primary thermometry techniques is important in view of their possible future application to the practical realization of the newly defined kelvin [12], allowing metrological laboratories across the world to realize a thermodynamic temperature standard by choosing the method which is best suited to the particular facilities, experience and knowledge available in the host institution.…”

“…Unless otherwise stated, all uncertainties in this work are standard uncertainties with coverage factor k = 1, corresponding to a 68% confidence interval. [6]; CODATA-06 [15]; LNE-09 [16]; NPL-10 [17]; INRiM-10 [18]; LNE-11 [4]; NIM-11 [19]; CODATA-10 [14]; NPL-13 [2,3]; NIM-13 [20]; LNE-15 [5];…”

The NIST Johnson Noise Thermometry System for the Determination of the Boltzmann Constant

“…based on the acoustic properties of gases with less than 1 × 10 −6 relative uncertainty [2,3]. An alternative technique using dielectric constant gas thermometry [4,5] recently produced a value for k with a relative uncertainty of 1.9 × 10 −6 [6].…”