Correction of NPL-2013 estimate of the Boltzmann constant for argon isotopic composition and thermal conductivity

Abstract

In 2013, a team from NPL, Cranfield University and SUERC published an estimate of the Boltzmann constant based on precision measurements of the speed of sound in argon. A key component of our results was an estimate of the molar mass of the argon gas used in our measurements. To achieve this we made precision comparison measurements of the isotope ratios found in our experimental argon against the ratios of argon isotopes found in atmospheric air. We then used a previous measurement of the atmospheric argon isotope ratios to calibrate the relative sensitivity of the mass spectrometer to different argon isotopes. The previous measurement of the atmospheric argon isotope ratios was carried out at KRISS using a mass spectrometer calibrated using argon samples of known isotopic composition, which had been prepared gravimetrically.We report here a new measurement made at KRISS in October 2014, which directly compared a sample of our experimental gas against the same gravimetrically-prepared argon samples. We consider that this direct comparison has to take precedence over our previous more indirect comparison. This measurement implies a molar mass which is 2.73(60) parts in 10 6 lighter than our 2013 estimate, a shift which is seven times our 2013 estimate of the uncertainty in the molar mass.In this paper we review the procedures used in our 2013 estimate of molar mass; describe the 2014 measurement; highlight some questions raised by the large change in our estimate of molar mass; and describe how we intend to address the inconsistencies between them. We also consider the effect of a new estimate of the low pressure thermal conductivity of argon at 273.16 K. Finally we report our new best estimate of the Boltzmann constant with revised uncertainty, taking account of the new estimates for the molar mass and the thermal conductivity of the argon.

A determination of the molar gas constantRby acoustic thermometry in helium

“…To calculate the perturbation due to the finite conductivity of the surface at 273.16 K, we correct this result by first subtracting the increase in surface resistivity due to the insertion of the microphones (previously measured at 296 K) with the intermediate result ×10 -8 m, in good agreement with other determinations for the same type of copper [3,4]. Finally, we correct our estimate of the expected resistivity at 273.…”

“…The influence of outgassing might be minimised by continuously flushing the internal measuring volume at a high flow rate. However, a systematic dependence of speed of sound on the flow-rate was previously reported for argon [3,4], possibly due to thermal gradients induced by the expansion of the gas jet as it enters the cavity [15]. To assess such possible influence of the flow rate on the measured speed of sound, in a preliminary test at 300 kPa, 273.16 K, we varied the flow rate in four steps between 10 sccm and 100 sccm while continuously recording the resonance frequencies of three radial modes, observing no significant variation of the measurand within the limited relative precision of 0.3 ppm.…”

“…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];…”

“…In contrast to other experiments which recently achieved accurate determinations of k using ellipsoidal or cylindrical cavities [3,5,10], the internal geometry of our assembled resonator was designed to be nearly spherical. Given this …”