Acoustic Resonator Experiments at the Triple Point of Water: First Results for the Boltzmann Constant and Remaining Challenges

Abstract

We report on two sets of isothermal acoustic measurements made with argon close to the triple point of water using a 50 mm radius, thin-walled, diamondturned quasisphere. Our two isotherms yielded values for the Boltzmann constant, k B , which differ by 0.9 parts in 10 6 , and have an average value of k B = (1.380 649 6 ± 0.000 004 3) × 10 −23 J · K −1 . The relative uncertainty is 3.1 parts in 10 6 , and the average value is 0.58 parts in 10 6 below the 2006 CODATA value (Mohr et al. Rev Mod Phys 80:633, 2008), and so the values are consistent within their combined (k = 1) uncertainties.

Determination of the Boltzmann constant using a quasi-spherical acoustic resonator

“…The shaded area spans the uncertainty u(k B_CODATA ). The experimental determinations by Pitre et al [7] in 2009, by Sutton et al [2] in 2009 and by Gavioso et al [8] in 2010 were, respectively, obtained at the Laboratoire National de Métrologie et d'Essai-Conservatoire National des Arts et Métiers (LNE-CNAM), at the National Physical Laboratory (NPL) and at the Istituto Nazionale di Ricerca Metrologica (INRiM), by measuring the speed of sound in He and Ar with quasi-spherical resonators. The value from the study of Zhang et al [9] was obtained with a cylindrical acoustic resonator.…”

“…In this work, the average radius of BCU3 has been determined from measurements of the frequencies and half-widths of nine microwave triplets, corrected to take into account three effects: (i) the microwave penetration depth using measured half-widths of the resonances, as described by Sutton et al [2], (ii) the inlet and outlet gas ducts and the two microwave antennas using the extensive study of the effects of probes and holes in a quasi-spherical resonator (QSR) performed by Underwood et al [22], and (iii) the shape of the QSR, using second-order theory [21] and our measurements of the frequency splitting of the microwave triplets. The determination of the equivalent radius and its uncertainty budget was accomplished in four steps.…”

“…The value is deduced from measurements of the velocity of sound in argon, as in the work performed by Moldover et al at the National Institute of Standards and Technology (NIST) in 1988 [1]. However, several fundamental modifications and improvements have been made to measure and control the parameters that influence the measurement of k B [2,3].…”

Measurement of the Boltzmann Constant k B Using a Quasi-Spherical Acoustic Resonator

“…The shaded area spans u (k B_CODATA ). The determinations of 2009 by Pitre et al [7] and by Sutton et al [2], and of 2010 by Gavioso et al [8] were, respectively, obtained at LCM (LNE-CNAM), at NPL, and at INRiM, by measuring the speed of sound in He and Ar with quasi-spherical resonators. The value from Zhang et al [9] was obtained at NIM with a cylindrical acoustic resonator For an accurate determination of the speed of sound in a dilute gas, methods involving the measurement of the resonance frequencies of standing waves in cavities of simple geometry remain unsurpassed.…”

“…However, several fundamental modifications and improvements have been made in this new experiment to measure and control the parameters that influence the measurement of k B [2,3].…”