Progress in INRiM Experiment for the Determination of the Boltzmann Constant with a Quasi-spherical Resonator

Abstract

Current progress in the INRiM experiment for the determination of the Boltzmann constant k B by means of acoustic thermometry is reported. Particularly, the microwave determination of the volume of a triaxial ellipsoidal resonator with an inner radius of 5 cm which was designed at LNE-CNAM is discussed. For the same cavity, acoustic measurements in helium at T w over the extended pressure range between 50 kPa and 1.4 MPa are reported and these results are compared with the predictions of a model which accounts for several perturbing effects. The procedures, methods, and results obtained in the calibration of several capsule-type SPRTs used in the experiment are briefly illustrated, together with the estimate of the temperature uniformity of the experiment.

A determination of the molar gas constantRby acoustic thermometry in helium

“…Also, the half-width of mode (0,7) shows an anomalous increase below 100 kPa. As reported in previous work with helium [6,42] these anomalous trends are a consequence of the overlap from neighboring nonradial modes in the acoustic spectrum. Due to the elevated number of components in these multiplets, with different associated amplitudes and phases, the consequences of overlapping are extremely hard to predict, apart from the general expected features that these effects will increase proportionally to p -2 , due to increase of the mode half-widths, and that the combination of phases within the single components of the multiplets may result, depending on the mode and the pressure in an increase, or a decrease of the frequency and half-width of neighbouring radial modes.…”

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

“…We conclude that the insertion of the microphones did not modify the inner QSR volume in a significant way. In [31], the authors have obtain the same conclusion.…”

Second-order boundary corrections to the radial acoustic eigenvalues for a spherical cavity

“…The superscripts in parentheses indicate the order of the approximation. As part of the effort to re-determine k B , de Podesta, et al [7] and Gavioso, et al [8] measured the resonance frequencies and half-widths of the radial acoustic modes of gas-filled quasi-spherical cavities with extraordinary precision. In [7] the gas was argon, and in [8] the gas was helium.…”

“…As part of the effort to re-determine k B , de Podesta, et al [7] and Gavioso, et al [8] measured the resonance frequencies and half-widths of the radial acoustic modes of gas-filled quasi-spherical cavities with extraordinary precision. In [7] the gas was argon, and in [8] the gas was helium. Surprisingly, both groups found that, at low pressures and low frequencies, the measured half-widths g m were narrower than the half-widths g calc calculated using the first-order boundary layer correction and other, smaller perturbations.…”