Shell Perturbations of an Acoustic Thermometer Determined from Speed of Sound in Gas Mixtures

Abstract

With the goal of achieving a better understanding of gas-shell coupling perturbations in the acoustic resonators used at INRiM for the determination of the Boltzmann constant, we measured the variation of their acoustic and microwave resonances induced by changing the composition of a binary He-Ar mixture which filled the cavity at constant temperature and pressure. As a consequence of the progressive dilution of a sample of initially pure He with Ar, the radial acoustic modes of the resonator spanned decreasing frequency intervals, partially overlapping, for several modes. In addition to the expected breathing mode of the shell, the results evidenced the presence of several other shell resonances at lower and higher frequencies, confirming that the elastic response of the assembled resonator significantly differs from that of a simple spherical shell. Experimental results are reported for two resonators which differ in design, dimensions, and constructing material. In spite of their being preliminary and susceptible of significant improvement, these results favor the interpretation of acoustic thermometry measurements with pure gases.

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

“…In addition to the expected breathing frequency of the shell calculated at 19.3 kHz from the model in [9], the measurements in the He/Ar mixture evidenced the presence of several other shell resonances at a lower frequency (Fig. 6 in [24]), with a predominant peak located around 16.7 kHz.…”

“…The characterization of the acoustic performance of TCU2v2 was started in February 2010 by recording the resonance frequencies of several radial modes while the composition of the gas flowing through the cavity was slowly (over a period of 1.5 months) varied from pure He to pure Ar and the molar density of the gas was maintained constant at 690 kPa and 273.16 K. The scope of this time-consuming test, which has been described elsewhere [24] was to investigate the acoustic coupling effects between the gas and the cavity shell. In addition to the expected breathing frequency of the shell calculated at 19.3 kHz from the model in [9], the measurements in the He/Ar mixture evidenced the presence of several other shell resonances at a lower frequency (Fig.…”

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

“…This experimental technique allows the measurement of the thermal expansion of spherical cavities in acoustic thermometry, and has successfully been applied in several experiments [14][15][16][17][18][19]. The radius a(p, T TPW ) of the cavity can be obtained using…”

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

“…This experimental technique allows determination of the thermal expansion of spherical cavities in acoustic thermometry, and has successfully been applied in several experiments, as shown in [13][14][15][16][17][18]. The accuracy in the determination of microwave eigenfrequencies, used to determine the cavity dimensions, can be improved removing the degeneracy associated with the microwave eigenfunctions, and adopting a quasi-spherical geometry for the shape of the resonant cavity, and in particular, that of a triaxial ellipsoid [19,20].…”