Internal consistency in the determination of the Boltzmann constant using a quasispherical resonator

Abstract

The use of a combined microwave and acoustic resonator to determine the Boltzmann constant, kB, permits several checks on the internal consistency of the data. Using measurements in argon gas in the NPL-Cranfield quasispherical copper resonator (NPLC-2), we describe four distinct types of internal consistency check. Firstly, we estimate kB using six distinct acoustic resonances varying in frequency from 3.55 kHz to 21.77 kHz. We thus span a wide range of systematic corrections, most notably in the effect of the thermal boundary layer (TBL), which varies strongly with mode. Secondly, the same theory which predicts the TBL corrections to the acoustic resonance frequencies also predicts the widths of the resonances. By comparing the measured and theoretically-expected widths we can place limits on the effect of any un-modeled physics. Thirdly, the equivalent radius of the resonator (∼62.03 mm) is inferred from analysis of 8 TM microwave resonances and the spread of the radius values inferred from each mode is a measure of how well the resonator has been modeled. Finally, the microwave data can be used to check the inferred density of gas within the resonator. Based on measurements of the dielectric permittivity of the argon gas, pressure discrepancies greater than ±6 Pa can be detected at all pressures up to 700 kPa. Taken together, these four checks improve confidence in the final estimate for kB and restrict the types of systematic error which may affect the result.