The Research Of Non-ideal Factors In Boltzmann Constant K_B Measurement

Acoustic resonance method is the most accurate way to measure Boltzmann constant kB and determine thermodynamic temperatures. Measurement of ideal resonance frequencies in the acoustic resonator is the key factor. The resonance frequencies can be shifted, and become the resonance peaks with certain widths due to the acoustic field in the resonator can be disturbed by the non-ideal factors. In order to kB with relative uncertainties of 1×10-6 or less. Therefore, the non-ideal factors must be corrected rigidly. This paper investigated on the perturbations from imperfect cylindrical Geometry for the cylindrical resonator both in theory and experiment. The main contents is detailed below:Calculated the impedance and perturbation for the axial resonance frequencies of cylindrical resonator of diaphragm which is used to stick the piezoceramics transducer when the frequencies covered a range of 400 Hz≤fg≤4000 Hz.. Also, designed the diaphragm- impedance measurement model and experimental system. Measured the impedance and perturbations of diaphragm covered the same frequency range. The results showed that the diaphragm impedance can be measured accurately. The measured result agreed well with the calculated results. The calculated perturbation for the ideal axial resonance frequency is less than 0.15×10-6 base on first-order acoustic perturbation theory when thickness of diaphragm td is 0.33 mm.Measured the perturbations of gas-filled ducts mounted on the top endplate of the cylindrical resonator with change of ducts lengths for (200),300),(400),(500) axial resonance frequencies when p is from 50 kPa to 500 kPa. The results showed that the curves of ducts perturbations was quiet similar between calculated results and measured results, and the absolute deviations was within±25 ppm at each duct length. Also, the calculated results showed that the perturbation was damping out with lengthening the ducts lengths. The perturbation is approximately 1×10-6 when duct length is 2 m.Deduced the formula of duct perturbation for ideal radial resonance modes of cylindrical resonator base on first-order acoustic perturbation theory. Calculated the perturbations of duct for (001) ideal radial resonance mode. The results areΔf/f=-0.04×10-6 andΔg/f=14.15×10-6 respectively. Also, analyzed the influences of duct perturbations for ideal radial resonance modes as a function of length, internal diameter and fixed-position of duct.