Microwave measurements of the length and thermal expansion of a cylindrical resonator for primary acoustic gas thermometry

Abstract

In the application of acoustic gas thermometry to determine the Boltzmann constant and thermodynamic temperatures using resonant cavities, the internal dimensions or the thermal expansion of the cavity have to be known accurately. For this purpose, measurement of the microwave resonances has proved to be an accurate and convenient experimental technique for dimensional measurement of acoustic resonators. We report measurements of the length and longitudinal thermal expansion of a prototype cylindrical cavity made of oxygen-free copper. We studied four non-degenerate transverse magnetic modes for three isotherms at 243, 258 and 273 K. Two procedures were investigated for calculating the length and longitudinal thermal expansion of the cavity at the temperatures examined. The results from both methods agree well. The relative standard uncertainties for the measurements of length and longitudinal thermal expansion are less than 0.47 × 10−6 and 0.04 × 10−6, respectively, from 243 to 273 K. The low uncertainty achieved here provides confidence to pursue a determination of the Boltzmann constant and thermodynamic temperature with a cylindrical cavity and microwave techniques.