Progress Towards an Acoustic Measurement of the Molar Gas Constant at INRIM

Progress in developing an experiment for the determination of the molar gas constant R and the Boltzmann constant k at INRIM is reported. The experiment involves simultaneous measurements of the acoustic and microwave resonance frequencies of a stainless steel spherical resonator for which its hemispheres were deliberately misaligned. For the present work, these frequencies were measured in helium near 273.16 K, in the pressure range from 100 to 800 kPa. From microwave data, the radius of the resonator was determined as a function of pressure with an estimated uncertainty of 6.0 ppm. Using acoustic data and the microwave determination of the resonator radius, the speed of sound in helium was deduced, and these values were compared with those predicted by recent accurate ab initio calculations. Over most of the pressure range, the present values agreed with the ab initio values within the uncertainty of the measurements (standard uncertainty of approximately 7.0 ppm). Many suggestions for reducing the uncertainty are provided.