Progress Towards an Acoustic/Microwave Determination of the Boltzmann Constant at LNE-INM/CNAM

Abstract

The Boltzmann constant k will be re-determined by using the simple, exact connection between the speed of sound in noble gases (extrapolated to zero pressure) and the thermodynamic temperature T, the molar mass of the gas M, and the universal gas constant R. The speed of sound will be determined in a spherical cavity of known volume V by measuring the acoustic resonance frequencies. This acoustic method led to the CODATA-recommended value of k; however, the CODATA value of k came from measurements using an almost perfectly spherical, stainless-steel-walled cavity filled with stagnant argon. The steel cavity’s volume was determined by weighing the mercury of well-known density required to fill it. In contrast, a copper-walled, quasi-spherical cavity (intentionally slightly deformed from a sphere), filled with helium gas that is continuously refreshed by a small helium flow that will mitigate the effects of outgassing, will be used. The volume of the copper cavity will be determined by measuring the microwave resonance frequencies and/or by three-dimensional coordinate measurements. If the microwave method is satisfactory, the measurement of k will be based on the ratio of the speed of sound in helium—obtained by acoustic resonance measurements—to the speed of light, obtained by microwave resonance measurements. This method exploits the theorem that the frequency ratios are independent of the details of the shape of the quasi-spherical cavity. Here, progress at LNE-INM/CNAM towards a better mechanical design and better understanding of the excess of the half-widths of the acoustic and microwave measurements are reported.