An apparatus based on a spherical resonator for measuring the speed of sound in gases and for determining the Boltzmann constant

The Spanish Metrology Institute and the Research Group TERMOCAL of the University of Valladolid are involved in a European project for which the main target is the determination of the Boltzmann constant k B. We have set-up an acoustic gas thermometer, which consists of a stainless steel spherical resonator, 4 cm nominal radio, in an adiabatic enclosure. The temperature stability and uniformity obtained are about 0.1 mK. This system allows performance of measurements of acoustic and microwave resonance frequencies. Microwave measurements characterize the resonator volume. Both hemispheres, joined by a flange in the equatorial band, can be misaligned up to 50 µm, splitting degenerate microwave modes in suitable triplets. Acoustic radial resonances in helium and argon can be used to compute the zero-density limit at the speed of sound at T TPW. Kinetic theory of gases and hydrodynamics reveals k B from this speed of sound value. In this article, a description of the apparatus and the first results using argon will be presented.