A determination of the Boltzmann constant from speed of sound measurements in helium at a single thermodynamic state

Abstract

We report on acoustic and microwave measurements made with a purified helium sample maintained close to a single thermodynamic state (Texp ∼ 273.16 K, pexp ∼ 410 kPa) within a 2.1 L volume stainless steel spherical cavity. From these measurements and ab initio calculations of the non-ideality and the refractive index of helium, we determine a value for the Boltzmann constant kB which is consistent with the recommended 2006 CODATA value: (kB − k2006)/k2006 = (−7.5 ± 7.5) × 10−6. We discuss the current limits of the experiment and the prospects of a further reduction in the uncertainty associated with the determination of kB.