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

We report on acoustic and microwave measurements made with a purified helium sample maintained close to a single thermodynamic state ( T exp ∼ 273.16 K, p exp ∼ 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 k B which is consistent with the recommended 2006 CODATA value: ( k B − k 2006 )/ k 2006 = (−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 k B .