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) similar to 273.16K, p(exp) similar to 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) x 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).