Correlations among acoustic measurements of the Boltzmann constant

Abstract

We review correlated uncertainties among the accurate determinations of the Boltzmann constant that used the techniques of primary acoustic gas thermometry (AGT). We find correlated uncertainty contributions from four sources: (1) the uncertain chemical and isotopic compositions of the test gases that lead to an uncertain average molar mass, (2) measurements of the temperature, (3) measurements of the shape and dimensions of the cavity resonators, and (4) fitting acoustic resonance frequencies as a function of the pressure. Molar-mass-dependent uncertainties are correlated among those measurements that used argon with isotopic abundances determined using an isotopic standard prepared at the Korea Research Institute of Standards and Science in 2006. Correlated, cavity-dependent uncertainties result from using the same cavity for more than one measurement. Small, correlated uncertainties propagate into all the AGT determinations of when acoustic resonance frequencies are fit for using uncertain literature data for the Avogadro constant and for the thermal conductivity and the higher acoustic virial coefficients of helium or argon.