Determination of the Boltzmann constant using a quasi-spherical acoustic resonator

Abstract

The paper reports a new experiment to determine the value of the Boltzmann constant, k(B)=1.3806477(17)×10(-23) J K(-1), with a relative standard uncertainty of 1.2 parts in 10(6). k(B) was deduced from measurements of the velocity of sound in argon, inside a closed quasi-spherical cavity at a temperature of the triple point of water. The shape of the cavity was achieved using an extremely accurate diamond turning process. The traceability of temperature measurements was ensured at the highest level of accuracy. The volume of the resonator was calculated from measurements of the resonance frequencies of microwave modes. The molar mass of the gas was determined by chemical and isotopic composition measurements with a mass spectrometer. Within combined uncertainties, our new value of k(B) is consistent with the 2006 Committee on Data for Science and Technology (CODATA) value: (k(B)(new)/k(B_CODATA)-1)=-1.96×10(-6), where the relative uncertainties are u(r)(k(B)(new))=1.2×10(-6) and u(r)(k(B_CODATA))=1.7×10(-6). The new relative uncertainty approaches the target value of 1×10(-6) set by the Consultative Committee on Thermometry as a precondition for redefining the unit of the thermodynamic temperature, the kelvin.