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

• Published in: Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences physical, and engineering sciences, 2011-10, Vol.369 (1953), p.4014-4027
• Main Authors: Pitre, Laurent, Sparasci, Fernando, Truong, Daniel, Guillou, Arnaud, Risegari, Lara, Himbert, Marc E.
• Format: Article
• Language: English
• Subjects: Acoustic measurement; Acoustic Resonance; Argon; Boltzmann Constant; Helium; International System Of Units; Kelvin Redefinition; Metrology; Microwave Resonance; Microwaves; Quasi-Sphere; Resonators; Supersonic transport; Temperature measurement
• ISSN: 1364-503X; 1471-2962
• DOI: 10.1098/rsta.2011.0197

The paper reports a new experiment to determine the value of the Boltzmann constant, , with a relative standard uncertainty of 1.2 parts in 106. kB 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 kB is consistent with the 2006 Committee on Data for Science and Technology (CODATA) value: (knewB/kB_CODATA−1)=−1.96×10−6, where the relative uncertainties are and ur(kB_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.