A determination of the molar gas constant<i>R</i>by acoustic thermometry in helium

Abstract

We have determined the acoustic and microwave frequencies of a misaligned spherical resonator&#13;\nmaintained near the temperature of the triple point of water and filled with helium with carefully&#13;\ncharacterized molar mass M = (4.002 6032 ± 0.000 0015) g mol-1, with a relative standard uncertainty&#13;\nur(M) = 0.37×10-6. From these data and traceable thermometry we estimate the speed of sound in our&#13;\nsample of helium at TTPW = 273.16 K and zero pressure to be u0&#13;\n2 = (945 710.45 ± 0.85) m2 s-2 and&#13;\ncorrespondingly deduce the value R = (8.314 4743 ± 0.000 0088) J mol-1 K-1 for the molar gas&#13;\nconstant. We estimate the value k = R/NA = (1.380 6508 ± 0.000 0015) × 10-23 J K-1 for the Boltzmann&#13;\nconstant using the currently accepted value of the Avogadro constant NA. These estimates of R and k,&#13;\nwith a relative standard uncertainty of 1.06 × 10-6, are 1.47 parts in 106 above the values recommended&#13;\nby CODATA in 2010.