A determination of the molar gas constant R by acoustic thermometry in helium

We have determined the acoustic and microwave frequencies of a misaligned spherical resonator maintained near the temperature of the triple point of water and filled with helium with carefully characterized molar mass M = (4.002 6032 ± 0.000 0015) g mol−1, with a relative standard uncertainty ur(M) = 0.37 × 10 –6. From these data and traceable thermometry we estimate the speed of sound in our sample of helium at TTPW = 273.16 K and zero pressure to be u0 = (945710.45 ± 0.85) 2 m2 s−2 and correspondingly deduce the value R = (8.314 4743 ± 0.000 0088) J mol−1 K−1 for the molar gas constant. We estimate the value k = R/NA = (1.380 650 8± 0.000 0015) × 10 –23 J K−1 for the Boltzmann constant using the currently accepted value of the Avogadro constant NA. These estimates of R and k, with a relative standard uncertainty of 1.06 × 10−6, are 1.47 parts in 106 above the values recommended by CODATA in 2010.