Progress toward redetermining the Boltzmann constant with a fixed-path-length cylindrical resonator
Jintao Zhang, H. Lin, X.J. Feng, J.P. Sun, Keith A. Gillis, Michael R. Moldover, Y.Y. Duan
We used a single, fixed-path-length cylindrical-cavity resonator to measure c0 = (307.8252 ± 0.0012) m•s−1, the zero-density limit of the speed of sound in pure argon at the temperature of the triple point of water. Three even and three odd longitudinal modes were used in this measurement. Based on the ratio M/γ0 = (23.968644 ± 0.000033) g•mol−1, determined from an impurity and isotopic analysis of the argon used in this measurement and our measured c0, we obtain the value kB = 1.380 650 6×10−23 J•K−1 for the Boltzmann constant. This value of kB has the relative uncertainty ur(kB) = 7.6×10−6 and is fractionally, (0.12 ± 7.8)×10−6 larger than the value recommended by CODATA in 2006. (The uncertainty is one standard uncertainty.) Several, comparatively large imperfections of our prototype cavity affect the even longitudinal modes more than the odd modes. Our models for these imperfections are approximate. To assess possible effects of the approximations, we analyzed the data for the 3 odd modes only. The result for kB was fractionally smaller than the 2006 CODATA value by (5.0 ± 5.5)×10−6. This suggests that an improved cavity will significantly reduce the uncertainty of c0.