Progress Toward Redetermining the Boltzmann Constant with a Fixed-Path-Length Cylindrical Resonator

A single, fixed-path-length cylindrical-cavity resonator was used to measure c (0) = (307.825 2 +/- 0.001 2) m center dot 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/gamma (0) = (23.968 644 +/- 0.000 033) g center dot mol(-1), determined from an impurity and isotopic analysis of the argon used in this measurement and the measured c (0), the value k (B) = 1.380 650 6 x 10(-23)J center dot K-1 was obtained for the Boltzmann constant. This value of k (B) has a relative uncertainty u (r)(k (B)) = 7.9 x 10(-6) and is fractionally, (0.12 +/- 8.1) x 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. The models for these imperfections are approximate, but they suggest that an improved cavity will significantly reduce the uncertainty of c (0).