Progress toward redetermining the Boltzmann constant with a fixed-path-length cylindrical resonator

Published

May 20, 2011

Author(s)

Jin-Tao Zhang, H. Lin, X.J. Feng, J.P. Sun, Keith A. Gillis, Michael R. Moldover, Y.Y. Duan

Abstract

We used a single, fixed-path-length cylindrical-cavity resonator to measure c₀ = (307.8252 ± 0.0012) m&#8226s⁻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&#8226mol⁻¹, determined from an impurity and isotopic analysis of the argon used in this measurement and our measured c₀, we obtain the value k_B = 1.380 650 6×10⁻²³ J&#8226K⁻¹ for the Boltzmann constant. This value of k_B has the relative uncertainty u_r(k_B) = 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 k_B 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.

Citation

International Journal of Thermophysics

Volume

32

Issue

7-8

Pub Type

Journals

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Citation

Zhang, J. , Lin, H. , Feng, X. , Sun, J. , Gillis, K. , Moldover, M. and Duan, Y. (2011), Progress toward redetermining the Boltzmann constant with a fixed-path-length cylindrical resonator, International Journal of Thermophysics, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=907610 (Accessed December 26, 2024)