The progress towards re-determining the Boltzmann constant k B using two fixed-path, gas-filled, cylindrical, acoustic cavity resonators is described. The difference in the lengths of the cavities is measured using optical interferometry. Thus, a literature value for the density of mercury is not used, in contrast with the presently accepted determination of k B . The longitudinal acoustic resonance modes of a cylindrical cavity have lower quality factors Q than the radial modes of gas-filled, spherical cavities, of equal volume. The lower Qs result in lower signal-to-noise ratios and wider, asymmetric resonances. To improve signal-to-noise ratios, conventional capacitance microphones were replaced with 6.3 mm diameter piezoelectric transducers (PZTs) installed on the outer surfaces of each resonator and coupled to the cavity by diaphragms. This arrangement preserved the shape of the cylindrical cavity, prevented contamination of the gas inside the cavity, and enabled us to measure the longitudinal resonance frequencies with a relative standard uncertainty of 0.2 × 10 −6 . The lengths of the cavities and the modes studied will be chosen to reduce the acoustic perturbations due to non-zero boundary admittances at the endplates, e.g., from endplate bending and ducts and/or transducers installed in the endplates. Alternatively, the acoustic perturbations generated by the viscous and thermal boundary layers at the gas-solid boundary can be reduced. Using the techniques outlined here, k B can be re-determined with an estimated relative standard uncertainty of 1.5 × 10 −6 .

The length is one of the key parameters for a cylindrical acoustic resonator used for measurement of the Boltzmann constant. A research project has been conducted in the National Institute of Metrology (NIM), China, for the re-determination of the Boltzmann constant with a fixed-path cylindrical acoustic resonator. This paper describes the procedure for the length determination. The excess fraction method was applied to accurately obtain the length of the resonator. This method is performed in a two-step procedure. First, the length is coarsely determined as L 1 with an uncertainty of 1.5 µm in the length division of NIM. Second, the result of the coarse measurement is further interpolated by the dual wavelength laser interferometer with a resolution of 1 nm, which is composed of a 633 nm He-Ne laser and a 657 nm semiconductor laser. A Michelson wavemeter has been constructed for calibration of the wavelength of the semiconductor laser. The length variation of the resonator has to be measured from room temperature to the triple point of water (TPW). As a result, the laser interferometer can be also used as a precise dilatometer. The result and the measurement uncertainty of the length measurement are given in this paper.