There is currently great interest in the international metrological community for new accurate determinations of the Boltzmann constant k _B, with the prospect of a new definition of the unit of thermodynamic temperature, the kelvin. In fact, k _B relates the unit of energy (the joule) to the unit of the thermodynamic temperature (the kelvin). One of the most accurate ways to access the value of the Boltzmann constant is from measurements of the velocity of the sound in a noble gas. In the method described here, the experimental determination has been performed in a closed quasi-spherical cavity. To improve the accuracy, all the parameters in the experiment (purity of the gas, static pressure, temperature, exact shape of the cavity monitored by EM microwaves, etc.) have to be carefully controlled. Correction terms have been computed using carefully validated theoretical models, and applied to the acoustic and microwave signals. We report on two sets of isothermal acoustic measurements yielding the value k _B = 1.380 647 74(171) × 10⁻²³ J · K⁻¹ with a relative standard uncertainty of 1.24 parts in 10⁶. This value lies 1.9 parts in 10⁶ below the 2006 CODATA value (Mohr et al., Rev. Mod. Phys. 80, 633 (2008)), but, according to the uncertainties, remains consistent with it.

We evaluate a quasi-spherical, copper, microwave cavity resonator for accurately measuring the relative dielectric permittivity ${\epsilon }_{\mathrm{r}}\mathrm{(p,T)}$ of helium and argon. In a simple, crude approximation the cavity’s shape is a triaxial ellipsoid with axes of length $\text{a,1.001a}$ and $\text{1.005a}$ , with $\text{a=5\hspace{0.5em}}\mathrm{cm}$ . The unequal axes of the quasi-sphere separated each of the triply degenerate microwave resonance frequencies of a sphere ${\mathrm{(f}}_{11}^{\mathrm{TM}}{\mathrm{,f}}_{12}^{\mathrm{TM}}{\mathrm{,\dots ,f}}_{11}^{\mathrm{TE}}{\mathrm{,f}}_{12}^{\mathrm{TE}}\mathrm{,\dots )}$ into three nonoverlapping, easily measured, frequencies. The frequency splittings are consistent with the cavity’s shape, as determined from dimensional measurements. We deduced ${\epsilon }_{\mathrm{r}}\mathrm{(p,T)}$ of helium and of argon at $\text{289\hspace{0.5em}}\mathrm{K}$ and up to $\text{7\hspace{0.5em}}\mathrm{MPa}$ from the resonance frequencies $f_{\ln }^{\sigma }$ , the resonance half-widths $g_{\ln }^{\sigma }$ , and the compressibility of copper. Simultaneous measurements of ${\epsilon }_{\mathrm{r}}\mathrm{(p,T)}$ with the quasi-spherical resonator and a cross capacitor agreed within ${\text{1×10}}^{\text{−6}}$ for helium, and for argon they differed by an average of only ${\text{1.4×10}}^{\text{−6}}$ . This small difference is within the stated uncertainty of the capacitance measurements. For helium, the resonator results for ${\epsilon }_{\mathrm{r}}\mathrm{(p,T)}$ were reproducible over intervals of days with a standard uncertainty of ${\text{0.2×10}}^{\text{−6}}$ , consistent with a temperature irreproducibility of $\text{5\hspace{0.5em}}\mathrm{mK}$ . We demonstrate that several properties of quasi-spherical cavity resonators make them well suited to ${\epsilon }_{\mathrm{r}}\mathrm{(p,T)}$ determinations. Ultimately, a quasi-spherical resonator may improve dielectric constant gas thermometry and realize a proposed pressure standard based on ${\epsilon }_{\mathrm{r}}\mathrm{(p,T)}$ .

The principles and techniques of primary refractive-index gas thermometry (RIGT) are reviewed. Absolute primary RIGT using microwave measurements of helium-filled quasispherical resonators has been implemented at the temperatures of the triple points of neon, oxygen, argon and water, with relative standard uncertainties ranging from 9.1 × 10⁻⁶ to 3.5 × 10⁻⁵. Researchers are now also using argon-filled cylindrical microwave resonators for RIGT near ambient temperature, with relative standard uncertainties between 3.8 × 10⁻⁵ and 4.6 × 10⁻⁵, and conducting relative RIGT measurements on isobars at low temperatures. RIGT at optical frequencies is progressing, and has been used to perform a Boltzmann constant measurement at room temperature with a relative standard uncertainty of 1.2 × 10⁻⁵. Uncertainty budgets from implementations of absolute primary microwave RIGT, relative primary microwave RIGT and absolute primary optical RIGT are provided.