Thermodynamic Temperatures of the Triple Points of Mercury and Gallium and in the Interval 217 K to 303 K

We measured the acoustic resonance frequencies of an argon-filled spherical cavity and the microwave resonance frequencies of the same cavity when evacuated. The microwave data were used to deduce the thermal expansion of the cavity and the acoustic data were fitted to a temperature-pressure surface to deduce zero-pressure speed-of-sound ratios. The ratios determine (T–T₉₀), the difference between the Kelvin thermodynamic temperature T and the temperature on the International Temperature Scale of 1990 (ITS-90). The acoustic data fall on six isotherms: 217.0950 K, 234.3156 K, 253.1500 K, 273.1600 K, 293.1300 K, and 302.9166 K and the standard uncertainties of (T−T₉₀) average 0.6 mK, depending mostly upon the model fitted to the acoustic data. Without reference to ITS-90, the data redetermine the triple point of gallium T_g and the mercury point T_m with the results: T_g/T_w = (1.108 951 6 ± 0.000 002 6) and T_m/T_w= (0.857 785 5 ± 0.000 002 0), where T_w = 273.16 K exactly. (All uncertainties are expressed as standard uncertainties.) The resonator was the same one that had been used to redetermine both the universal gas constant R, and T_g. However, the present value of T_g is (4.3 ± 0.8) mK larger than that reported earlier. We suggest that the earlier redetermination of T_g was erroneous because a virtual leak within the resonator contaminated the argon used at T_g in that work. This suggestion is supported by new acoustic data taken when the resonator was filled with xenon. Fortunately, the virtual leak did not affect the redetermination of R. The present work results in many suggestions for improving primary acoustic thermometry to achieve sub-millikelvin uncertainties over a wide temperature range.