Further Estimates of $(T-T_{90})$ Close to the Triple Point of Water

Abstract

Recent advances in primary acoustic gas thermometry (AGT) have revealed significant differences between temperature measurements using the International Temperature Scale of 1990, $T_{90}$, and thermodynamic temperature, T. In 2015, we published estimates of the differences $(T-T_{90})$ from 118 K to 303 K, which showed interesting behavior in the region around the triple point of water, $T_\mathrm{TPW}=273.16$ K. In that work, the $T_{90}$ measurements below $T_\mathrm{TPW}$ used a different ensemble of capsule standard platinum resistance thermometers (SPRTs) than the $T_{90}$ measurements above $T_\mathrm{TPW}$. In this work, we extend our earlier measurements using the same ensemble of SPRTs above and below $T_\mathrm{TPW}$, enabling a deeper analysis of the slope $\mathrm{d}(T-T_{90})/\mathrm{d}T$ around $T_\mathrm{TPW}$. In this article, we present the results of seven AGT isotherms in the temperature range 258 K to 323 K. The derived values of $(T-T_{90})$ have exceptionally low uncertainties and are in good agreement with our previous data and other AGT results. We present the values $(T-T_{90})$ alongside our previous estimates, with the resistance ratios W(T) from two SPRTs which have been used across the full range 118 K to 323 K. Additionally, our measurements show discontinuities in $\mathrm{d}(T-T_{90})/\mathrm{d}T$ at $T_\mathrm{TPW}$ which are consistent with the slope discontinuity in the SPRT deviation functions. Since this discontinuity is by definition non-unique, and can take a range of values including zero, we suggest that mathematical representations of $(T-T_{90})$, such as those in the mise en pratique for the kelvin (Fellmuth et al. in Philos Trans R Soc A 374:20150037, 2016. doi:10.1098/rsta.2015.0037), should have continuity of $\mathrm{d}(T-T_{90})/\mathrm{d}T$ at $T_\mathrm{TPW}$.