Primary thermometry at 4 K, 14 K, and 25 K applying dielectric-constant gas thermometry

This short note is a supplement to the paper 'Primary thermometry from 2.5 K to 140 K applying dielectric-constant gas thermometry' (2017 Metrologia 54 141-7). It deals with thermodynamic temperature measurements at the boiling point of the heavy isotope of helium (He-4, 4 K) and the triple points of hydrogen (14 K) and neon (25 K). This is of special interest because recent data published in this temperature range have an unexpectedly large spread. The results presented in this short note show that the International Temperature Scale of 1990, ITS-90, is thermodynamically correct at 4 K and 14 K, but too high by about half a millikelvin at 25 K. Furthermore, care is given to two aspects of dielectric-constant gas thermometry in the low-temperature range. First, dielectric-constant gas thermometry can be applied for practical primary thermometry. The measurement of only one isotherm in one day yields a temperature value with an uncertainty order of a few tenths of a millikelvin. Second, the use of recent ab initio values for the virial coefficients of helium as a measuring gas can reduce the efforts significantly. Even one data pair of pressure and dielectric constant can yield a thermodynamic temperature value of uncertainty less than a factor of two larger compared to the uncertainty of the usually used fit evaluation. For 4 K and 25 K, the achieved final uncertainty for T is still larger than the realization uncertainty of T (90). Thereby in the case of 14 K, both uncertainties are comparable.

Automated summary

This note provides a supplement to a paper on thermometry at low temperatures, focusing on the accuracy of the International Temperature Scale of 1990 at different reference points. It demonstrates that dielectric-constant gas thermometry can be effectively used for practical primary thermometry and employing ab initio values for virial coefficients of helium can significantly reduce measurement efforts. Despite achieved uncertainties, the realization uncertainty at certain temperatures compared to the ITS-90 is discussed.