# Reproducibility of the Helium-3 Constant-Volume Gas Thermometry and New Data Down to 1.9 K at NMIJ/AIST

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## Abstract

This study confirms reproducibility of the International Temperature Scale of 1990 (ITS-90) realized by interpolation using the constant-volume gas thermometer (CVGT) of National Metrology Institute of Japan (NMIJ)/AIST with \(^{3}\)He as the working gas from 3 K to 24.5561 K by comparing the newly obtained results and those of earlier reports, indicating that the CVGT has retained its capability after renovation undertaken since strong earthquakes struck Japan. The thermodynamic temperature *T* is also obtained using the single-isotherm fit to four working gas densities (\(127\,\hbox {mol}\cdot \hbox {m}^{-3}\), \(145\,\hbox {mol}\cdot \hbox {m}^{-3}\), \(171\,\hbox {mol}\cdot \hbox {m}^{-3}\) and \(278\,\hbox {mol}\cdot \hbox {m}^{-3})\) down to 1.9 K, using the triple point temperature of Ne as a reference temperature. In this study, only the second virial coefficient is taken into account for the single-isotherm fit. Differences between *T* and the ITS-90 temperature, \(T-T_{90}\), reported in earlier works down to 3 K were confirmed in this study. At the temperatures below 3 K down to 2.5 K, \(T-T_{90}\) is much smaller than the standard combined uncertainty of thermodynamic temperature measurement. However, \(T- T_{90}\) seems to increase with decreasing temperature below 2.5 K down to 1.9 K, although still within the standard combined uncertainty of thermodynamic temperature measurement. In this study, *T* is obtained also from the CVGT with a single gas density of \(278\,\hbox {mol}\cdot \hbox {m}^{-3}\) using the triple-point temperature of Ne as a reference temperature by making correction for the deviation from the ideal gas using theoretical values of the second and third virial coefficients down to 2.6 K, which is the lowest temperature of the theoretical values of the third virial coefficient. *T* values obtained using this method agree well with those obtained from the single-isotherm fit. We also found that the second virial coefficient obtained by the single-isotherm fit to experimental results agrees well with that obtained by the single-isotherm fit to the theoretically expected behavior of \(^{3}\)He gas with the theoretical second and third virial coefficients at four gas densities used in the present work.

## Keywords

Constant-volume gas thermometer Helium-3 ITS-90 Low temperature Thermodynamic temperature Virial coefficient## Notes

### Acknowledgements

The authors are grateful to S. Takasu who operated CVGT and discussed its functions. The authors thank Dr. Moldover for his valuable advice related to theoretical results of the virial coefficients of \(^{3}\)He. The authors also thank members of the Thermometry Group and the Frontier Thermometry Group of NMIJ/AIST for valuable discussion.

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