Highly-accurate second-virial-coefficient values for helium from 3.7 K to 273 K determined by dielectric-constant gas thermometry

Since the redefinition of the base unit kelvin via fixing the Boltzmann constant in 2019, it has been possible to realise the unit applying different gas-thermometry methods in accordance with the 'Mise en pratique for the definition of the kelvin in the SI'. For this application, the use of data for the gas properties resulting from ab initio calculations is of special interest because it makes primary thermometry much easier. But since a rigorous estimation of the uncertainty of theoretical calculations is at least very complex, if not impossible, a check of the results by a comparison with highly-accurate experimental values is mandatory. Such a check is performed for the second virial coefficient of helium, which is a widely used measuring gas, in the temperature range from 3.7 K to 273 K. For obtaining highly-accurate second-virial-coefficient values (relative uncertainty at a few tenth of a percent level or even better), isotherms were measured with the PTB dielectric-constant gas thermometer. The highly-accurate isotherm data were evaluated by fitting, applying an extended working equation for the dependence of the gas pressure on the dielectric constant. The comparison with the results of the latest ab initio calculations shows coincidence within the combined uncertainty estimates.

Automated summary

Since the redefinition of the kelvin in 2019 via fixing the Boltzmann constant, different gas-thermometry methods have been used to realise the unit. The use of data from ab initio calculations makes primary thermometry easier, but rigorous estimation of the uncertainty of theoretical calculations is complex. A comparison with highly-accurate experimental values is necessary to check the results.