Dielectric-Constant Gas Thermometry and the Relation to the Virial Coefficients

At PTB new dielectric-constant gas thermometry (DCGT) measurements were performed at the temperature of the triple point of water. As discussed recently in an accompanying paper, the main goal was the determination of the Boltzmann constant \(k\) as a contribution to the international efforts directed to a new definition of the base unit kelvin via fixing the value of  \(k\) . Besides the linear term in the series expansion used for fitting the results of measurements of DCGT isotherms that reveals \(k\) , in this paper the higher-order terms are analyzed. For retrieving highly accurate virial coefficients of helium from the data obtained at gas pressures up to 7 MPa, an extended DCGT working equation is developed. Applying this equation, information is deduced on the viral coefficients up to the fourth density virial coefficient. Finally, comparisons with the latest ab initio calculations for the second and third density virial coefficients as well as the second dielectric virial coefficient are performed.