Highly-accurate density-virial-coefficient values for helium, neon, and argon at 0.01 °c determined by dielectric-constant gas thermometry

Abstract

The dielectric-constant gas thermometer of Physikalisch-Technische Bundesanstalt (PTB) developed for measuring the Boltzmann constant with a relative uncertainty of 1.9 parts per million was used for determining the virial coefficients of the three noble gases, helium, neon, and argon, at the triple point of water (0.01 °C). For this purpose, isotherms were measured up to a maximum pressure of 7 MPa. The evaluation of the highly accurate data by fitting is required to derive an extended working equation for the dependence of the gas pressure on the dielectric constant. The following values have been obtained for the second B and third C virial coefficients, with the standard uncertainties given in parentheses as a multiple of the last digit, considering literature data for the dielectric virial coefficients: helium: BDCGTHe0.01 °C=11.925715 cm3/mol, CDCGTHe0.01 °C=113.4958 cm6/mol2; neon: BDCGTNe0.01 °C=10.994528 cm3/mol, CDCGTNe0.01 °C=215.815 cm6/mol2; argon: BDCGTAr0.01 °C=-21.233144 cm3/mol, CDCGTAr0.01 °C=1143.339 cm6/mol2. These values are compared with the results of the latest ab initio calculations of the second and third virial coefficients.