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

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: B 0.01 C=11.925715 cm/mol, C 0.01 C=113.4958 cm/mol; neon: B 0.01 C=10.994528 cm/mol, C 0.01 C=215.815 cm/mol; argon: B 0.01 C=-21.233144 cm/mol, C 0.01 C=1143.339 cm/mol. These values are compared with the results of the latest ab initio calculations of the second and third virial coefficients.