A simple realistic and precise empirical intermolecular potential is proposed for helium. It possesses nearly the correct Hartree–Fock repulsion as well as the correct long range behavior. It was fitted to recent accurate intermediate temperature second virial coefficients and thermal conductivity data as well as high temperature viscosity values. It is able to predict second virial coefficients over an extended temperature range from 1.5 to 1475 K. Above 100 K it reproduces substantially all of the transport properties to within experimental error in a manner superior to all other potentials in existence. Below 100 K where the transport data are less reliable, it produces a good representation of the isotopic differences in the viscosity. It also predicts differential cross sections reasonably well. In spite of a few remaining discrepancies, when all the different macroscopic properties are considered, the potential produces the best representation of the helium interaction available at this time.
Expressions for the virial coefficients B(T) and C(T) of 4He gas between 2.6 K and 300 K have been derived from a surface fit to low-temperature gas-thermometry data constrained at higher temperatures. The resulting expressions are shown to be in agreement with various experimental data over the whole temperature range within the accuracy of the data, and also with present theoretical calculations of B(T).
In considering the second virial coefficient corrections for low temperature helium gas thermometry, the ITS-90 has incorporated data fits for the 4He and 3He second virial coefficients. An alternative is to use second virial coefficients calculated from recent interatomic potential functions for helium. We compare several functions using different computer codes to assess the accuracy of the calculations. The most recent function is the HFD-B2 of Aziz and Slaman. In the literature it is found that the potentials developed by different authors using their respective codes indicate a spread of only 0,4 cm3/mol at the lowest experimental temperature (2,6 K) for 4He. When calculations based on these same potentials are performed with the same code, the spread is nearly twice as large. However, calculations based on the two codes which have undergone recent improvements produce a spread of less than 0,01 cm3/mol when based on the same potential. For 3He, there is a relative difference between potential functions of 0,4 cm3/mol down to the lowest temperature of 1,5 K. There is a larger systematic difference between the calculations and the data fit which indicates that there is a contribution from the third virial in the latest 3He second virial coefficient data.
Results of measurements of the 3He virial coefficient 3B (T) between 1.5 K and 20.3 K at the Kamerlingh Onnes Laboratory (KOL) and of a theoretical calculation of 3B (T) are reported. The uncertainty in the experimental data ranges from ± 1.0 cm3/mol at 1.5 K to ± 0.2 cm3/mol at 20.3 K. Experiment and calculation are shown to be in agreement to within 1 cm3/mol at 1.5 K and 0.3 cm3/mol at 20.3 K. A comparison with the few existing data is made.
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