The compressibility factors and second virial coefficients for helium-nitrogen mixtures at low temperature and high pressure
Canfield, Frank B., Jr
Doctor of Philosophy
The Burnett method was used to determine the volumetric behavior of helium, nitrogen, and six evenly spaced helium-nitrogen mixtures at low temperature and high pressure. Compressibility isotherms were determined for both of the pure components and all of the mixtures at 0, -50, -90, -115, -130, and -140°C. Two series of expansions were made in order to accurately define each isotherm. The maximum pressure for the first series of expansions was maintained at 500 atm for each isotherm, and sufficient expansions were carried out to reduce the final pressure to 2--3 atm. The results were expressed in terms of the compressibility factors at the experimental pressures, the Leiden reciprocal volume series coefficients, and the compressibility factors at forty-three even values of pressure ranging from 1 to 500 atm. A total of approximately twelve hundred experimental compressibility factors were determined. From an error analysis developed specifically for the Burnett method, the maximum error in the experimental compressibility factors was estimated to be about one-tenth percent. The results of the experimental investigation were used to calculate the second virial coefficients, the interaction second virial coefficients, the third virial coefficients, the interaction third virial coefficients, the Lennard-Jones (12:6) potential parameters for nitrogen, the quantum mechanical Lennard-Jones (12:6) potential parameters for helium-nitrogen, and the fugacity coefficients for both of the pure components and all of the mixtures. The values of the second virial coefficients for the pure components were found to be in excellent agreement with similar values obtained from other methods by different investigators. Thus the Burnett method was established as an accurate way to determine second virial coefficients at low temperature. The existing data for gaseous mixtures were combined with the present results to study the mixing rules which have been proposed to predict the interaction parameters of the unlike species from known data for the pure components. The geometric mean and average rules were found to predict the correct values of the interaction second virial coefficients when the difference in the molecular size of the interacting species was small; however, for systems such as He-N2 and He-A, they predicted values which were fifteen to twenty percent too small. The mixing rule proposed by Srivastava and Madan was investigated where sufficient data were available over an extended range of temperature. In such cases one experimental value of the interaction second virial coefficient was used to supplement their rule. The predicted values of the interaction second virial coefficients were in good agreement with the experimental values for the six systems studied. An empirical rule was also developed for use with the Srivastava and Madan rule. Second interaction virial coefficients were predicted with these rules and compared with similar predictions based on the geometric mean and average rules for twelve systems. The average deviation between the experimental and predicted values was 5.1 cm3/mole for the empirical correlation and 8.8 cm3/mole for the geometric mean and average rules.