A new numerical method for conversion of sonic second virial coefficients to density second virial coefficients

Abstract

A new numerical method has been developed for calculation of density second virial coefficients, B(T), from sonic velocity measurements in gases at low pressures. Unlike existing methods, this procedure requires no model assumption as to the form of the temperature variation of B(T). Rather it gathers additional information by differencing the measured acoustic second virial coefficient in accordance with a new mathematical approximation. While two higher-ordered terms in the complete identity must be ignored to initiate the numerical calculations, the magnitude of these terms can later be estimated from the initial determination of B(T). By such an iterative procedure, the method can be made exact or, from a second viewpoint, the initial estimate allows calculation of the errors in the method itself. The new method is simple and easy to use as it employs only standard numerical techniques. It requires a digital computer program; although limited calculations can be made on a modern hand-held calculator. The objectives of this research are (1) to prove that our method is more accurate than existing methods for extracting second density virial coefficients from sonic velocity data, (2) to illustrate that the new numerical method is much simpler in convening sonic velocity data to second density virial coefficients and finally (3) to show that with the new method, no model assumptions for the temperature profile need to be made to get accurate results.