Burnett second virial coefficients

Expansion methods are often used for measuring gas densities. In these methods, a sample is expanded from a small volume to a larger volume (where the ratio of volumes is accurately known), holding the temperature constant and measuring the pressure ratio. Typically, multiple expansions are used (a successive expansion technique known as the Burnett method is popular), with the final state being at a pressure sufficiently low that the density is accurately known by other means (such as correction of the ideal-gas law by the second virial coefficient). The Burnett expansion method may achieve uncertainties in density as low as 0.01%. 

Values of the second virial coefficient of ethylene for temperatures between 0° and 175°C have been determined to an estimated accuracy of 0.2 cm3/mol or less from low-pressure Burnett PVT measurements. Our values, from —167 to —52 cm3/mol, agree within an average of 0.2 cm3/mol with those recently obtained by Douslin and Harrison from a distinctly different experiment. This close agreement reflects the current state of the art for the determination of second virial coefficient values. The data and error analysis of the Burnett method are discussed. 

The effects of systematic errors are best studied by analyses of accurate Burnett data with superimposed simulated errors. For a relative pressure offset of 0.003%, which is comparable with the accuracy of piston gauges, the ethylene second virial coefficient of —167 cm3/mol changes only by 0.02 cm3/mol. Thus, this type of error is largely cancelled in the Burnett method. An offset in N of 11 ppm, which is comparable with the N variation we expect, changes the same second virial coefficient by 0.1 cm3/mol. Errors resulting from truncation of the series... 

In Figure 5, we present a comparison of our preferred values for the ethylene second virial coefficient with comparable state of the art results obtained by Douslin and Harrison (2). The experimental method and data analysis used by Douslin are independent from ours. In Douslin s experiment, all of the variables required for the calculation of the compressibility factor are measured, whereas in the Burnett method only two variables are measured. Aslo, in this experiment the same sample of gas is retained for the entire experiment in the Burnett isothermal method, the sample is changed for each sequence of measurements. Furthermore,... 

This gave a very reasonable fit to the second virial coefficient data then available, but more recent, accurate values from Burnett and speed of sound measmements indicate that the coefficients need to be re-determined. Even so, this method is very valuable for estimating second virial coefficients where data are lacking. 

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