Discrimination between equations of state

Abstract

Eight isothermal equations of state are analyzed to yield quantitative measures of the degrees to which equation pairs can be discriminated for real data, data of limited span and precision. Calculated curves allow one to assess the span and precision necessary in P-V data to allow unambiguous discrimination of various pairs. Some discussion is presented of bias and systematic error which may arise in least squares fitting. Using exact synthetic data, we also illustrate for seven equation pairs the very large relative systematic errors in parameter and standard deviation estimates which arise from such fitting of data of limited span with an incorrect but 'close' equation model. General conclusions following from these results are discussed. Although the present work is principally concerned with discrimination between equations of state, its results are pertinent to the more general problem of choosing a 'best' analytical model (linear or nonlinear) to represent experimental results.