Fitting an Equation of State to Experimental Data

Fitting an equation of state to experimental data basically involves several steps. The first step is to assign an experimental uncertainty Oj to each data point j to which the equation of state is fitted. This step requires analysis of the available data. Because information on the uncertainty of published data is not always reliable and often incomplete, assigning a suitable uncertainty also requires information on the uncertainty of the measured independent variables, such as temperature T and pressure p. The correlator has to assess the available data set by detailed comparisons with measurements of properties obtained from methods that suffer from quite different sources of systematic error. Often 

If the uncertainty of a data point is known, a weighted residual can be calculated. If the experimental data point is, for example, a pressure measured as a function of temperature and density [a typical p p, T) data point] the relative residual Cj becomes 

Pj calc, 7 (meas),p(meas),n —/7y meas, 7 (meas),p(meas)  

The parameter Cj for the point j is unity when the deviation between the value, in this case pressure, calculated from the equation of state py calc, T (meas), p (meas), n and the experimental value p jmeas, T (meas), p (meas) is equal to the experimental uncertainty Opj. Typically, for a reference equation of state, the should be less than unity for almost all data (typically 95 % of the points if a is considered to be equal to two times the standard deviation as appropriate for an expanded uncertainty at a confidence interval of 0.95). In eq 12.1 the calculated pressure depends on the parameter vector n, thus on the coefficients of the equation of state that are fitted. In practice, the dimensionless compression factor Z is commonly used instead of the pressure. Thus, the residual becomes 

Zyjcalc, r(meas),p(meas)j g, n - Z, meas, r(meas),p(meas)  

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