To adjust some data to a curve you need the data and the curve family.
In your case the data isn't experimental, it is intra or extrapolated data based also in a model (which gives the curve family) and some few experimental data points. But the origin of the calculus could be very complicated. Programs like FactSage starts with the EOS of pure substances and interaction matrix coefficients for mixtures; a model for mixtures, actually a function of the states, and a model for the equilibrium, reactions, etc.
But this isn't important, it's only to discard the curves family search based in how the data is obtained. So, your data are only that: points in some space, and you want a curve (or surface or anything) to adjust.
There are two kinds of curve fitting: situations where you want to assign a physical meaning to the obtained parameters, and sitations where you whant only reproduce the physical propertie under study to eval anywhere where you define as the domain, not only in the given points.
When you search a curve with few parameters you probably are more interesting in the physical meaning of those parameters. But this is not your case, so the number of parameters is not important, you can handle a lot of adjust parameters.
This is the case for the EOS in programs like REFPROP from NIST: they write polynomials with several parameters (usually in the range of 20-40 terms) to adjust the a function with variables T and P representing the EOS in some region for the substance. Sometimes this fuction is the volume, but not always.
In this case the "curve family" is a polynomial. But there are "theoretical" reasons to take polynomials: The algorithm to eval the function and they derivatives are very easy (Horner's method) and the error is easy to handle and take under control. The number of terms is given by the data pressicion and the -usually- fortran routines.
Programs like Hysys, which modelates also pure and mixed substance, have usually different EOS models for the same substance. One very general is the Peng-Robinson equations, with few parameters and a low level degree polynomial: only 3 roots, and only one with sense.
Even the paramaters for long equations can have some kind of interpretation as the virials of some model, they are enough complicated to not be used as a model representation, only in very high level texts, and are taken as pure mathematics expressions in the practice.
So, what you need to specify your "family curves" is first chose a short or a long model. You must to jusfify also your selection: for few parameters models you must to provide some physical interpretation of the parameters, and for several parameters model you must to study the numerical pressicion of your software and your hardware. This not meaning a fully study, only gives to the reader enough backgraund if it is needed.
Also there are avaible predefined models for properties like cp(T), thermal cond (T) and this kind of calculations that have "predefined" equations, numbered: eq 98, eq 102 and eq 104 are the more usual! This shorts models search only a way to interpolate values, but not assign physical sense to the parameters: isn't the purpose.
In resume: you must to search a family of curves and gives a few reasons to choose this. In the practice you can search in the literature which model choose another people and see why this is done.
Your work is complete when you provide a few justification of the general model (the curve family), the particular model (the parameters for the selected curve family) and the maximun relative or absolute error that the original data set is evaluated with your model. This last thing is very important, and can be evaluated as the maximun of the errors for each data point.
Regards. Alvaro.
