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Additional info for Volume Properties: Liquids, Solutions and Vapours

Example text

Of the infinite series in amount-ofsubstance density. For instance, B ; RT (1:203) C À B2 ; etc: ðRT Þ2 (1:204) B0 ¼ C0 ¼ These two virial equations are known to converge at different rates, hence for a given degree of truncation they provide different extents of approximation to the true volumetric behaviour. 11)], the theoretical importance of the virial expansion lies in the fact that its coefficients are explicitly related to the intermolecular potential-energy functions. Specifically, the second virial coefficient B depends on pairwise interaction between molecules, the third virial coefficient C depends on the interaction in clusters of three molecules, and so forth.

The selection of any primary thermodynamic function/ fundamental property relation depends on which set of independent variables best simplifies the problem to be solved. In physical chemistry by far 14 Chapter 1 the most useful set of independent variables is {T,P,{ni}}, because, in principle, temperature, pressure and composition are easily measured and controlled. Thus, for chemists, the Gibbs energy nG ¼ f(T,P,{ni}) is of central importance. 50)], of which ! @ðnGÞ mi  (1:55) @ni T;P;nj a i is the preferred one.

E. e. nS ¼ f (nU,nV,{ni}). These sets of variables are called the corresponding canonical (or natural) variables. All thermodynamic equilibrium properties of any system can be derived from these functions, and it is for this reason that they are called primary functions or cardinal functions or fundamental functions. In both the energy and entropy representations the extensive quantities are the mathematically independent variables, while the intensive parameters are derived, a situation which does not conform to experimental practice.

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