Abstract
Perturbation theory of liquids and distribution function theories of liquids (as typified by the Percus–Yevick theory) are examined. It is shown that the energy equation, relating the pair distribution function to the internal energy, may be integrated to yield an expression for the free energy which is similar to that obtained from perturbation theory. The equation of state resulting from this approach, based on the energy equation, is shown to be better than that obtained from the pressure or compressibility equations. Finally, the similarity between perturbation theory and distribution function theories is exploited to provide simple improvements to either approach.
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