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The consistency of several approximate radial distribution functions of fluids is examined in the sense that the pressure and the internal energy derived from them satisfy the thermodynamical relation \ (T (pT) = V (ET^{2}) \), where T, p, V and E have the usual meanings. It is found that the original form of Green's linear theory is the only one which satisfies the above relation. It is also shown that Green's theory can be improved further without breaking the above relation.
Kazuo Hiroike (Mon,) studied this question.
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