Abstract
Molecular dynamics simulations on the Lennard-Jones system are performed to obtain the pVT and UVT relations. An extended van der Waals equation of state (EOS) is derived by statistical mechanics on the perturbation approximation. A hard sphere system is used as the reference system. The attraction energy term in the canonical ensemble partition function is extended by a cluster expansion. The new EOS includes three parameters, two of which are the interaction parameters in the Lennard-Jones interaction. The last parameter is the effective volume of the hard sphere system. The extended van der Waals EOS reproduces the pVT and UVT relations, at least qualitatively, whereas the original van der Waals EOS can explain only the pVT relation.
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