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Using the extended thermodynamic perturbation theory of Wertheim, closed simple analytic expressions for the internal energy and pressure of the primitive model of water are derived and examined in detail. The equation of state, which has a form of a perturbed hard sphere equation, exhibits the same anomaly in temperature dependence of the isothermal compressibility as real water. The low value of the critical compressibility factor is in close agreement with the experimental value for real water.
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Nezbeda et al. (1990) studied this question.
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