Use of the velocity of sound in predicting the PVT relations

Thermodynamic properties of fluids are generally calculated from the PVT relations through equations of state. The majority of existing equations of state require the critical properties or intermolecular potential energy parameters as their input data. In many cases, such properties are neither available nor they can be accurately estimated.

One accessible and accurately measurable property of substances is the velocity of sound. In this report a method is introduced through which one can predict the PVT behavior of fluids using the velocity of sound data. A general mathematical relationship,

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expressing the velocity of sound, c, in terms of the hard-core velocity of sound, c_hs, and thermodynamic properties is derived. One may use this equation to extract PVT data from cVT data, or vice versa. As an example the virial coefficients, the Lennard-Jones intermolecular potential parameters, and the constants of the van der Waals equation of state for a number of pure fluids are calculated using the velocity of sound data. Utility of this method is particularly attractive for such compounds as heavy hydrocarbons, unstable fluids, and newly designed molecules for which intermolecular parameters and critical properties are not available.