![]() The general solution to this set of equations has not been found yet, except for the gaseous phase under low pressures (Trusler et al. However, the speed of sound in a fluid is connected to these properties through the set of nonlinear partial differential equations of the second order. While the speed of sound itself is a piece of useful information about a fluid, other thermodynamic properties like the density and the heat capacity, which may be derived from it, make the speed of sound even more useful. The speed of sound is the property of a fluid which is measured with an exceptional accuracy (Ewing and Goodwin, Estrada-Alexanders and Trusler, Costa Gomes and Trusler, Trusler and Zarari, and Estrada-Alexanders and Trusler ). The boundary values of are specified along the same isotherm and along another isotherm with a higher temperature, at several values of. The initial values of and are specified along the isochore in the limit of the ideal gas, at several isotherms distributed according to the Chebyshev points of the second kind. This set of equations is solved as the initial-boundary-value problem. The values of are generated by the reference equation of state, while the values of are derived from the speed of sound, by solving another set of differential equations in domain in the transcritical temperature range. The initial values of and are specified along the isotherm with the highest temperature, at a several values of. The set of differential equations connecting these properties with the speed of sound is solved as the initial-value problem in domain. A numerical procedure for deriving the thermodynamic properties, , and of the vapor phase in the subcritical temperature range from the speed of sound is presented. ![]()
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