Thermodynamic Properties of Vapors from Speed of Sound

摘要

A numerical procedure for deriving the thermodynamic properties(Z,cv, andcp)of the vapor phase in the subcritical temperature range from the speed of sound is presented. The set of differential equations connecting these properties with the speed of sound is solved as the initial-value problem inT-ϕdomain(ϕ=ρ/ρsat). The initial values ofZand∂Z/∂Tρare specified along the isothermT0with the highest temperature, at a several values ofϕ[0.1, 1.0]. The values ofZare generated by the reference equation of state, while the values of∂Z/∂Tρare derived from the speed of sound, by solving another set of differential equations inT-ρdomain in the transcritical temperature range. This set of equations is solved as the initial-boundary-value problem. The initial values ofZandcvare specified along the isochore in the limit of the ideal gas, at several isotherms distributed according to the Chebyshev points of the second kind. The boundary values ofZare specified along the same isothermT0and along another isotherm with a higher temperature, at several values ofρ. The procedure is tested on Ar, N2, CH4, and CO2, with the mean AADs forZ,cv, andcpat 0.0003%, 0.0046%, and 0.0061%, respectively (0.0007%, 0.0130%, and 0.0189% along the saturation line).