Thermodynamic Properties of Vapors from Speed of Sound

Abstract

A numerical procedure for deriving the thermodynamic properties (Z, cv, and cp) 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 in T-ϕ domain (ϕ=ρ/ρsat). The initial values of Z and ∂Z/∂Tρ are specified along the isotherm T0 with the highest temperature, at a several values of ϕ [0.1, 1.0]. The values of Z are generated by the reference equation of state, while the values of ∂Z/∂Tρ are derived from the speed of sound, by solving another set of differential equations in T-ρ domain in the transcritical temperature range. This set of equations is solved as the initial-boundary-value problem. The initial values of Z and cv 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. The boundary values of Z are specified along the same isotherm T0 and along another isotherm with a higher temperature, at several values of ρ. The procedure is tested on Ar, N2, CH4, and CO2, with the mean AADs for Z, cv, and cp at 0.0003%, 0.0046%, and 0.0061%, respectively (0.0007%, 0.0130%, and 0.0189% along the saturation line).