Thermodynamic Properties of Vapors from Speed of Sound

Muhamed Bijedić,Sabina Begić

doi:10.1155/2014/231296

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).

Highlights

The speed of sound is the property of a fluid which is measured with an exceptional accuracy (Ewing and Goodwin [1], Estrada-Alexanders and Trusler [2], Costa Gomes and Trusler [3], Trusler and Zarari [4], and Estrada-Alexanders and Trusler [5])
The lines of constant φ are generated in advance by the Peng-Robinson equation of state (Peng and Robinson [14]), except the line φ = 1.0 which is generated by the corresponding reference equation of state
Since the compressibility factor is calculated before the speed of sound is required, in each integration step, the latter is interpolated along the isotherms with respect to the pressure (p = ZρRT/M)

Summary

Introduction

The speed of sound is the property of a fluid which is measured with an exceptional accuracy (Ewing and Goodwin [1], Estrada-Alexanders and Trusler [2], Costa Gomes and Trusler [3], Trusler and Zarari [4], and Estrada-Alexanders and Trusler [5]). That procedure is applied to the transcritical temperature range in order to generate the initial conditions of the Neumann type, which are used for deriving the compressibility factor and the heat capacity of a vapor in the subcritical temperature range. In this way, the main disadvantage of the approach based on the numerical integration is minimized, because only a few data points of the compressibility factor from other sources are needed to cover the whole gaseous phase except the region around the critical point. While the derived properties of a gas in the transcritical temperature range have a very good agreement with the corresponding reference data they are not discussed in this paper (see Table 7)

Theory

Results and Discussion

Conclusions