Thermodynamic Equilibrium of the Saturated Fluid with a Free Surface Area and the Internal Energy as a Function of the Phase-Specific Volumes and Vapor Pressure

Albrecht Elsner

doi:10.4236/eng.2015.79053

Abstract

This study is concerned with describing the thermodynamic equilibrium of the saturated fluid with and without a free surface area A. Discussion of the role of A as system variable of the interface phase and an estimate of the ratio of the respective free energies of systems with and without A show that the system variables given by Gibbs suffice to describe the volumetric properties of the fluid. The well-known Gibbsian expressions for the internal energies of the two-phase fluid, namely for the vapor and for the condensate (liquid or solid), only differ with respect to the phase-specific volumes and . The saturation temperature T, vapor presssure p, and chemical potential are intensive parameters, each of which has the same value everywhere within the fluid, and hence are phase-independent quantities. If one succeeds in representing as a function of and , then the internal energies can also be described by expressions that only differ from one another with respect to their dependence on and . Here it is shown that can be uniquely expressed by the volume function . Therefore, the internal energies can be represented explicitly as functions of the vapor pressure and volumes of the saturated vapor and condensate and are absolutely determined. The hitherto existing problem of applied thermodynamics, calculating the internal energy from the measurable quantities T, p, , and , is thus solved. The same method applies to the calculation of the entropy, chemical potential, and heat capacity.

Highlights

We are concerned here with electrically and magnetically neutral single-component matter under steady-state equilibrium conditions which are thermodynamically defined in the immediate vicinity of the critical point and below it
This gas mass in thermodynamic equilibrium existing in two phases is called a saturated fluid
By means of the expression given for the volume function d (μ T ) d ( p T ) many thermodynamic relations are verified in the Appendix, this in turn being evidence for the correctness of the volume function used

Summary

Introduction

We are concerned here with electrically and magnetically neutral single-component matter under steady-state equilibrium conditions which are thermodynamically defined in the immediate vicinity of the critical point and below it. The equilibrium in the case A > 0 is discussed where there is a third fluid phase, called the interface phase To it is assigned the free interface energy Fi , which is identified with − A⋅γ ( γ surface tension), so that the ratio Fi F can be numerically estimated. This result, which can be deduced from internal energy functions being subject to Nernst’s theorem at absolute zero, is noteworthy, because the said quantities have been treated in Applied Thermodynamic Theory for more than a century as temperature functions with arbitrarily specified constants. By means of the expression given for the volume function d (μ T ) d ( p T ) many thermodynamic relations are verified in the Appendix, this in turn being evidence for the correctness of the volume function used

Description of the Thermodynamic Equilibrium of the Real Gas

Two-Phase Equilibrium without and with a Free Surface Area

The Thermodynamic Zero of Thermodynamic Functions

The Unsolved Problem in Applied Thermodynamics

Results and Discussion