Nonequilibrium thermodynamic postulates

The linear phenomenological equations are valid within the nonequilibrium thermodynamics postulates made in 3.5.3. The summary of the assumptions are ... 

Displacements toward equilibrium are irreversible or, more descriptively, one way only. An elegant discipline describing these displacements is irreversible thermodynamics, sometimes called nonequilibrium thermodynamics. The four fundamental postulates of irreversible thermodynamics are (1) ... 

Thermodynamics of nonequilibrium (irreversible) processes is an extension of classical thermodynamics, mainly to open systems. Unfortunately, the Second Law of classical thermodynamics cannot be applied directly to systems where nonequilibrium (i.e., thermodynamically irreversible) pro cesses occur. For this reason, thermodynamics of nonequilibrium processes has used several principal concepts that are supplementary to the classical thermodynamics postulates. In contrast to the postulates, many of the con cepts in thermodynamics of nonequilibrium processes can be mathe maticaUy substantiated by considering, for example, the time hierarchy of the processes involved. 

Individual film mass transfer coefficients may be determined by the following considerations. According to postulates of nonequilibrium thermodynamics [78], the general equation that relates the flux, J, of the solute to its concentration, C, and its derivative, is [79]... 

The linear nonequilibrium thermodynamics approach mainly is based on the following four postulates ... 

If the steady state concentrations of the components are shifted, but not too far from their equilibrium values, the interconnection between the fluxes and chemical forces (chemical affinities, in our case) should satisfy the well-known linear relationships that are usually postulated in the linear thermodynamics of irreversible processes [15-18]. We do not consider here the phenomenological equations of nonequilibrium thermodynamics. For details the reader can refer to numerous excellent monographs and review articles devoted to the applications of nonequilibrium thermodynamics in the description of chemical reactions and biological processes (see, for instance, [22-30]). In many cases, the conventional phenomenological approaches of linear and nonlinear nonequilibrium thermodynamics appear to be useful tools for the... 

In the above formal development, we found that Gibbs stability condition from equilibrium thermodynamics and Prigogine s stability condition from nonequilibrium thermodynamics for a chemically reactive system emerge from the statistical mechanical treatment of nonequilibrium systems. Unlike the stability conditions of Gibbs and Prigogine, the inequalities (384), (385), (396), and (397) are not postulates. They are simple consequences of the statistical mechanical treatment. Moreover, these inequalities apply to both equihbrium and nonequilibrium systems. 

While Eq. (26) is an eight-parameter equation, its use can be justified in terms of the postulates of nonequilibrium thermodynamics and it includes the terms to estimate the correct free energy of the reaction. 

The third approach is called the thermodynamic theory of passive systems. It is based on the following postulates (1) The introduction of the notion of entropy is avoided for nonequilibrium states and the principle of local state is not assumed, (2) The inequality is replaced by an inequality expressing the fundamental property of passivity. This inequality follows from the second law of thermodynamics and the condition of thermodynamic stability. Further the inequality is known to have sense only for states of equilibrium, (3) The temperature is assumed to exist for non-equilibrium states, (4) As a consequence of the fundamental inequality the class of processes under consideration is limited to processes in which deviations from the equilibrium conditions are small. This enables full linearization of the constitutive equations. An important feature of this approach is the clear physical interpretation of all the quantities introduced. 

In 1902, T. W. Richards found experimentally that the free-energy increment of a reaction approached the enthalpy change asymptotically as the temperature was decreased. From a study of Richards data, Nernst suggested that at absolute zero the entropy increment of reversible reactions among perfect crystalline solids is zero. This heat theorem was restated by Planck in 1912 in the form The entropy of all perfect crystalline solids is zero at absolute zero.f This postulate is the third law of thermodynamics. A perfect crystal is one in true thermodynamic equilibrium. Apparent deviations from the third law are attributed to the fact that measurements have been made on nonequilibrium systems. 

The free-volume concept dates back to the Clausius [1880] equation of state. The need for postulating the presence of occupied and free space in a material has been imposed by the fluid behavior. Only recently has positron annihilation lifetime spectroscopy (PALS see Chapters 10 to 12) provided direct evidence of free-volume presence. Chapter 6 traces the evolution of equations of state up to derivation of the configurational hole-cell theory [Simha and Somcynsky, 1969 Somcynsky and Simha, 1971], in which the lattice hole fraction, h, a measure of the free-volume content, is given explicitly. Extracted from the pressure-volume-temperature PVT) data, the dependence, h = h T, P), has been used successfully for the interpretation of a plethora of physical phenomena under thermodynamic equilibria as well as in nonequilibrium dynamic systems. 

Summary. Basic thermodynamic concepts were introduced in this section which form a very general framework to formulate two basic thermodynamic laws also at nonequilibrium conditions. Only three primitive notions of work, heat, and empirical temperature and several simple general properties of thermodynamic systems and universe were sufficient for this purpose. In the following two sections, we postulate the First and the Second Laws of thermodynamics and deduce the consequences. Because they are formulated in terms of heat, work, empirical temperatures, and cyclic processes (including those which are ideal) their direct experimental confirmation is possible. 

Summary. The Second Law was postulated as a simple general statement on heat exchange in cyclic processes. It was demonstrated that when this statement is combined with the properties of thermodynamic systems and universe introduced in Sect. 1.2 the existence of the absolute temperature and entropy follows, even out of equilibrium. The entropy should satisfy an inequality (1.21) which can be viewed as an alternative form of the Second Law and is called the entropy inequality. However, enttopy need not be unique especially in complex (nonequilibrium) systems or processes and even the ttansferability of the proof of its existence at such conditions remains unclear. Even in such cases the supposed existence of entropy can give important information on possible behavior which can be subjected to experimental testing. 

In equilibrium thermodynamics model A and in model B not far from equilibrium (and with no memory to temperature) the entropy may be calculated up to a constant. Namely, in both cases S = S(V, T) (2.6)2, (2.25) and we can use the equilibrium processes (2.28) in B or arbitrary processes in A for classical calculation of entropy change by integration of dS/dT or dS/dV expressible by Gibbs equations (2.18), (2.19), (2.38) through measurable heat capacity dU/dT or state Eqs.(2.6>, (2.33) (with equilibrium pressure P° in model B). This seems to accord with such a property as in (1.11), (1.40) in Sects. 1.3, 1.4. As we noted above, here the Gibbs equations used were proved to be valid not only in classical equilibrium thermodynamics (2.18), (2.19) but also in the nonequilibrium model B (2.38) and this expresses the local equilibrium hypothesis in model B (it will be proved also in nonuniform models in Chaps.3 (Sect. 3.6), 4, while in classical theories of irreversible processes [12, 16] it must be taken as a postulate). 

In this chapter, we will mainly consider the Gibbsian thermodynamics of phase equilibria relevant to problems in hydrocarbon reservoirs and use its concepts in the other chapters to solve practical problems. The thermodynamics of equilibrium processes also provide the framework for nonequilibrium and irreversible thermodynamics. It is our intention that the material covered in this book should be self-contained. The postulational approach introduced by Callen (1985), and Tisza (1966) is, therefore, adopted to make brief the presentation of basic concepts and equations. 

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