Thermodynamic potentials open systems

A fundamental corollary of the Glansdorf Prigogine criterion (3.2) is a potentiality of the formation of ordered structures at the occurrence of irreversible processes in the region of nonlinear thermodynamics in open systems that are far from their equilibrium. Prigogine created the term dissipative structures to describe the structures that arise when some controlling parameters exceed certain critical values and are classified as spatial, temporal, or spatial temporal. Some typical dissipative structures are discussed in Sections 3.5 and 4.6. 

The first law of thermodynamics for open systems applies the transport of work dl heat dQ mass dm, with its enthalpy h and external energy (kinetic and potential energy) across the system boundaries equals the change in internal energy dtJ and external energy d a in the system. 

The unsteady-state balance equation for this system (air within the engine housing) is the first law of thermodynamics for open systems with changes in kinetic and potential energies neglected. Also, the temperature and composition of the system contents are assumed independent of position and no phase changes occur. This gives the equation... 

The heat associated with a specific polymerization reaction depends on the temperatures of both the monomers and polymer. A standard basis that is consistent for treating polymerization heat effects results when the products of polymerization and the monomers are all at the same temperature. Consider a calorimeter method of measurements of heat of polymerization of monomers. The initiator is mixed with the monomer, and the system is a continuous flow CSTR. The polymerization reactions take place in the CSTR. The polymerization products enter a devolatilizer where the monomers are vaporized and removed from the product mix and recycled back to the reactors. The CSTR is water cooled to bring the monomers/polymer to the reactor temperature. There is no shaft work performed by the process. The CSTR is built, so that changes in potential and kinetic energy are negligible. The first law of thermodynamics for open systems can be written for the system as... 

Note that the energy terms in parentheses in Eq. (5.73) (internal plus macrokinetic plus potential) represent the total macroscopic energy of the fluid and, thus, Eq. (5.73) is the general differential form of the first law of thermodynamics for open systems. 

Regarding the electrode/electrolyte interface, it is important to distinguish between two types of electrochemical systems thermodynamically closed (and in equilibrium) and open systems. While the former can be understood by knowing the equilibrium atomic structure of the interface and the electrochemical potentials of all components, open systems require more information, since the electrochemical potentials within the interface are not necessarily constant. Variations could be caused by electrocatalytic reactions locally changing the concentration of the various species. In this chapter, we will focus on the former situation, i.e., interfaces in equilibrium with a bulk electrode and a multicomponent bulk electrolyte, which are both influenced by temperature and pressures/activities, and constrained by a finite voltage between electrode and electrolyte. 

Whether a reaction is spontaneous or not depends on thermodynamics. The cocktail of chemicals and the variety of chemical reactions possible depend on the local environmental conditions temperature, pressure, phase, composition and electrochemical potential. A unified description of all of these conditions of state is provided by thermodynamics and a property called the Gibbs free energy, G. Allowing for the influx of chemicals into the reaction system defines an open system with a change in the internal energy dt/ given by ... 

In open systems consisting of several components the thermodynamic properties of each component depend on the overall composition in addition to T and p. Chemical thermodynamics in such systems relies on the partial molar properties of the components. The partial molar Gibbs energy at constantp, Tand rij (eq. 1.77) has been given a special name due to its great importance the chemical potential. The corresponding partial molar enthalpy, entropy and volume under the same conditions are defined as... 

The inverse of H determines the geometric compliance matrix (Nalewajski, 1993, 1995, 1997, 1999, 2000, 2002b, 2006a,b Nalewajski and Korchowiec, 1997 Nalewajski et al., 1996, 2008) describing the open system in the Qi,F)-representation. The relevant thermodynamic potential is defined by the total Legendre transform of the system BO potential, which replaces the state-parameters (N, Q) with their energy conjugates (/a, F), respectively ... 

In a closed system when temperature and pressure are constant, the sum of chemical potentials of all components is fixed in contrast, in an open system, the chemical potential of all components is influenced by both the thermodynamic parameters of the phases and various parameters outside the system. The main relationship among phases, components, and physical conditions is given by the phase rule. 

With an open system to which electrodes are attached, we can study the stability of interface morphology in an external electric field. A particularly simple case is met if the crystals involved are chemically homogeneous. In this case, Vfij = 0, and the ions are essentially driven by the electric field. Also, this is easy to handle experimentally. The counterpart of our basic stability experiment (Fig. 11-7) in which the AO crystal was exposed to an oxygen chemical potential gradient is now the exposure of AX to an electric field from the attached electrodes. In order to define the thermodynamic state of AX, it is necessary to apply electrodes with a predetermined... 

With electrochemical methods, we determine thermodynamic potentials of components in systems which contain a sufficiently large number of atomic particles. Since the systematic investigation of solid electrolytes in the early 1920 s, it is possible to change the mole number of a component in a crystal via the corresponding flux across an appropriate electrolyte (1 mA times 1 s corresponds to ca. 10 s mol). Simultaneously, the chemical potential of the component can be determined with the same set-tip under open circuit conditions. Provided both the response time and the buffer capacity of the galvanic cells are sufficiently small, we can then also register the time dependence of the component chemical potentials in the reacting solids. ... 

Consider a two-phase system of fixed total volume, with constant T and p (an open system with respect to matter flow), as illustrated in Fig. C.5. Under these conditions, the function Cl = E — TS — piNi — P2N2 is the appropriate thermodynamic potential. For any small variation at equilibrium, such as an infinitesimal variation... 

The chemical potential is defined as an intensive energy function to represent the energy level of a chemical substance in terms of the partial molar quantity of free enthalpy of the substance. For open systems permeable to heat, work, and chemical substances, the chemical potential can be used more conveniently to describe the state of the systems than the usual extensive energy functions. This chapter discusses the characteristics of the chemical potential of substances in relation with various thermodynamic energy functions. In a mixture of substances the chemical potential of an individual constituent can be expressed in its unitary part and mixing part. 

Thus, another approach consists in selecting some boundary conditions and properties. It is obvious that all exact correlation functions must satisfy and incorporate them in the closure expressions at the outset, so that the resulting correlations and properties are consistent with these criteria. These criteria have to include the class of Zero-Separation Theorems (ZSTs) [71,72] on the cavity function v(r), the indirect correlation function y(r) and the bridge function B(r) at zero separation (r = 0). As will be seen, this concept is necessary to treat various problems for open systems, such as phase equilibria. For example, the calculation of the excess chemical potential fi(iex is much more difficult to achieve than the calculation of usual thermodynamic properties since one of the constraints it has to satisfy is the Gibbs-Duhem relation... 

The foam film/has a core of aqueous solution and two surfactant monolayers. The thermodynamic description of such an open system (at constant temperature T, total volume V and chemical potentials i = 1,2, 3) implies the use of the Si-potential formalism with [19]... 

When the system is out of full thermodynamic equilibrium, its non-equilibrium state may be characteristic of it with gradients of some parameters and, therefore, with matter and/or energy flows. The description of the spontaneous evolution of the system via non equilibrium states and prediction of the properties of the system at, e.g., dynamic equilibrium is the subject of thermodynamics of irreversible (non-equilibrium) processes. The typical purposes here are to predict the presence of solitary or multiple local stationary states of the system, to analyze their properties and, in particular, stability. It is important that the potential instability of the open system far from thermodynamic equilibrium, in its dynamic equilibrium may result sometimes in the formation of specific rather organized dissipative structures as the final point of the evolution, while traditional classical thermodynamics does not describe such structures at all. The highly organized entities of this type are living organisms. 

In real situations surface and volume changes are often made with systems that are at equilibrium with their environment, characterized by a set of chemical potentials p, rather than keeping In ] fixed, as in [2.2.7 and 8j. In other words, area changes in open systems are considered. In statistical thermodynamics the conversion from closed to open implies the transition from the canonical to the grand canonical ensemble. The characteristic function of the latter is nothing other than the sum of the bulk and surface mechemical work terms (see [1.3.3.12] and [I.A6.23D which are the quantities of interest ... 

In any experimental setup that constitutes an open system, what is measured is the heat exchange with the surrounding media, which includes the exchange of matter and a certain amount of work. In this case, one is tempted to introduce thermodynamic potentials, i.e., to introduce entropy. Nevertheless, we feel it more prudent to find a way to relate the experimental data with the internal energy without introducing any additional hypothesis. 

As a first illustration we consider the model discussed in Section 1.3.3, namely a fluid of simple molecules confined between chemically striped solid surfaces (see Fig. 5.2). As before in Section 5.4 we treat the confined fluid as a thermodynamically open system. Hence, equilibrium states correspond to minima of the grand potential 11 introduced in Eqs. (1.66) and (1.67). The fluid fluid interaction is described by the intermolecular potential ug (r) introduced in Eq. (5.38) where the associated shifted-force potential is introduced in Eq. (5.39). The fluid substrate interaction is described by 1 1 (x, z) in the continuum representation [see Eq. (5.68)], where x replaces x because of the misaligmncnt of the sul)stratcs relative to each other [see Eq. (5.103)]. 

The sulfur-sodium polysulfide system has received the attention of electrochemists but few of the studies have been under conditions comparable to sodium-sulfur battery operating conditions. The thermodynamics of the system have been studied by means of open-circuit potentials (17,27), and dynamic measurements have been made in fused salts (28). The most pertinent studies are those of sulfur-polysulfide electrochemistry in the actual sulfur-polysulfide melts (24, 29, 35). The results of these studies seem to indicate that both the oxidation and reduction reactions are rapid, although the oxidation reaction is hindered by the formation of an insulating sulfur film. These studies also concluded that the electrode reaction sequences were quite complex because of the multitude of polysufide species. As the system becomes better characterized more quantitative descriptions are possible as evidenced by a recent work which modeled the resistive drop through an actual sulfur impregnated graphite electrode in order to correlate the spatial distribu-... 

Fluctuations of observables from their average values, unless the observables are constants of motion, are especially important, since they are related to the response functions of the system. For example, the constant volume specific heat of a fluid is a response function related to the fluctuations in the energy of a system at constant N, V and T, where N is the number of particles in a volume V at temperature T. Similarly, fluctuations in the number density (p = N/V) of an open system at constant p, V and T, where p is the chemical potential, are related to the isothermal compressibility Kj, which is another response function. Temperature-dependent fluctuations characterize the dynamic equilibrium of thermodynamic systems, in contrast to the equilibrium of purely mechanical bodies in which fluctuations are absent. 

The chemical potential p, has an important function in the system s thermodynamic behavior analogous to pressure or temperature. A temperature difference between two bodies determines the tendency of heat to pass from one body to another while a pressure difference determines the tendency for bodily movement. We will show that a difference in chemical potential can be viewed as the cause for chemical reaction or for mass transfer from one phase to another. The chemical potential p greatly facilitates the discussion of open systems, or of closed systems that undergo chemical composition changes. 

Having derived the open system potential quantity, L, we must now admit that it is not much used, any more than are the other thermodynamic potentials apart from G. You never see tables of AL in the way that you see tables of AG or AH (you never see tables of AU either, but that doesn t mean it s not important). It is not used probably because it is unfamiliar, and the number of real applications may be limited. One application is discussed by Ghiorso (1987) and used by Ghiorso and Carmichael (1987). They used L to calculate the equilibrium composition of melts at given values of T, P and i.e., values of fo fixed by various buffer assemblages. 

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