Thermodynamics equilibrium criterion

Vesicles [10, 11] these aggregates of insoluble natural or artificial amphiphiles in water can have various shapes (spherical, cylindrical). Depending on the preparation conditions, small unilamellar or large multilamellar vesicles can be produced. The structures meet the self-organization criterion, because they are, albeit on a long time scale, dynamic and not in thermodynamic equilibrium, which would in many cases be a macroscopically phase separated lamellar phase. 

An important use of the free energy function is to obtain a simple criterion for the occurrence of spontaneous processes and for thermodynamic equilibrium. According to the second law of thermodynamics,... 

The criterion for thermodynamic equilibrium between two phases of a multicomponent mixture is that for every component, i ... 

A Criterion of Thermodynamic Equilibrium between Two Phases Equality of Electrochemical Potentials. It has been stated that ihe total driving force responsible for Ihe flow or transport of a species j is the gradient d lj/dx of its electrochemical potential. However, when there is net flow or flux of any species, this means that the system is not at equilibrium. Conversely, for the system to be at equilibrium, it is essential that there be no drift of any species—hence, that there should be zero gradients for the electrochemical potentials of all the species. It follows, therefore, that, for an interface to be at equilibrium, the gradients of electrochemical potential of the various species must be zero across the phase boundary, i.e.,... 

A simple conclusion follows Thermodynamic equilibrium exists at a nonpolarizable interface. Hence, one can immediately apply the criterion of thermodynamic equilibrium to a nonpolarizable interface. That is, from Eq. (6.38),... 

Constraint Conditions Thermodynamic Potential Criterion of Spontaneity Criterion of Equilibrium... 

Kait is the so-called fracture toughness parameter. It was first discussed by Griffith [A. A. Griffith (1920)] and describes the mechanical equilibrium of the crack, but not the thermodynamic equilibrium of the unstable crystal. Rewriting the criterion given by Eqn. (14.32) in terms of Eqn. (14.30) one finds... 

To treat solid-solid reactions, Wagner introduced the concepts of local equilibrium and counterdiffusion of cations between the solids. The latter concept forms the basis for Darken s subsequent introduction of the interdiffusion coefficient, which was discussed in Section 2.4. To maintain a state of local equilibrium, the exchange fluxes across the interface must be large compared to the net transport of matter across the boundary. This is analogous to the criterion that the forward and reverse reaction rates be the same, or nearly so, for a reversible reaction to be considered at thermodynamic equilibrium. 

For the HPLC separation of low molecular weight organic compounds and various biomacromolecules, the near-equilibrium criterion has generally been assumed for the binding and desorption behaviour. Changes in thermodynamic parameters due to polypeptide- or protein-ligate interaction can thus be depicted in terms of the Gibbs-Helmholtz relationship, namely,... 

Near thermodynamic equilibrium, similar linear relationships are also valid for elementary chemical processes, as well as for stepwise processes where the rates are proportional to the difference between the thermodynamic mshes of the initial and final reaction groups (see Section 1.4.2). Here, the criterion of proximity to thermodynamic equilibrium is relationship jA jl < RT, where Arij is the affinity for the transformation of reaction group i to reaction group j. In fact, while... 

The Prigogine Criterion (Theorem) of the Evolution for Systems that Are Close to their Thermodynamic Equilibrium... 

The intimacy criterion above (15, 15A) involves physical parameters, a reaction rate, and a quantity based on thermodynamic equilibrium. It thus presents a link between rate process variables and thermodynamics. 

For the description of /-independent phases with k components, we therefore need f(k - 1) independent data on composition. To these we still have to add data on temperature and pressure, so we have altogether/( - l) + 2 intensive data, if the temperature and pressure are equal in the whole system. If the system considered is in equilibrium, the intensive criterion of the thermodynamic equilibrium must be fulfilled, fhus the chemical potentials of all the k components in all the/phases have to be equal. This criterion thus defines fhe number of binding conditions between the intensive variables. This number is kif- 1), because the number of binding conditions is one less than the number of phases. Then the difference between both the quantities defines the number of intensive variables, which are independent in a system with A components and/phases being in equilibrium -the variance, or the number of degrees of freedom v... 

The key then is to somehow calculate the probability with which a specific quantum state contributes to the average values. As far as thermal systems in thermodynamic equilibrium are concerned, this is the central problem addressed by statistical thermodynamics. W( therefore begin our discuasion of some core elements of statistical thermodynamics at the quantum level but will eventually turn to the classic limit, because the phenomena addressed by this book occur under conditions where a classic description turns out to be adequate. We shall see this at the end of this chapter in Section 2.5 where we introduce a quantitative criterion for the adequacy of such a classic description. 

The surface area expansion process in Figure 3.5 must obey the basic thermodynamic reversibility rules so that the movement from equilibrium to both directions should be so slow that the system can be continually relaxed. For most low-viscosity liquids, their surfaces relax very rapidly, and this reversibility criterion is usually met. However, if the viscosity of the liquid is too high, the equilibrium cannot take place and the thermodynamical equilibrium equations cannot be used in these conditions. For solids, it is impossible to expand a solid surface reversibly under normal experimental conditions because it will break or crack rather than flow under pressure. However, this fact should not confuse us surface tension of solids exists but we cannot apply a reversible area expansion method to solids because it cannot happen. Thus, solid surface tension determination can only be made by indirect methods such as liquid drop contact angle determination, or by applying various assumptions to some mechanical tests (see Chapters 8 and 9). 

Cathodic protection is the process whereby the corrosion rate of a metal is decreased or stopped by decreasing the potential of the metal from Ecorr to some lower value and in the limit to E M, the thermodynamic equilibrium half-cell potential. At this potential, iox M = ired X[ = i() xi- and net transfer of metal ions to the solution no longer occurs. This is the criterion for complete cathodic protection (i.e., E = E m). 

It occurred that the term phase extended onto microscopic objects has a rather conditional meaning. Because of this the main criterion used to separate colloidal systems and polymer solutions, i.e., viewing true solutions as thermodynamically equilibrium systems, was no longer significant. The studies on polymer solutions indicated that the latter often contained molecular aggregates and that ideal solutions obeying the statistical theory of dissolution of flexible chains, were rarely encountered. 

Certain equilibrium states of thermodynamic systems are stable to small fluctuations others are not. For example, the equilibrium state of a simple gas is stable to all fluctuations, as are most of the equilibrium states we will be concerned with. It is possible, however, to carefully prepare a subcooled liquid, that is, a liquid below its normal solidiflcation temperature, that satisfies the equilibrium criteria. This is an tin-.stable equilibrium. state because the slightest disturbance, such as tapping on the. side of the containing ve.s.sel, will cause the liquid to freeze. One sometimes encounters mixtures that, by the chemical reaction equilibrium criterion (see Chapter 13). should react however, the chemical reaction rate is so small as to be immeasurable at the temperature of interest. Such a mixture can achieve a state of thermal equilibrium that is stable with respect to small fluctuations of temperature and pressure. If, however, there is a sufficiently large, but temporary, increase in temperature. so that die rate of the chemical reaction is appreciable for some period of time) and then the system... 

To illustrate the use of this equilibrium criterion, consider the very simple, initially nonuniform system shown in Fig. 7.1-1. There a single-phase, single-component fluid in an adiabatic, constant-volume container has been divided into two subsystems by an imaginary-boundary. Each of these subsystems is assumed to contain the same chemical species of uniform thermodynamic properties. However, these subsystems are open to the flow of heat and mass across the imaginary internal boundary, and their temperature and-pressure need not be the same. For the composite system consisting of the two subsystems, the total mass (though, in fact, we will use number of moles), internal energy, volume, and entropy, all of which are extensive variables, are the sums of these respective quantities for the two subsystems, that is. 

The thermodynamic requirement for any type of phase equilibrium is that the composition of each species in each phase in which it appears be such that the equilibrium criterion... 

The mathematical statement of the second law provides, as a corollary, a criterion for thermodynamic equilibrium. It is clear that a thermodynamic system must be in an equilibrium state if there are no natural processes by which it can proceed from its specified state to another state. Thus, a state of a thermodynamic system is an equilibrium state if all virtual variations in state fail to satisfy the inequality... 

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