Thermodynamic equilibrium, criterion stability

It is worth reminding here that particularly this value of , was introduced earlier (see Chapter VII, 1) in the criterion describing equilibrium between peptization and coagulation and thermodynamic stability of system towards coagulation. In agreement with eq. (VII. 1), a disperse system is stable when ux < p kT / I/2 Z, which at (5 15 to 20 and Z 3 to 4 constitutes approximately 7 to 15 kT. 

The results show the important effect of the substitution on the equilibrium as a function of the electronic properties of the functional groups, especially in the C3 and C7 sites of the triazolopyridine ring. Therefore, deprotonation produces an effect qualitatively similar to the substitution by electron-releasing groups. The position of protonation and the effect of protonation and deprotonation on the isomeric equilibrium have been discussed and some results are coherent with the experimental data described in the literature. From the results of the specific study of the regioselective reaction of lithiation it can be deduced that the process could be explained by a thermodynamic criterion due to the relative stability of the lithio derivatives. 

A) Thermodynamics of the Active-Passive Transition If faced with the task of deciding whether a particular metal would be suitable as a fabrication material In a given environment, one likes to know a) what kinds of spontaneously occurring reactions are expected and b) what Is the magnitude of the rate of metal dissolution. The latter Is the real criterion In making the decision and Is usually evaluated through experimentation. The former provides a yes or no answer regarding the stability of the metal and falls within the scope of equilibrium thermodynamics. 

The local equilibrium assumption was the basis on which the Brussels school developed a global thermodynamic theory. Use of this assumption makes possible the macroscopic evaluation of entropy production and entropy flow terms with macroscopic thermodynamic methods. The assumption states that "there exists within each small mass element of the medium a state of local equilibrium for which the local entropy, s, is the same function of the local macroscopic variables as at equilibrium state" (Glansdorff and Prigogine, 1971, p. 14). In other words, each small element of a system may be treated as a state near equilibrium but need not necessarily be at equilibrium. This does not mean that the system as a whole need be near equilibrium thus, neighboring local elements may differ in parameters (temperatures, chemical affinities, etc.) which are reflected in the function describing their local entropy. The additional assumption is made that the sum of the criteria of local stability for each element corresponds to the global stability criterion for the whole system. 

The minimum entropy production theorem dictates that, for a system near equilibrium to achieve a steady state, the entropy production must attain the least possible value compatible with the boundary conditions. Near equilibrium, if the steady state is perturbed by a small fluctuation (8), the stability of the steady state is assured if the time derivative of entropy production (P) is less than or equal to zero. This may be expressed mathematically as dPIdt 0. When this condition pertains, the system will develop a mechanism to damp the fluctuation and return to the initial state. The minimum entropy production theorem, however, may be viewed as providing an evolution criterion since it implies that a physical system open to fluxes will evolve until it reaches a steady state which is characterized by a minimal rate of dissipation of energy. Because a system on the thermodynamic branch is governed by the Onsager reciprocity relations and the theorem of minimum entropy production, it cannot evolve. Yet as a system is driven further away from equilibrium, an instability of the thermodynamic branch can occur and new structures can arise through the formation of dissipative structures which requires the constant dissipation of energy. 

At equilibrium, or in the linear nonequilibrium domain, equation (9) is a direct result of the second law of thermodynamics, and inequality (8) is derived as a sufficient criterion for stability. In the nonlinear range of nonequilibrium thermodynamics, as long as the local equilibrium assumption remains valid, inequality (8) is assumed and becomes the starting point from which equation (9) is derived as a sufficient stability criterion. Far from equilibrium, if a(82s)... 

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