Thermodynamically-equivalent systems

Consider one closed chemical system A. It is composed, to begin with, of a mixture of a certain number of components in known quantities. This system evolves spontaneously at constant pressure and temperature. In general, with the exception of oscillating systems, this system approaches a state of equilibriiun. In order for this to happen, a number of reactions occur which, at any given moment, are each characterized by their fractional extent 

The concept of thermod5mamically-equivalent systems is used, in particular, when studying sets of several reactions, using the predominant-reaction method. The method is very frequently used for calculating the state of equilibrium of ionic reactions in an aqueous solution - e g. calculating the pH of a solution. 

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A variant of the method is particularly widely used for quickly performing the calculations for ionic solutions the predominant reaction method, which is based on the concept of thermodynamically-equivalent systems. The method is usually described when studying these ionic reactions, for which it is very often employed. 

However, let note, that the assumption about independence of the osmotic pressure of semi-diluted solutions on the length of a chain is not physically definitely well-founded per se it is equivalent to position that the system of strongly intertwined chains is thermodynamically equivalent to the system of gaped monomeric links of the same concentration. Therefore, both Flory-Huggins method and Scaling method do not take into account the conformation constituent of free energy of polymeric chains. 

The notion of thermodynamic tree (the graph, each point of which represents the set of thermodynamically equivalent states) was introduced by Gorban (1984) where he also revealed the possibilities of applying this notion for analysis of the chemical kinetics equations. In the work by Gorban et al. (2001, 2006) the authors consider the problems of employing thermodynamic tree to study the physicochemical systems using MEIS. 

As before, the requirement that all fi s refnaln constant implies that the adjacent phases should be infinitely large, so as not to become depleted if large new areas are created. We shall restrict ourselves to systems where this premise is satisfied. As 2° = yA and 2° = y. the grand potential per unit area is the thermodynamic equivalent of the mechanical interfacial tension, interpreted as a force per unit length. 

Note that pfp, V2/2, and gz have units of m2/s2=J/kg=energy/mass, while pf pV2j2, and pgz have N/mz=J/m3=energy/volume, p = 1/v being the density. Since the electric energy Ue generated in a system is thermodynamically equivalent to work done on the system,... 

Chemical equilibrium model Most reactive transport formulations use the mass action law to solve the chemical equilibrium equations. In this formulation an alternative (though thermodynamically equivalent) approach is used, based on the minimization of Gibbs Free Energy. This approach has a wider application range extending to highly non-ideal brine systems. 

It can therefore be seen that the potential is dependent on the hydrogen ion concentration, that is on the pH of the solution. The Nernst equation applies only to a thermodynamically reversible system but an equivalent expression involving the hydrogen ion concentration applies to all reductions or oxidations. 

Figure 3.5ob represents a system comprising, at the initial instant, a monomer and an inert diluent (IjMWL) which are thermodynamically equivalent to each other except for the ability for polymerization so, one parameter = 0.45 characterizes the interaction in the NP+(LMWL+mononier) system. 

We may reduce any system for thermodynamic cooling into four main operational phases, which are at any rate, thermodynamically interconnected, whose processes may not be combined with each other or be replaced by thermodynamically equivalent steps. 

We shall see, as an example, a simple counterflow cold exchanger connecting the cold and warm ends between (B) and (D) is the nearest realistic equivalent to a Carnot cycle. The idealized constant-mass flow system in a perfect counterflow heat regenerator operating with an idealized gas is thermodynamically equivalent to the adiabatic expansion paired with the adiabatic compression in the Carnot cycle, since the following intrinsic energy transfer is fulfilled in terms of a reciprocal isobaric transformation. (See Fig. 2)... 

The complex distribution system that results from the frontal analysis of a multicomponent solvent mixture on a thin layer plate makes the theoretical treatment of the TLC process exceedingly difficult. Although specific expressions for the important parameters can be obtained for a simple, particular, application, a general set of expressions that can help with all types of TLC analyses has not yet been developed. One advantage of the frontal analysis of the solvent, however, is to produce a concentration effect that improves the overall sensitivity of the technique. The primary parameter used in TLC is the (Rf) factor which is a simple ratio of the distance traveled by the solute to the distance traveled by the solvent front. The (Rf) factor will always be less than unity. If a standard is added to the mixture, then the ratio of the (Rf) factors of the solute to that of the standard is termed the (Rx) factor and is thermodynamically equivalent to the separation ratio (a) in GC or LC. In a similar manner, the capacity ratio (k ) of a solute can be calculated for TLC from its (Rf) factor. Resolution is measured as the distance between the centers of two spots to the mean spot width. Alternative expressions for the resolution can be given in terms of the (Rf) factor and the plate efficiency. The plate efficiency is taken (by analogy to GC and LC) as sixteen times the square of the ratio of the retention distance of the spot to the spot width, but the analogy between TLC and the techniques of GC and LC can only be used with extreme caution. The so called... 

The synthesis of partially thermally coupled column configurations for a multicomponent distillation has b n studied in the context of the thermodynamic equivalent structures. There has been formulated a conqtlete space of the possible thermodynamic equivalent alternatives of the partially coupled (PC) configurations for multicomponent mixtures. A formula is presented to calculate the number of all the partially coupled schemes for any n-conqx)nent mixture. The formulated alternatives of all the possible arrangements of PC configurations provide a complete subspace for optimal design of multicomponent distillation systems not only for the economics, but also for column equipment designs. 

Obviously, the thermodynamic equivalent partially coupled column configurations have formulated a unique search space of the possible thermally coupled alternatives for optimal design of distillation systems for multicomponent separations. 

At equilibrium, each reaction reaches a limit extent or equilibrium extent. Now we construct another system, B, mixing the same components as before, with the quantities identical to those obtained when the reactions in system A have each attained a given fractional extent. This system B will, imder the same conditions of temperature and pressiu-e, obviously attain the same state of equilibrium as the previous system. We say that the two systems A and B are thermodynamically equivalent. We can even state that the second system, B, is closer to equilibrium than system A. 

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