Transport and reaction in the light of irreversible thermodynamics

We have already seen in Section 4.2 that, in the case of a chemical reaction, the entropy production, which is zero at equilibrium, can be described at nonequilibrium as a product of the driving force (affinity A), which we will regard in what follows as being given, and the corresponding rate (reaction rate U). This can be generalized for different processes (k) to 

Since the rate disappears in the equilibrium (X=0), it follows that a = 0 and, as the equilibrium is approached, the higher terms become less important, so that we are left with the linear relationship  

Of course, the choice of the driving force is not unequivocal. This is even the case if only one independent driving force is relevant, as assumed in the text. For simplicity we restrict to one dimension. Instead of X (e.g. if dilute (9/5x)p) it is also possible to introduce X as driving force, with X cs X(9X /9X)equiiibrium (e.g. d/dx)c = (5/Ax)p(c/RT)). However the range of validity is altered. 

If uncharged particles are concerned, such as, for example, sugar molecules in aqueous solution or germanium atoms in silicon, the process is reduced to a pure diffusion (V/x = V i), and 

A comparison with Pick s law (Table 6.1) permits the identification 

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