Prigogine’s theorem

The extended principle of Le Chdtelier and Prigogine s theorem thus leads to the conclusion that if k out of n forces X1( Xj . X are maintained at fixed values by means of external constraints the system will ultimately reach a state of minimum entropy production that is truly stationary this will be termed a steady-state condition of order k. 

Provide a proof of Prigogine s Theorem in which you maintain the vectorial notation throughout. 

Steady state conditions obtain when the fluxes and forces giving rise to irreversible phenomena in a system remain time-invariant, whereas the properties of the surroundings change. We now render this idea more precise by introducing Prigogine s Theorem Let irreversible processes take place through imposition of n forces X, X2,. ,X that result in n fluxes J, Ji,---, Jn- Let the first k forces remain fixed at values Xj, X ,..., then it is claimed that the rate of entropy production 0 is minimized when the fluxes Jk+i Jk 2, Jn ah vanish. We first prove the theorem and then discuss its relevance to steady state conditions. As before, we set 9 = Jj Xj, to construct the phenomenological... 

Examine more closely the proof of Prigogine s theorem and make due allowance for the fact that one must deal properly with vectorial quantities. This may be done by putting the relations into component forms. 

This value of cr would correspond to steady-state value, since it is minimum according to Prigogine s theorem. The values of for different steady states are summarized in Table 4.1. 

Steady-state conditions obtain when the fluxes and forces giving rise to irreversible phenomena in a system remain time-invariant, while the properties of the surroundings change. We render this concept more precise by introducing Prigogine s theorem let irreversible processes take place... 

MSN. 112. T. Petrosky and II. Prigogine, Poincare s theorem and unitary transformations for classical and quantum systems, Physica, 147A, 439 60 (1987). 

The term Extensive Phase Rule is our own terminology, and may prove confusing to geochemists more used to seeing it referred to as Duhem s Theorem. As expressed by Prigogine and Defay (1965), p. 188, Duhem s Theorem says... 

Here, Aj are intermediate compounds, and S is a solvent molecule. Show the relationship between chemical potentials and concentrations of the reaction intermediates S in the stationary mode of the process. Write the expression for the rate of entropy production. Formulate the Prigogine theorem on the rate of entropy production in the stationary state for the case of the given system. To what extent is this theorem apphcable for the given system at the temperature 300 K if the affinity of stepwise reaction R <— P equals 2 kJ/mol 30 kJ/mol ... 

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