Non-equilibrium Thermodynamics of Heterogeneous Systems. Signe Kjelstrup
velocities calculated using only neutral components and the one calculated using charged components. As we do not use fluxes in the barycentric frame of reference in this book, this does not lead to any complications in our analysis.
Also the measurable heat flux is different in the two descriptions. We have
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(4.49) |
The difference is the enthalpy of the charge carrier carried along by the electric current. We note that Jq and Js, both in the laboratory frame of reference, are the same whether one uses charged or uncharged components. In view of the fact that hCl− is not measurable, it is appropriate to call Jq′,uncharged as measurable. De Groot and Mazur named Jq′,charged the reduced heat flux.
Finally, we show, again for the same example, that both descriptions give the same entropy production. To simplify the system further we neglect the contribution due to the displacement current. This is the case considered by de Groot and Mazur [23] in Chapter XIII. On p. 344 in Eq. (40), they give the entropy production in a system with no magnetic field,
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(4.50) |
In the analysis of de Groot and Mazur, all fluxes are in the barycentric frame of reference. For a system in mechanical equilibrium, one may replace all of them by their value in the laboratory frame of reference. The difference is a term which is zero, according to Gibbs–Duhem’s equation. The fact that the expression is correct in an arbitrary frame of reference if the system is in mechanical equilibrium, is called Prigogine’s theorem [18]. Using Eq. (4.41) for the ion fluxes, we obtain
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(4.51) |
This is the expression we gave in Eq. (4.14) for the case that there is no polarization and no chemical reaction.
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