Читать книгу Non-equilibrium Thermodynamics of Heterogeneous Systems - Signe Kjelstrup - Страница 35

In an electroneutral system, the electric current density j is independent of the frame of reference. The measurable heat flux J′q is also independent of the frame of reference. The total heat flux, the mass fluxes and the entropy flux depend on the frame of reference. In the laboratory or the wall frame of reference, we denote these fluxes by Jq, Jk and Js. In any other frame of reference, they become

(4.27)

All frames of reference defined above can be used for v_ref .

We consider in this book systems that are in mechanical equilibrium. The hydrostatic pressure is then constant and there are no shear forces. The Gibbs–Duhem’s equation for constant pressure is

(4.28)

By substituting J_q,ref, J_j,ref and J_s,ref into Eqs. (4.13)–(4.15), we find, using Gibbs–Duhem’s equation, that the term proportional to v_ref gives a zero contribution to the entropy production. This result is Prigogine’s theorem [23].

Gibbs–Duhem’s equation gives a possibility to eliminate a thermodynamic force. Galilean invariance gives a possibility to eliminate a mass flux. One property is a consequence of the other, as we have seen above. De Groot and Mazur [23] used systematically the barycentric frame of reference, because they also treated hydrodynamic phenomena. In this frame of reference, the sum of the mass (diffusion) fluxes is zero, see above. The total heat flux J_q,bar equals the heat flux Jq used by de Groot and Mazur.