Continuum physics by Peter Hertel

By Peter Hertel

Stability Equations -- fabric Equations -- Linear reaction concept -- Examples

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We shall discuss this effect later in the section on charge transport. There are more sources of internal energy production, for instance by radioactivity. Here we concentrate on a relation between the heat current density J u and other fields which will drive it. Let us assume a situation without electric fields and without concentration gradients first. Thermodynamic equilibrium is characterized by constant pressure, constant temperature, constant electric potential and constant chemical potentials.

Entropy also flows if there is a heat current. The heat current is weighted by the inverse temperature. The smaller the temperature, the more entropy is conducted. The third term on the right hand side of Eq. 123) says that entropy is also transported by diffusion. A diffusion current is weighted by the ratio of negative chemical potential and temperature. The volumetric production rate of entropy will be discussed in the following subsection. It is more than an expression of fields which we have introduced before.

Recall that the amount of NA particles is a mole4 in terms of chemistry. R D NA kB is the universal gas constant,5 M D NA m the average molar mass. With this Eq. 10) R is the universal gas constant. Pressure p, temperature T and mass density % are fields. 3 Newtonian Fluid Medium The dissipative contribution Ti 00k must be a symmetric tensor which behaves nonstandard under time reversal. It describes friction. There is no friction if neighboring material points travel with the same velocity. Hence, the dissipative contribution to the stress tensor will depend on velocity gradients.

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