Читать книгу Non-equilibrium Thermodynamics of Heterogeneous Systems - Signe Kjelstrup - Страница 16

The entropy balance of the system and the expression for the entropy production can be used for control of the internal consistency of the thermodynamic description. The change of the entropy in a volume element in a homogeneous phase is given by the flow of entropy in and out of the volume element and by the entropy production inside the element:

(2.18)

where we take the entropy flux in the x-direction. In the stationary state, there is no change in the system’s entropy density, s, and

(2.19)

By integrating over the system’s extension, keeping its cross-sectional area Ω constant, we obtain

(2.20)

The left-hand side is obtained from σ, which is a function of transport coefficients, fluxes and forces, Eqs. (1.1)–(1.3). The right-hand side of this equation, the difference in the entropy flows J_s^o − J_sⁱ, can be calculated from the knowledge of the heat flux, and of the entropy carried by components into the surroundings. These quantities do not depend on the system’s transport properties. The two calculations must give the same result. Chapter 19 gives an example of such a comparison. Other examples were given by Kjelstrupet al. [32], see also Zvolinschi et al. [95].