Gibbs’ vector relations

Furthermore, it is noted that the first three terms in the brackets on the RHS of (2.452) are similar to the terms in the Gibbs-Duhem relation (2.451). However, two of these three terms do not contribute to the sum. The pressure term vanishes because js = 0. The two enthalpy terms obviously cancel because they are identical with opposite signs. Moreover, the last term in the brackets on the RHS of (2.452), involving the sum of external forces, is zero = 0- Oue of the two remaining terms, i.e., the one containing the enthalpy, we combine with the q term. Hence, the modified entropy flux vector (1.171) and production terms (1.172) become ... 

Let us find the vector Xjj orthogonal to the hypersurface of the phase transition at point D in the space of the ehemieal potentials. The Gibbs-Duhem relations (32) at constant temperature, on the gas and on the liquid sides of the phase transition, may be expressed as follows ... 

The starting point for the rigorous derivation of the diffusive fluxes in terms of the activity is the entropy equation as given by (1.174), wherein the entropy flux vector is deflned by (1.175) and the rate of entropy production per unit volume is written (1.176) as discussed in Sect. 1.2.4. To eliminate S from the Gibbs-Duhem relation formulated in terms of specific quantities (2.324) we need the definitions of H = mH and G = mG ... 

This equation shows the pressure difference Ap needed to keep two phases in mechanical equilibrium, if the interface has a radius of curvature r. One shoidd distinguish here between thermodynamic equilibrium and mechanical equilibrium. The former is defined by the condition of minimum Gibbs energy of the system. The latter represents the condition that the vector sum of all forces acting on the interface is zero. When the interface is flat, r goes to infinity and Ap 0. In the present example, the pressure in each capillary is related to the height of the liquid, since... 

---