The enthalpic contribution is calculated for the whole solid-solvent in the CC carbonized without treatment acid, with values between -0.12 and 2.78 J with an opposite behavior to that of the ion Ni(II) enthalpic contribution in the mixture, complying with the Gibbs-Duhem equation
Direct Solution of the Isothermal Gibbs-Duhem Equation
for Multicomponent Systems.
The graduate textbook covers the Gibbs-Duhem equation
, temperature-composition diagrams, configurational entropies, Helmholtz energy minimization, total Gibbs energy, Ellingham diagrams, and analytical representation of thermodynamic properties.
(3) is not consistent with restrictions given by Gibbs-Duhem equation
and by Onsager's reciprocity relations.
together with the differential [dg.sup.E] from Equation (3) and the Gibbs-Duhem equation
in the form (Sandler, 1999c):
In his first thesis Duhem had shown the usefulness of the concept of thermodynamic potential, and he deduced what is now known as the Gibbs-Duhem equation
. In the following years he consolidated his scientific reputation, working on the interaction of electric currents, and the theory of saline solutions as well as making a rigorous analysis of the foundations of thermodynamics.