The entropy production rate for a distillation column is a t a minimum when the driving forces for separation are uniformly distributed along the column. This theoretical result was derived for separation of binary mixtures having linear flux-force relations with coefficients which vary with temperature and composition. The entropy production rate was first calculated numerically for separation of a n ideal and a nonideal mixture. The application of the principle, called the principle of equipartition of forces, was then demonstrated by analyzing the effect of distributed heating in a column with a n ideal mixture. A reduction in the entropy production rate per m3 of product formed of up to 7% was found for the system plus surroundings, after seeking equipartition of forces with minimum changes in the apparatus.Abstract published in Advance A C S Abstracts, June 15, 1995.
A new method for modeling electrode surfaces, applied to aluminum electrolysis, is presented. The method uses nonequilibrium thermodynamics for surfaces and describes the fluxes, the overpotential, and the dissipated energy at the surfaces in a new way. Examples are given for the interface anode-and cathode-bath to show how the model may be used to predict surface properties based on observed phenomena and the total energy dissipated in the cell. The method predicts apparent discontinuities at the surfaces in electrical properties, as well as in temperature and in chemical potentials. The overpotential is viewed as a discontinuity in electrical potential. Local surface heating or cooling effects can be simulated, and the results can be used to estimate surface properties. The calculations show that excess surface temperatures of magnitude 0.1 K can occur under certain surface conditions. If the excess surface temperature is of magnitude 1 to 10 K, unrealistically high dissipated energy at the surfaces results. At the anode surface, electrical conductivities as small as l0 times their respective bulk values lead to the measured value for anodic overpotential. Even smaller conductivities lead to larger overpotentials, and a typical anode effect value results if the electrical conductivities are smaller than io times their respective bulk values.
The thermoelectric power of a cell with platinum electrodes and a carbon conductor was determined. The electromotive force (emf) was measured as a function of the temperature difference between the electrodes at temperatures varying from 310 ЊC to 970 ЊC. From these measurements, the transported entropy of electric charge in carbon was found to vary from Ϫ1.7 to Ϫ1.9 J/(K mole) at temperatures around 300 ЊC, from Ϫ2.0 to Ϫ2.3 J/(K mole) at temperatures around 550 ЊC, and from Ϫ3.4 to Ϫ3.7 J/(K mole) at temperatures around 950 ЊC. This transported entropy had not before been determined for temperatures above 550 ЊC. Also, it is shown how the previously neglected surface properties can be taken into account to interpret the measurements. In the Hall-Héroult cell, the anode is made of a similar kind of carbon. Hence, the transported entropy found above can be used to describe the often neglected coupling between transport of heat and electric charge in this electrode. It is shown that the calculated electric potential profile through a coal sample will change significantly if the coupling is neglected, but the calculated temperature profile is independent of whether the coupling is neglected. New equations are also developed that can be used to evaluate the importance of the coupling in other systems.
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