Peltier effects in electrode carbon
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INTRODUCTION
MOST aluminum production is made in Hall–He´roult cells. According to Grjotheim et al.,[1] a typical value for the total energy consumption in the cell is 14 kWh/kgAl. In contrast, the theoretical minimum energy requirement is 7 kWh/kgAl. The aluminum industry is, hence, interested in minimizing the excess energy consumption. A method to describe this excess energy consumption is nonequilibrium thermodynamics (NT), as described by de Groot and Mazur,[2] and later by Førland et al.[3] In this work, NT will be used to calculate profiles of temperature and electrical potential through the anode coal in a Hall– He´roult cell. Once this is known, the excess energy consumption, or dissipated energy, in the anode coal can be calculated. This knowledge of the locations and sources of the dissipated energy is the first step toward reducing it. To calculate the profiles of temperature and electrical potential, a coupling coefficient between these two kinds of transport is needed. It is called the Peltier effect. If the Peltier effect is divided by temperature, the transported entropy of electric charge results. The transported entropy has been determined in several materials before, such as in salt melts, in solid salts, or in metals. In salts, the electric charge is carried by ions, and the transported entropy is typically around 100 J/(K mole). One example is the transported entropy of copper ions in liquid CuCl, determined to be 109 5 1 J/(K mole) at 900 K by Pezzati et al.[4] The transported entropy in solid salts are of the same magnitude as in molten salts, one example being the transported entropy of copELLEN MARIE HANSEN, formerly Research Assistant, Department of Physical Chemistry, The Norwegian University of Science and Technology, is Project Engineer, Prediktor, P.O. Box 296, N-1601 Fredrikstad, Norway. ESPEN EGNER, formerly Master’s Student, Department of Physical Chemistry, The Norwegian University of Science and Technology, is Project Engineer, Saga Petroleum ASA, N-1301 Sandvika, Norway. SIGNE KJELSTRUP, Professor, is with the Department of Physical Chemistry, The Norwegian University of Science and Technology, N-7034 Trondheim, Norway. Manuscript submitted November 7, 1996. METALLURGICAL AND MATERIALS TRANSACTIONS B
per ions in solid CuCl at 573 K, which was determined to be 136 5 2 J/(K mole) by Mogilevski and Usmanov.[5] R. Haase[6] and J. Agar[7] have tabulated transported entropies in several metallic conductors. One example is the transported entropy in solid silver, which was found to be 20.20 J/(K mole) at 800 K. The values for several other electronic conductors, like lead, copper, and platinum, are of the same magnitude. The determination of the transported entropy of electric charge in carbon was done in a cell where carbon was the conductor, and the electrodes were made of platinum. The Peltier effect is related to the processes taking place at the electrode-conductor interfaces, so a special form of NT (NT for surfaces) is used.[8] A preliminary form of parts of this work, relatin
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