Effect of space charge and nonuniform temperature on a solid state galvanic cell
Abstract The complete set of differential equations of nonequilibrium thermodynamics has been solved for a solid state galvanic cell consisting of single electrolyte sandwiched between electrodes. Electroneutrality is not assumed anywhere, and it is therefore possible to assess the effects of nonzero space charge in the electrolyte near the electrodes. A special transformation of concentration variables into a neutral part and a charge part facilitates both the analytical and the numerical solution of the mathematical problem. Formulas are obtained for the electric field, the ionic concentration, the space charge, the cell potential, and the efficiency of the cell at steady state. Inclusion of appropriate temperature gradient terms in all equations permits evaluation of the effects of nonuniform temperature on all cell properties including efficiency. For specificity, numerical results are obtained for the particular galvanic cell consisting of cerium oxide doped with calcium oxide as the electrolyte contained between oxygen electodes. Efficiency is enhanced — more current is produced with less ohmic loss — if the product Q ∗ (ΔT) is negative, with Q ∗ the heat of transport of the electrolyte and ΔT the temperature difference between the cathode and the anode.