The “Vicious Cycle” in Secondary Batteries—A Mathematical Approach

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Abstract
Equations relating voltage, temperature, heat capacity, time, and current have been derived for a cell on constant‐potential charge. Assuming the cell to be fully charged and thermally isolated from its surroundings, thereby retaining all of the electrical energy supplied to it, the equations derived are and where is the current, the time, the absolute temperature, the applied voltage, the voltage corresponding to the fraction of the electrical energy converted into chemical energy, the activation energy for the electrode reaction, α the transfer coefficient, η the activation overpotential, and To the initial current and temperature, respectively, and the heat capacity of the cell. The equations have been verified experimentally. The case where cooling occurs is also considered.

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