Joule heating rate need not equal I2R, where R is the Ohmic resistance: The case of voltaic cells
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The electrolyte within a charging or discharging voltaic cell, carrying current [Formula Presented] has time-dependent carrier densities. Therefore the energy conservation argument that equates the total rate of Joule heating P to the rate of decrease of electrical energy is inappropriate because it neglects changes in chemical energy. Explicit study of two systems (the lead-acid cell and the Zn-Cu cell) shows that the Joule heating resistance [Formula Presented] differs from the Ohmic resistance [Formula Presented][Formula Presented] is the voltage drop across the electrolyte). [Formula Presented] can be greater than or less than unity. [Formula Presented] involves only the current-carrying ions, whereas [Formula Presented] involves all of the ions. 1999 The American Physical Society.
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