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I keep seeing entropy change (or reversible effects) and irreversible effects (Joule heating) when reading about charging and discharging of Li-ion batteries. I understand the Joule heating part (the irreversible), but I have troubles understanding the reversible effects. What's going on in the structure of the electrodes that the process is reversible? As far as I know, reversiblities come from the fact that there is no friction or other losses. If one isolates a single ion, the charging or discharging, in my interpretation, would look roughly like in the figure below:

ion leaving electrode

What happens inside the battery during this charge and discharge that would make one think of reversibility? And why is entropy important in this case? And why would a reversible process release heat?

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I think your diagram seems plausible; the physical process happening here is when charging an applied potential difference (voltage) causes lithium ions to leave the crystal lattice and migrate to the cathode. When the battery discharges, the reverse happens, and lithium ions rejoin the anode.

The definition of reversibility is the infinitesimal change in some thermodynamic quantity in the system with respect to its surroundings without increasing the entropy. The electrode is crystalline, so Li+ ions can rejoin the lattice without increasing the configurational entropy, whilst infinitesimally changing the chemical potential.

If the temperature is low enough for crystallisation to be entropically and energetically favourable with respect to dissolving, then the free energy of the system will be reduced by adding an ion to the crystal lattice. The chemical potential induced by charging causes the lithium ions to return to the anode when discharging.

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  • $\begingroup$ Thank you! Nice explanation of the process. Can you please explain why this reversible process is generating heat (more heat than the joule effect, actually)? $\endgroup$ – Physther Feb 4 '17 at 16:31
  • $\begingroup$ I think the heat generated is the heat of crystallisation. When a lithium ion rejoins the crystal lattice, the creation of new bonds releases energy. $\endgroup$ – Paraquat Feb 4 '17 at 17:22
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I think it has to do with the equation heat dq=TdS so since gibbs dG=SdT+VdP+mudN we know S or entropy is partialG partialT and also gibbs= -nFE so S=partialE partialT and heat is TdS so TpartialE partialT* nF. In short TdS is the reversible heat

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    $\begingroup$ Welcome to chemistry.se! Unfortunately this is just a bunch of formulas with no real explanation. $\endgroup$ – Martin - マーチン♦ Sep 27 at 23:32
  • $\begingroup$ I meant its called the reversible heat because the reversible heat is defined as TdS so dQrev=TdS=ITPartialEPartialT. Which is what he asked why is this term in the Bernardi Heat Generation equation called the reversible heat becz it is TdS $\endgroup$ – ChemEng Sep 27 at 23:57

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