Reversible heating in electric double layer capacitors

TL;DR

This paper compares different models of reversible heating in electric double layer capacitors, showing that a combined Poisson-Nernst-Planck and heat equation aligns with thermodynamic predictions in slow charging conditions, challenging previous approximative models.

Contribution

It demonstrates that a coupled Poisson-Nernst-Planck and heat equation accurately predicts temperature changes, clarifying the thermodynamic consistency of reversible heating models in capacitors.

Findings

The combined model recovers thermodynamic predictions in slow charging limit.

It shows disagreement with the prevalent approximative model in literature.

The study clarifies the theoretical understanding of reversible heating in capacitors.

Abstract

A detailed comparison is made between different viewpoints on reversible heating in electric double layer capacitors. We show in the limit of slow charging that a combined Poisson-Nernst-Planck and heat equation, first studied by d'Entremont and Pilon [J. Power Sources {\bf 246}, 887 (2014)], recovers the temperature changes as predicted by the thermodynamic identity of Janssen, H\"{a}rtel, and van Roij [Phys. Rev. Lett. {\bf 113}, 268501 (2014)], and disagrees with the approximative model of Schiffer, Linzen, and Sauer [J. Power Sources {\bf 160}, 765 (2006)] that predominates the literature.