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# Journal of Non-Equilibrium Thermodynamics

Founded by Keller, Jürgen U.

Editor-in-Chief: Hoffmann, Karl Heinz

Managing Editor: Prehl, Janett / Schwalbe, Karsten

Ed. by Michaelides, Efstathios E. / Rubi, J. Miguel

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1437-4358
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# A Symmetric Van ’t Hoff Equation and Equilibrium Temperature Gradients

D. P. Sheehan
Published Online: 2018-06-21 | DOI: https://doi.org/10.1515/jnet-2017-0007

## Abstract

Thermodynamically isolated systems normally relax to equilibria characterized by single temperatures; however, in recent years several systems have been identified that challenge this presumption, demonstrating stationary temperature gradients at equilibrium. These temperature gradients, most pronounced in systems involving epicatalysis, can be explained via an underappreciated symmetry in the Van ’t Hoff equation.

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For the sake of illustration, let the number of epicatalytically active surface sites on S1 and S2 be ${\mathit{\sigma }}_{\ast }={10}^{16}\text{ }{\text{m}}^{-2}$ and the reaction energy be $\mathrm{\Delta }\mathit{E}=0.5\text{ }\text{eV}=8×{10}^{-19}\text{ }\text{J}$, typical of hydrogen-bonded dimers like methanol and formic acid [37]. Let the average cycling time ${\mathit{\tau }}_{\mathit{c}}$ be the thermal transit time for room-temperature 100 amu molecules (typical for volatile species) to cross the S1–S2 gap of thickness 10−6 m, that is, ${\mathit{\tau }}_{\mathit{c}}\simeq \frac{{\mathit{x}}_{\mathit{g}}}{{\mathit{v}}_{\mathit{t}\mathit{h}}}\simeq {10}^{-8}\text{ }\mathrm{s}$. With these, the areal power density for the STG device is estimated to be $\mathcal{P}\simeq {10}^{6}\text{ }{\mathrm{W}\mathrm{/}\mathrm{m}}^{2}$. This, of course, will be reduced by unavoidable convective, radiative, and conductive backflows.

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Revised: 2018-05-25

Accepted: 2018-05-28

Published Online: 2018-06-21

Citation Information: Journal of Non-Equilibrium Thermodynamics, ISSN (Online) 1437-4358, ISSN (Print) 0340-0204,

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