Entropic considerations on the Two-Capacitor Problem

TL;DR

This paper explores the thermodynamic aspects of the Two Capacitor Problem using the Free Electron Gas Model, revealing entropy increase and irreversibility during discharge.

Contribution

It introduces a thermodynamic analysis of the Two Capacitor Problem, focusing on entropy and irreversibility using a quantum statistical model.

Findings

Discharge process results in positive entropy change.

The process is confirmed to be thermodynamically irreversible.

Energy exchange with a heat reservoir is integral to the analysis.

Abstract

In the present work we study the well-known Two Capacitor Problem from a new perspective. Although this problem has been thoroughly investigated, as far as we know there are no studies of the thermodynamic aspects of the discharge process. We use the Free Electron Gas Model to describe the electrons' energy levels in both capacitors in the low temperature regime. We assume that the capacitors and the resistor can exchange energy freely with a heat reservoir. We assume that the resistance is large enough to consider an isothermal heat exchange between the resistor and the heat reservoir. Thereby we obtain a positive entropy variation due to the discharge process, corroborating its irreversibility.