Entropic considerations in the two-capacitor problem

Abstract

We study the well-known two-capacitor problem from a new perspective, focusing on the thermodynamic aspects of the discharge process. The free electron gas model is used to describe the electrons' energy levels in both capacitors in the low temperature regime. We assume an isothermal heat exchange between the resistor and the heat reservoir. Even in this limiting case, we obtain a positive entropy variation due to the discharge, which points out the irreversibility of this process. Keywords: two-capacitor problem, entropy.Estudamos o problema bem conhecido dos dois capacitor através de uma nova perspectiva, com foco nos aspectos termodinâmicos do processo de descarga. O modelo de gás de elétrons livresé usado para descrever os níveis de energia dos elétrons nos dois condensadores no regime de baixas temperaturas. Consideramos uma troca de calor isotérmica entre o resistor e o reservatório térmico. Mesmo nesse caso limite, obtém-se uma variação positiva da entropia devidoà descarga, apontando o caráter irreversível desse processo. Palavras-chave: problema de dois capacitores, entropia.

On the Dynamics of Transition of a Classical System to Equilibrium State

“…In such systems, energy dissipation or energy transfer is a crucial quantity for the system to be able to undergo a transition from non-equilibrium to final equilibrium state [9] [10] [11] [12] [13]. A well-known system which demonstrates the role and mechanisms of energy dissipation during its transition from a non-equilibrium to an equilibrium state is the two-capacitor problem which has been under investigation by many authors [14]- [21]. Classical systems, which involve energy dissipation in their transition from non-equilibrium to equilibrium state, have re-cently attracted much attention of many authors [22] [23] [24] [25] [26].…”

Fourier-Series Representation of Discontinuous Functions and Its Physical Applications

“…this problem[29] [30] [31][32]. The essence of the problem amounts to the problem of charging a capacitor of capacitance C by a power supply of electromotive force 0 V with a series resistor of resistance R. At the end of charging, the energy stored in the capacitor will be dissipated regardless of the value of R. In ref [30],.…”