Evaluating the Gouy-Stodola Theorem in Classical Mechanic Systems: A Study of Entropy Generation

TL;DR

This paper investigates the application of the Gouy-Stodola theorem to a simple pendulum, analyzing how entropy generation relates to energy dissipation under non-conservative forces.

Contribution

It demonstrates the connection between entropy generation and energy dissipation in a classical mechanical system using the Gouy-Stodola theorem.

Findings

Entropy generation is zero in ideal conservative systems.

Non-conservative forces increase entropy generation proportional to energy dissipation.

Greater non-conservative force strength leads to higher entropy variation.

Abstract

We propose to apply the entropy generation $(\dot S_{gen}$) concept to a mechanical system: the well-known simple pendulum. When considering the ideal case, where only conservative forces act on the system, one has $\dot S_{gen}=0$, and the entropy variation is null. However, as shall be seen, the time entropy variation is not null all the time. Considering a non-conservative force proportional to the pendulum velocity, the amplitude of oscillations decreases to zero as $t$ grows. In this case, $\dot S_{gen}>0$ indicates that it is related to energy dissipation, as stated by the Gouy-Stodola theorem. Hence, as shall be seen, the greater the strength of the non-conservative force, the greater are both the energy dissipation and the time rate of entropy variation.