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

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.