Use of the Gouy–Stodola Theorem in Classical Mechanic Systems: A Study of Entropy Generation in the Simple Pendulum

Abstract

Both classical mechanics and thermodynamics live in the core of physics. They are two different aspects of the same thing, one can say. The thermodynamic equivalent of a mechanical system is one of the main achievements of the 19th century. Regarding only thermodynamics, the introduction of entropy, roughly defined in many textbooks as the unuseful energy present in a physical system, is a victory of Rudolf Clausius. Unlike energy, entropy can be produced in a physical system under certain conditions. We can act to increase the degree of disorder (statistical mechanics) in a physical system. Here, we propose to apply the entropy generation [Formula: see text]) concept to the simple pendulum by using a very unknown result: the Gouy–Stodola theorem. When considering the ideal case, where only conservative forces act on the system, one has [Formula: see text], and the entropy variation is null. However, as shall be seen, the entropy variation is not null all the time. Considering a nonconservative force proportional to the pendulum velocity, the amplitude of oscillations decreases to zero as [Formula: see text] grows. Then, [Formula: see text] may be related with the energy dissipation, as stated by the Gouy–Stodola theorem. Hence, as shall be seen, the greater the strength of the nonconservative force, the greater are both the energy dissipation and the time rate of entropy variation.