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Equivalence of the Kelvin–Planck statement of the second law and the principle of entropy increase
Abstract
We present a demonstration of the equivalence between the Kelvin-Planck statement of the second law and the principle of entropy increase. Despite the fundamental importance of these two statements, a rigorous treatment to establish their equivalence is missing in standard physics textbooks. The argument is valid under very general conditions, but is simple and suited to an undergraduate course.
... Once aware that the temperature T e in (1) is that of the heat reservoir with which the system exchanges the heat dQ, the principle of entropy increase can effectively be derived from the Clausius relation. The procedure is as shown in [1]. Consider a given system A undergoing a reversible or irreversible process i f followed by a reversible one f i leading A back to its initial state, during which the system entropy change -S S i f is given by ...
... becomes the mathematical formulation of the principle of entropy increase [1,6]: ...
... Even though the Clausius relation leads to the principle of entropy increase, a demonstration of the equivalence between this principle and the Kelvin-Planck statement of the second law is meritorious. Sarasua and Abal [1] would have fully achieved that goal if they had not imposed the total insulation of the system in process i f, having thus obtained an incomplete demonstration. In fact, from (3) and as Mello and Rodríguez [6] pointed out, only thermal insulation (d = Q 0) [8] is required to obtain (4) from (3), and thus there is no need for mechanical insulation: work can be exchanged with surroundings. ...
This comment addresses the paper by Sarasua and Abal (2016 Eur. J. Phys. 37 055103). Driven by an incorrect interpretation of the Clausius relation, those authors demonstrated the equivalence of the Kelvin-Planck statement of the second law and the principle of entropy increase. In addition to the necessary clarification of the Clausius relation, we propose an improved version of the demonstration made in the aforementioned paper, since the one carried out therein is restrictive. Our aim is to clarify issues that, being didactically and pedagogically relevant, are also subtle.
... This is a reply to the comment by Anacleto on our recently published work [1]. Although Anacleto asserts that the demonstration of the equivalence between the Kelvin-Planck statement of the second law and the principle of entropy increase is meritorious, he criticizes the work in the following two aspects. ...
... Although Anacleto asserts that the demonstration of the equivalence between the Kelvin-Planck statement of the second law and the principle of entropy increase is meritorious, he criticizes the work in the following two aspects. First, he states that the demonstration proposed in [1] is incomplete, because we imposed the total insulation of the system to formulate the second law. Second, he asserts that our criticism about the derivation of the principle of entropy increase found in common textbooks is inappropiate because the temperature that appears in the Clausius relation is the temperature of the heat reservoir, instead of the temperature of the system. ...
... Non-bonding energy changes in the models over time: (a) ungrafted model; (b) grafted model. FIG. 4. Total energy changes in the models over time: (a) ungrafted model; (b) grafted model.energy of the system gradually increased with increasing temperature, which is consistent with the principle of entropy increase.36 ...
In order to improve the thermal stability of insulation paper cellulose in micro-water environment, the molecular simulation was used to compare and analyze the thermal stability of polysiloxane-grafted cellulose with 3% micro-water content in the present study. The static mechanics, glass transition temperature and number of hydrogen bonds are used to characterize the thermal stability of insulating paper cellulose in this paper. First, analysis of the mechanical properties of the model demonstrated that the value of the elastic moduli (E) and bulk moduli (K) of the grafted model were greater than those of the ungrafted model at each temperature. Second, the glass transition temperature of the grafted model was 60 K higher than that of the ungrafted model. Finally, the analysis of the radial distribution function (RDF) and hydrogen bonding showed that polysiloxane-grafted insulation paper cellulose can reduce the number of hydrogen bonds formed between the water molecules and the cellulose chains, which can reduce the damage caused to the cellulose chains by the water molecules. Therefore, the present study shows that the polysiloxane-grafted insulation paper cellulose can improve its thermal stability in micro-water environment.
We discuss the representation of thermodynamic processes in diagrams. Although the idea that it is impossible to represent non-quasistatic processes is correct and consensual, it is surprising that we sometimes find in the literature such processes represented somehow, in contradiction with, for instance, the concept of equilibrium state. At other times, the justification given for process representation does not help clarify the difference between reversible and quasistatic processes. In this paper we address the errors inherent to such procedures and also, paradoxically, propose the representation of non-quasistatic processes using the concept of identical processes.
Encouraging ‘active learning’ in the large lecture theatre emerges as a credible recommendation for improving university courses, with reports often showing significant improvements in learning outcomes. However, the recommendations are based predominantly on studies undertaken in mechanics. We set out to examine those claims in the thermodynamics module of a large first year physics course with an established technique, called interactive lecture demonstrations (ILDs). The study took place at The University of Sydney, where four parallel streams of the thermodynamics module were divided into two streams that experienced the ILDs and two streams that did not. The programme was first implemented in 2011 to gain experience and refine logistical matters and repeated in 2012 with approximately 500 students. A validated survey, the thermal concepts survey, was used as pre-test and post-test to measure learning gains while surveys and interviews provided insights into what the ‘active learning’ meant from student experiences. We analysed lecture recordings to capture the time devoted to different activities in a lecture, including interactivity. The learning gains were in the ‘high gain’ range for the ILD streams and ‘medium gain’ for the other streams. The analysis of the lecture recordings showed that the ILD streams devoted significantly more time to interactivity while surveys and interviews showed that students in the ILD streams were thinking in deep ways. Our study shows that ILDs can make a difference in students’ conceptual understanding as well as their experiences, demonstrating the potential value-add that can be provided by investing in active learning to enhance lectures.
In order to undestand how the complex concept of entropy emerged,we propose a
trip towards the past reviewing the works of Clausius, Boltzmann, Gibbs and
Planck. In particular, since the Gibbs's work is not very well known, we
present a detailed analysis, recalling the three definitions of the entropy
that Gibbs gives. May be one of the most important aspect of the entropy is to
see it as a thermodynamic potential like the other thermodynamic potentials as
proposed by Callen. We close with some remarks on entropy and irreversibility.