Joaquim Anacleto

Thermodynamical interactions: subtleties of heat and work concepts

This paper focuses on the determination of the final equilibrium state when two ideal gases, isolated from the exterior and starting from preset initial conditions, interact with each other through a piston. Depending on the piston properties, different processes take place and also different sets of equilibrium conditions must be satisfied. Three cases are analysed, namely, when (case 1) the piston is a heat conductor and free to move, (case 2) the piston allows heat conduction but its position is fixed, and (case 3) the piston is free to move but it is adiabatic (so no heat can be exchanged). Cases 1 and 2 have straightforward solutions, but it is shown that case 3 leads to an undeterminable final state. Even though this last situation seems to be strange and difficult, mechanical and thermodynamical analyses are performed. It is shown that the determinability of the final state depends on whether friction is considered or not. Carried out numerically, both analyses provide consistent results and not only do they enable an interesting and useful discussion regarding the concepts of energy, heat, work and entropy, but they also reinforce some ideas which were recently published.

Dissipative work in thermodynamics

This work explores the concept of dissipative work and shows that such a kind of work is an invariant non-negative quantity. This feature is then used to get a new insight into adiabatic irreversible processes; for instance, why the final temperature in any adiabatic irreversible process is always higher than that attained in a reversible process having the same initial state and equal final pressure or volume. Based on the concept of identical processes, numerical simulations of adiabatic irreversible compression and expansion were performed, enabling a better understanding of differences between configuration and dissipative work. The positive nature of the dissipative work was used to discuss the case where the dissipated energy ends up in the surroundings, while the invariance of such work under a system–surroundings interchange enabled the resulting modification in thermodynamical quantities to be determined. The ideas presented in this study are primarily intended for undergraduate students with a background in thermodynamics, but they may also be of interest to graduate students and teachers.

Work reservoirs in thermodynamics

We stress the usefulness of the work reservoir in the formalism of thermodynamics, in particular in the context of the first law. To elucidate its usefulness, the formalism is then applied to the Joule expansion and other peculiar and instructive experimental situations, clarifying the concepts of configuration and dissipative work. The ideas and discussions presented in this study are primarily intended for undergraduate students, but they might also be useful to graduate students, researchers and teachers.

On the Clausius equality and inequality

This paper deals with subtleties and misunderstandings regarding the Clausius relation. We start by demonstrating the relation in a new and simple way, explaining clearly the assumptions made and the extent of its validity. Then follows a detailed discussion of some confusions and mistakes often found in the literature. The addressed points include the issue of temperature in the Clausius relation and closely related concepts, such as heat, reversibility and reservoir. The ideas presented in this study are primarily intended for graduate students and teachers, and may also be of interest to undergraduate students with a solid background in thermodynamics.

When an adiabatic irreversible expansion or compression becomes reversible

This paper aims to contribute to a better understanding of the concepts of a reversible process and entropy. For this purpose, an adiabatic irreversible expansion or compression is analysed, by considering that an ideal gas is expanded (compressed), from an initial pressure Pi to a final pressure Pf, by being placed in contact with a set of N work reservoirs with pressures decreasing (increasing) in a geometric or arithmetic progression. The gas entropy change ΔS is evaluated and it is clearly shown that ΔS > 0 for any finite N, but as the number of work reservoirs goes to infinity the entropy change goes to zero, i.e. the process becomes reversible. Additionally, this work draws attention to the work reservoir concept, which is virtually ignored in the literature, and to its analogy with the commonly used heat reservoir concept. Finally, it complements and reinforces an earlier study dealing with irreversible cooling or heating so that the synergy created by the two studies is important from both theoretical and educational standpoints.

From free expansion to abrupt compression of an ideal gas

Using macroscopic thermodynamics, the general law for adiabatic processes carried out by an ideal gas was studied. It was shown that the process reversibility is characterized by the adiabatic reversibility coefficient r, in the range 0 ≤ r ≤ 1 for expansions and r ≥ 1 for compressions. The particular cases of free expansion and reversible adiabatic processes correspond to r = 0 and r = 1, respectively. To conclude the interpretation of r, the relation between r and the variation of the system entropy was also obtained. Comparison between this study and one restricted to expansions following a microscopic point of view showed not only equivalent interpretations but also that our approach is more general, since it also comprises compressions, provides an objective relation between r and entropy change and considers instantaneous varying values of the adiabatic reversibility coefficient. Finally, simulations of selected adiabatic processes are performed and numerical calculations of r are presented. This paper is intended primarily for the undergraduate student, although a comparison with the aforementioned work also requires a background in thermodynamics and kinetic theory.

Ampère–Maxwell law for a conducting wire: a topological perspective

The integral form of Ampere–Maxwells law for an arbitrarily-shaped wire is recast from a topological perspective, eliminating the need to use conduction current and displacement current terms to determine the magnetic field circulation around an arbitrarily-shaped loop. A generalized flux of the electric field is defined, enabling Ampere–Maxwells law for magnetic field circulation to be written in a form which parallels that in the absence of conduction current. It is hoped that this work has educational interest since it provides an example of how topology can simplify the formulation of physical laws. The ideas presented herein are primarily intended for undergraduate students of electromagnetism, but may also be of interest to graduate students and teachers.

Sobre a primeira lei da termodinâmica: as diferenciais do calor e do trabalho

We treat some subtleties concerning the First Law of Thermodynamics and discuss the inherent difficulties, namely the interpretation of the heat and the work differentials. By proposing a new differential equation for the First Law, which is written using both system and neighborhood variables, we overcome the mentioned difficulties and establish a criterion for the definition of heat and work.

Entropy change of an ideal gas determination with no reversible process

As is stressed in literature [1], [2], the entropy change, DS, during a given irreversible process is determined through the substitution of the actual process by a reversible one which carries the system between the same equilibrium states. This can be done since entropy is a state function. However this may suggest to the students the idea that this procedure is mandatory. We try to demystify this idea, showing that we can preserve the original process. Another motivation for this paper is to emphasize the relevance of the reservoirs concept, in particular the work reservoir, which is usually neglected in the literature2. Starting by exploring briefly the symmetries associated to the first law of Thermodynamics, we obtain an equation which relates both the system and neighborhood variables and allows entropy changes determination without using any auxiliary reversible process. Then, simulations of an irreversible ideal gas process are presented using Mathematica©, which we believe to be of pedagogical value in emphasizing the exposed ideas and clarifying some possible misunderstandings relating to the difficult concept of entropy [4].

Symmetry of the adiabatic condition in the piston problem

This study addresses a controversial issue in the adiabatic piston problem, namely that of the piston being adiabatic when it is fixed but no longer so when it can move freely. It is shown that this apparent contradiction arises from the usual definition of adiabatic condition. The issue is addressed here by requiring the adiabatic condition to be compatible with the invariance of total entropy under a system–surroundings interchange. This paper also strengthens some recently published ideas concerning the concepts of heat and dissipative work, and is primarily intended for teachers and graduate students, as well as for all who are interested in this fascinating problem.