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- Herausgeber: Bentham Science Publishers
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
The second law of thermodynamics is an example of the fundamental laws that govern our universe and is relevant to every branch of science exploring the physical world. This reference summarizes knowledge and concepts about the second law of thermodynamics and entropy. A verbatim explanation of chemical thermodynamics is presented by the author, making this text easy to understand for chemistry students, researchers, non-experts, and educators.
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Seitenzahl: 421
Veröffentlichungsjahr: 2017
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An Account Of Thermodynamic
Entropy
Authored by:
Alberto Gianinetti
BENTHAM SCIENCE PUBLISHERS LTD.
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Preface
The second law of thermodynamics is one of the most fundamental laws that govern our universe and is relevant to every scientific field studying the physical world. Nonetheless, the second law’s application makes constant reference to entropy, one of the most difficult concepts to work with, and this is the reason why they are discussed almost exclusively in highly specialized literature.
Thermodynamic entropy has been rigorously examined by classical, statistical, and quantum mechanics, which provide several mathematical expressions for calculating it under diverse theoretical conditions. However, the concept of entropy is still difficult to grasp for students and even more for educated laymen. As a scientist in plant biology, I fall into the second category with regards to this subject. Indeed, I first wrote this introductory book for myself; to approach my work with greater awareness about its physicochemical implications, I felt I needed better insight into the thermodynamic considerations that underpin spontaneous processes and allow plants, as well as humans, to achieve and improve the capability to exploit the environment to their benefit. When I consulted the literature on this topic, I found that although there are very many papers and books on the subject, the thorough explanation that I was looking for was scattered throughout them. I then began taking notes, and when I was finally satisfied I realized that, once organized and suitably presented, they were potentially interesting for other people looking for detailed, but not too advanced, clarifications on entropy and the second law of thermodynamics. I believe that a better understanding of these concepts requires a more satisfactory verbal explanation than is generally provided, since, in my opinion, a verbal approach is the one closer to the understanding capability of students and non-experts. This is why this book is focused on providing a verbal account of entropy and the second law of thermodynamics. In this sense, I deem that, beside to the basic mathematical formulations, a consistent explanation in verbal terms can be very useful for the comprehension of the subject by people who do not have a full understanding of it yet. Thus, I eventually came out with the present work, targeted to students and non-experts who are specifically interested into this matter and have a basic knowledge of mathematics and chemistry.
With this book I attempt to offer an account of thermodynamic entropy wherein verbal presentation is always a priority. Basic formal expressions are utilized to maintain a rigorous scientific approach to the matter, though I have always tried to explain their meaning. The essential outlines for a verbal account of thermodynamic entropy are summarized in the last chapter. Such an outline is how I wish I had been taught the core concepts of this matter when I was first introduced to it. Therefore, I hope it can be of help for a general introduction to the second law of thermodynamics and the basic concept of entropy. The main text of the present work aims to demonstrate the validity of the proposed verbal presentation from a rigorous, scientific point of view, but it also represents a resource for insights on specific topics since the verbal approach is adopted throughout the text. Several examples illustrate the concept of entropy in its different expressions. A number of notes provide further clarification or insight into the content in the main text and the reader may skip them on a first reading.
With regard to the contents of the this work, I have highlighted that the best way to conceive thermodynamic entropy that I found in the literature was that of a function of “energy spreading and sharing” as suggested by physicist Harvey S. Leff. Herein I try to take this line of thought further to verbally unravel the concept of thermodynamic entropy and to provide a better verbal account of it. I propose that a useful definition of entropy is “a function of the system equilibration, stability and inertness”, and that the tendency to an overall increase of entropy set forth by the second law of thermodynamics should be meant as “the tendency to the most probable state”, that is, to a macroscopic state whose distribution of matter and energy is maximally probable (according to the probabilistic distributions of matter and energy, and also considering the eventual presence of constraints). Thus, with time, an isolated system settles into the most equilibrated, stable, and inert condition that is actually accessible. I have provided a wide overview to introduce the rationale for these definitions and to show that they are consistent throughout the various levels and applications of the concept of entropy. The key idea is to extract from known formal expressions of entropy the essential verbal outlines of this concept and to use them to elaborate a verbal presentation of entropy that can be of general utility to non-experts, as well as to educators.
Conflict of Interest
The authors confirm that they have no conflict of interest to declare for this publication.
Acknowledgements
Declared none.
Introduction
Alberto GianinettiAbstract
Basic concepts are defined, such as what thermodynamics aims to, what a system is, which are the state functions that characterize it, what a process is.
Thermodynamics deals with the overall properties of macroscopic systems as defined by state functions (that is, physical properties that define the state of a body) such as: internal energy, E; temperature, T; volume, V; pressure, P; and number of particles1, N. In addition to these properties, which are easy to understand, macroscopic systems are also characterized by specific values of entropy, a further state function that is more difficult to comprehend. Entropy can be calculated in many diverse theoretical conditions by several mathematical expressions; however, the concept of entropy is still difficult to grasp for most non-experts. A troublesome aspect of entropy is that its expression appears to be very different depending upon the field of science: in classical thermodynamics, the field where it was first defined, the conceptualization of entropy is focused on heat transfer; in classical mechanics, where many of the first studies were performed, entropy appears to be linked to the capability of an engine to produce work; its nature was then more precisely explained by statistical mechanics, which deals with the microscopic structure of the thermodynamic systems and studies
how their particles affect the macroscopic properties of these systems; finally, quantum mechanics, by focusing on the quantization of energy and particles states, showed that the probabilistic nature of entropy, already highlighted by statistical mechanics, is closely dependent on the non-continuous nature of the universe itself. This works aims to show that, eventually, all these different aspects of entropy, which are necessarily linked to each other, can be better understood by considering the probabilistic nature of entropy and how it affects the properties of macroscopic systems, as well as the processes by which they interact.
A first exigency is then to define a macroscopic system. According to Battino et al. [2] a system is “any region of matter that we wish to discuss and investigate”. The surroundings consist of “all other matter in the universe that can have an effect on or interact with the system”. Thus, “the universe (in thermodynamics) consists of the system plus its surroundings”. The same authors notice that “there is always a boundary between the system and its surroundings and interactions between the two occur across this boundary, which may be real or hypothetical” [2]. In any case, a thermodynamic system, which typically includes some matter, is a part of the universe that is clearly defined and distinguishable from all the other parts of the universe. The presence of solid boundaries around the system is an obvious aid in the identification of the system, but it is not a necessary one. A gas inside a vessel is traditionally seen as a good, simple thermodynamic system. An aquarium can be another quite well defined thermodynamic system, although the presence of fish and other organisms would greatly complicate its thermodynamic properties and entropy in particular. The Earth, even though it is not surrounded by solid boundaries, represents a thermodynamic system too since it is something that is clearly defined and distinguishable by the remaining universe: beyond its stratosphere there is extended empty space that separates our planet from other systems. Although some energy and matter can move through the theoretical boundary that divides the Earth from empty space, these can be precisely identified as transfers of energy and matter from/to the Earth system, which maintains its identity. It can then be immediately noted that the identification of a system is essentially a theoretical step, since the Earth can contain innumerable smaller systems, e.g. vessels containing fluid, like an aquarium, but also each cell of a fish in an aquarium is clearly an enclosed system with physical boundaries.
Hence, a system must be clearly delimited to be studied, but the rules that govern a system must also hold for any macroscopic parcel of matter with corresponding properties and conditions. Simply put, a system is just an identifiable parcel of the universe. It is worthy to note, therefore, that any parcel inside a system has, with the rest of the system, the same relationship that holds between an open system and its surroundings. So, for a system to be equilibrated it is necessary that all of its parcels, however sorted out, are equilibrated with the rest of the system, just like a thermodynamic system equilibrates with its surroundings if there is no insulating barrier between them.
What is particularly relevant to the study of entropy is that the system that is under consideration has to be macroscopic, that is, it must include a huge number of particles. This is because of the above-mentioned probabilistic nature of entropy, which can really be appreciated when, in the presence of a large number of particles, the probabilities become determining for every feature of the system; that is, the intensive state functions of the system (i.e., those that do not depend on the system size, but, rather, on the distributions of particles and energy across the system), which emerge as overall properties from the statistical average behaviours of all the constituting particles, can be sharply defined and statistical fluctuations due to random effects of the particles are so small that they can be neglected. Of course, the concept of entropy holds true for every system, including very small ones consisting of only a few particles. However, some statistical approximations and mathematical simplifications that are ordinarily used for large systems, cannot be applied when dealing with very small ones. Notably, in every system, intensive state functions like temperature, density and pressure, which are widely used to characterize large systems, can undergo instantaneous fluctuations. However, whereas such fluctuations are negligible in large systems, as we will see, they become relevant for very small ones. In fact, in very small systems, intensive state functions can attain ample inhomogeneities across the system itself, or between the system and its external environment if they are connected, even at equilibrium. Hence, very small systems cannot be accurately described by single average values for these parameters, which, thus, lose their physical meaning. The exact probabilistic distributions of particles and energy have to be considered for these systems, whose physical description requires, therefore, mathematical formulations that are much more complicate and less intuitive. So, though the verbal account of the entropy that will be provided in the last chapter is always valid, the formulations that must be used for precise quantification of entropy changes are more intuitive when large systems, like the ones we commonly are used to deal with in everyday life, are considered.
In addition, for the sake of simplicity, systems are also assumed to be at temperatures much higher than absolute zero, since some quantum effects that complicate the characterization of a macroscopic system arise at low temperatures, where the nature of the particles becomes more similar to that of a packet of waves than to an ideal, spherical, and dense unit of matter (actually, matter particles remain wavepackets even at high temperatures, but then they can be treated as if they were ideal, spherical, and dense units of matter).
Thermodynamic systems can be classified according to their capability to interact with the outside. An isolated system neither transfers energy or matter with the rest of the universe nor it changes its volume; a closed system can transfer energy to/from the outside and/or change its volume; an adiabatic system can change its volume, but cannot exchange energy or matter with the outside environment; an open system can transfer both energy and matter with the rest of the universe and can change volume too.
When studying the interaction of a thermodynamic system with its outside (obviously not in the case of an isolated system), it is important that the state functions of the system are known, and even the outside environment has to be clearly defined, since any interaction can cause a different result depending upon the conditions of the environment surrounding the system. Therefore, the state functions of the surroundings, at least those involved in the studied interaction, have to be defined as well. In many cases, temperature, pressure, or chemical potential for a given interaction must be defined for change in the system, specifically in the entropy, to be computed. Thus, the surroundings often act as a thermal reservoir that assures that the temperature remains constant. Analogously, in some processes, the pressure or the chemical potential is held constant. In this way, the interactions between a system and its surroundings can be measured and any change in the state functions can be properly accounted for. These interactions are called processes and are studied by thermodynamics to understand how the states of a system and its surroundings interact, as well as how physical processes generally occur. Clearly, in everyday phenomena, the theoretical and experimentally rigorous conditions assumed by thermodynamics do not commonly occur. Nevertheless, as is usual in science, results of experiments conducted in rigorously controlled conditions help us understand what factors are involved in a given phenomenon and thereby provide guidance to comprehend all similar phenomena that happen in the physical universe. Theoretical analysis assists us in defining to which actual instances such a general inference can be extended. Hence, if we understand how thermodynamic properties, and specifically entropy, affect systems and processes that are exactly defined from a theoretical point of view, we can then try to extend these findings to correctly interpret all the systems and processes of the universe.
Entropy in Classical Thermodynamics: The Importance of Reversibility
Alberto GianinettiAbstract
The concept of entropy is introduced within the context of classical thermodynamics where it was first developed to answer the questions: What happens when heat spontaneously goes from hot bodies to cold ones? To figure out this change, the transfer process must have some peculiar features that make it reversible. First of all, to be studied, systems and processes must be conceptualised as occurring at equilibrium conditions, or in conditions close to equilibrium. A first description of equilibrium is provided.
Heat vs. Work
Alberto GianinettiAbstract
The idea of transferring energy from/to a system is expanded to include work in addition to heat. Work is an alternative form by which the energy of a system can be transferred.
