Entropy concept

Environmental protection and resource use have to be considered in a comprehensive framework, and all of the relevant economic and natural scientific aspects have to be taken into consideration. The concepts of entropy and sustainability are useful in this regard. The entropy concept says that every system will tend toward maximum disorder if left to itself. In other words, in the absence of sound environmental policy. Earth s energy sources will be converted to heat and pollutants that must be received by Earth. The concept of sustainability has to do with... 

To obtain a better grasp of the essential character of the entropy concept, let us examine in more detail a few transformations that occur spontaneously even though At/ = 0 in each case (Fig. 6.10). 

Some of the historical reluctance to assimilate the entropy concept into general scientific thinking, and much of the introductory student s bewilderment, might have been avoided if Clausius had defined entropy (as would have been perfectly legitimate to do) as... 

Once you begin to get a feel for the enthalpy and entropy concepts, you ll probably learn to eyeball a reaction and tell whether or not it will proceed spontaneously. There are some patterns that you can study to help you remember the different possible relationships between enthalpy, entropy, and free energy. You can learn these conceptually or from a mathematical perspective. All of the relationships are based on Equation 17.7 ... 

The concept of entropy and its dependence on randomness, led to the interpretation of thermodynamic properties in terms of atomic or molecular arrangements. Earlier also, there were attempts to correlate, rather logically, the temperature with molecular motion. But till the evolution of entropy concept, thermodynamics studied properties of system at macro-level only. The latter interpretations with atomic and molecular arrangements came to be discussed under Statistical Thermodynamics. ... 

If the introduction of entropy concepts is a sign of the maturity of a field of research, it can be concluded from this survey that our present concepts on adsorption and chemisorption have now reached their ultimate stage of refinement. But the evolution from energy to entropy is very recent history. 

The entropy concept allows us to define two new extensive thermodynamic variables the Helmholtz Free Energy, F, which is the maximum amount of work a system can do at constant temperature (isothermal changes) and the Gibbs Free Energy, G, which is the maximum amount of work a system can do at constant pressure (isobaric changes) and is a minimum for closed systems at equilibrium with a fixed temperature and pressure. 

Head loss thus represents useable energy lost from the system and may be thought of as a measure of change in entropy. Likewise, the irreversible process of dissolving minerals in the aquifer system has an entropy change associated with it. One way in which the physical and chemical processes within such a system can be compared is through use of entropy concepts. 

Now suppose a chamber of slow and hence cold molecules is connected with a chamber of warm, fast moving molecules. Soon, the two chambers will have the same mix of fast and slow molecules. But if you begin with two chambers containing the same mixture and connect them, you will never find one chamber collecting all the fast molecules and the other the slow ones. Newtonian physics was reversible, but the world he was describing was not. To cope with this fact, enshrined of course in the second law of thermodynamics and the entropy concept, we need to introduce directional time designated here as -ft. 

We apply the presented maximiun entropy concept within this example for the modeling of the soil parameters and evaluate the influence of the parameter imcertainties on the failure probability. The limit state function of the bearing failure of a simple strip foimdation with pure vertical loading can be derived based on Terzaghi (1943) and Meyerhof (1953) as... 

However, such discussions tend to be rather long and abstract, and exactly how conclusions about irreversible heat transfers in Carnot cycles get transferred to irreversibility in chemical reactions requires even more discussion. This detracts from the task attempted here - the shortest possible, intuitively clear, development of the concepts necessary to use thermodynamics in solving Earth science problems. Readers who want to know more about the historical development of the entropy concept and its deeper meaning must consult the many excellent treatises on this subject. 

There is a tendency for PMs to be discipline specific. Physicists, for example, often use PMs based on information theoretic and entropy concepts. These metrics appear to have seen limited use in chemistry, and the interested reader is referred to Ref. 246 for an application example, and Chapters 5 and 6 of Ref. 13 for a theoretical discussion. 

Such non-zero values of fJf are associated with the internal energy barriers to rotation. Thus in contrast to the Gaussian entropy concept... 

ACp are constant, then, from Eq 4.34, the conclusion can be drawn that value of ASg increases due to transition from unfilled to filled material. At the same time, for the system PMMA-glass beads, constant values of T2 were obtained which, together with ACp = const, indicates approximate constancy of ASg for all samples. From this discussion, it follows that the application of the iso-entropy concept to describe the glass transitions in filled polymers needs additional development. 

Chapter 4. Second law deals with the concept entropy, which is the basis for solving equilibrium problems in physical chemistry. Through the entropy concept of the second law, equilibrium conditions for substance systems is developed and the apphcation of these conditions is illustrated by solution of practical problems within material science. 

Through the Boltzmann relation, the macroscopic entropy concept of classical thermodynamics is connected with the molecular statistic quantity 1 that specifies the number of micro states corresponding to the same macro state. In many cases, this relationship can be used for simple, qualitative estimates of the properties and behaviour of the substances. 

The power and importance of the entropy concept were not evident to Clausius contemporaries when he introduced it in 1865. Indeed, Clausius himself did not view entropy as the basic concept for understanding the second law. He preferred to express the physical meaning of that law in terms of the concept of disgregation, another word that he coined, which he interpreted in molecular and mechanical terms ([Clausius, 1862] see [Klein, 1969[). Clausius restricted his use of entropy to its convenient role as a summarizing concept. In the memoir where it was introduced, he kept the original thermodynamic concepts, heat and work, at the center of his thinking and derived the experimentally useful consequences of the two laws without using the entropy function. 

Rudolf Julius Emanuel Clausius, German physicist, K6slin (now Koszalin) 2.1.1822, fBonn 24.8.1888 one of the developers of the mechanical theory of heat his achievements encompass the formulation of the second law and the introduction of the entropy concept. 

We will describe below the SE formalism in detail and explain how it can be used to estimate chemical information content based on histogram representations of feature value distributions. Examples from our work and studies by others will be used to illustrate key aspects of chemical information content analysis. Although we focus on the Shannon entropy concept, other measures of information content will also be discussed, albeit briefly. We will also explain why it has been useful to extend the Shannon entropy concept by introducing differential Shannon entropy (DSE) to facilitate large-scale analysis and comparison of chemical features. The DSE formalism has ultimately led to the introduction of the SE-DSE metric. 

There are other metrics of information content, and several of them are based on the Shannon entropyAbout 10 years after introduction of the Shannon entropy concept, Jaynes formulated the maximum entropy approach, which is often referred to as Jaynes entropy and is closely related to Shannon s work. Jaynes introduction of the notion of maximum entropy has become an important approach to any study of statistical inference where all or part of a model system s probability distribution remains unknown. Jaynes entropy, or relations, which guide the parameterization to achieve a model of minimum bias, are built on the Kullback-Leibler (KL) function, sometimes referred to as the cross-entropy or relative entropy function, which is often used and shown (in which p and q represent two probability distributions indexed by k), as... 

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