The Concept of Entropy

In this chapter we present the rudiments of this approach, not so that the reader can become proficient in statistical thermodynamics (a considerably more thorough introduction is required for that) but to show how entropy is related to statistical considerations. Statistical mechanics does not exactly explain what entropy is, but rather provides a model, quite different from the thermodynamic model, that contains a parameter identical to the entropy of the thermodynamic model in every measurable respect. Equating a parameter in one model with a parameter in another model may not be completely satisfactory as an explanation, but there is no doubt that the statistical point of view is of considerable help in gaining an intuitive grasp of entropy. There is no doubt in our minds that a familiarity with this point of view is essential to a good understanding of thermodynamics. As Nash (1972) says  

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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... 

Deals with the concept of entropy, which serves as a means of determining whether or not a process is possible. Defines the zero entropy state for any substance in a single, pure quantum state as the absolute zero of temperature. 

Today, the Second Law, as applied to chemical systems, is firmly associated with the concept of entropy as expressed in the 1865 statement of Clausius and given mathematically by equation (2.41). 

When ammonium nitrate, NH jNOj, dissolves in water, it absorbs heat. Consequently, its standard enthalpy of solution must be positive. This means that the entropy change caused by ammonium nitrate going from solid to solution must increase for the process to proceed spontaneously. This is exactly what one would expect based on the concept of entropy as a measure of randomness or disorder. 

In thermodynamics, entropy enjoys the status as an infallible criterion of spontaneity. The concept of entropy could be used to determine whether or not a given process would take place spontaneously. It has been found that in a natural or spontaneous process there would be an increase in the entropy of the system. This is the most general criterion of spontaneity that thermodynamics offers however, to use this concept one must consider the entropy change in a process under the condition of constant volume and internal energy. Though infallible, entropy is thus not a very convenient criterion. There have, therefore, been attempts to find more suitable thermodynamic functions that would be of greater practical... 

The work of Ludwig Boltzmann (1844-1906) in Vienna led to a better understanding, and to an extension, of the concept of entropy. On the basis of statistical mechanics, which he developed, the term entropy experienced an atomic interpretation. Boltzmann was able to show the connections between thermodynamics and the phenomenon of order and chance events he used the term entropy as a measure... 

We start by introducing the concept of entropy S to explain why some reactions occur spontaneously, without needing additional energy, yet others do not. The sign of A 5 for a thermodynamic universe must be positive for spontaneity. We explore the temperature dependence of A5. 

We have already seen the way processes occur with an attendant increase in disorder. We now introduce the concept of entropy. The extent of energetic disorder is given the name entropy (and has the symbol S). A bigger value of S corresponds to a greater extent of energetic disorder. 

Our goal in this chapter is to help you learn the laws of thermodynamics, especially the concepts of entropy and free energy. It might be helpful to review Chapter 6 on thermochemistry and the writing of thermochemical equations. The concept of Gibbs free energy (G) will be useful in predicting whether or not a reaction will occur spontaneously. Just like in all the previous chapters, in order to do well you must Practice, Practice, Practice. 

Based on the change in enthalpy, you would expect that water would always freeze. Use the concepts of entropy and free energy to explain why this phase change is favourable only below 0°C. 

The concept of entropy-enthalpy compensation resulting in the critical conditions of enthalpic interactions and the molar mass independent sample retention turned out useful also for the understanding several other coupled methods of polymer HPLC. It is accepted [195,196] that the polymer species tend to elute at the critical conditions also when either eluent strength or quality change within the HPLC system in the course of the HPLC experiment that is in the continuous and local gradient methods (Sections 16.5.3, 16.5.4, and 16.5.6). Irrespective of the problems and limitations of LC CC, its concept belongs to the important breakthroughs in polymer HPLC. 

The foundation of irreversible thermodynamics is the concept of entropy production. The consequences of entropy production in a dynamic system lead to a natural and general coupling of the driving forces and corresponding fluxes that are present in a nonequilibrium system. 

In thermodynamics, a measure of disorder is entropy, S. Low entropy means little disorder high entropy means great disorder. We need to express the concept of entropy quantitatively but even at this stage, with entropy being no more than another name for disorder we can see that the tendency of energy and matter to become more disordered can be expressed more formally as... 

In contrast to the conservation of internal energy (Eq. 2.1, the first law of thermodynamics), the entropy of the Universe always increases (Eq. 2.5), which is an alternative definition of the second law of thermodynamics. Inherent in the concept of entropy is a preferred direction for spontaneous change (AS rr > 0). For example, at 1 bar pressure, ice melts at 10°C, water freezes at —10°C, and not vice versa. A spontaneous process leads from a state of lower probability to a state of higher probability, and equilibrium is the state of maximum probability (Pitzer, 1995). 

For good accounts of the history and meaning of the concept of entropy, see (a), (b) (a) von Baeyer HC (1998) Maxwell s demon. Why warmth disperses and time passes. Random House, New York, (b) Greenstein G (1998) Portraits of discovery. Profiles in scientific genius, chapter 2 ( Ludwig Boltzmann and the second law of thermodynamics ), Wiley, New York... 

Equation 4.28 maximizes 2, the number of ways the energy can be distributed consistent with the known total energy. This led to the concept of entropy,... 

We know that the concept of entropy is the fundamental consequence of the second law of thermodynamics. There are two other functions, which utilize entropy in their derivations. These two functions are free energy function and work function. These functions like the internal energy, heat content and entropy are fundamental thermodynamic properties and depend upon the states of the system only. 

Rudolf Clausius in the 1860s introduced the concept of entropy. 

The enthalpy change, AH, is the change in heat associated with a process. However, the concept of entropy is based on the randomness or disorder of a system, and it can be illustrated by reference to Figure 4.5. 

Equation (1.77) shows that disorganization and randomness increase entropy, while organization and ordering decrease it, and equilibrium states have the maximum value of fl. In the above system, fl reaches its maximum value when , = n2. In parallel, the increase in entropy corresponds to the increase in the number of microscopic states or states with higher probability. The concept of entropy as a measure of organized structures is attracting scientists from diverse fields such as physics, biology, and communication and information systems. 

Equation (1.89) determines the rate of entropy production due to irreversibility within a control volume. The concept of entropy production is elaborated further in the next section. 

Clausius himself, later on, introduced the concept of entropy. Studies on entropy led to the evolution of the Third Law of Thermodynamics in 1906 by Nemst (1907). This was many times debated and revised till 1912, when Plank (1927) went back to practically the same statement as that of Nemst. 

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. ... 

The concept of Entropy was found to remain valid irrespective of the path the heat took to flow from source to sink, i.e., either through the heat engine or directly from chemical reaction into the atmosphere. Thus, for any real process occurring in real system, there is a net increase in the entropy of system and surroundings taken together. 

From this relationship evolves the concept of Entropy. ... 

The concept of Entropy would be discussed in detail in the next chapter. 

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