Entropy as a measure of disorder

Using the statistical mechanical approach, we have been able to rederive equations (6.18)-(6.20) without any mention of steam engines or idealized Carnot cycles. These equations form the basis for much of the rest of thermodynamics, as we have already begtm to see in Chapter 5. These few relationships are so useful because they serve as pointers or criteria for the spontaneous direction of any process. Hopefully the statistical approach clarifies much of this, in the sense that we conceive of entropy as a measure of disorder or randomness. The most random permissible state is also the most probable statistically. It is self-evident that spontaneous processes head in the most probable direction by doing so, they maximize entropy. 

As we have previously seen (see Sections 2.5, 2.6, and 3.11), the maintenance of an ordered state requires energy expenditure, energy extracted from the environment. Entropy has previously been introduced (Section 2.5) as a concept of disorder. Thus, information storage (as an ordered state) and thermodynamic entropy (as a measure of disorder) are somehow related inversely. Shannon s definition of information is (Shannon and Weaver, 1949 Gatlin, 1972 Loewenstein, 1999) ... 

Virtually since the beginning, however, a popular viewpoint has been to see entropy as a measure of disorder. Helmholtz used the word Unordnung (disorder) in 1882. This results from familiar relationships such as S > liquids > S soiids, and the universally positive entropy of mixing. We used this relationship in the previous section when we spoke of degree of mixed-upness. However the disorder analogy can involve a serious fallacy, as made clear by Lambert (1999 see also http //www.entropysite.com). 

Entropy is sometimes said to he a measure of disorder. According to this idea, the entropy increases whenever a closed system becomes more disordered on a microscopic scale. This description of entropy as a measure of disorder is highly misleading. It does not explain why entropy is increased by reversible heating at constant volume or pressure, or why it increases during the reversible isothermal expansion of an ideal gas. Nor does it seem to agree with the freezing of a supercooled hquid or the formation of crystalline solute in a supersaturated solution these processes can take place spontaneously in an isolated system, yet are accompanied by an apparent decrease of disorder. 

Thus we should not interpret entropy as a measure of disorder. We must look elsewhere for a satisfactory microscopic interpretation of entropy. 

Unfortunately, the picture of entropy as a measure of disorder has been misapplied to simations that are not molecular. For example, imagine your desk with books and papers placed carefully to give an orderly arrangement. Later, as you work, your books and papers become strewn about—your desk becomes disordered. This has sometimes been described as a spontaneous process in which entropy increases. Of course, the books and papers do not move spontaneously—you move them. In fact, there is essentially no difference between the thermodynamic entropies of the ordered and disordered desks. All that has happened is that normal-sized objects (books and papers) have been moved by you from human-defined order to human-defined disorder. 

For convenience (and in accordance with our understanding of entropy as a measure of disorder), we take this common value to be zero. Then, with this convention, according to the Third Law,... 

Entropy is often described as a measure of disorder or randomness. While useful, these terms are subjective and should be used cautiously. It is better to think about entropic changes in terms of the change in the number of microstates of the system. Microstates are different ways in which molecules can be distributed. An increase in the number of possible microstates (i.e., disorder) results in an increase of entropy. Entropy treats tine randomness factor quantitatively. Rudolf Clausius gave it the symbol S for no particular reason. In general, the more random the state, the larger the number of its possible microstates, the more probable the state, thus the greater its entropy. 

The Second Law of thermodynamics states that for a chemical process to be spontaneous, there must be an increase in entropy. Entropy (S) can be thought of as a measure of disorder. 

In physical chemistry, entropy has been introduced as a measure of disorder or lack of structure. For instance the entropy of a solid is lower than for a fluid, because the molecules are more ordered in a solid than in a fluid. In terms of probability it means also that in solids the probability distribution of finding a molecule at a given position is narrower than for fluids. This illustrates that entropy has to do with probability distributions and thus with uncertainty. One of the earliest definitions of entropy is the Shannon entropy which is equivalent to the definition of Shannon s uncertainty (see Chapter 18). By way of illustration we... 

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. 

A simple statement of the Second Law is natural processes are accompanied by an increase in the entropy of the universe. There are several other statements of the Second Law in the chapter Notes. As noted above, entropy is a measure of disorder the greater the extent of disorder, the greater the entropy. The Second Law tells us that things change spontaneously in a way that increases disorder. At equilibrium, entropy is maximized and disorder reigns. 

Ions or molecules flowing down their concentration gradients is one aspect of a very general statement known as the Second Law of Thermodynamics. The Second Law is a mathematical statement to the effect that all real processes increase the disorder, captured in a quantity known as entropy, of the universe. Entropy is a measure of disorder or randomness and may be thought of as negative information. 

This limitation, imposed by a scientific law called the second law of thermodynamics, can be difficult to understand. It involves a concept known as entropy, which can be thought of as a measure of disorder. Entropy must increase in natural processes in other words, processes naturally go from order to disorder (as observed by anyone who has bought a shiny new bicycle or automobile and watched it fade, corrode, break down, and finally fall apart—usually just after the warranty expires). The second law of thermodynamics requires a heat engine to vent some heat into the environment, thereby raising entropy. This loss is unavoidable, and a heat engine will not operate without it. No one will ever buy a car powered by a gasoline engine that does not exhaust, and lose, some of its heat. 

The standard entropies S° of gases are much larger than those of solids and liquids (Section 2.3). This may be understood by the somewhat simplistic view of S° as a measure of disorder at the molecular level. The molecules of gases have much greater freedom of translational motion, and hence are less ordered, than those of liquids and especially solids. Consequently, for oxidation of a solid metal to a solid oxide with consumption of gaseous oxygen... 

Entropy is a measure of disorder. The largest negative entropy of solution in Table 3.1 is generally considered as evidence of the creation of structure (increased order) within the body of water. More recently it has been suggested that the creation of a cavity can explain the entropy decrease. Large heat capacity changes also indicate the structuring effect of the solute on the water molecules. The size of the solute molecule has a substantial effect on solubility. 

Entropy change (AS) (Section 2.6) Entropy is a measure of disorder. Processes that increase the disorder in a system (AS > 0) are favored. Epoxide (oxirane) (Section 10.10) A three-membered cyclic ether. 

Although the enthalpy is a measure of order in the system, the entropy is a measure of disorder. The second law of thermodynamics states that a spontaneous event results in an increase in entropy. Hence, a favorable process always results in an increase in disorder. The entropy is defined as ... 

It is well known that the entropy is a measure for the disorder of a system. It is clear that the entropy can serve also as a measure for the order of a system. However, the fact that we can understand entropy as a measure of symmetry is rather emphasized rarely. 

For large numbers of particles, then, probability favors random arrangements. Using this insight, we can tentatively define entropy as a measure of the randomness or disorder of a system. However, we still have to establish a definition that can be used quantitatively and from a molecular perspective. To do this, we turn to a branch of physical chemistry called statistical mechanics, or statistical thermodynamics, where we find a subtle addition to the definition. The probability of events that must be counted is not the number of ways particles can be arranged... 

The Boltzmann relation provides a statistical interpretation of the entropy. The greater the number of accessible states, the less our knowledge of the system and the more randomness or disorder in the system. This entropy is a measure of disorder. The tendency of the entropy to increase reflects the tendency of thermodynamic systems to increase in disorder just as an initially ordered deck of cards increases in disorder during a game of cards. 

What is transported One of the peculiarities of the thermal energy variety is to think of the thermal conduction in terms of energy transported, when other domains consider entities as the transported quantity (charges, momenta, etc.). According to their definition, as entities bear energy, there is no physical consequence due to this disparity. There are naturally historical reasons for this, but also a conceptual difficulty in our modern minds to view the entropy as a quantity able to be transported. This is certainly due to the influence of the statistical definition of entropy as a measure of order/disorder in the system, considered as a whole with implicitly a uniform entropy distribution. 

Entropy is often described as a measure of disorder or randomness. These terms should be used with a great deal of caution, however, because they are subjective and can lead to erroneous conelusions. It is preferable, instead, to view the change in entropy of a system in terms of the change in the number of microstates of the system. 

Two factors namely, enthalpy of solution and entropy of solution AS, govern the dissolution of a substance in a solvent. A negative enthalpy of solution is always favourable for solution formation. The entropy factor, AS, also plays an important role. In fact, solution formation is largely governed by this factor. Entropy is a measure of disorder or randomness. The process of solution is always accompanied by an increase in disorder or randomness. When enthalpy of solution is highly endothermic, no solution is formed i.e., the solute does not mix with the solvent. 

The thermodynamic function, entropy, is a state function (like enthalpy and internal energy), which may be thought of as a measure of disorder or randomness. 

Entropy is a thermodynamic state function (often described as a measure of disorder) that is related to the number of microstates in a system. 

The enthalpy of mixing AH is the heat consumed (AH > 0) or generated (AH < 0) during the mixing, at constant pressure. If the mixing is exothermic, then the enthalpic term will drive the system towards miscibility. As the entropy provides a measure of disorder or randomness, and the systems always incline to a uniform distribution of energy, ASm is always positive and therefore the entropic term is favorable for mixing. 

Entropy can be regarded as a measure of disorder. That is, the higher the value, the higher the level of disorder. A closed system tends towards higher entropy and therefore a higher disorder. For example, two layers of coloured balls in a box shaken will generate a level of randomness and disorder, and will not return to their original state without the intervention of more work in their separation. See first law of thermodynamics. 

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