Chemistry
Entropy
Entropy is a measure of the disorder or randomness in a system. In chemistry, it is associated with the dispersal of energy and the number of ways a system can be arranged. An increase in entropy indicates a spontaneous process, while a decrease in entropy requires an input of energy.
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eBook - ePub- Patrick E. McMahon, Rosemary McMahon, Bohdan Khomtchouk(Authors)
- 2019(Publication Date)
- CRC Press(Publisher)
25 ThermodynamicsEntropy and Free EnergyI GENERAL CONCEPTS OF Entropy The Entropy of a system (symbol = S(system) ) is a measure of the disorder, or randomness, of that system. The larger the Entropy value the greater the randomness, or disorder, of the system; the smaller the Entropy value, the lesser the randomness or disorder (or, equivalently, the smaller the Entropy value, the more ordered the system).Entropy measures the statistical probabilities of specific system configurations vs. all possible configurations (termed the degrees of freedom).Randomness, or disorder, always represents the more probable arrangement of matter. The result is that Entropy always increases in the direction of increasing probability of the arrangement of matter within a system.Entropy is a state function, the change in Entropy of any system depends only on the initial and final states and not on how the change occurs. Randomness, or disorder, in a system of matter is related to the number of arrangements in which the matter can exist. General trends for a specific amount of matter are:(1)
No longer available |Learn more- (Author)
- 2014(Publication Date)
- White Word Publications(Publisher)
Statistical mechanics demonstrates that Entropy is governed by probability, thus allowing for a decrease in disorder even in a closed system. Although this is possible, such an event has a small probability of occurring, making it unlikely. Even if such event were to occur, it would result in a transient decrease that would affect only a limited number of particles in the system. Definitions and descriptions Thermodynamic Entropy is more generally defined from a statistical thermodynamics viewpoint, in which the molecular nature of matter is explicitly considered. Alternatively Entropy can be defined from a classical thermodynamics viewpoint, in which the molecular interactions are not considered and instead the system is viewed from perspective of the gross motion of very large masses of molecules and the behavior of individual molecules is averaged and obscured. Historically, the classical ther-modynamics definition developed first, and it has more recently been extended in the area of non-equilibrium thermodynamics. Statistical thermodynamics The interpretation of Entropy in statistical mechanics is the measure of uncertainty, or mixedupness in the phrase of Gibbs, which remains about a system after its observable macroscopic properties, such as temperature, pressure and volume, have been taken into account. For a given set of macroscopic variables, the Entropy measures the degree to which the probability of the system is spread out over different possible microstates. In contrast to the macrostate, which characterizes plainly observable average quantities, a microstate specifies all molecular details about the system including the position and velocity of every molecule. The more such states available to the system with appreciable probability, the greater the Entropy. More specifically, Entropy is a logarithmic measure of the density of states:
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
Statistical mechanics demonstrates that Entropy is governed by probability, thus allowing for a decrease in disorder even in a closed system. Although this is possible, such an event has a small probability of occurring, making it unlikely. Even if such event were to occur, it would result in a transient decrease that would affect only a limited number of particles in the system. Definitions and descriptions Thermodynamic Entropy is more generally defined from a statistical thermodynamics viewpoint, in which the molecular nature of matter is explicitly considered. Alternatively Entropy can be defined from a classical thermodynamics viewpoint, in which the molecular interactions are not considered and instead the system is viewed from perspective of the gross motion of very large masses of molecules and the behavior of individual molecules is averaged and obscured. Historically, the classical thermody-namics definition developed first, and it has more recently been extended in the area of non-equilibrium thermodynamics. Statistical thermodynamics The interpretation of Entropy in statistical mechanics is the measure of uncertainty, or mixedupness in the phrase of Gibbs, which remains about a system after its observable macroscopic properties, such as temperature, pressure and volume, have been taken into account. For a given set of macroscopic variables, the Entropy measures the degree to which the probability of the system is spread out over different possible microstates. In contrast to the macrostate, which characterizes plainly observable average quantities, a microstate specifies all molecular details about the system including the position and velocity of every molecule. The more such states available to the system with appreciable probability, the greater the Entropy. More specifically, Entropy is a logarithmic measure of the density of states: where k B is the Boltzmann constant, equal to 1.38065×10 −23 J K −1 .
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Orange Apple(Publisher)
Statistical mechanics demonstrates that Entropy is governed by probability, thus allowing for a decrease in disorder even in a closed system. Although this is possible, such an event has a small probability of occurring, making it unlikely. Even if such event were to occur, it would result in a transient decrease that would affect only a limited number of particles in the system. Definitions and descriptions Thermodynamic Entropy is more generally defined from a statistical thermodynamics viewpoint, in which the molecular nature of matter is explicitly considered. Alternatively Entropy can be defined from a classical thermodynamics viewpoint, in which the molecular interactions are not considered and instead the system is viewed from perspective of the gross motion of very large masses of molecules and the behavior of individual molecules is averaged and obscured. Historically, the classical thermo-dynamics definition developed first, and it has more recently been extended in the area of non-equilibrium thermodynamics. Statistical thermodynamics The interpretation of Entropy in statistical mechanics is the measure of uncertainty, or mixedupness in the phrase of Gibbs, which remains about a system after its observable macroscopic properties, such as temperature, pressure and volume, have been taken into account. For a given set of macroscopic variables, the Entropy measures the degree to which the probability of the system is spread out over different possible microstates. In contrast to the macrostate, which characterizes plainly observable average quantities, a microstate specifies all molecular details about the system including the position and velocity of every molecule. The more such states available to the system with appreciable probability, the greater the Entropy. More specifically, Entropy is a logarithmic measure of the density of states: where k B is the Boltzmann constant, equal to 1.38065×10 −23 J K −1 .
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
Standard textbook definitions The following is a list of additional definitions of Entropy from a collection of textbooks. • a measure of energy dispersal at a specific temperature. • a measure of disorder in the universe or of the availability of the energy in a system to do work. Interdisciplinary applications of Entropy Although the concept of Entropy was originally a thermodynamic construct, it has been adapted in other fields of study, including information theory, psychodynamics, ther-moeconomics, and evolution. ________________________ WORLD TECHNOLOGIES ________________________ Thermodynamic and statistical mechanics concepts • Entropy unit - a non-S.I. unit of thermodynamic Entropy, usually denoted e.u. and equal to one calorie per Kelvin per mole, or 4.184 Joules per Kelvin per mole. • Gibbs Entropy - the usual statistical mechanical Entropy of a thermodynamic system. • Boltzmann Entropy - a type of Gibbs Entropy, which neglects internal statistical correlations in the overall particle distribution. • Tsallis Entropy - a generalization of the standard Boltzmann-Gibbs Entropy. • Standard molar Entropy - is the Entropy content of one mole of substance, under conditions of standard temperature and pressure. • Residual Entropy - the Entropy present after a substance is cooled arbitrarily close to absolute zero. • Entropy of mixing - the change in the Entropy when two different chemical substances or components are mixed. • Loop Entropy - is the Entropy lost upon bringing together two residues of a polymer within a prescribed distance. • Conformational Entropy - is the Entropy associated with the physical arr-angement of a polymer chain that assumes a compact or globular state in solution. • Entropic force - a microscopic force or reaction tendency related to system organization changes, molecular frictional considerations, and statistical va-riations. • Free Entropy - an entropic thermodynamic potential analogous to the free energy.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
Ambiguities in the terms disorder and chaos , which usually have meanings directly opposed to equilibrium, contribute to widespread confusion and hamper comprehension of Entropy for most students. As the second law of thermodynamics shows, in an isolated system internal portions at different temperatures will tend to adjust to a single uniform temperature and thus produce equilibrium. A recently developed educational approach avoids ambiguous terms and describes such spreading out of energy as dispersal, which leads to loss of the differentials required for work even though the total energy remains constant in accordance with the first law of ______________________________ WORLD TECHNOLOGIES ______________________________ thermodynamics (compare discussion in next section). Physical chemist Peter Atkins, for example, who previously wrote of dispersal leading to a disordered state, now writes that spontaneous changes are always accompanied by a dispersal of energy. Relating Entropy to energy usefulness Following on from the above, it is possible (in a thermal context) to regard Entropy as an indicator or measure of the effectiveness or usefulness of a particular quantity of energy. This is because energy supplied at a high temperature (i.e. with low Entropy) tends to be more useful than the same amount of energy available at room temperature. Mixing a hot parcel of a fluid with a cold one produces a parcel of intermediate temperature, in which the overall increase in Entropy represents a “loss” which can never be replaced. Thus, the fact that the Entropy of the universe is steadily increasing, means that its total energy is becoming less useful: eventually, this will lead to the heat death of the Universe. Ice melting example The illustration here is a classic example in which Entropy increases in a small universe, a thermodynamic system consisting of the surroundings (the warm room) and system (glass, ice, cold water).
eBook - PDFChemistry
Structure and Dynamics
- James N. Spencer, George M. Bodner, Lyman H. Rickard(Authors)
- 2011(Publication Date)
- Wiley(Publisher)
In some cases, such as the melting of a solid or the breaking apart of a larger molecule into smaller molecules, an increase in disorder can be readily inferred. Because Entropy is a state function, the change in Entropy that occurs as a system is transformed from some initial state to some final state can be calculated as follows. When a process produces an increase in the disorder of the universe, the Entropy change, ¢S univ , is positive. 13.3 Entropy and the Second Law of Thermodynamics As noted in Section 7.1, thermodynamics is the study of energy and its transfor- mations. The first law of thermodynamics, discussed in Chapter 7, provides us with ways of understanding energy changes in chemical reactions. The second law of thermodynamics helps us determine the direction in which natural processes such as chemical reactions should occur. The role that disorder plays in determining the direction in which a natural process occurs is summarized by the second law, which states that for a process to occur, the Entropy of the universe must increase. The term universe means everything that might conceivably have its Entropy altered as a result of the process. The second law of thermodynamics can therefore be written as follows. This statement means that processes for which ¢S univ 7 0 will occur naturally, but that processes for which ¢S univ 6 0 will probably never occur. If ¢S univ 0, the process may occur in either direction. It is important to recognize that the second law of thermodynamics describes what happens to the Entropy of the universe, not the system. The universe is divided into two components, the system and its surroundings. The change in the Entropy of the universe is the sum of the change in the Entropy of the system and the surroundings. Chemists generally choose the chemical reaction in which they are interested as the system. The term surroundings is then used to describe the environment that is altered as a consequence of the reaction.
eBook - PDF- Lokesh Pandey(Author)
- 2020(Publication Date)
- Arcler Press(Publisher)
This can be understood as the distribution of the thermal energy among the thermal microparticles that may be moving randomly in space. The Entropy can be considered as the measure of the thermal energy in its random and redistributed form which has been integrated over a certain range of temperature. The redistribution may have taken due to the transfer of heat or a heat generation which is irreversible in nature and has taken place due to the degradation of energy. The generation of heat may have more than one aspect to look forward to and may be elusive in nature. This redistribution may take place within a structure of material system in space as per the absolute temperature level and may be given by: dS = dQ sys /T = m C sys dT/T The unit of this may be J/K. The Entropy of a system may also be given as the measure of the thermal disorder which is given in relation to the logarithm of the number of all the thermal and dynamic microstates, given by W, which is based on the position and the moment of the microparticles and expressed as S = k B ln W Some people like to introduce the concept of Entropy as the measure of the disorder or the randomness and state that the destruction of Entropy is brought about when some order is created, giving the example of the manner in which life evolved. However, it may be noted that at the time of any of the processes, which may be natural or man-made and which may be of creating or destroying any order or disorder, that is the transformation of any structure of material, the work potential may be regarded as always being dissipated into heat and in such a case the generation of Entropy will always be there.
eBook - PDFUnearthed
The Economic Roots of Our Environmental Crisis
- Kenneth M. Sayre(Author)
- 2010(Publication Date)
- University of Notre Dame Press(Publisher)
A mathematical (thus quantitative) measure of order in operating systems is explained in the appendix to this chapter. Its purpose, as al-ready indicated, is to show that Entropy in the form of degraded struc-ture or disorder is subject to quantitative measurement no less than Entropy in the form of degraded energy. Readers not concerned with this matter may pass over the appendix without losing track of the continu-ing discussion. 2.6 Entropy and Randomness Discussion of Entropy in chapter 1 was confined to expended energy, which is energy no longer capable of work. Work is done when physical occurrences are brought about by other physical occurrences rather than occurring randomly (section 1.2). A standard example of energy incapable of further work is the low-grade heat expended by metabolic activity (e.g., the body heat of living animals). Another conception of Entropy was introduced into the discussion at the beginning of the present chapter. This second conception equates Entropy with disorder. In photosynthesis, solar energy is expended in creating biomass that provides chemical energy to plant-eating or-ganisms. The highly ordered wave structure of sunlight is converted into chemical structure, which then is further degraded into the waste Ent ropy and Disorder 23 products of metabolic activity. This process of increasing degradation culminates in the nondirectional wave structure of black-body radiation by which fully expended energy from the sun is eventually returned to space. The conceptions of Entropy as expended energy and as structural disorder can be further integrated in terms of a third conception equat-ing Entropy with randomness. This conception was implied in our dis-cussion of orderliness in the preceding section but needs to be more explicitly articulated. On one hand, random events are events whose oc-currence exhibits no particular order. The Entropy present in disorder thus is equivalent to that present in random occurrences.
eBook - PDFThermal Physics
Entropy and Free Energies
- Joon Chang Lee(Author)
- 2011(Publication Date)
- WSPC(Publisher)
Chapter 5 Entropy as a Measure of Disorder 5.1 Introduction Can we describe Entropy in any other terms more accessible by the general public? Such descriptions do exist and are the subject of this chapter. Generalize Eq. (4.21) to all situations where the the state of mat-ter is constantly changing amongst 1 , 2 , 3 ,... with frequency (probability) p 1 ,p 2 ,p 3 ,... , respectively. The functional D { p 1 ,p 2 , · · · } = -C summationdisplay i p i ln p i (5.1) is regarded as a measure of ‘disorder’. Here the Boltzmann constant has been replaced with a constant. This has been widely practiced in physics, and for a good reason. It is important to understand in what sense the term ‘disorder’ is used. Shannon arrived at the same equation for his information theory. There are those who wish to develop thermal physics based on the information theory and call Entropy ‘uncertainty’ or ‘missing information’. It is therefore equally important to understand in what sense they use the term ‘uncertainty’. 5.2 Order and Disorder According to this description, Entropy is a measure of disorder and nature tends to change irreversibly from an ordered state to a more disordered state. The usual examples given include the way unruly children mess up neatly ordered chairs in their classroom and the way monkeys might mess up a well-ordered library catalog. This description associates disorder with a state of affairs which can be realized in many different ways, that is, a large 141 142 Entropy as a Measure of Disorder number of microstates, and it associates order with a state of affairs which can be realized only in a small number of ways, that is, a small number of microstates. According to the film “Amadeus”, Mozart effectively said that there is in fact only one way to compose an opera based on the story of The Marriage of Figaro, namely, the way in which he composed it. In other words, there is only one microstate which achieves the maximum musical order possible for the story.
eBook - PDFThe Road to Maxwell's Demon
Conceptual Foundations of Statistical Mechanics
- Meir Hemmo, Orly R. Shenker(Authors)
- 2012(Publication Date)
- Cambridge University Press(Publisher)
We begin with the notion of Entropy. 7.2 Entropy In thermodynamics, Entropy designates the degree to which the energy of a system is exploitable in order to produce work. In the passage from thermodynamics to mechanics, the notion of exploitability of energy translates into the notion of the degree of control that one has over the energy in a given system. If one can control the way in which energy flows in a system and changes its form, one can, naturally, exploit this energy more easily. In thermodynamics, the convention is to associate low Entropy with high exploitability of energy, and high Entropy with low exploitability of energy. In statistical mechanics this convention is pre- served: low Entropy is associated with high control over the system’s energy, and high Entropy denotes low control over energy. How can the notion of control be expressed in terms of statistical mechanics? In mechanics, the real physical state of a system is its microstate, which is represented in the state space by a mathematical point. Since the 154 Entropy positions and velocities of particles are real numbers that can have any value in a given interval of the continuum, describing the exact microstate requires an infinite amount of information about the system’s microstate, and this is practically impossible. Because the degree of precision with which we can know the state of the system is finite, this means that we cannot determine the system’s exact microstate but can – at best – determine a set of microstates to which the system’s microstate belongs; in other words, we can only determine its macrostate. And if our know- ledge of the system’s state is limited in this way, then ipso facto so is our ability to control this state (with the exception of the spin echo experi- ments). The result is that we cannot prepare a system in a predetermined microstate but – at best – prepare it in a predetermined macrostate.
Index pages curate the most relevant extracts from our library of academic textbooks. They’ve been created using an in-house natural language model (NLM), each adding context and meaning to key research topics.
