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Entropy (energy dispersal)
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In physics and physical chemistry, the thermodynamic concept of entropy has heretofor been commonly defined as a scalar measure of the disorder of a thermodynamic system. This entry sets out a variant approach to entropy, namely as a measure of energy dispersal or distribution at a specific temperature. Under this new approach, changes in entropy can be quantitatively related to the distribution or the spreading out of the energy of a thermodynamic system, divided by its temperature.
The energy dispersal approach to teaching entropy was developed to facilitate teaching entropy to students beginning university chemistry and biology.
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In physics and physical chemistry, the thermodynamic concept of entropy has heretofor been commonly defined as a scalar measure of the disorder of a thermodynamic system. This entry sets out a variant approach to entropy, namely as a measure of energy dispersal or distribution at a specific temperature. Under this new approach, changes in entropy can be quantitatively related to the distribution or the spreading out of the energy of a thermodynamic system, divided by its temperature.
The energy dispersal approach to teaching entropy was developed to facilitate teaching entropy to students beginning university chemistry and biology. This new approach also avoids ambiguous terms such as disorder and chaos, which have multiple everyday meanings, and tend to confuse students.
Problem: entropy as disorder is hard to teach
The term "entropy" has been in use from early in the history of classical thermodynamics, and with the development of statistical thermodynamics and quantum theory, entropy changes have been described in terms of the mixing or "spreading" of the total energy of each constituent of a system over its particular quantized energy levels.
Such descriptions have tended to be used together with commonly used terms such as disorder and chaos which are ambiguous, and whose everyday meaning is the opposite of what they are intended to mean in thermodynamics. Not only does this situation cause confusion, but it also hampers the teaching of thermodynamics. Students were being asked to grasp meanings directly contradicting their normal usage, with equilibrium being equated to "perfect internal disorder" and the mixing of milk in coffee from apparent chaos to uniformity being described as a transition from an ordered state into a disordered state. Studies found that few understood what these terms were intended to convey.
The description of entropy as the amount of "mixedupness" or "disorder," as well as the abstract nature of the statistical mechanics grounding this notion, can lead to confusion and considerable difficulty for those beginning the subject. Even though courses emphasised microstates and energy levels, most students could not get beyond simplistic notions of randomness or disorder. Many of those who learned by practising calculations did not understand well the intrinsic meanings of equations, and there was a need for qualitative explanations of thermodynamic relationships.
Solution: entropy as energy dispersal
To overcome the difficulties described in the previous section, entropy can be exposited in terms of "energy dispersal" and the "spreading of energy," while carefully avoiding all mention of "disorder" and "chaos" except when explaining misconceptions. All explanations of where and how energy is dispersing or spreading have been recast in terms of energy disperal, so as to emphasise the underlying qualitative meaning.
In this approach, the Second law of thermodynamics becomes "Energy spontaneously disperses from being localized to becoming spread out if it is not hindered from doing so." Illustrative examples include everyday experiences such as a rock falling, a hot frying pan cooling down, iron rusting, air leaving a punctured tire, and ice melting in a warm room. Entropy is then depicted as a sophisticated kind of "before and after" yardstick — measuring how much energy is spread out/T as a result of a process such as heating a system. Entropy also measures how far energy spreads after something happens, in a process such as gas expansion or fluids mixing (at a constant temperature). The equations are explored with reference to the common experiences, but emphasizing that in chemistry, the energy that entropy measures as dispersing is internal energy, which beginners can most clearly understand as "motional energy," the translational, vibrational, and rotational energy of molecules.
By means of such concrete examples, this approach can explain entropy to those who have difficulty in grasping mathematical abstractions. The statistical interpretation, related to quantum mechanics, describes how energy is distributed (quantized) among molecules on specific energy levels, with all the energy of the macrostate always in only one microstate at one instant. Entropy is described as measuring the energy dispersal for a system by the number of accessible microstates, the number of different arrangements of all its energy at the next instant. Thus, an increase in entropy means more microstates in the Final than in the Initial one, and hence more possible arrangements for a system's total energy at any instant. Here, the greater "dispersal of the total energy of a system" means the existence of so many possibilities.
Continuous movement and molecular collisions are visualised as bouncing balls blown by air as used in a lottery can then lead on to showing the possibilities of many Boltzmann distributions and continually changing "distribution of the instant," and so on to the idea that when the system changes, dynamic molecules will have a greater number of accessible microstates. In this approach, all everyday spontaneous physical ocurrences and chemical reactions are depicted as involving some type of energy flows from being localized or concentrated, to becoming spread out to a larger space, always to a state with a greater number of microstates.
The new approach provides a good basis for understanding the conventional approach, except in very complex cases where the qualitative relation of energy dispersal to entropy change can be so inextricably obscured that it is moot. Thus in situations such as in the entropy of mixing when the two or more different substances being mixed are at the same temperature and pressure so there will be no net exchange of heat or work, the entropy increase will be due to the literal spreading out of the motional energy of each substance in the larger combined final volume. Each component's energetic molecules become more separated from one another than they would be in the pure state, when they were colliding only with identical adjacent molecules, leading to an increase in its number of accessible microstates.
Variants of the energy disperal approach have been adopted in number of undergraduate chemistry texts, mainly in the United States. For a list of American first-year university chemistry texts that have adopted this approach, see here. A distinguished advanced text, Physical Chemistry by Peter Atkins of Oxford University and Julio De Paula, has followed suit. Starting with the 8th edition, Atkins and De Paula describe entropy in terms of dispersal of energy, without mentioning "disorder."
Websites have made the energy dispersal approach accessible not only to all students of chemistry, but also to the lay public seeking a basic intuitive understanding of thermodynamic entropy. For example, is a page setting out the qualitative simplicity of the notion of entropy.
History of energy disperal
The exact origin of "energy dispersal" as a description of entropy change is not certain. Its first appearance is believed to have been in William Thomson's (Lord Kelvin) 1852 article "On a Universal Tendency in Nature to the Dissipation of Mechanical Energy." Thomson distinguished between two types or "stores" of mechanical energy: "statical" and "dynamical." He discussed how these two types of energy can change from one form to the other during a thermodynamic transformation. When heat is created by any unreversible process (such as friction), or when heat is diffused by conduction, mechanical energy is dissipated, and it is impossible to restore the initial state.
In the mid 1950s, with the development of quantum theory, researchers began speaking about entropy changes in terms of the mixing or "spreading" of the total energy of each constituent of a system over its particular quantized energy levels, such as by the the reactants and products of a chemical reaction.
In 1984, the Oxford physical chemist Peter Atkins, in a book The Second Law, written for laypersons, presented a nonmathematical interpretation of what he called the "infinitely incomprehensible entropy" in simple terms, describing the Second Law of thermodynamics as "energy tends to disperse," but then relapsed into confusing and problematic terminology by writing about a "collapse into chaos" and "the corruption of the quality of energy." His analogies included an imaginary intelligent being called "Boltzmann's Demon," who relentlessly runs around reorganizing and dispersing energy, in order to show how the W in Boltzmann's equation relates to energy dispersion. This dispersion is transmitted via atomic vibrations and collisions, and other verbal arguments. Atkins wrote: "each atom carries kinetic energy, and the spreading of the atoms spreads the energy…the Boltzmann equation therefore captures the aspect of dispersal: the dispersal of the entities that are carrying the energy."
Stanley Sandler, in his 1989 Chemical and Engineering Thermodynamics, described how given any thermodynamic process, a quantity TS can be interpreted as the amount of mechanical energy that has been converted into thermal energy by viscous dissipation, dispersion, and other system irreversibilities. In 1997, John Wrigglesworth described spatial particle distributions as represented by distributions of energy states. According to the second law of thermodynamics, isolated systems will tend to redistribute the energy of the system into a more probable arrangement or a maximum probability energy distribution, i.e. from that of being concentrated to that of being spread out. By virtue of the First law of thermodynamics, the total energy does not change; instead, the energy tends to disperse from a coherent to a more incoherent state. In his 1999 Statistical Thermodynamics, M.C. Gupta defined entropy as a function that measures how energy disperses when a system changes from one state to another. Other authors defining entropy in a way that embodies energy dispersal are Cecie Starr and Andrew Scott.
In a 1996 article, the physicist Harvey S. Leff set out what he called "the spreading and sharing of energy." Another physicist, Daniel F. Styer, published an article in 2000 showing that "entropy as disorder" was inadequate. In an article published in the 2002 Journal of Chemical Education, Frank L. Lambert argued that portraying entropy as "disorder" is confusing and should be abandoned. He has gone on to develop detailed resources for chemistry instructors, equating entropy increase as the spontaneous dispersal of energy, namely how much energy is spread out in a process, or how widely dispered it becomes – at a specific temperature.
Further reading
- Carson, E. M., and Watson, J. R., (Department of Educational and Professional Studies, Kings College, London), 2002, "" University Chemistry Education - 2002 Papers, Royal Society of Chemistry.
- Frank L. Lambert, 2002, "" Journal of Chemical Education 79: 187-92. Updated version
- Leff, Harvey S., 2007, "Entropy, Its Language and Interpretation," Foundations of Physics 37(12): 1744-66.
Texts using the energy dispersal approach
- , W. H. Freeman ISBN 0-7167-8759-8
- --------, Physical Chemistry for the Life Sciences. Oxford University Press, ISBN 0-19-928095-9; W. H. Freeman, ISBN 0-7167-8628-1
- Bell, J., et al., 2005. Chemistry: A General Chemistry Project of the American Chemical Society, 1st ed. W. H. Freeman, 820pp, ISBN 0-7167-3126-6
- Brady, J.E., and F. Senese, 2004. Chemistry, Matter and Its Changes, 4th ed. John Wiley, 1256pp, ISBN 0-471-21517-1
- Brown, T. L., H. E. LeMay, and B. E. Bursten, 2006. Chemistry: The Central Science, 10th ed. Prentice Hall, 1248pp, ISBN 0-13-109686-9
- Ebbing, D.D., and S. D. Gammon, 2005. General Chemistry, 8th ed. Houghton-Mifflin, 1200pp, ISBN 0-618-39941-0
- Ebbing, Gammon, and Ragsdale. Essentials of General Chemistry, 2nd ed.
- Hill, Petrucci, McCreary and Perry. General Chemistry, 4th ed.
- Kotz, Treichel, and Weaver. Chemistry and Chemical Reactivity, 6th ed.
- Moog, Spencer, and Farrell. Thermodynamics, A Guided Inquiry.
- Moore, J. W., C. L. Stanistski, P. C. Jurs, 2005. Chemistry, The Molecular Science, 2nd ed. Thompson Learning. 1248pp, ISBN 0-534-42201-2
- Olmsted and Williams, Chemistry, 4th ed.
- Petrucci, Harwood, and Herring. General Chemistry, 9th ed.
- Silberberg, M.S., 2006. Chemistry, The Molecular Nature of Matter and Change, 4th ed. McGraw-Hill, 1183pp, ISBN 0-07-255820-2
- Suchocki, J., 2004. Conceptual Chemistry 2nd ed. Benjamin Cummings, 706pp, ISBN 0-8053-3228-6
External links
- A large website, maintained by Frank L. Lambert, with to work on the energy disperal approach to entropy.
- on energy dispersal
- Frank Lambert's essays on entropy and energy dispersal:
- "" A presentation of entropy from the viewpoint of energy dispersal, aimed at undergraduate chemistry students.
- ""
- ""
- ""
- "" An outline contrasting "thermodynamic" and "configurational" ("positional") entropy in chemistry.
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