Dr. John M. Garland, M.D. and Ph. D. from Manchester University (U.K.), has informed me that his remarkable article -- an analysis of cancer that involves consideration of energy dispersal (entropy increase) and the spread of cancer to distant sites (in fractal terms) -- has been accepted by the Elsevier journal, "Critical Reviews in Oncology and Hematology" for publication in a couple of months. We have communicated frequently over the past two years, but of course the content and its magnitude (51 pages of ms. with 155 references) are totally his accomplishment. (The abstract is at http://dx.doi.org/10.1016/j.critrevonc.2013.04.001.)
He summarized it for me thus:
This article arose from considering that the variety of different entities thought to induce cancer is huge, but that all cancer cells energetically behave identically; they become highly motile, proliferate seemingly without control, and their internal organisation becomes increasingly degenerate. So, if this energetic behavior is universal, why is there not a universal mechanism?
Until now, cancer induction is viewed/represented as from a deranged biochemical pathway, usually by mutation, whose components are arranged linearly and end in cancer-prone targets, for example DNA replication control or cytoskeletal activity. There are problems with this, for example: on the molecular scale, how different pathways intersect; how many are needed for a given effect; how all the myriad of biochemical pathways normally “fit together”; and progression and development of the universal phenotype. The first clue to cancer universality lies in the apparent switch from regulated structure and behavior to generalized increased dynamic activities at structural expense; as structure degenerates, dynamic activities such as motility and migration, replication and indeed clinical poor outcomes, increase.
Fundamental to all biochemical pathways is the constant flow of energy in chemical reactions. The interaction of that flow with the environment in which they take place is crucial and inter-dependent. Thus, building cell structure or undertaking dynamic activity are always dependent on energy flow, the greater the energy available the more likely it is that a reaction will take place. However, in the process of structure-building the overall energy available for dispersal elsewhere becomes “locked in” while in dynamic activity it is constantly being dispersed or spread out. Cells normally co-ordinate these options through numerous checks and balances – always with the possibility of random distribution of energy in or out of the cell. Thus, an unintended/unusual shift in cellular conditions could potentially favor dynamic activity that does not favor structure-building but rather random energy dispersal -- already suggesting a universal clue to cancer.
The interior of a cell is astronomically variable and for a cell to function the environments managing all biochemical pathways must somehow be coherently organized. Nature widely uses a very simple tool, fractal geometry, to generate re-iterated “levels” of organization and which can deal with huge spatial variation. Clouds and snowflakes are examples. All different, but overall the same shape regardless of size. If we now apply fractal geometry to the distribution of energy flow in cells, they will self-assemble into fractal “corridors” where the components/reactions are decided by the amount of energy they dissipate or minimal energy states. This fractal “map” of energy dispersal is continuously changing according to energy demand, as in melting/freezing snowflakes, formation of clouds, generation of river patterns. The significance of this organization is that all parts are dynamically seamless; new areas can be added at different levels, and there are an infinite number of components that can fit into the same “space” (in the model termed Domains which at any level are absorbed into the next tier). The video files in the on-line article illustrate the creation of fractals which can be very easily conceived as energy flows arising from domains. However, and crucially for this model, every biochemical reaction is connected, in some way by its pattern of energy flow to every other. Further, pathways need not be linearly-ordered nor consecutive and components self-assemble according to ‘normal’ energetic criteria (see reference 155, Jun & Wright, Nat. Rev. Microbiol.8, 600, 2011). This provides the key to a universal framework both for normal cell operation and also for cancer; in cancer, the fractal network of energy dispersal is simply skewed towards maximizing that energy flow randomly in dissipation rather than involving orderly structure and function.
The final element concerns the enormous unpredictable variability within cells; there are so many things going on at once. Chaos theory deals mathematically with unpredictability, and chaos can be linked to fractal geometry through descriptions of unpredictable behaviors which influence fractal formation. If this linkage is applied to fractal entropy, cell organisation is inherently stable overall because these variables effectively cancel each other. For cancer, however, the situation is different. Cancer-inducing agents all share the property of being permanently active (i.e. they uniformly favor the random dispersal of energy rather than its use in creating structure) whether in a suppressive or activation mode. The effect of this is to replace variability with a constant dissipative component and permanent re-alignment of energy flow toward random dispersal. Over time the network becomes increasingly focused on dissipation and activities with the highest abilities, i.e. dynamic activity, lead to the self-generating progressive disturbances recognized in cancer.
Many aspects of the model are amenable to testing, for example using mathematical modelling or exploring how enzyme systems energetically self-assemble in complex mixes.
[In the Acknowledgements section of Dr. Garland's article, he refers to "Professor F. Lambert (Occidental College, USA)" and then concludes with "This paper is dedicated to Professor Lambert for his work on the fundamental applications of entropy."]
An ex-student has just referred me to an important article by two professors in a Japanese university, http://onlinelibrary.wiley.com/doi/10.1111/j.1749-6632.2009.05166.x/full#b9. It deals with the errors of many economics experts, from Georgescu-Roegen of 40 years ago up to the present, in their naïve attempts to connect economics to thermodynamics. Paragraph 2.6 in that article - about my view of entropy in thermo - is a neat summary.
Josh Floyd (whose important article about misapplying entropy ‘everywhere’ is cited in the Archives of this website for April 2008 – just scroll down!) had previously castigated Georgescu-Roegen on Amazon.com (awarding his book with one star – only because Amazon doesn’t permit 0 stars!): http://www.amazon.com/The-Entropy-Law-Economic-Process/product-reviews/1583486003/ref=cm_cr_dp_qt_hist_one?ie=UTF8&filterBy=addOneStar&showViewpoints=0
Floyd also evaluated Rifkin’s “Entropy Entropy Entropy” correctly in Amazon.com with Amazon’s one star (i.e., 0 stars!) in http://www.amazon.com/Entropy-A-New-World-View/product-reviews/0670297178/ref=cm_cr_dp_qt_hist_one?ie=UTF8&filterBy=addOneStar&showViewpoints=0
Most important: I have just discovered Floyd’s thought-provoking ‘continuing’ web page “Beyond This Brief Anomaly”. Its address is that: http://beyondthisbriefanomaly.org/
A statement about the importance of entropy as energy dispersal in a chemical reaction is in the sixth edition of Vollhardt and Schore’s “Organic Chemistry” text:
“If the enthalpy of a reaction depends strongly on changes in bond strength, what is the significance of ΔS°, the entropy change? You may be familiar with the concept that entropy is related to the order of a system: Increasing disorder correlates with an increase in the value of S°. However, the concept of “disorder” is not readily quantifiable and cannot be applied in a precise way to scientific situations. Instead, for chemical purposes, ΔS° is used to describe changes in energy dispersal. Thus, the value of S° increases with increasing dispersal of energy content among the constituents of a system. Because of the negative sign in front of the TΔS° term in the equation for ΔG°, a positive value for ΔS° makes a negative contribution to the free energy of the system. In other words, going from lesser to greater energy dispersal is thermodynamically favorable.
What is meant by energy dispersal in a chemical reaction? Consider a transformation in which the number of reacting molecules differs from the number of product molecules formed. For example, upon strong heating, 1- pentene undergoes cleavage into ethene and propene. This process is endothermic, primarily because a C–C bond is lost. It would not occur, were it not for entropy. Thus, two molecules are made from one, and this is associated with a relatively large positive ΔS°. After bond cleavage, the energy content of the system is distributed over a greater number of particles. At high temperatures, the –TΔS° term in our expression for ΔG° overrides the unfavorable enthalpy, making this a feasible reaction.”
Professor Leff has not only completed the publication of his five articles in the Physics Teacher mentioned below, but made them fully available online at http://www.csupomona.edu/~hsleff/selpubs.html.
Already, one author of a physics text has stated that he will use Leff's approach to entropy in it.
Professor Leff’s articles
Please click the Archive section of this site for June 2008 for a full introduction:
Physicist Harvey S. Leff (Professor Emeritus of the California State Polytechnic University, Pomona) published the first article that quantitatively presented the idea of entropy involving the dispersal or spreading of a system’s energy, with entropy as a measure of such spreading, in 1996 (Am. J. Phys. 1996, 64, 1261-1271). When I learned about it in 1999, I inserted a Note to it in my “Entropy Is A Cracked Crutch” ms. (published in February 2002) and gave more proper credit as the lead reference in my next article, “Entropy Is Simple, Qualitatively” (October 2002),
Now Professor Leff has begun a series of five articles in the Physics Teacher. As might be expected, because they are intended for physicists, they will be far more rigorous mathematically and theoretically than my qualitative approach to entropy. The first article appeared in the January 2012 issue: H. S. Leff, Phys. Teach., “Removing the Mystery of Entropy and Thermodynamics --- “Part I”, 50, 28-31 (2012); in February appeared “Part 2”, 50, 87-90 (2012). The subsequent Parts will be published monthly
Online article – why the concept of entropy was considered so difficult – and why it isn’t.
In October, the editors of an online scientific journal invited me to develop a guest editorial. It is online at lambert2011.pdf. I chose what might appear to be an egregious title, "The Conceptual Meaning of Thermodynamic Entropy in the 21st Century", but it is not. As stated in the last lines, a majority of the future leaders in US chemistry by mid-century will have been introduced to entropy via this concept of its being a measure of energy dispersal.
The initial goal of the brief article was to explain why brilliant physicists and chemists of the past century failed to explain entropy clearly - i.e., failed to develop an adequate conceptual explanation for the success of dS = dq/T. Certainly, the ‘driving force’ in this relationship is simple: the nature of q, energy. A common property of energy is that all types – including molecular energy -- tend to spread out, disperse in space if constraints are lessened or removed. It was simply unfortunate that Boltzmann's "disorder" comments of 1898 became the dominant “meaning” of entropy for so long.
This journal reports the number of downloads of its articles on its index page. Surprisingly, the number for this editorial exceeded 1300 by late February. (It is a legitimate count ! I had suspicions that the Journal may have manipulated them, but a friend who can access such arcane matter sent me a list of 800 when I asked him.)
As I mentioned two years ago, a truly excellent text, the 2nd edition of Burdge’s “Chemistry” was published. Now, with Dr. J. Overby, Burdge’s text has been revised to present an ’atoms first’ approach for those who prefer it..
Both texts are unusually good in their depiction of entropy. Not only have all references to entropy as “disorder” been eliminated but, far beyond this, “what entropy is” is uniquely handled.
Featured throughout each text are 16 two-page “Visualizing Chemistry” (large drawings/illustrations) of important points, many extended to online animations available to student users. That feature in the thermodynamics chapter depicts six examples of system change that are correlated with entropy change and ‘particles in a box’ energy levels – volume increase, temperature increase, molecular complexity change, molar mass, phase change, and chemical reaction. Many good texts only attempt to show such differences via energy levels for volume expansion and temperature increase. None supplement with animation as do Burdge or Burdge and Overby..
Further, I am impressed by the wide utility of the text for a large span of students’ competence – specifically re my focus on the presentation of entropy. Due to information I have received from instructors in the classroom, almost all students readily accept the concept of entropy as measuring how widely spread in space or in additional particles, the energy of molecules (or that which is supplied to them) becomes. However, too many students of average ability ‘get stuck’ when microstates are introduced in any meaningful detail.
Burdge barely mentions the word, microstate – her ‘particle in a box’ energy levels are left at that, as greater spreading out of energy – volume increase, closer levels; temperature increase, more occupancy of higher levels, etc. I think this is optimal, because it is clear over the whole span of students’ abilities in gen chem. (And, if desired, in a very short discussion only for students going on to physical chemistry, a basic relation of numbers of energy levels/microstates and entropy change can be elucidated.)
An article about carbon nanotubes – tiny hollow tubes of carbon atoms (ca. 25 to 100 thousandth of the thicknessof a human hair) – whose properties of rapidly absorbing water were found to be related to entropy and enthalpy changes appeared in a recent issue of the Proceedings of the National Academy of Sciences. (The complete article is available via http://www.pnas.org/content/108/29/11794)
The PNAS abstract below uses the words entropy and enthalpy in a traditional manner. Following it, my expansion of the abstract in terms of viewing entropy as energy spreading out to the surroundings due to hydrogen bonds being broken when water molecules move into minute CNTs (and seeing that enthalpy increases in one particular CNT size because stronger hydrogen bonds are formed) – more clearly explains exactly what happens.
Entropy and the driving force for the filling of carbon nanotubes with water
Tod A. Pascala,b, William A. Goddarda,b,1, and Yousung Junga,1 a Graduate School of Energy, Environment, Water, and Sustainability, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea; and b Materials and Process Simulation Center, California Institute of Technology, Pasadena CA 91125 Contributed by William A. Goddard, May 25, 2011.
AbstractThe spontaneous filling of hydrophobic carbon nanotubes (CNTs) by water observed both experimentally and from simulations is counterintuitive because confinement is generally expected to decrease both entropy and bonding, and remains largely unexplained. Here we report the entropy, enthalpy, and free energy extracted from molecular dynamics simulations of water confined in CNTs from 0.8 to 2.7 nm diameters. We find for all sizes that water inside the CNTs is more stable than in the bulk, but the nature of the favorable confinement of water changes dramatically with CNT diameter. Thus we find (i) an entropy (both rotational and translational) stabilized, vapor-like phase of water for small CNTs (0.8–1.0 nm), (ii) an enthalpy stabilized, ice-like phase for medium-sized CNTs (1.1–1.2 nm), and (iii) a bulk-like liquid phase for tubes larger than 1.4 nm, stabilized by the increased translational entropy as the waters sample a larger configurational space. Simulations with structureless coarse-grained water models further reveal that the observed free energies and sequence of transitions arise from the tetrahedral structure of liquid water. These results offer a broad theoretical basis for understanding water transport through CNTs and other nanostructures important in nanofluidics, nanofiltrations, and desalination.
My ‘translation’ of the above abstract of fundamental CNT research – in terms of entropy as a measure of energy spreading out in the surroundings in a process and enthalpy as energy becoming incorporated in stronger chemical bonds in a process:
Water spontaneously flows into extremely small carbon nanotubes (CNTs) -- but why should it? What is the ‘driving force’? Carbon does not attract water!
Each molecule of ‘bulk’ or ordinary water (or ice) is about 0.3 nm (nanometers) in diameter and is strongly attracted to two other water molecules by 4 hydrogen bonds, HBs.
Two HBs are due to the H atoms of a particular water molecule being attracted to the (lone electron pairs) of another water molecule. Two additional HBs are formed between the lone pairs of that ‘particular’ water molecule, acting as acceptors in being attracted to the H atoms of a third water molecule. However, all water molecules are rapidly and ceaselessly breaking such bonds while instantly forming similar hydrogen bonds with other water molecules as they continually move in any body of water – whether a large tank, a beaker, or a thimble.
Of course, there is no attraction between water molecules and the carbon walls of a CNT, so any water molecules within a CNT that are touching the walls cannot be attracted to them as they were previously hydrogen-bonded to adjacent water molecules. Thus, each water molecule next to the CNT walls must lose one or two hydrogen bonds in entering the tube – and the amount of energy in that loss as similar water molecules enter must be spread out to the surroundings: to the tube walls, to outside molecules. Clearly, this process of greater energy dispersal in space compared to bulk water is favored – it is an increase in entropy.
Because of the size restrictions inside the smallest CNTs, e.g., those with an 0.8 nm diameter, only about “two plus” water molecules per cross-section of the CNT, with three or fewer such “cross-sections” per nm of the CNT length is probable. This means that the energy of some 12 hydrogen bonds in the water per nm of the length of the tube, must be dispersed from bulk water if/when it moves into such a CNT – a comparatively large spreading out of energy as/after water molecules enter, and thus a very favored process energetically: the cause of spontaneous movement of water into 0.8 nm CNTs is an entropy increase.
Also, because there are fewer H-bonds on each water molecule – i.e., considerably less attraction between each molecule in the chain/line/assembly of water molecules in the CNT than in “bulk water” – those water molecules in an 0.8 nm CNT are slightly freer to move than in bulk water, a little bit more like a gas than like a liquid (i.e., a “vapor-like phase” in the scientific abstract).
Surprisingly, a slight difference in diameter causes quite different arrangements for the water molecules. In 1.1-1.2 nm diameter CNTs, the water that enters and is ‘lined up’ the length of the tubes has enough space for more molecules per nm of tube length (but more hydrogen bonding between adjacent molecules than in 0.8 nm tubes). Thus, their limited motion due to slightly more hydrogen bonding causes them to line up (“stack up”) less freely than in bulk water -- almost as though they were in an ice-like structure. But such firmer bonding arrangements compared to bulk water is an enthalpy increase. Again, although here aided by stronger bond formation rather than only HB breakage, movement of water molecules into a 1.2-1.2 nm diameter CNT is energetically preferred to their remaining in bulk water.
In CNTs larger than 1.4 nm, relatively fewer molecules -- but still a very substantial number -- have some of their hydrogen bonds broken as they enter >1.4 nm CNTs compared to smaller CNTs. Therefore, despite a lesser quantity, this decrease in inter-molecular bonding results in the dispersal of some bond energy to the surroundings – i.e., an increase in entropy of the ‘universe’ of surroundings and system, when water molecules enter the larger CNTs.
I worked hundreds of hours on several sites in Wikipedia in 2006 and some in 2007. However, because no one can put their own bio in Wikipedia, it is quite an honor that an important Wikipedia administrator has installed my bio -- with the only recent picture that I have -- too much of a smile and all. Click on: Wikipedia Frank L. Lambert.
It was just reported to me that the Dean of a university wrote a blog item in 2009 about my ‘Gutenberg Method' of teaching referring way back to its being featured by the editor of the Journal of Chemical Education in 1963. JCE1963.pdf Below is an excerpt, with corrections and citations added by me.
Dean of Academic Support Services, Johnson C. Smith University
Earlier this week, I wrote about two physics instructors who use vodcasting as a technique to replace traditional lectures with a more engaged classroom experience. I came across another article today (again on Reddit) from
the 1960s 1986, where a Professor Morrison lays out his case for what he calls The Gutenberg Approach. This piece is paired with a letter from 2008 an editorial from the Journal of Chemical Education of 1963 about the discovery and use of this method, where Frank L. Lambert gives the following summary of the problem as he sees it:
The lecture system was crazy for teaching organic chemistry. What are professors doing in a lecture? They’re outlining and explaining the important points (and wasting time mentioning even obvious points) of the text on the blackboard. But why? Gutenberg invented movable type. That made printed textbooks available 500 years ago — even now in chemistry rather than alchemy! Students don’t read them? Of course not, if the whole course is dependent on what the prof puts on a blackboard! Students can’t pick out the most important ideas and facts from a 500-page text (in 1948, or thousand-page now) by themselves. They’re beginners.
[W]hy not give them something a bit better than the [class] notes on the day or the week before the class, not really an outline of the text but more of a guide to what’s important and what’s not in each day’s text assignment. Then the students could read a day’s assignment and know what to look out for as the key points, realizing that the professor is not going to outline it on the board. Instead, she or he will explain in detail a few complex things in the assigned pages, answer any questions about them, and show how to conquer problems like those in the text, always open to questions and for back and forth with student.
(The discovery of 'The Gutenberg Method' is attached.)
Robert T. Morrison, co-author of the leading organic chemistry text for some 30 years, died in April. (We were friends in our graduate school days at the University of Chicago.) If you teach organic or have taken a course in it, you should read his lecture against lecturing (as mentioned by Dr. Eubanks, previously) — the funniest ever given seriously at a University of Chicago conference, or any other!
The 2nd edition of Burdge’s Chemistry was published in late January. It is truly excellent. Not only have all references in the previous edition to entropy as “disorder” been eliminated but, far beyond this, the introduction to “what entropy is” is superbly handled. Featured throughout the text are 16 two-page “Visualizing Chemistry” (large drawings/illustrations) of important points, almost all extended to online animations available to student users. That feature in the thermodynamics chapter depicts seven examples of system change that are correlated with entropy change and ‘particles in a box’ energy levels – volume increase, temperature increase, greater mass of molecules, lesser or greater structural complexity (i.e., the latter with more energetic modes), etc. Most good texts only attempt to show such differences via energy levels for volume expansion and temperature increase. None supplement with animation.
Further, I am impressed by the wide utility of the text for a large span of students’ competence – specifically re my focus on the presentation of entropy. Due to information I have received from instructors in the classroom, almost all students readily accept the concept of entropy as measuring how widely spread in space the energy of molecules becomes. However, too many of average ability ‘get stuck’ when microstates are introduced in any meaningful detail.
Burdge does not go into microstates at all – her ‘particle in a box’ energy levels are left at that, as greater spreading out of energy – volume increase, closer levels; temperature increase, more occupancy of higher levels, etc. I think this is optimal, because it can become clear for all levels of ability in a class, especially with Burdge’s visual aids. Then, an hour or two only with those students going on to physical chemistry (linking energy dispersal in space with the increased number of accessible microstates and the Boltzmann equation, plus the Boltzmann with Clausius’ entropy) is adequate preparation for chemistry majors’ later course.
I have finally read a book that I was told had become popular, “Entropy Demystified”. It is a 217-page disaster to anyone wanting to understand entropy and the second law. Most of the lengthy evaluations that praise the book on Amazon.com seem to have been written by the author's best friends, several being mature physicists – rather than by persons trying to understand entropy for the first time. The following is more objective than those "reviews": giving it a rating of “no stars” out of a possible five. (However, Amazon.com, for a reason you might guess J, increased that rating to “one star”.)
Fifty years ago, Arieh Ben-Naim, as every student in a physics or chemistry class of that era, was mystified by his introduction to entropy and the second law of thermodynamics. Although he became a professor of chemistry at the University of Jerusalem before retiring 15 years ago, Ben-Naim has evidently not kept up with the teaching of those topics in current chemistry texts. Thus, he seems unaware that most general chemistry texts currently published in the US (16) and three in physical chemistry now clearly and simply present entropy and the second law (Check “May 2009” in this website).
Therefore, his 217 pages of “Entropy Demystified” that are necessary to develop his personal viewpoint (an information theory variant, not present in any US undergraduate chemistry textbook) can be clarified by 3-4 pages in each of the chemistry texts listed in this site at “May 2009” with their ISBN numbers.
In fact, a conceptual summary of the second law and entropy for all chemistry students and many non-scientists can be abstracted from these texts in two sentences: “Energy of all types in chemistry changes – if it is not hindered – from being localized in one volume to becoming more dispersed, spread out, distributed in space (and abstractly at one instant, in any one of many more energy quantum states, microstates, than were accessible before the change).” Then, “entropy change is the quantitative measure of how much more widely distributed the initial energy becomes in a spontaneous process in chemistry.” Thus, in real processes, energy literally spreads out in space, and abstractly, at each instant, is in one microstate of a maximally probable number of quantum states (microstates) that are consistent with a final macrostate at equilibrium.
Unfortunately, Professor Ben-Naim’s fundamental error, summarized on page 204 but vitiating all previous pages, is his misinterpretation of what happens in real systems of molecules, especially in the simple isothermal expansion of ideal gases or in their mixing or expansion. These cases have misled him to focus on the lack of change in the total energy of the system, rather than on what is actually the fundamental cause of all thermodynamic entropy change in chemistry: the increased spreading of the initial energy of actual molecules in space when constraints are removed – e.g., their spontaneously moving into a greater volume from a smaller volume (with unchanged energy) in a process such as expansion or mixing. This is what traditional thermodynamic entropy readily measures and, as just stated, can be readily understood.
Ben Naim admits, in italics, the disconnect between information and the second law on page 203 of “Entropy Demystified” by writing “a measure of information cannot be used to explain the Second Law of Thermodynamics.” This is true, indeed. The connection between the second law and information is tenuous.
Contrast this with the modern view in beginning collegiate chemistry texts, e.g. “whenever a product-favored chemical or physical process occurs, energy becomes more dispersed...This is summarized in the second law of thermodynamics, which states that the total entropy of the universe ... is continually increasing.” (Moore, Stanitski, and Jurs; 3rd edition.) A popular physical chemistry text that is used world-wide states “...the Second Law of thermodynamics, may also be expressed in terms of another state function, the entropy, S. ...entropy...is a measure of the energy dispersed in a process...” (Atkins and de Paula, 8th edition.)
The connection between the second law, spontaneous chemical reactions or physical processes, dispersal of energy, and entropy is integral, tight, and widely accepted in chemistry books. It does not require 200 pages for its justification.
In “what’s new” for August 2007 I described my article that showed how texts that introduced ‘positional’ (configurational) entropy to students would totally mislead them: beginners are taught that “matter tends to become dispersed” and that there are two “types” of entropy rather than one. Equally disastrous to students’ understanding is a focus on the ‘probability’ of molecules’ positions as the sole factor in entropy increase.
[Entropy increase is first enabled by molecular motional energy (rapidly moving or vibrating molecules); only then is entropy increase actualized by the probability of a maximal dispersal/distribution of that energy – in space, within each microstate of a greater number of accessible microstates.]
A far more fundamental article by Professor E. I. Kozliak has just been published in the September issue of the Journal of Chemical Education, “Overcoming Misconceptions about Configurational Entropy in Condensed Phases”. (He had previously resolved the old problem of incorrectly understanding “residual entropy” as simply due to molecules’ locations in space.)
A minority of US general chemistry texts for majors still describe entropy in terms of “disorder” – an unfortunate subjective concept whose source appears to be a naïve statement by Boltzmann (boltzmann.html). Now, however, most ‘gen chem’ texts have discarded this non-scientific view and describe both entropy (e.g. standard molar entropy) and entropy change as measuring the result of energy becoming dispersed in physical or chemical processes – literally spreading more widely in space, while abstractly dispersing on additional energy levels in a conventional “particle in a box” diagram of one microstate. (The latter, of course, then directly implies a greater number of microstates, W, in any final macrostate.)
It was eight years ago that the ms. outlining the above approach was accepted for publication (that now, revised and corrected, is available at this site: entropy_is_simple.
There have been some noteworthy improvements in texts’ treatment of entropy in terms of energy dispersal. A few will be mentioned here. In May will be listed the 21 chemistry texts that no longer define entropy as “disorder” but rather emphasize molecular energy dispersal, concretely in space or abstractly on more energy levels in each microstate, as a useful approach to understanding standard entropy and entropy change.
Levine, in his new 6th edition of “Physical Chemistry”, well develops entropy, S, as a measure of the probability of a thermodynamic state. On page 101, he states “…order and disorder are subjective concepts, whereas probability is a quantitative concept. It is therefore preferable to relate S to probability rather than to disorder.” Then, he summarizes, “…it is the distribution of energy (which is related to entropy) that determines the direction of spontaneity.”
The final sentence of the preceding section is “The website entropysite.com contains several articles criticizing the increasing-disorder interpretation of entropy increase and promoting the increasing-dispersal-of-energy interpretation.”
To be cited by Levine is indeed an honor.
McMurry and Fay have completely discarded “disorder” from the 5th edition of their text. However, they emphasize randomness as the key to understanding entropy rather than a start to that goal: It is energy that is being carried by randomly moving molecules as far as they are allowed to move that results in a probable energy distribution, a final equilibrium state.
Chang, in his 10th edition of “Chemistry” has also eliminated any mention of “disorder” in connection with entropy in this most recent of a distinguished series.
Kotz, Treichel and Townsend in their 7th edition have markedly improved their previous introduction of spontaneity and entropy, with an even more clear and complete exposition. They surpass several authors who still separate the dispersal of energy from the dispersal of molecules. Matter, in chemistry, never spreads out without the intervention of energy (macro matter), unless it is a carrier of energy (molecular matter above 0K).
Hill, Kolb, and McCreary in their 12th edition of “Chemistry for Changing Times” have now adopted their introduction of entropy as “a measure of the dispersal of energy in a system…” with no reference whatsoever to ‘disorder’.
Unfortunately, I had not seen a copy or excerpts from the 2008 2nd edition of Gilbert, Kirss, Foster and Davies “Chemistry: The Science in Context” until last week. The authors have remarkably improved their treatment of thermodynamics in this edition. Not only have they completely eliminated any mention of “disorder” in connection with entropy, but their presentation of spontaneous processes and entropy is unusually well done.
Admittedly from anecdotal evidence, but not only from my geographical area, I am becoming convinced that the majority of students in general chemistry classes are ‘overtaught’ about microstates. In contrast to those texts emphasizing ‘positional entropy’ and spending an inordinate amount of time and space on probability to introduce microstates, Gilbert and his collaborators directly present energy levels and simple statements about arrangements on energy levels as their four-paragraph intro to the Boltzmann equation. This is characteristic of their entire thermo chapter — well-presented and sufficient — but not too much.
A standard molar entropy, S0, is the absolute (i.e., not ‘relative’) measure of the entropy of a substance at 298.15 K. It is extremely important because these S0 values are essential for so many areas of chemistry and chemical engineering to predict the outcome of reactions via the Gibbs equation, its most simple form being
The January 2009 issue of the Journal of Chemical Education contains an unusually important article by physics professor Harvey S. Leff and me — important because it shows a surprisingly simple linear correlation. The S0 of 77 solid substances, widely differing in type — e.g.,from Cu to NaCl to UF4 to C20H42 — and the quantity of enthalpy, ∆H0, added to them while they were heated from 0 K to 298.15 K are closely linked.
The equation is:
There is no “mystery” to entropy here, no place for old subjective terms like “disorder”, or such new terms as “missing information” ! Entropy in this most fundamental case is simply a measure of the spreading of energy within a cooler substance from its warmer surroundings when it is heated — starting with the cooler substance near 0 K and summed up, degree by degree, to 298.15 K, the ‘standard’ temperature.
The amount of spreading/energy dispersal depends upon the material in which the spreading occurs and the amount of energy added to it.
A fundamental article about “residual entropy” by Professor E. I. Kozliak and me is now available here. Residual entropy, the entropy remaining in crystals of some compounds even near absolute zero, e.g. CO, N2O and H2O, has traditionally been accounted for (and counted) just from the number of different molecular arrangements in the crystal. From this, chemists have felt that entropy can depend only on a “position in space”, regardless of a substance’s internal energy. Unfortunately, residual entropy has been the ‘poster boy’ of an example of “positional entropy”.
In a previous article, Kozliak showed that the results from counting procedures in residual entropy calculations are identical to those from considering the different forms on different energy levels — a novel focus on entropy values as related to energy distributions in substances like CO, rather than on the number of arrangements of the molecules, their “positions in space”.
In this 2008 article, Kozliak shows how residual entropy is inherently coupled to the corresponding latent heat which would be released upon cooling if a reversible path were available. That such a process is not fanciful for CO or N2O (although not yet achieved) is illustrated by the actual release of energy at very low temperatures by ice, when a small amount of KOH is added as a ‘catalyst’ and ice XI is formed that has no residual entropy.
I failed to announce a most important publication about entropy, “Entropy, Its Language, and Interpretation”. It was written by Professor Emeritus of Physics Harvey S. Leff (of the California State Polytechnic University, Pomona) and appeared in Foundations of Physics, 2007, 37 (12), 1744-1766. The abstract is available here and, of course, the full article is in the journal or online through one’s institutional library.
As indicated by its length and the eminence of the journal, this article is both thorough and theoretically sound in presenting the increase in entropy as fundamentally a spreading of energy spatially during processes and its greater temporal spreading over accessible microstates after such an entropy increase.
“Temporal spreading” means that a system’s total energy (e.g., that of an ideal gas) in a single microstate at one instant in time — a particular arrangement of its molecular energies on quantized energy levels — will change, in the next instant of time, to a different arrangement/microstate. Then, if after a process there is a greater number of accessible microstates than before, a few or many different microstates are more likely to be reached from an initial microstate in a second of time or so over which a measurement is made. It can be seen that this is a “greater temporal spreading of the system's energy” in the sense of a “temporal dance” over the same number but probably a few or many more different microstates than prior to the process.
The notion of temporal speading that increases with the number of accessible microstates (W) is consistent with, and provides a new interpretation for the Boltzmann entropy, S = kB ln W, where kB is Boltzmann’s constant.
It is appropriate to see entropy’s symbol S as shorthand for spreading, a coincidental memory aid for beginning students.
I am indebted to Professor Leff for aid over the past six years. We have just collaborated on a very important article (to be published within the next five months) that should convince the last doubters of the value of our viewpoint.
Joshua Floyd, with a background in engineering and now teaching at the Australian Graduate School of Entrepreneurship in the Swinburne University of Technology, Victoria, Australia, has published a brilliant and scholarly article, "Thermodynamics, entropy and disorder in futures studies". Its abstract is below. (The article is accessible via college or university library e-journal services.) He discusses the manifold misuse of the second law of thermodynamics over many years and by many economists, IT specialists, serious professionals involved in futures studies, and not-as-serious popularizers. The major error in most of their writing is an assumption that this law, derived from studies of the energetic behavior of atoms and molecules, applies to “order or disorder” in the material objects with which we all must deal
Futures 39 (2007) 1029-1044. Abstract
The conceptual bases of futures studies are constrained by physical reality only to the extent that we construct these according to our best understanding of physical principles. This places a burden on futures practitioners to ensure that engagement and use of these principles is sufficiently robust to protect the plausibility of their work. The second law of thermodynamics is widely recognized as having fundamental implications for the nature of our physical reality. It is also widely misinterpreted, leading to distorted understanding of this reality. Thermodynamic principles are frequently referred to in the futures literature, and are sometimes fundamental to the futures thinking underlying the work. Reflecting the widespread misunderstanding of the second law, usage in the futures literature is usually problematic. This has implications for the value of the work, and also for the credibility of the field. In this article, the problem is demonstrated, and an updated interpretation of the second law is introduced. The origin of the problem is examined from historical and scientific perspectives within the thermodynamics field. The updated interpretation's implications are examined in the context of futures and other transdisciplinary perspectives.
1. Introduction: thermodynamics in futures studies
2. An introduction to the problem, and to a response
3. Understanding the problem: some history and science of thermodynamics
4. Reinterpreting the second law: the futures studies context
In his new book “Notes From the Holocene (A Brief History of the Future), Dorion Sagan, science author and eldest son of the late Carl Sagan, writes:
“Publications in the Journal of Chemical Education by Occidental College professor emeritus Frank L. Lambert have drawn attention to the century-old non-scientific mantra, entropy-as-disorder, altering the modern textbook landscape. [By April 2007, authors of eighteen chemistry textbooks] had deleted their previous identification of entropy as “disorder”. The new texts describe the second law as being fundamentally a matter of energy dispersal. If energy is not hindered, it spreads out.”
Invited to speak as a registrant at the International Thermodynamics Symposium at MIT on October 4-5, Sagan opened his remarks in the Session, “Foundations of the Second Law”, with the above quotation from his book.
In addition to the 16 chemistry textbooks described in March 2006 and December 2005, two more texts now introduce entropy in terms of energy dispersal within a system or in the universe of a system plus its surroundings.
In contrast to the Second Law chapter of the 7th edition, which had some 27 instances of using "order to disorder" as a rationale for change, "disorder" and "disorderly" are mentioned only 3 times in the new 8th edition. Atkins, with co-author dePaula, now state that their view of entropy "summarized by the Boltzmann formula is consistent with our previous statement [earlier in the chapter, re the dispersal of energy in classical thermodynamics] that the entropy is related to the dispersal of energy.
First-year college chemistry textbooks since about 1960 have used the 1898 description of thermodynamic entropy as “disorder”. In the February 2002 issue of the Journal of Chemical Education I showed that treating entropy change as “disorder” was not based on modern science and could mislead students. In the October 2002 Journal I urged that entropy be presented as the quantity of dispersal of energy/T or by the change in the number of microstates.
Textbooks do not alter their presentation of basic concepts readily nor rapidly. Thus, for the following 15 texts to delete “entropy is disorder” from their new editions within three years of my calling for such a drastic change is perhaps without precedent. Further, for all of them now to describe the meaning of entropy in various terms of the spreading or dispersing of energy (in some, quantified by Boltzmann's number of microstates) shows the utility of this concept in good teaching.
The first edition of Suchocki's "Conceptual Chemistry" (Benjamin Cummings) introduced the second law as "Order Tends to Disorder". His 2nd edition (2004) does so as "Entropy Is a Measure of Dispersed Energy"..."This fits with our everyday experience...." Then, with ΔSoReact, Suchocki can lead even this group of students to understand the direction of chemical reactions.