Stories to Make Thermodynamics and Related Subjects More Palatable

In the Classroom

Stories to Make Thermodynamics and Related Subjects More Palatable Lawrence S. Bartell Department of Chemistry, University of Michigan, Ann Arbor, MI 48109; [email protected]

For more than 40 years I taught physical chemistry at Iowa State University and the University of Michigan. Students had invariably entered the course having heard horror stories about how tedious and impossibly difficult thermodynamics and physical chemistry can be. In fact, our student newspaper, the Michigan Daily, once published an article on courses offered by the University of Michigan and singled out physical chemistry as the most difficult course in the entire university. Naturally, that presented a real challenge of how to break the ice. I found that the only way I could keep the students alert and receptive to ideas in lectures on thermodynamics and related fields was to tell them stories from time to time. These stories illustrated aspects of principles, recounted the personalities of some of the architects of thermodynamics and related fields, or reviewed steps and missteps in the development of these fields. Since it turned out that the stories were much easier for students to remember than simple recitations of principles and facts, they seemed a good idea. I also posed several scientific puzzles (1), encouraging students to apply their imagination about how they could be resolved using the basic framework we had already established. Sometimes, I even offered extra credit for correct answers. In student evaluations of my teaching it was my stories that got the most favorable mention. It has now been over seven years since I last taught. But some of my young colleagues come to me for suggestions about teaching, and I have told them some of the stories that illustrated the points they asked about. Several years ago Roald Hoffmann and Dudley Herschbach lectured at a workshop on chemical education at the University of Michigan, and both stressed the importance of telling stories (or, as Herschbach put it, “parables”) to the students. All of this prompted me to try to recall and record the stories I told. Since most of them are true, however, they aren’t parables. For what it is worth I offer the stories I remember, indicating where in a course on thermodynamics and related subjects they might fit. I also record several of the more interesting paragraphs written by others that I read to the class. Thermodynamics

relates, and the more extended is its area of applicability. Therefore, the deep impression which classical thermodynamics made upon me. It is the only physical theory of universal content concerning which I am convinced that, within the framework of the applicability of its basic concepts, it will never be overthrown (for the special attention of those who are skeptics on principle).

The following is from the Preface to Thermodynamics, by Lewis and Randall (3). There are ancient cathedrals which, apart from their consecrated purpose, inspire solemnity and awe. Even the curious visitor speaks of serious things, with hushed voice, and as each whisper reverberates through the vaulted nave, the returning echo seems to bear a message of mystery. The labor of generations of architects and artisans has been forgotten, the scaffolding erected for their toil has long since been removed, their mistakes erased, or have become hidden by the dust of centuries. Seeing only the perfection of the completed whole, we are impressed as by some superhuman agency. But sometimes we enter such an edifice that is still partly under construction; then the sound of hammers, the reek of tobacco, the trivial jests bandied from workman to workman, enable us to realize that these great structures are but the result of giving to ordinary human effort a direction and a purpose. Science has its cathedrals, built by the efforts of a few architects and of many workers. In these loftier monuments of scientific thought a tradition has arisen whereby the friendly usages of colloquial speech give way to a certain severity and formality. While this may sometimes promote precise thinking, it more often results in the intimidation of the neophyte [aside to students—that’s you]. Therefore we have attempted, while conducting the reader through the classic edifice of thermodynamics, into the workshops where construction is now in progress, to temper the customary severity of the science in so far as is compatible with clarity of thought.

How rare it is to encounter such prose in scientific writing!

Introduction.—Before launching into the principles of thermodynamics it is a good idea to read to the students a few classic passages to increase their appreciation of thermodynamics as a topic well worth the trouble of studying. Even though Einstein has been dead for a half-century, all students still regard him as legendary and his opinions as profound. The following remarks of Einstein are appropriate (2). Consequently, these obituary notes can limit themselves in the main to the communicating of thoughts which have played a considerable role in my endeavors. … A theory is the more impressive the greater the simplicity of its premises, the more different the kinds of things it

First Law of Thermodynamics Joule’s role in the formulation of the first law is invariably covered in courses. A personal glimpse of his experience when he introduced his radically new ideas on the nature of heat adds a realistic note about the faltering way science tends to advance. Joule’s classic talk (4).—When Joule was 28, having obtained new and more precise results demonstrating the conservation of energy, he forwarded a paper to be presented at the British Association Meeting at Oxford in August 1847. But the chairman suggested that, owing to the press of business, Joule should not read the paper but instead give a verbal description of his experiments. “This I endeavored to do,” Joule wrote

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later, “and, discussion not being invited, the communication would have passed without comment if a young man had not arisen in the Section, and by his intelligent observations created a lively interest in the new theory.” So it was a 23-yearold kid who made Joule’s paper the sensation of the meeting, as well it should have been in the first place in view of its historic importance. This bright young man was William Thomson, later known as Lord Kelvin. Still, Thomson’s comments persuaded few of those present, including Faraday, of the correctness of the revolutionary new views, for they contradicted Carnot and the long-entrenched caloric theory. After the meeting Joule and Thomson chatted for awhile. Joule didn’t mention that he was about to get married (why should he?) and Thomson didn’t mention that he was about to go to Switzerland on holiday (why should he?). Two weeks later Thomson, while strolling along the valley of the Chamonix, saw a young man coming toward him carrying what looked like a long stick. On closer approach the man turned out to be Joule, with a long thermometer, and he was walking to the top of a neighboring waterfall. If his ideas were right there would be a difference in temperature of the water between the bottom and the top, due to the dissipation of kinetic energy at the bottom of the fall. Evidently a honeymoon could not interrupt Joule’s passion for science—first things first, after all. This chance meeting cemented a warm friendship between Joule and Thomson and led to a lifelong collaboration. What Joule’s waterfall experiment yielded besides a lasting friendship with a scientific genius is not known. In any event, it is doubtful that a persuasive result could have been derived in such a way. On “established” ideas when insufficient facts are known (5).— Lord Kelvin was such a brilliant scientist that he became perhaps the principal authority in matters of the physical universe. He applied the known laws of heat dissipation to the problem of the earth’s temperature. From the known temperature increase with distance below the surface, he deduced that the earth was not nearly old enough for Darwin’s estimates of the duration of certain geological processes or for his theory of the origin of the species to operate. He also estimated the possible active lifetime of the sun from its energy output, assuming that the energy source was gravitational infall. The result was more or less consistent with his conclusions about the age of the earth. Late in Kelvin’s life radiochemists confirmed the antiquity of the earth proposed previously by geologists. Kelvin remained adamant that while the earth might perhaps be 20 million years old and just possibly an order of magnitude older, it could not possibly be billions of years old. What he had not reckoned with, of course, was the steady evolution of heat from the radioactive elements deep within the earth or the nuclear reactions powering the sun. Kelvin also disputed Maxwell’s theory of the electromagnetic nature of light, and proclaimed that heavier-than-air aircraft were impossible. This is not to disparage his genius and his enormous accomplishments, or even his genuine modesty. Even such giants can err, and that, itself, is a lesson worth learning. Conservation of Matter and Energy Earth older than the Universe?—When I was a university student there was a strange paradox. According to radiochemists in collaboration with geologists, the world was about 5 billion years old. But astrophysicists (Hubble et al.) found from 1060

the rate at which the universe was expanding that it could not have been expanding for more than about two billion years. In other words, the big bang believed to produce the universe occurred after the earth was born—the earth was older that the universe in which it sat, if chemists were to be believed! Many physicists, of course, were complacent about this discrepancy because, after all, what is the opinion of a chemist or geologist compared with that of a physicist? But some physicists did worry, and that is the point of this story. We all now take for granted the conservation of energy and mass. But extraordinary facts call for extraordinary ideas! The distinguished physicists Bondi, Gold, and Hoyle proposed a steady-state universe that would look to astronomers just like Hubble’s expanding universe but, in the steady-state universe, matter would be generated spontaneously as the universe expanded (6 ). In that way the expanding universe could go on forever, always looking much the same, and the earth could, indeed, be five billion years old. Later, astronomers discovered that the Cepheid variable stars they used to judge distances had been miscalibrated and the universe was actually several times older than the earth. Moreover, other evidence (microwave radiation, cosmic abundances of the elements, etc.) is generally considered to confirm the big bang theory and the antiquity of the universe. But the moral of the story is that the conservation of mass was seriously challenged by competent scientists even during the lifetime of scientists alive today. Of course, the big bang itself is the quintessential example of matter appearing out of nothingness. Is conservation of energy only statistical?—Additional challenges to conservation were encountered in β emission by radioactive atoms. It happens that some of a nuclide’s β-rays are much more energetic than others even though all of the nuclei are believed to be identical, before decay. To account for this observation the prominent physicists Bohr, Kramers, and Slater wrote a paper suggesting that energy is conserved, not in individual events on the atomic scale but only statistically, on the average (7). To Wolfgang Pauli this solution to the β problem was so ugly that he postulated the emission of another particle, later named the neutrino, which carried off enough energy in each decay to balance the energy emitted by the β-ray (8). It was supposed that the nearly massless, uncharged neutrino was undetectable, which suggested to many that it was pure fiction. Even Pauli felt a bit ashamed at the time to postulate a solution that could not be tested. But as everyone now knows, the neutrino has been detected and several neutrino observatories exist around the world. So it turns out that the laws of conservation of mass and energy are more robust than many feared, even in comparatively recent history. Is mass conserved when an atom bomb explodes?—Yes! See ref 1. Can perpetual motion machines be built?—Backyard inventors even today keep coming up with machines that they claim produce more energy than it takes to run them. Several years ago a couple of Ann Arbor self-educated inventors announced such an invention and the Ann Arbor paper, to its discredit, gave the inventors a long, uncritical feature article. The U.S. Patent Office has an official policy of not accepting for examination any applications for perpetual motion machines. Neither will the National Bureau of Standards (now called NIST) waste its time on such claims. Several years

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In the Classroom

Second Law and Equilibrium On entropy and the teaching of thermodynamics.—An interesting article by W. Brostow discusses the “myth” that entropy is a name given to a quantitative measure of disorder (10). Parts of it should be read to students after they have had a bit of experience with entropy and its uses, not only or not even mainly because it is helpful, scientifically. The principal rationale for this diversion is that it delights students since it (rightly) pokes fun at teachers of thermodynamics and makes students feel less guilty about not mastering the subject right away. To set the stage I read from Cokcen’s Thermodynamics, page 140 (although a large fraction of the other books on the subject would serve as well): “An increase in the entropy of a system is always accompanied by a corresponding increase in the randomness of a system. Thus, a solid crystalline substance, in which the atoms are arranged in some sort of geometric pattern, becomes more random upon melting since molecules can move more freely in the liquid.” I show that the second sentence can be wrong by drawing the phase diagram of 3He (Fig. 1). Helium is remarkable in that it would not freeze at atmospheric pressure even if it could be cooled to absolute zero. It can be crystallized at low

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ago, however, congressmen (who are considerably more at home with common law than with the first law) forced the Bureau of Standards to reverse its policy (9). A Mississippi inventor, a backwoods high-school dropout with no formal scientific training, claimed he had the solution to America’s energy crisis. He had invented a machine that ran on electricity but, in the process, produced far more energy than it consumed. He applied for a patent, was turned down, and sued the U.S. Patent and Trademark Office. He was uncommonly charismatic and persuasive, an appealing character that TV news and talk shows could not resist featuring. He convinced lawyers and congressmen that such a useful creation of American ingenuity should be rewarded and the Patent Office should seriously consider his claim—despite its reactionary policy. A federal judge then ordered the inventor to turn over his perpetual motion machine to the Bureau of Standards for tests of his claims. When the NBS found the machine to be a very inefficient generator, using substantially more energy than it produced, even that failed to silence the inventor. Initially the inventor seems to have been genuinely convinced he had discovered a new principle and that his machine performed as he claimed it did. Nevertheless, after conventional science had proved him wrong, he seems to have evolved, in the words of Park (9) “from foolishness to fraud”, hoping at least to fleece a lot of rich investors. He even succeeded in convincing senators to reopen his case and hold a special hearing about the abuse of power of the Patent Office. Again, it was not testimony by scientists with impeccable reputations that cost him his case. It was the disclosure, by former astronaut John Glenn, of a conflict of interest in the parties giving testimony in support of the inventor’s claims, that killed it. However, it is worrying that such firmly established principles as the laws of thermodynamics presented by nationally recognized scientists and officials of trusted government laboratories should be less persuasive to our lawmakers in Washington than charismatic quacks who appeal to desires for a cheap solution to our energy problems.

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T/K Figure 1. Low-temperature phase diagram of 3He. The upper field represents crystalline He and the lower, liquid He. Below about 0.3 K and above 30 bar, it can be seen that the liquid can be frozen by heating it! Data from ref 12.

temperature, however, if it is subjected to a pressure of about 30 bar. For 3He at low T, the P-vs-T solid–liquid coexistence line in the phase diagram curves downward for awhile before beginning to increase (12). That means the solid exists at a higher temperature than the liquid at a given pressure. Therefore, it is clear that heat must be fed into the liquid to freeze it! In other words, the crystalline phase has the higher entropy! Then I read from Brostow (10), part of his section on “Entropy and Disorder”: We mean here, of course, the persistent myth that ‘entropy is a name given to a quantitative measure of disorder.’ McGlashan [13] has explained that phrases like this are meaningless, except in the three special cases of mixtures of perfect gases, mixtures of isotopes, and crystals at temperatures near thermodynamic zero.—And yet, even today the myth seems to be still alive. The reason for this seems to lie in the fact that one tries to connect an indeed exact notion, entropy, with something called disorder, which is loose and subjective and for which no definition exists. The disorder story discussed above represents, unfortunately, only one aspect of an otherwise grave problem: bad textbooks of thermodynamics. At first glance, writing a book on thermodynamics is a very easy task. This science has existed for so long, and so many books have already been written, that one can simply extract pieces from several books and sell the compilation as a ‘new’ book. This depressing hypothesis seems to be confirmed by (i) the proliferation of books on thermodynamics; (ii) the obsolescence of many of them—and (iii) the errors and mistakes—there seems to be no other discipline of the physical sciences, quoting McGlashan [13] so ‘incredibly badly presented, for the most part by people who do not understand it.’ The consequences are well known: the frustration of students who, while suspecting some coherent structure and even beauty in thermodynamics, are unable to comprehend it. A characteristic opinion of a student is quoted by Andrews [14]: ‘To me, thermodynamics is a maze of vague quantities, symbols with superscripts, subscripts, bars, stars, circles,


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In the Classroom etc., getting changed along the way, and a dubious method of beginning with one equation and taking enough partial differentials until you end up with something new and supposedly useful (if that doesn’t work you try graphing). I have the impression, however, that to other people, thermodynamics is a logical study of the effects of temperature and pressure on matter and on energy.’

By this time students are practically cheering! I have to say that I think Brostow is too severe in his rejection of the notion that entropy is related to disorder but, to say it again, I included his remarks in my lectures because it lifted the spirits of the students. On Raoult’s law.—According to all physical chemistry textbooks I know, two empirical auxiliary laws are invoked to flesh out applications of the three principal laws of thermodynamics. The two auxiliary laws are the ideal gas law and the law of ideal solutions (Raoult’s law or Henry’s law, either of which can be derived from the other via the Gibbs–Duhem relation). Let us examine whether this characterization is correct. First we review the validity of Raoult’s law. The following story is good at getting students indignant with “rigid, unimaginative, authorities” but also at putting established laws into perspective. Many years ago one of my colleagues who was a brilliant young thermodynamicist was studying activity coefficients of components in various solutions. He discovered in an aqueous solution of propyl alcohol that even in very dilute solutions (the range in which Raoult’s law is supposed to apply), Raoult’s law simply failed. Obviously this anomaly deserved to be investigated because, if true, it would overthrow a great deal of what had been written. So my colleague had his students purify and repurify the alcohol by repeated fractional distillations, and the anomaly remained, strong as ever. Finally, after meticulous testing and retesting, having convinced himself that the effect was reproducible and real—he wrote a manuscript describing his findings and submitted it to a standard journal in the field. He was dismayed to find it rejected at once by some referee. The referee said he didn’t know what the mistake was but it was in my colleague’s work, not in Raoult’s law, and that was that! My colleague was indignant. Just because every crow you have seen has been black doesn’t prove that the next one will also be black! Is it fair for established authorities (probably men past their ability to think creatively?) to play God with young people’s science? Smarting from this attack on his competence, my colleague went back to the laboratory, and this time, subjected the alcohol to a battery of chemical purifications including treatment with sulfuric acid. And what do you suppose he found? Raoult’s law was now obeyed faithfully in the limit of dilute solutions! Of course the authority was correct. We can state this more strongly in the particular case of Raoult’s law. All physical chemistry text books I am aware of regard Raoult’s law as an empirical law, adopted as an auxiliary law in addition to the ideal gas law. On the other hand, Fermi, in his interesting little book on thermodynamics (15), proves that Raoult’s law must be obeyed. The way he does it is to evaporate a solution completely (any solution at all, heated to whatever temperature and with whatever pressure lowering might be required) and by the mathematical continuity of thermodynamic functions, show that if the vapor is ideal, Raoult’s law must hold for the solution. Now, we know that 1062

the ideal gas law must hold for warm gases at low pressure and we can derive the ideal gas law for gases under such conditions. Therefore, we do not have to invoke two separate auxiliary laws. One is sufficient. We can deduce that Raoult’s law is a consequence of the ideal gas law, and the ideal gas law is firmly founded on mechanical principles. So authorities must not be dismissed lightly! On Henry’s law.—When I joined the faculty of Iowa State University, my colleagues quipped that I had better stress Henry’s law when I taught. This was because our department chairman had made a substantial amount of money after noticing that carbon dioxide is significantly soluble in cream. In accordance with Henry’s law, he found that the higher he made the pressure of carbon dioxide over cream, the greater was the amount of gas that dissolved in the cream. He discovered this when he worked in the cow barns of a large state university to put himself through college. Whatever led him to the discovery is unclear, except that he was a very bright and curious sort. Having observed the ability of CO2 under pressure to dissolve in cream, he also discovered that, if he released the pressure suddenly, the gas would quickly escape, whipping the cream into as fine a froth as ever was produced by the normal whipping process. Although he recognized the commercial potential of this phenomenon of the self-whipping of cream, he soon noticed that the carbonic acid in the cream soured it. As a well-schooled chemist he knew that laughing gas, N2O, had physical properties very like those of CO2 but lacked the acidity and, moreover, was nontoxic. True to his expectations, laughing gas worked perfectly. He had invented “instant whip”. He even designed the container and nozzle arrangement that produced whipped cream on demand. To put the working of the world into perspective, however, I should point out that his commercial success was less than he had hoped for. He was too poor to hire a good patent attorney when he patented his product. An enterprising scoundrel came out with a product that adulterated the laughing gas with a bit of carbon dioxide—not enough to sour the cream but enough to break the patent and take over the lion’s share of the market. On the volatility of tungsten.—When I first joined the department of chemistry at Iowa State University, I was given no start-up package and had no resources to begin a research program (for political reasons I was not given an appointment in the Ames Laboratory of the U.S. Atomic Energy Commission, a laboratory with lavish resources that supported all of the other physical chemists). Therefore, it was suggested that I join two physicists who were attempting, without success, to evaporate tungsten and molybdenum on various surfaces in order to study the optical properties of the pure elements and mixed films of the two. I ultimately succeeded in evaporating tungsten by switching from the original brass furnace (!) to a heated tungsten filament in a high-vacuum system, making sure that the filament did not come into contact with any volatile material (16 ). In the process I found just how extraordinarily nonvolatile tungsten really is, and how marvelous the laws of thermodynamics are in allowing one to relate something that is very difficult to measure to something that is much easier. Indeed, this is the essence of the power of thermodynamics. As it turned out, the best outcome of this work was to provide a spectacular illustration of exactly this point for students. The following story sets the stage.


In the Classroom

When I was an undergraduate student with no longer an attention span than most students, my mind wandered during physical chemistry lectures and, staring at the water faucet on the lecture bench, I daydreamed that if metal atoms were as large as flies, I would be able to see them buzzing around the faucet. It was only their truly small size, I supposed, that kept the faucet from evaporating away perceptibly. But when I began to study tungsten I was forced to a very different conclusion! Suppose the faucet were made of tungsten. How many atoms per liter do you imagine there are at the equilibrium vapor pressure of tungsten at room temperature? Better, how large a volume do you need in order to have just one tungsten atom, on average, in equilibrium? One liter? Guess again. One chemistry building? One Earth’s volume? One solar system? No, much, much larger! Let us take the radius of the visible universe to be 109 light years. That represents a truly immense volume, but even that is not enough to hold one gaseous tungsten atom in equilibrium with the metal at room temperature. I’ve forgotten the volume actually needed, but it is something like 1016 universes. It is not a bad calculation for students to do as a special exercise. How could one possibly measure such a volume? There is no way to measure it, but one can calculate it using the Clapeyron equation, knowing the melting point, heat of fusion, boiling point, heat of vaporization, and heat capacity. If an accurate answer is not needed (of course, it would be useless), the simple Clausius– Clapeyron equation should suffice, applied first to the liquid and then to the solid to extrapolate to the vapor pressure at room temperature. It is truly impressive how nonvolatile tungsten really is! Which of course has something to do with its use as filaments in light bulbs. On the difficulty of teaching phase diagrams.—This story is best told after teaching phase diagrams, a construction for which I was all too often unsuccessful in conveying the meaning. That this problem is not uncommon is illustrated by the following story. One day, when I was a consultant to a major petroleum corporation, I was discussing recent work with a small group of Ph.D. scientists. In reviewing the properties of finely divided tungsten–rhenium catalysts, the scientists wondered if the individual particles were of the pure metals or were a solid solution of the two. When it was suggested that the quickest way to get an idea would be to look at the tungsten–rhenium phase diagram, most of the scientists had forgotten what phase diagrams are—as completely as my own students. This story comforts students who find phase diagrams difficult and suggests that we should try to find a better way to teach the subject. Surface Science Introduction.—I think it is unfortunate that all too many physical chemistry teachers skip over the subject of surface science during the term concentrating mainly on thermodynamics. After all, surface science offers many nice examples of applications of thermodynamics. Moreover, and quite apart from the important technological applications of surface science, there is the historical significance of the field. Science taught without history is rather sterile. The reason for this significance is that surface science gives a two-dimensional view of the world, whereas the science of bulk material presents

a three-dimensional view. When the two sources of information are played together, it becomes possible to learn the approximate size of molecules and their range of interaction. This was known by some scientists long before many wellknown scientists (including Mach and Ostwald) accepted the reality of atoms and molecules! I usually started surface science with a couple of stories. In one, two patrons were enjoying a conversation over foamy mugs of beer in a bar when one of them said “Bill, you’d better get yourself to a doctor right away! You’ve got diabetes.” The friend had noticed that every time Bill breathed onto his beer the foam wilted away. That phenomenon illustrates surfaceactive agents. The foam on beer (bubbles filled with carbon dioxide) is stabilized by a beer protein film in much the same way as soap bubbles are thin films of water stabilized by monomolecular layers of soap. Surface-active agents that are responsible for the foam stabilization are substances whose molecules have polar groups (water-loving) and organic groups (water-hating) and therefore tend to aggregate at the surface of a solution. So, suds are thin water bubbles whose surfaces are covered by a layer of molecules anchored to the water by their “hydrophilic” groups. What is exposed to the outside world (and also to the air inside the bubble) are organic groups. What has this to do with diabetes? Diabetics may be in a state of ketosis in which they produce acetone by metabolism, and this volatile substance is breathed out. Acetone has fatty ends (methyl groups) and a polar carbonyl group that is so water-loving it displaces the beer protein from the foam surface. But acetone is unable, itself, to stabilize foam. Fortunately, Bill did go to the doctor. A closely related incident happened when I was on the faculty of Iowa State University of Agriculture and the Mechanic Arts. In the spring there was a bad time when cows ate alfalfa before it was suitable for cattle feed. The trouble was that it started to ferment in the cows’ stomachs, and the carbon dioxide liberated created a foam. This foam was stabilized by protein from the immature alfalfa and caused cow bloat, a serious condition in which the cow swells up like a balloon! The only known treatment (and I used to get disgustingly graphic when telling this story) was to take a sharp nail, ram it through the cow’s side, and stand back as the rotten gas spewed out. The agriculture people came to the chemists to ask for advice. The surface chemists suggested feeding the cows the dishwashing detergent ALL, a deliberately nonfoaming detergent designed to avoid filling a kitchen with suds when a dishwasher is used. It might displace the alfalfa protein in the cows’ stomachs and deflate them. Unfortunately, this treatment hadn’t worked by the time I left the faculty. On the size of molecules.—Who was the first person to measure the size of molecules? Benjamin Franklin came very close to that honor. His scientific prowess in other areas is well known, and he is the first person of record to carry out scientifically designed experiments that, with a quick calculation he did not make, could have given the first estimate of molecular dimensions (17 ). In fact, the world had to wait another century for the answer. Franklin, like many before him, became interested in the wave-calming effect that oil had when spread on water. But what Franklin did, and published at the suggestion of a clergyman, was to note just how far his oil (probably olive oil or whale oil) spread on water. He was astonished to


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find that a teaspoon quickly spread over a half-acre of water, then stopped spreading. The spreading gave a spectacular 107fold increase in area. Franklin could tell how far the oil spread because of its calming effect on waves. He wrote “I think it a curious inquiry, and I wish to understand whence it arises.” The idea of molecules was not well developed at the time but it was supposed by many that matter was particulate. If Franklin had speculated that the oil spread until its thickness was reduced to one molecule (which is the explanation), he could have computed the length of a molecule from the thickness of the film, since thickness times area equals volume, and he knew the volume and area. His results yield about 20 Å, a rather good estimate. Then, by making any plausible guess about the shape of molecules, he could have estimated the order of magnitude of how many molecules there are in, say, a cubic centimeter of material. When Franklin was carrying out his experiments, Avogadro had not yet formulated the idea of moles and molecular weights. Therefore, Franklin could not have estimated Avogadro’s number. Oil films reveal their presence on water by greatly lowering the surface tension. Because this has a very conspicuous effect on the amplitude of waves in ponds and rivers, Franklin took delight in playing tricks on his friends. He would tell them he was going to cast a magic spell on the stream they were walking beside, then would walk upstream many paces. When he waved his cane as if it were a magic wand, lo and behold, the stream suddenly became much smoother! Of course, in the tip of his cane was a reservoir for a bit of oil. A brief note to put Franklin into a historical context that surprises many: he was born 50 years before Mozart. When Franklin first went to England, he was promised a meeting with Isaac Newton. This meeting never came about, though Newton lived for about three years after Franklin’s visit. Most people think of Franklin as a publisher and statesman of stature but in his time, he was also considered a world-class scientist by others, including his friends Priestley and Lavoisier. He was a musician (he invented the “glass harmonica” an instrument with an ethereal sound for which even Mozart wrote a small composition) and a composer, as well. (In my opinion, however, Franklin’s musical compositions were pretty dreadful.) A very rough estimate of Avogadro’s number can be made from the surface tension, γ, and heat of vaporization, ∆Hv, of a liquid. By dividing one mole of the liquid into N cubes (for sake of example) and taking the cube edges to be L, the area of the liquid is increased by 6NL 2. To separate the cubes, the cost in work would be 6NL 2 γ. Note that NL 3 is the molar volume of the liquid. Therefore, if one equates this energy to the molar heat of vaporization, N becomes Avogadro’s number, NA, and L, the molecular size. Both quantities can be estimated crudely in this way. As another example, let the force holding a cylinder or “bar” of a liquid together be equated to the cross-sectional area A times the internal pressure (available from the thermodynamic equation of state). Then the work to separate the “bar” into two pieces (so as to produce a new area A + A), is 2A γ = force × distance. Since everything is known except the effective distance, this distance representing the range of molecular forces can be calculated. It turns out to be of the order of magnitude of several angstrom units. These two crude but very simple estimates actually give the correct orders of magnitude for the molecular properties! 1064

Just how accessible to our mechanical sensibilities molecular sizes really are can be brought home in laboratory experiments with Langmuir–Blodgett layers on water. Students can deposit a counted number of molecular layers on a slide. The number of layers laid down can be counted by the number of times the slide is withdrawn through the monolayer on water, then put back and withdrawn again. Each withdrawal and each insertion back through the film adds a layer of molecules. It is easy to see the development of interference colors, from which the thickness can be calculated. It is even possible to build up a multilayer until the thickness of the deposit on the slide can be measured with micrometer calipers, and hence the length of the molecules can be measured by ordinary devices. There is another noteworthy story about Langmuir films on water (17), films one molecule thick, as were Franklin’s olive oil films, but whose areas are measurable in a small, inexpensive “Langmuir trough”. Such films can be produced by adding to the water surface droplets containing minute amounts of oil dissolved in a volatile solvent. A contemporary of Langmuir was Evert Gorter, a Dutch M.D. who was not formally trained in physical chemistry. Gorter was aware that membranes of living cells seemed to be made of lipids (phospholipids, oils with polar groups somewhat like Franklin’s oil). He and his assistant, Grendel, dissolved the membranes of blood corpuscles in a volatile solvent, then measured the area occupied by a monolayer on water corresponding to corpuscle. What he found for blood corpuscles from a variety of animals (including humans) was that the area of the lipid per corpuscle spread on water was twice the area of a blood cell. From this he correctly inferred that cell membranes are bilayers, which present their polar groups to the outside and inside of the cells. The lipid molecules in the bilayer, then, are joined organic tail to organic tail. Although he published this correct structure and composition of cell membranes in 1925, it was approximately a half-century before his findings were accepted by biological scientists (16 ). In between a Ph.D. and an academic job, I was invited by the Simonize Company to study their wax films manufactured for automobile polish (today’s automobile paint is so much more durable that car wax is all but extinct). At the time Simonize had little idea of how thick its films were or what structure they had. Conventional surface-chemical tools told them little. After several fruitless tests by more conventional techniques, I devised one of the first ellipsometers ever used in surface chemistry. An ellipsometer is an optical device able to measure film thicknesses to fractions of an angstrom unit. It turned out that a really well buffed Simonize film was much thinner than had been suspected. It was approximately the length of the carnauba wax molecules used in the preparation! Out of curiosity I deposited fatty ester molecules onto a metal substrate by evaporation of a dilute solution and found by diffracting electrons from the film that the long molecules were standing up in the film. Then, when I stroked them gently with Kleenex, I found that this made them lie down, nearly parallel to the surface. It really gives one a feeling of intimacy with molecules to see them obeying orders like a pet dog. But the most remarkable thing was the protection these scant layers could give to lacquer films. In order to use the


In the Classroom

ellipsometer with films on lacquer (automobile paints of the day were sometimes lacquer) I had to prepare lacquer films about 100 Å (10 nm) thick on a metal surface because reflection from the metal was essential for ellipsometry. These films were so flimsy that they tore at the slightest touch by the gentlest tissues available. But when just one layer of wax molecules was deposited onto the thin lacquer films, you could rub as hard as you wished with tissues without any damage to the underlying lacquer film. Obviously one layer of soft wax molecules does not provide an armor plate to protect the underlying film. What was provided was lubrication. Remember that molecular forces are very short in range, much less than one layer of wax molecules. To the outside world, the surface is slippery wax, not lacquer. The moral of the story is obvious. If we somehow alter surfaces by just one molecular layer, we can profoundly change the properties of a surface (friction, wetting, catalytic properties, etc.) Changes can be beneficial or harmful to properties of a product. Therefore the great importance of surface science to industry. Kinetic Theory History of the kinetic theory (4).—Students learn about Maxwell’s development of the kinetic theory of gases, but the real story of the first formulation of the kinetic theory of gases is more depressing than the one recorded in textbooks. John Waterston (1811–1883), a brilliant but unknown young man, worked out the essentials of the kinetic theory some 15 years before Maxwell. His long manuscript was turned down as nonsense by the referees of the prestigious journal he submitted it to. Worse, it was his only copy, and the journal would not return it. Authorities can be and often are reactionary and unimaginative. This trouble so bothered Waterston that he developed a contempt for scientific colleagues and dropped out of science. His original paper was, however, archived by the Royal Society so that its priority is verifiable. Much later, the distinguished physicist Lord Rayleigh consulted the archives and wrote at length on the important contents of Waterston’s first paper, confirming the originality and ingenuity of his approach. He then offered a cynical moral to the story: “The history of this paper suggests that highly speculative investigations, especially by an unknown author, are best brought before the world through some other channel than a scientific society, which naturally hesitates to admit into its printed records matter of uncertain value. Perhaps one may go further and say that a young author who believes himself capable of great things would usually do well to secure the favorable recognition of the scientific world by work whose scope is limited, and whose value is easily judged, before embarking upon higher flights.” In this respect one thinks of the unknown young Indian scientist Bose, whose manuscript treating electromagnetic radiation by a strange new statistics was rejected by British journals. His writings met with little success until he sent his paper to Einstein. The rest is history. Einstein recognized the genius of it, translated it from English into German, and had it published in the Zeitschrift für Physik. He then generalized the treatment (now referred to as Bose–Einstein statistics) to the case of material gases, and predicted, among other things, the Bose–Einstein condensation, which has recently burst so spectacularly into the news.

Gas viscosity.—Experience with molasses in January and high-viscosity oils and polymers leads students to an intuition about effects of temperature, molecular length, and concentration on viscosity that is contradicted by properties of gases. The counterintuitive behavior of gas was predicted before it was measured (18), helping to nail down the kinetic theory. Unlike motor oil, a gas increases in viscosity when heated, and the viscosity is decreased as molecular sizes increase. Moreover, increasing the gas density leaves the viscosity unchanged ! The charming way Moore in his early editions of Physical Chemistry (19) introduced gas viscosity leads to a very easy way to understand it, estimate it, and explain its somewhat surprising properties. Without this charm and without pointing out how differently gases respond to changes in temperature, concentration, and molecular dimensions, viscosity appears to be a dull subject. Since gas viscosity gives us a measure of the collisional area of molecules per mole, this can be played against the molar volume of the liquid to estimate Avogadro’s number, another reason for the historic importance of gas transport properties. Recall that, in the early days of the kinetic theory, many of the most influential scientists did not believe in molecules. More Morals about Authority The following stories cast interesting sidelights on scientists when the advances in physical chemistry they introduced are discussed. Impact on Arrhenius.—When Arrhenius was a student, he proposed his perceptive treatment of what we today call ionic solutes. But many or most scientists of the time did not believe that salts are composed of positive and negative ions or that the interaction of a solvent with salts, acids, and bases might produce ions in solution. This, despite earlier definitive suggestions by Clausius to the contrary. Nevertheless, the scholars on the committee of Arrhenius could not prove him wrong. Besides, in his thesis, Arrhenius had been somewhat vague and careless in his exposition (20). So the committee compromised: their solution was to award him the lowest passing grade. In reality, such a grade was a grave punishment, for it prevented Arrhenius from being offered an academic position in Sweden. Nevertheless, when it became clear that the famous physical chemist in Germany, Wilhelm Ostwald, was greatly impressed by the achievements of Arrhenius and offered him a position, Sweden relented and admitted him into the ranks of Swedish scientists, where he flourished. So Arrhenius felt the sting of authority—until a higher authority prevailed. Impact on Einstein.—Another story involving authority is about Albert Einstein. His performance in what we would call graduate school was somewhat indifferent in the eyes of his teachers because, as Einstein himself reports in his brief autobiographical sketches (2), he hardly ever went to lectures. Instead, he went to the library and studied the primary literature. Therefore, he was not regarded as a really serious scholar, and his performance on the few examinations given to him was less than fully stellar. Consequently, the only position he could find, and that through the special influence of the family of a friend, was as patent office examiner. In 1905, after he had been at the patent office for a few years, he published an astonishing outburst of papers. In them


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he developed the special theory of relativity, the statistical mechanical theory of fluctuations including the first quantitative treatment of Brownian motion, and several seminal ideas on the quantum theory of matter and radiation, including the photoelectric law. Because his contributions were so remarkable, Einstein became well known quite soon, and within a few years he was being nominated for the Nobel Prize by some of the most famous scientists in the world. But the Nobel committee kept turning him down, year after year. Finally some previous Nobel laureates wrote that the failure to award Einstein the Prize was becoming an embarrassment to the Nobel committee. Still the committee refused to award Einstein the Prize. Some of Einstein’s predictions were not yet confirmed, and some were contested by less talented scientists. But the Nobel committee finally found a compromise. It awarded Einstein the prize for his contributions to theoretical physics, citing his photoelectric law! And do you know who the committee member was who kept vetoing Einstein’s award? It was Arrhenius! I think there is a moral in this story somewhere…. On the reputation of Gibbs.—J. Willard Gibbs was a man of independent means when he lectured (without pay) at Yale University. He carried out research of extraordinary depth in thermodynamics and statistical thermodynamics and invented vector calculus in the bargain. He published mainly in the Transactions of the Connecticut Academy. Although this journal was not widely read, Gibbs submitted reprints to the most distinguished European scientists of the time, including Maxwell, who immediately recognized their importance and beauty. In his later years Maxwell spent considerable time carefully constructing, with his own hands, a model of Gibbs’s thermodynamic surfaces, a cast of which, shortly before his death, he sent to Gibbs. At the time, American universities were just beginning to try to build up their faculties in the sciences. Many chairmen of physics and chemistry departments wrote to the best-known scientists in Europe for advice on whom to import from Europe for their departments. Often enough they received the reply “Why don’t you consider the American, Gibbs? His work is outstanding!” After awhile Gibbs began to receive offers to move from Yale, and at attractive salaries. When the New Haven townspeople heard of this state of affairs, they got together a stipend to offer Gibbs if he stayed at Yale. And so he did. Vulnerability of and imperfections of true authorities.— Troublesome controversies are mentioned above. The giants Gibbs, Newton, and Einstein particularly suffered from this vexing source of aggravation. When Gibbs developed vector calculus he was subjected to savage attacks by those who preferred the more tedious methods of the day. This caused him much anguish. Newton also encountered acrimonious criticism. He wrote that, if he had known what a litigious lady natural science was, he never would have entered the field. Einstein said it more simply. He remarked that if he were beginning again, he would become a plumber or peddler. When covering gas laws, it might be remarked that the springiness of air (its resistance to compression) was well known to Newton, a contemporary of Boyle. Newton recognized that he could calculate the speed of sound in air via the elasticity of air. Gifted in abundance though he was, his calculated velocity did not agree with experiments! We now realize that Newton 1066

took the isothermal elasticity when he should have taken the adiabatic elasticity. Otherwise his theory was correct. Newton also outlined in his Principia (21) some “Rules of Reasoning in Philosophy” His Rule II: Therefore to the same natural effects we must, as far as possible, assign the same causes. As to respiration in a man and in a beast; the descent of stones in Europe and in America; the light of our culinary fire and of the sun.

Newton’s rule is an excellent one but his last example is somewhat misguided in the light of today’s knowledge. On Boltzmann’s tomb is inscribed his statistical prescription for entropy: S = k log W Boltzmann’s contributions to statistical science were enormous. Yet he became regarded by many well-placed colleagues as a has-been, a man whose science was of equivocal value. Even in recent times a popular play in Germany was about a fumbling old professor whose work was held in contempt, and the misinformed playwright based his character’s life on Boltzmann’s. Today we regard Boltzmann as one of the most creative founders of the science of statistical thermodynamics. But in Boltzmann’s day he received more criticism than he could bear—so much that he was driven to suicide. Many of the above stories dealing with human nature and human activities are unhappy ones. But not all stories in chemistry are negative, of course. A wealth of happy stories can be found, for example in the book Serendipity, by R. M. Roberts (22). Another (short) story about personalities. At a recent physics seminar the speaker remarked that although Faraday conceived of the existence of the “field” in electromagnetic phenomena, he was unable to understand the mathematical development of his concept by Maxwell “because of the fact that he was the child of a blacksmith!” To this remark was replied that humble beginnings do not preclude proficiency in mathematics. The great mathematician Fourier was the 19th child of a poor tailor! Now that Fourier has been mentioned, his experience gives another example of how acknowledged authorities often fail to recognize the virtue of important new ideas. Fourier’s publication of his seminal work on Fourier series and boundary value problems was delayed for 24 years owing to hostile reviews by Lagrange. Concluding Remarks Motivated by the response of colleagues and students, I submitted this collection of stories in the hope that it would encourage teachers to tell more stories. Some teachers are so gifted they can hold students spellbound. Lacking such charisma, I found that stories are a useful substitute. Not only do they offer an effective and relatively painless way to convey ideas, they also make lecturing more fun for the teacher. Literature Cited 1. Bartell, L. S. J. Chem. Educ. 2001, 78, 1067–1069. 2. Einstein, A. In Albert Einstein: Philosopher-Scientist, 3rd ed.; Schilpp, A., Ed.; Cambridge University Press: Cambridge, 1969. 3. Lewis, G. N.; Randall, M. Thermodynamics and the Free Energy of Chemical Substances; McGraw-Hill: New York, 1923.


In the Classroom 4. Borse, H.; Motz, L. The World of the Atom; Basic Books: New York, 1966; Vol. I. 5. Smith, C.; Wise, M. N. Energy and Empire. A Biographical Study of Lord Kelvin; Cambridge University Press: Cambridge, 1989. 6. Bondi, H.; Gold, T. Mon. Not. R. Astron. Soc. 1948, 108, 252. Hoyle, F. Ibid., 1948, 108, 372. 7. Bohr, N; Kramers, H. A.; Slater, J. C. Philos. Mag. 1924, 47, 785. 8. Wolfgang Pauli: Scientific Correspondence with Bohr, Einstein, Heisenberg: 1930–1939; von Meyenn, K., Ed.; Springer: Berlin, 1985; Vol. II. 9. Park, R. Voodoo Science; Oxford University Press: Oxford, 2000. 10. Brostow, W. Science 1972, 178, 121. 11. Gokcen, N. A. Thermodynamics; Techscience, Inc.: Hawthorne, CA, 1975; p 140. 12. McClintock, P. V. E.; Meridith, D, J.; Wigmore, J. K. Matter at Low Temperatures; Wiley: New York, 1984; p 18.

13. McGlashan, M. L. J. Chem. Educ. 1966, 43, 226. 14. Andrews, F. C. Thermodynamics: Principles and Applications; Wiley-Interscience: New York, 1971; p 3. 15. Fermi, E. Thermodynamics; Dover: New York, 1959. 16. Bartell, L. S. Adv. Mol. Struct. Res. 1999, 5, 1–23. 17. Tanford, C. Ben Franklin Stilled the Waves; Duke University Press: Durham, NC, 1989. 18. The Scientific Papers of James Clerk Maxwell; Niven, W. D., Ed.; Dover: New York, 1952; Vol. 2, pp 1–78. 19. Moore, W. J. Physical Chemistry, 3rd ed.; Prentice Hall: Englewood Cliffs, NJ, 1962; p 225. 20. Servers, J. W. Physical Chemistry from Ostwald to Pauling. The Making of a Science in America; Princeton University Press: Princeton, NJ, 1990. 21. Newton, I. Principia; Cajori, F., Translator; University of California Press: Berkeley, 1943; p 398. 22. Roberts, R. M. Serendipity. Accidental Discoveries in Science; Wiley: New York, 1989.


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Stories to Make Thermodynamics and Related Subjects More Palatable

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