Jerry A. Bell
Simmons College Boston, Massachusetts 021 15
I 1
Content and Context Entropy principle experiments in a course for non-science students
During the Fall Semester of 1972, I gave a course for non-science students, Order and Change, which was aimed a t giving the students a feel for the concept of entropy and for how to analyze natural events to see the entropic control. The lecture material was based on many sources (1-4). Although the laboratory work was not always novel, the interpretation and context of the experiments was different from the usual. This is a report on the way the context for these experiments was developed and how they were used both to test and to expand the context. The approach is not limited to the particular experiments we chose and could he adapted to another set within the same kind of interpretive framework for students with similar aims. My approach throughout the course was always to begin with observations and systems that were familiar to at least several of the students and then to proceed in a more-or-less Socratic manner to scrutinize them carefully and together develop and test models to explain them. The students were very adept a t seeing analogies and interrelationships between their model testing and other exneriences (nerhans more so than science maiors. whose ;ision is sdmewh'at narrowed by the feeling that they will be ~enalizedfor "unscientific" observations): for examde, the; were able to see the carrespondence &tween a dif-. fraction grating and the play of color from the surface of long-playing records or between a glass of ice water and a solid-liquid system of moth halls. I began with no fixed ideas about specific topics to he covered (except, of course, that the general aim was to develop the entropy concept), so that the work we did largely arose from these class discussions. How this worked and the experiments we did are described below. Most college students, science and non-science majors alike, are familiar with and have accepted the atomicmolecular model of matter (even if they have only the haziest concept of its origins). Beginning with a discussion of possible observable consequences of the model, the students and I decided that Brownian motion of dust motes in the air was one candidate. I directed this discussion to lead to a laboratory investigation, by microscopy, of Brownian motion of particles suspended in water and the discovery that the particle density varied with height above the bottom of the container (5-7). The particles were 0.81-u diameter latex heads. a clinical reaeent sold as '0.81 ~ a t e x , "contained on n microscope slide'm a well, ahout 250 r deep, formed u,ith cover glasses and stopcock grenie. I'hotomicrograpbs were taken at various heights. Each student analyzed one or two of these and pooled her darn with her classmates. Quantitative analysis of these results, carried out in a group discussion period, led to the formulation of a logarithmic relationship between particle density and height. rAlthough the class did not determine Avoeadro's number. these data -give 4 X loz3 molecules/ mole.) Two problems for non-science students became apparent during this experiment. The first is that it is difficult for them to make an easy connection between the purposely limited and controlled laboratory world and the
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more complex interactive world of their experience. This places a greater burden on the instructor to make the connections before the experiment is performed or its impact will be lost.' The second is that the concept of logarithms is so foreign and mysterious as to he a serious pedagogical stumbling block toward understanding the physical relationships expressed in this mode. This is curious in that the exponential concept was not so objectionable, especially when presented as the result of a compounding effect. I conclude that necessary relationships should simply he left in their exponential form and treated quantitatively, when necessary, using computers or calculators that give exponentials directly. Since we bad accepted a model incorporating random molecular motion, we thought it wise to know more about random behavior; we chose to study coin tossing, by computer simulation. Computers generally have a random number generator which can he used to "toss coins" and give the numbers of heads and tails for a given number of tosses (or coins tossed). The results of the class study on systems ranging from 10 to 105 coins were graphed to show (1)the marked narrowing of the distrihution curves as the number of coins increases, (2) the wide variations from the "most probable" distrihution when only small numhers are involved, (3) the large absolute deviations from the "most probable" distrihution even as the fractional deviations become too small to plot, and (4) the actual numbers involved when we say "a large number of tosses." The result, of course, is that this random process gives a predictable result with less and less relative deviation as the number of events involved grows. (Students suggested that the sequence of heads and tails-for the smaller numbers of tosses-he given as well as the totals; with this change an introduction to microstates and configurations is possible in this very simple system.) We examined the consequences of a very simple model for the Brownian motion system by asking what the result would be if the particles were simply randomly distributed between two compartments, the bottom and top halves of the container. If it were a purely random process, the results of the coin tossing experiment predict an equal distrihution between the two compartments. Obviously this is not the case; nature can tell up from down,in that system, presumably, the students decided, because of the effect of gravity. Are there any other cases in which such a binary decision is made where the effect of an external force can he tested? We decided to find out whether such an effect could explain why plants grow uprather than in random directions when they germinate. I t is easy to see by microscopic examination that there are many kinds of granules
'It may seem inconsistent that the students found it difficult to relate laboratory concepts to the "real world," while being able to see experimental interrelationships very well. However, the differentiation here is between abstract-centered and problem-centered relationships; the latter is where they shone. For a discussion, in a quite different context, of this sort of distinction, see Ref. (17).
suspended in the cell fluid of a seed; so the system is not ta, different from that already studied. The model of the germinating cell is again a two chamber model, with the particles suspended in the cell fluid under the influence of gravity and the motion of the seed (8). We grew cucumber seeds in vermiculite on a uniformly lighted platform about 2 ftz and 3 in. deep that was rotated continuously at 60 rpm. (Smaller versions of geotropic experiments can be carried out in Petri dishes, hut the quantitative effects are more difficult to see.) We found that the stems of the plants grew a t an angle and the roots grew in the opposite direction. Analysis of the measured angles of growth, distances from the center of rotation, and rate of rotation quantitatively confirmed that the stems of the germinating cucumbers were growing in opposition to the net force, R, the resultant of gravitational, 6, plus centrifugal, p, forces. (Since the direction of growth is opposite to that which one might intuitively predict for such an experiment without this analysis and model, the results are very convincine.) Althoueh bv. no means a conclusive test. the . results were ronsistent with our hypothesis that the source of seeds' information is [he non-random distribution of' cellular particles in the force field to which the seed is subjected.=
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At this point we needed to refine our view of the molecular world (since we had been looking upon molecules as simply very small, structureless particles) to see if other processes could he understood. We spent some time considering wave effects (diffraction patterns) and their relevance to atoms and molecules (the deBroglie hypothesis); ultimately we used the tangent sphere model and electrostatic attraction (4, 9, 10) to rationalize molecular formulas, structures, and some physical properties (crystallinity, hydrogen bonding, etc.). But since this honding model produces an essentially static world, how were we to explain the changes that are going on all about us? An easy change to study is melting and freezing; we used two of the PSNS experiments (11) involving the temperature changes in a melt of p-dichlorobenzene and then in a melt plus the surroundings to show that energy is released from a system during a phase change even though the temperature of the system is constant. We thus discovered how important the surroundings may he in influencing changes that can occur. The staee was then set to discuss the effect of temDerature upon the change in number of microstates of a system when a eiven auantitv of enerav is added or subtracted. The modkl I chose to-develop% lecture and discussion was the random distribution of energy in closed systems of identical molecules which were fixed in space and had equal spacings between adjacent, quantized energy levels (identical, quantized harmonic oscillators) (1-3). By choosing systems for which we knew the answers (e.g., energy transfer from a body with high average energy per molecule to one with low average energy) we developed predictive procedures, based upon counting all possible microstates in small systems, for determining whether changes would or would not be spontaneous. The result, of course, was that spontaneous changes always move an isolated system toward that configuration (state) with which the largest number of microstates are associated. (We characterized this state interchangahly as the most disordered, the most random, or the state of highest entropy.) We noted, also, the similarity between the average populations of energy levels in small systems to the populations of latex heads in the gravitational field and made a leap of analogical faith (not uncommon in science), as-
sumed a logarithmic relationship between population distribution and average energy (a measure of temperature), and found that disorder (randomness) increased with increasing temperature in these closed systems. We studied the extension and contraction of rubber to demonstrate the utility of this model. First we stretched and contracted ruhber bands held to our lios. . . noted the accompanying temperature changes, formed a hypothesis concernine confirmrational and enerev distribution effects. and then 'tested Tt with a 20-ft "ruhLr hand" (a length of rubber tubing stretched coaxially within a long glass tube). It was very satisfying to he able to predict the surprising contraction of a rubber band under tension brought about by increasing its energy (by raising the temperature slightly with a stream of warm air directed through the glass tuhe).3 Having dealt with a complicated material like rubber, we felt confident to examine processes more closely associated with living systems. To begin, we all constructed hall-and-stick models of a molecule with a tetrahedral central atom and four different colored halls attached to the central atom, examined them all together, and noted the occurrence of two non-superimposahle, mirror-image structures. Could molecules discriminate on the basis of such subtle differences among one another? We studied the cleavage of a - and 8-ortho-nitophenylgalactoside (ONPG) catalyzed by hydroxide ion, an inherently indiscriminate species (describable essentially as a ball of electron density by our model) and hy the enzyme P-galactosidase (14). The base catalyzed reaction is essentially the same for both ol- and 8-ONPG; the enzyme is a much more efficient catalyst for the 8-ONPG and is, of course, completely inactive toward the a-ONPG. Our observations of the relatively narrow effective p H range for enzyme activity and the denaturing effect of modest temperature increases startled the students and made them pause to consider how delicately balanced are the processes that support living systems. Findine from our enzvme ex~erimentsthat life ~ r o cesses depend upon the brder-recognizing-order principle (16) and the generation and maintenance of order, we had to ask how order on a planetary scale could be maintained, using our model of a universe moving inexorably toward greater disorder. We easily recognized that the sun is the only external agent that could produce such an effect. The question remaining was the mechanism of the interaction. The photosynthetic process itself seemed too complex and not visual enough for our study, so we used an experimental analog to photosynthesis, methylene-blue (MB) photosensitized oxidation of 1,3-diphenylisobenzofuran (A) to o-dibenzoylhenzene (P) by singlet oxygen. The characteristics of this system are that it (1) uses an atmospheric gas as one of the reactants, (2) employs a sensitizer compound that absorbs the light energy and is not used up in the reaction, (3) can he followed visually (the initially green solution of A, yellow, and MB, blue, becomes blne as the reaction proceeds to produce colorless P), (4) is rapid and kinetically simple, and (5) demonstrates that a reaction going with a decrease in entropy can he driven by absorption of light energy (16).
2The qualitative effects of weightlessness, predicted on the basis of earth-based geotropic experiments like ours, are strikingly confirmed by satellite studies. A pamphlet, "Binsatellite II," NASA Facts, NF-3110-68, available from the Superintendent of Documents, US. Government Printing Office, Washington, D.C. 20402 60.351, shows the results of a number of experiments on ~ l a n t and s animals in the absence of external forces. 3The thermodynamics oi ruhhrr i i discussed in almost all thermodynamics tdxthooks, engines hare been built with ruhhrr as the working suhstanre (12.. and a suggested drmonstmtlun yew similar t o our experiment has appeared (131.
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We thus concluded the course by studying a complex system illustrating the same overall entropy control (since the enormous loss of matter and energy by the sun increases the total entropy of the universe far more than the small amount of ordering created locally on Earth) as the very simple systems with which we began. Along the way we had discussed other coupled processes and seen the natural limitations on the processes and machines man mieht create. The students' abilitv to w o w through a problem and develop testable modeis to rationalize o6servations and their evaluations of the course lead me to believe that this approach and the experimentation we carried out have made them more aware and better able to analyze the interrelationships which have to be accounted for in solving many of our problems and less willing to accept glib partial answers. Acknowledgment
I would like to thank the Division of Chemical Education (ACS)--DuPont Small Grants Program for support in developing the experiments we did in this course.
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Literature Cited 111 ~ c n t , ~ . ~ . , " ~ h e s e e o n d ~ a ~ , " o ~ f a1965, r d . partm. ~a~~~~k, 121 Nssh. L. K., "ChemThorma: A Statistical Appmaeh to Cla~riealChemical Thermodynamics," Addlmo-Wesley, hading, M a u , 1972. part I. 131 Craig, N. C., J.CHEM. EDUC.,47,342 11970). (41 Bent. H. A,. J . CHEM. EDUC.. 40. 446. 523 (1963): 42. 302, 348 (19G); 44. 512 (19671; d5.768I19681. I51 Perin. J. B.. ef al.. Cornofes Rendu. 146. Om 119031: IN. 475. 530 119081: 119. 477 (l9-B):" ~ f o m ~ , " DV& . ~ o s t m ~ d~ ~e w~ ~. o. r k , i 9 1 7 . (61 Slabaugh. W. H.. J.CHEM.EDUC., 42.471 (19651. d1.211 (?MI 171 , , Hpnw P S .1 CHRM F.nlF -~ , 181 Wsreiog, P. F., and Phillips, I. D. J., "The Control or Omwth and Differenfistion bn Plants," Pergsmon. Oxford, 1910, pp. llCL145. For some different geotropic vr s r i ~ n t l f arnerieon. i~ 222 1-6, erpriments, seo, also he ~ m a t ~ sciemut." June), 141 (1970). I91 Kimball, G.E.,andLochl,E.M., J.CHEM.EDUC.. 36.233119591. (101 Rioux,F., J.CHEM. EDUC.,S0,55011973). I111 "PSNS: An Aooroseh to Phvsiesl Science." John Wilev & Som. New York. 1969.. erperimenf~2-6and 2-7. (121 "The Amateur Scientist," S~ienfifkArnari~oq 224 1 ~ 4April). . 118 (19711. (131 Lasaiek, P.H., J.CHEM.EDUC.. 49.469(1972). 1141 Clark. J . M.. Jr., IEditor), "Erprimental Biachemiatry," W. H. Freeman. San Franeiaco. 1964, eroeriment 23. The croerimental oroeedure for the enzvmatic . also. Pederson, D. reaction was adapted for u r with commercisl e n r y m ~ See, M., J. CHEM. EDUC., 61, 268 119741. 1 would be happy to furnish s copy of the entinexperiment to anyonewhois interested. 115) Monod. J.. "Chenee and Necessity." Knopf, New York, 1971. p r t i ~ u l a d yChapter
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(161 Bell. J.A.. andMaeCillinsy, J . D . J . CHEM.EDUC.. 51.67711974) 1171 Dede, C., andHardin, J.. J.CHEM.EDUC., 50.683119731.
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