Research as an Influence on Teaching Kenneth R. Jolls Department of Chemical Engineering, lowa State University, Ames, IA 50011 Research and teaching need not be isolated functions in a university. Skills and experience acquired from research and other creative activity can enhance teaching and promote learning when their potential influence on pedagogy is recognized. This paper reports on research into a new form of computer-generated visual aid and the ways in which the results are being used to help students understand thermodynamics. The Problem All too often in our academic society the notions of teaching and research are treated as separate. if not mutuallv exclusive. activities. Professor Smith is known as a good teacher, and Professor Jones is recoenized for research. Whether these distinctions are correct in an absolute sense or whether they are the result of a less-than-enviahle performance in one or the other area is often obscured by our penchant for finding eood in everyone and our reluctance to criticize our colleames. i n simpler terms, we may expecr fewer research publlratiuns from Smith berause of histeaching nhilitier whileat thesame time we excuse Jones for mediocre lectures because of all the time he spends writing papers and working with graduate students. In reality neither of these extremes exists very often. Most of us teach. and most of us do some kind of research. althoueh obviously kith very different impacts on our students, t i e universitv, our profession, and knowledee in eeneral. But. because we are all possessed of finite c&acit& as well as being imperfect managers of our time, rarely do any of us realize that utopian mixture of the two that has come to epitomize the ideal academic person. So this presents a paradox. In one breath I have been critical of a svstem that isolates teachine from research and even reward; iLi practitioners. hut wen iiefore these words have died away I have admitted that at any ziren time must of us will be found in one or the other-of these two professorial states. In graduate school a t the University of Illinois I had the good fortune of working for a major professor who had what I have come to regard as the ideal point of view on this question. His name is Thomas Hanratty, and he is a distinguished researcher in the area of fluid mechanics. Sometime durine my last few months a t Illinois, after the decision to go into teaching had been irrevocably made, I asked Tom Hanratty how he felt about the teaching-versus-research issue. Hereplied without hesitation that. as far as he was concerned. research was teaching. The succeeding years have crystallized my own views on the matter and convinced me not only that he was right but also that the excitement we feel for a solved equation, a successful run, a functioning program, or a new result in our research can often carry over into the classroom to inspire our students and make learning equally as exciting for them. What I believe Tom Hanratty meant when he said "research was teaching" was that for him the two are inseparable. I think there is much wisdom in this idea, and I think that it can apply universally among those of us who teach. Let me paraphrase it simply. As academic men and women, much of our life is devoted to learning about things we do not understand. First as stuPresented at the Second Biennial 6. F. Ruth Chemical Engineering Research Symposium, lowa State University. Ames. March 8, 1979.
dents, then as teachers and researchers, we put our energies into grasping new ideas that often change the way we think about old concepts. Then, because we hear some responsibility for the future (and also to preserve our own work), we feel the need to pass this knowledge on to others. I doubt that there is a person in our profession who has not felt that certain elation. that little burst of eeo that roes along with telline someone else about a problemthat wejust solved, an exper; ment that finally worked, or a new idea that just occurred to US.
Ow students are iust like us. Thev, too. want to learn about things they do not Gnderstand. ~ut,'becausethey are on the order of a eeneration behind us, their experiences and associations &limited. I believe that they look to us for more than just facts and reflections of their textbooks. They also want to know Why?, Why not?, What if?, What else?, and so on. Surely the best means that we have to respond to such auestionsk to cite something in our own experience-often our own research experience. No amount of mathematical modelingor derivation can offer as con\,incing an argument about an urificc c d f i & n one's own experienre in measuring one. All t ~ the f predictive c.quatims and loy,icaI mechnnismi that one can call upon toeuplain critical hear tlux will not have the imnact of a live demonstration. F'veu the laws of thermodvnamics, with all their elegance, fairly beg for concrete exam~ l e to s lift them out of the abstract. Certainly none of us hasrhe hreadth of experience, whether from research or elsewhere. to hiehiieht everv lecture inall the ways I am suggesting. ~ uallt ofus can do ;omething special to make some lectures excitine for some students. and more often than not that "somethi~g"will have its origins in our research. Tom Hanratty does that with fluid mechanics. To hear him teach the subject is to experience his love for it. T o talk to his research students is to understand the excitement that he inspires in them. And to study hisresearch is to appreciate the benefits of staving involved in both aspects of an academic career. One Man's Solution This rather elaborate introduction may lead some to think that I have discovered the "final" solution. that ultimate correlation that factors in both research interests and teaching res~onsibilitiesand then points the wav for them to coexist. ~n'fortunately,I have not'been able tobbtain that in closed form -vet..and all that Ican reallvrenort " . are the results for one special, perhaps even limiting, case: my own. I t seems clear tome that style plays a major role in the way we teach and also in the way we modify and improve our teaching through some type of creative activity. My approach has been to develop a completely new research area related to pedagogy, and I offer the results below, both for their intrinsic value to students and as an example of one way to resolve the teaching-versus-research question. Before I began my first year of teaching I was asked by my prospective department head to list the courses that I would "like" to teach. I responded by saying "anything but thermodynamics," whereupon one of my first teaching assignments became a two-semester, undergraduate sequence in chemical engineering thermodynamics. The rather gruesome details of that first year's bout featuring me versus thermodynamics versus 35 chemical engineering seniors are probably beyond the scope of this presentation, and I will let the reader's imagination recreate the scene as it will. Even though I Volume 61 Number 5
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would have been appalled to have had a Gihhs or a van der Wads or a Prausnitz or a Van Ness (or even the reader) sittine in the back of my class, there were some useful things thai came out of that first year: 1) I did not understand thermodynamics. 2) If possible, my students understood even less ahout it. 3) Even when I did understand it. 1certainlv did not know how to go about teaching it.
We certainly have not explored all of these fully. Points (1) and (2) were addressed in the early papers cited above. Point (3) was considered by Willers ( 4 ) , and research into point (4) was supported by a grant from the National Science Foundation through its Local Course Improvement Program (5). But the purpose here is to look a t some of the work that has been finished, suggest how it might be useful in teaching, and then let imagination prescribe the future.
Now, the first two of these ideas should strike a familiar note. I believe vou either love "thermo" or vou hate it. You understand it q&e well or not a t all. You "get the idea" or you "miss it completelv." The third point;however, carries with i t some of that tacit arrogance of the new PhDfprofessor: "The textbooks aren't goodenough; I'm going to &me up with a better way." Actually, the textbooks are good enough. They just need a little help. I think that this is true not only in many of the engineering courses we teach but probably in other areas of science as well. T h e last thing we need in thermodynamics is another textbook, another system of nomenclature, or another way to symbolize the "partial molar Gibbs energy change." What we do need, I think, are better ways to verbalize fundamentally difficult concepts. What makes a subject like thermodynamics so hard is that i t contains so many intangibles. We can demonstrate fluid flow in a pipe. We can doexperiments showing heat transfer, gas absorption, process control, and so forth. But we cannot demonstrate enthalpy. We cannot go to a laboratory supply house and buy an entropy meter, and we certainly cannot have two scales on a hourdon gauge, one that reads in pressure and one that reads in fugacity. The tool that I have found to he most useful in focusing my own thinking and in helping me verbalize thermodynamic situations to students is the computer-drawn property diagram. I am sure that there are many thermodynamicists who feel that interpreting physical property relationships and thermodvnamic processes through geometry is a t least artifirial an(lperhitpseven too simpltstic for the college rlassroum. My. response is a pragmatic m e : after a decade and a half of staring a t vacant ixp&sions and grading exam solutions that hear little resemblance to the questions, I am willing to try anvthine he &mputer-drawn property diagrams that follow show the results of research ~ e r f o r m e dbv five students a t Iowa State Ilnivcrstty. Twochemical engineering project students, ('a11 Smetrh and l.es Jmsen, hclurd during the first stages of the work, and a graduate student; Gary ~ i ~ e rcompleted s, his MS research on the project ( 1 4 ) . The goals were simple enough: first, to learn how to construct thermodynamic property diagrams through the use of computer graphics; then, having done that, to produce some diagrams that would he useful in teaching; and finally, to organize and document these in such a way that others could use them with a minimum of effort. Currently, we are well into the third phase of the work. A considerable amount of time a t the beginning of the project was spent rederiving some fairly well-known principles in computer graphics. But this was necessary because we wanted to do more elaborate things than can typically he done with standard library graphics programs. For example, we wanted to he able to do the following:
The Results Today, more than a hundred years after van der Waals, it is probably difficult to become excited about another P-V-T diagram. But, as is always the case with research, we needed to start with something we already understood, so our first "guinea pig" was the ideal gas surface, shown in Figure 1for the range of properties characteristic of ethylene in the liquid and vapor states. Geometrically, this simplest of all thermodynamic equations of state comprises one symmetrical section of a hyperbolic paraboloid. Lines of constant temperature are hyperbolae, and lines of constant pressure and volume are straight lines, which give rise to what we call a ruled surface. I tell students that this is a three-dimensional graph of the pressure-volume-temperature properties of an ideal gas, and that the equation that generates the graph can be arrived a t from elementary kinetic theory if we assume that molecules are point masses in constant motion and that they exert no forces upon one another. I also tell them that they have been usine the ideal eas ever since thev heard of Bovle's " eauation . ~ a w a n Charles' d Law in high school chemistry. Now the first loeical auestion is. "How eood is it?" To answer this it would &em that we need experikental results. But I think that a more dramatic answer comes in the form of a yimilar diagram, covering the same range of proprrries, fur a '.real" gas tor more ~rolwrlv.a real fluid,. Figure 2 shows the most accurate portrayal of the P-V-T propekies of ethylene that has been reported to date. The generating equation is due to Bender (6)and is of the form of the Benedict-Webb-Ruhin equation with 20 constants. I tell the students that thisgraph, too, comes from an equation hut t h a t t h e level of accuracy is so great as to make it essentially the equivalent of experimental data for our purposes. In other words, I tell them that
~
~
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1) Display a thermodynamic phase surface (a function of two or more variables) in some desired orientation either with or
without the three-dimensional effect. 2) Show the interrelatiunships among eonstant-property lines, saturation curves, and other thermodynamically interesting
topographic features. 3) lntruduce same purely graphical procedures to make the diagrams more readable or more attractive. 4) Experiment with advanced techniques that might yield entirely new kinds of property representations.
394
Journal of Chemical Education
Figure 1. The pressure-volume-temperature(P-V-7) surfaceof an ideal gas as defined bv lines of constant oressure (isobars). constant volume lisocharesl. ana constant temperatre (wxnernm, Fuery po nl on tneclear surface oat s k s the e q ~ m o nPV = RT, as ver l e d 0 ) Ine c rcled. lnree-way ntersecl onat P = 625 ps a. T = 350 'Rand V :6 It3. lo-mo e !R = 10.731 n lnese unmJ
this is reallv the wav" nure . ethvlene behaves over the ranees of pressure, volume, and temperature shown, and then I describe the various areas of the diagram, the phases they denote, and the phase boundaries hetween them. Now in response to the question, "How good is the ideal gas law?" we can compare corresponding points on the two figures. At the points marked a (high temperature-low pressure) the volume predicted for the ideal gas is in error by less than 5%. At the near-saturation points /3 the error is nearly 20%, and a t the high temperature-high pressure points y the error is more than 30%.Qualitatively, there is also an enormous difference: the ideal gas does not condense. The entire two-phase region enclosed by the saturated-liquidlsaturated-vapor h(;rmdary on thr n r n d r r rlia~ratn1s ah&t from the sin~pler P- 1'-T surface, as is also a n \ indication of a critici~lpoint. Next. I ask thr utwstlm. "What can we do to rhe ideal gas " equation that will make i t predict, even qualitatively, the hehavior observed in nature?" The answer is that we can do what van der Waals did. Instead of having the entire molar volume free for molecular movement. we subtract an amount b that we see as inaccessible because of the molecules themselves and obtain a free volume equal to V - b. Then, instead of equating the pressure to the value P measured externally, we increase it hv an amount alV2 to account for the loss due to real intermolecular forces. Now, in place of the ideal gas equation for 1mole of gas PV = RT
(1)
we get the van der Waals equation (P++)(v-~)=RT
(2)
Figurr 3 shows thr rrst~ltof plotting eqn. (21o\,er thesame range of the P- V - T variables used in the previous figures. The contrast with the ideal a a s s ~ ~ r l a isdramatic. ce With nothing more than these "mech&ical" changes to eqn. (I),we generate a surface much more like the natural phase diagram for the real material. T o do this, of course, we had to choose the constants a and b so that the highest isotherm on the surface
Figure 2. The P-V-T surface for ethylene as generated by an equation of state due to Bender (6). The loci a! saturated-liquid states (those at the paint of m i z i n g ) and satuat&vapor states (lhose at lhe poim of condensing) wnnect at m e critical point. The ruled surface enclosed by lhe saturation curves represents mixtures of liquid and vapor that coexist in equilibrium. Pressure and temperature vary as unique functions of one another in this region, and volume denotes me combined volumes of me two saturated phases, presem respectively in amounts that sum to one mole. The fraction vapor of such a mixture is onen called lhe "quality."
displaying a horizontal tangent (i.e., where (dPldV)T = 0) would correspond to the real critical isotherm for ethylene (508.8 OR) and predict the actual critical pressure (736 psia). Figure 3 still does not look exactly like Figure 2 because it does not show the ruled surface that characterizes the saturation region. At this early stage of thermodynamics training, the tvnical -. student is not .nrenared . for the concents of Gihhs energy or fugacity that enter into the explanation of phase senaration. So I ask students simnlv . . to accent. . . on faith for the moment, that with more advanced thermodynamic reasoning a two-ohase reeion can he su~erimnnsedon the hasic van der ~ a a l s m o d e il f Figure 3 tdgive the net phase diagram of Figure 4 and a striking resemblance to nature. It is well known that the van der Waals equation gives poor numerical results over large regions of the P-V-T surface. Its critical compressibility isfar &eater than that of most of the equarion of materials WP deal with. Almost anv tw
