Misconceptions in school thermodynamics

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Misconceptions in school thermodynamics

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Misconceptions in school thermodynamics A H J O H N S T O N E , J J MACDONALD and G W E B B Department of Chemistry, University of Glasgow

This article is based on the results an of investigation(Macdonald 1976) of the conceptual difficulties experienced by pupils studying the topic of chemical equilibrium for the Scottish Certificate of Education in highergradechemistry(Scottish Certificate of Education Examination Board 1976) and for the Certificateof Sixth-Year Studies (CSYS) (Scottish Certificate of Education Examination Board 1976). The approach to chemical equilibrium at higher gradeis based on the conceptof equal and oppositerates of reaction while atCSYSlevela thermodynamics approach based on the concept of Gibbs free energy is employed. Conceptual difficulties experienced by pupils (and perhaps by teachers) with respect to the thermodynamics approach are discussed. Since the mid-1960s it has become fashionable to introduce thermodynamics in schools. Even in the traditionalsyllabusesthe first law hashadan honourable place under the guise of Hess’s law and thermochemistry for many years. The more recent innovations (Roberts and Watts 1976) boldly introduced the second and even the third laws with the attendant concepts of free energy and entropy. Free energyevenfoundits way into Nuffield 0-level chemistry, much to the delight of the sophisticates. Fewmodernsixth-formchemistrycoursesdonot include the three laws. These changes have not met with universal approval.Wright(1974)assertsthatthermodynamics has noplace in schoolsonthegrounds that its basic tenets are beyond the abilities of pupils of tenderage;sincethermodynamicsdoesnot invokemolecularmodels,hemaintainsthat it is quiteunsuitedtoelementaryteaching.Healso asserts that most teachers are not qualified to teach thermodynamics because of its inherent difficulties of ‘perfectly the scandalous because and inaccuracy’ of thermodynamics taught in most universities. 248

However, in thesamejournal,Ogborn (1974) defends the school position and accepts that conceptually difficult topics’ought tobetaught.He points out that, just as senior pupils are perfectly capable of appreciating the basic ideas of Newtoniandynamics,theyarealsocapable of appreciating the basic ideas of thermodynamics and using them to good effect. The problem, rather, is one of deciding how to go about. it. And the controversy has been, if anything, more hotly debated on the other side of the Atlantic (Strong 1971, Case 1971).

Feasibility of teaching thermodynamics It was decided that measurements should be made to test the feasibility of teaching thermodynamics in schools. The main goal was to examine the development of the idea of dynamic equilibrium through thermodynamics and to look for the misconceptions and the successes in the teaching of the subsumedconcepts of enthalpy,freeenergyand entropy.A‘thermodynamicsapproach’test was written and administered to 98 pupils in IO schools who had just completed the relevant part (section 2) of the CSYS syllabus. The test attempted to determine if pupils had successfully assimilated the variety of conceptualmaterialjustencountered: AH (in greater depth than at higher grade, with emphasisontheunderlyingdistinctionbetween potential and kinetic energy at the molecular level), AG, q rev (notmentioned as such in thesyllabus notes) or T A S and reversibility, A S and irreversibility, and K e q (A GO is not required by the Scottish syllabus.) of theresponsesselected by Aclosescrutiny pupilsshowedthatcertainmisconceptionswere generally prevalent. ( l ) It was found that the majority of these sixth formers did not appreciate that at the boiling point of a liquid the molecules in the gas phase had the same average kinetic energy as the molecules in the liquid phase. It is important that pupils have a clear idea of the distinctionbetweenpotentialenergyandkinetic energyatthemolecular level sincemost of the changes they deal with are at constant temperature (albeit at the macroscopic level) and are therefore potentialenergyones.It may bethattheearly teachingontheparticulatenature of matter intrudeshere.Juniorpupilsaretaughtthatthe particles in a solid hardlymove, while those in a liquid move more vigorously and those in a gas are moving even more violently. ( 2 ) About one pupil in six was still hampered by the idea that endothermic reactions could not be spontaneous. This is presumably carried over from theapparentlyuniversalrulethatsituationstend spontaneously to a positionof lower energy. Physlcs Education M a y 1 9 7 7

Whether this is tacitly and unwarrantedly assumed or is a result of the very heavy emphasis givento‘favourableandunfavourable’enthalpy changes during higher grade is not certain. What is certain is that there exists a tendency to compare relativemagnitudes of enthalpychanges in this fashion in discussions of ionizationenergies, electronaffinities,bonddissociationenergiesand lattice energies when in fact the determining energy change is a free energy one. In a sense, pupils may bebeingactivelymistaughtatthispoint in the higher grade syllabus, with repercussions later on. (3) There would appear to be some tendency for pupilstorelatethemagnitude of thefree-energy change to the rateof reaction (a reaction for which thefree-energychange is large is considered by about one pupil in four to occur rapidly). There is possibly a misconception to the effect that the net rate of reaction in system a tends tozeroas equilibrium is approached because the value of A G tends to zero. This misconception was not tested in the research study butit probably exists. Pupilswereprobablydrawingananalogyfrom themacrophysicalworldwherethefurtherthings fall, thefastertheygo, or eventhemoreenergy provided,thehigherthevelocity.This is another example along with(2) above in which the ‘common sense’ of physicsseemstoconflictwithchemical thermodynamics. (4) Morethan half thepupilshad difficulty in appreciatingthattheamount of heatreleased during a reaction varied with the amount of work the reaction was called upon to perform and that maximum heat is only evolved (or minimum absorbed) when no workis done by the reaction. ( 5 ) Two pupils in three confused the descriptive (rates) and prescriptive (thermodynamics) meanings of reversibility. The descriptive rates definition, that a reaction may proceed forwards or backwards, was showntobe well understoodatordinarygrade, though the simultaneous occurrenceof forward and reverse reactions at equal rate (a dynamic concept in conflict with the mechanical static concept) was not very well understood at higher grade, while the significance of thermodynamic reversibility in that it prescribes how a reaction is to be operatedis lost to most pupils. That a reaction is operated reversibly when a maximum demand is made of its optional work capability, with the consequence that it ‘proceeds infinitely slowly’, is not too difficult an idea to present concretely. But pupils tend to think that slowness is thecriterion of reversibility andare therefore all too ready to assert that a mixture of hydrogenandoxygen, for example, is reacting reversibly at room temperature simply because the reaction is occurring slowly. About half the pupils who took the test did not appear to know that a reaction could be held back by a kinetic barrier and Physlcs Education M a y 1 9 7 7

that this had nothing whatsoever to do with reversibility. ( 6 ) Approximately one pupil in four had no clear conception of the distinction between system and surroundings.

Pupils’ conceptionsof entropy (7) Entropy is generally interpreted as a measure

of disorder, which is in accordance with the requirements of the syllabus. This might or might not be conceptually sound, depending on how disorder is interpreted. Unfortunately, the test was not able to delvetoodeeplyintothe‘mystique’ of entropy becausethequestionswererestricted by syllabus content. However, this is probably one of the areas most worthy of investigation in science. This one concept more than any other is perhaps responsible for the unpopularity of thermodynamics: none of us likes that whichwe do not understand. Although questions in the test were set at a very superficial level with respect to this concept, one is leftwith theimpressionfromthetestresultsand from casual conversations with pupils and students that they have little or no conception of entropy. Somesuggestions to accountforthisare now offered. It is not too difficult to establish the meaning of qrevif done concretely to begin with. That qrevis equatable to T A S is much more difficult to explain. The programmed text, issued to schools before the test,adoptedthestrategy of explainingwhat AS was in terms of change in ‘disorder’, where disorder was very carefully defined as the number of accessible microstates. Entropy emerged as a value indicative of the number of accessible microstates, analogous in somerespectsto,andrequiringthe samesort of verbaltreatmentas, ‘pHvalue‘, a concept with which pupils were already familiar and which thereforeactedasthemental‘anchoring idea’ for the new concept. Pupils wereencouragedtotalkaboutentropy values andto resist thetemptationtotalkabout entropy in themanner in whichtheywouldtalk about mass and energy. The conventional approach atthispoint in thesyllabus is toexplainthe relationship A G = AH - TAS and to interpret TAS (with or without mention of qrev)as an energy termwhichhasto d o with disorder.Change in entropy is then deduced by dividing the energy term by temperature. (The performance of pupilswho followed the concretely based programmed text was overall significantly better at the 0.1%level than the performance of pupils who received conventional teaching.) Thereseemstobesometendencytoconfuse For example,pupils entropyandkineticenergy. were asked to consider a stretched elastic band at room temperature, which-when released249

contracts spontaneously. Given that the entropy of the rubber increasesas it contracts, one pupilin two considered that the temperature of the rubber must increase.Increase in entropy,therefore,seemsto equate with increase in temperature, perhaps through some misconceptual notionof disorder. It would seemalsothatdisorder is popularly misinterpreted as ‘chaos’. For example, the diffusion of twogasesto give ahomogeneous mixture is accompanied by an increase in entropy value indicative of increase the in total ‘permutational arrangements’ or microstates, which may be equated to increased disorder, which is valid enough. This however may be extended to the point where a haphazard array of tumbled building bricks is accorded‘greaterentropy’thantheoriginal orderedarray simply becausethearray is more disordered! (8) About three pupils in four consider that when Keq = 1 theequilibriummixtureconsists of 50% reactant and 50% product.Thismisconception probably results from the very superficial coverage given to the constant in section 2 of thesyllabus notes, and would probably be easily dispelled with any kind of treatment in depth.

BerthelotandThomsen in 1878. Itseemedtobe commonsensethatsystemsshouldmoveto positions of lower energy. Our pupils can be forgiven if they are making this wrong connection. This ‘rationalization’ process can also be seen when pupils are linking rate with free-energy change. The misuse of aconversedescribed in (5) is another understandableerror,anerrorcommon in most fields of human activity.

Is there a remedy?

Somewriterswould gladly banthermodynamics from schools, assuming that universityis the correct placeforthis,butthis is no remedywhen most graduatechemistsconfessthemselves baffled by their undergraduate experiences of thermodynamics. Teachers in both secondary and tertiary education would do well to consider that the cause of the misconceptions may bein their own failure to appreciate that their students will make problems for themselves out of what the teacher thinks is a perfectly lucid presentation. Teachers may have to teach consciously towards helping their students to makethecorrectconnectionstotheir existing knowledge and to warn their students against making the wrong ones. This teaching may not be Why should these problems exist? bad, but unsympathetic. It is possible that an early concrete and pictorial It would be easy to lay the blame for the existenceof presentation of essential thermodynamic concepts these problems on incompetent teachers, and some in a final year at school might become a necessary teacherswouldfreelyadmitthatthermodynamics preliminarytothemoreformaltreatmentat has always been a closed book to them. Here the university. It certainly is true that the universities indictmentwouldhavetobe levelled againstthe university educators who taught them. Anothereasy have had ample time and opportunity to demonstrate the effectiveness of their teaching of explanationwouldbetoassertthatpupils in the thermodynamics. The lackof confidence with which sixth form are not mature enough to appreciate the teachers approach the subject is perhaps testimony conceptual subtleties of the subject. This could in to the failureof the universitiesin this respect. part be true, but it would have to be proven; while There is probably a place for thermodynamics in by contrast the investigation (Macdonald 1976) has schools where it can be taught in small groups by shown that basic thermodynamic concepts can be discussiontechniques.Asensitiveteachershould taught with some success in school using, initially, a then be able to detect the misconceptions. A large concrete nonabstract approach. university lecture situation is certainly not the best When a student is presented with a new idea he medium for presentation of material of this kind in cantreat it in anumber of ways (Ausubeland that the teacher has little or no feedback until the Robinson 1969). He can place it in a compartment alongside his existing body of knowledge and not try examination, when it is too late. There is one other way in which teachers at all to incorporate it. Another possibility is that he can levels canbedeceived. If thetreatment of the attempt to attach the new knowledge to his existing thermodynamics is toomathematical, itis all too knowledgeandhemaymakequitewrongconeasytosetmathematicalquestionsandthen nections (Ausubel 1963). A third course is to mistakenlyequatemathematicalcompetence with incorporate his newknowledgecorrectlyinto his present knowledge and apply clear understanding to an understanding of the underlying thermodynamic concepts. the new concepts. The evidence we have presented could be used in Some of the problems listed earlier in this article supportofthe‘anti-thermodynamics in schools’ may havetheirorigin in thesecond of these position since we have purposely set out to isolate possibilities.Forexample,theideathatreactions misconceptions.Wecouldhavedoneasimilar havetobeexothermictobespontaneouswas exercise on many other concepts taught in science historically the accepted view of chemists such as 250

Physlcs Educatlor V a y 1 9 7 7

and we would have found a significant number of students in everycasewhohadfailedtocomprehendtheideascompletely.Butthisdoesnot mean that these ideas should not be taught. It may well bethatchanges in approachandinformed sympathetic teaching may prove to be beneficial. If teachersunderstandthematerialandunderstand how their students learn, they will be in a position to present it in an acceptable and intellectually honest way. It wouldbeapity if seniorpupils,many of whommayneverbeprofessionalscientists,were debarred from one of themostbeautiful,elegant and all pervading intellectual experiencesof science because we didnottrytomakethermodynamics understandable to them.

Celestial navigation with the stereographic projection D R HUTTON Physics Department, Monash University, Australia

REFERENCES Ausubel D P 1963 ‘Cognitive structure and the facilitation of meaningfulverballearning’ 1. Teach.Educ. 14 2 17-30 Ausubel D P andRobinson F G 1969 SchoolLearning (New York: Holt, Rinehart and Winston) Case J B 1971 Treating Chemical Equilibrium Mathematically in Secondary Schools ERIC ED043483 equilibrium and its Macdonald J J 1976 ‘Chemical conceptual difficulties’ M S c Thesis University of Glasgow Ogborn J 1974 Educ. Chem. 11 11 Roberts I F and Watts D S 1976 ‘The teaching of therrnodynamics at preuniversity level’Phys. Educ. 11 277-84 Scottish Certificate of Education Examination Board and Higher Grades1976 Chemistry-Ordinary Syllabuses and Notes 2nd edn (Glasgow: Gibson) Scottish Certificate of EducationExaminationBoard 1976 Certijcate ofSixth Year Srudies (Glasgow: Gibson) Strong L E 1971 ‘Chemistry and the liberal arts’ J . Chem. Educ. 48 562-5 Wright P G 1974 Educ. Chem. 11 9

One of the most rewarding culminations of study of positional astronomy is the ability to navigate by the stars,andmoststudents,perhapsmotivated by romantic feelings, work hard to achieve this ability. Success is also rewarding for the teacher, since it requires a good understandingof many of the more difficultconcepts of positionalastronomyparticularly in the areasof coordinate systems and time. Themajorexercise in celestialnavigation(e.g. Menzel et a1 1970) requires the calculation of the observer’s latitude and longitude given a standard time, the date, some celestial data (almanac) and somecelestialobservations, usually thesextant heights of two celestial objects (stars, planets, sun, moon).Fromtheobservedheightstwocircles of position on the earth’s surface centred at the correspondingsubstarpointsarecalculated,andthe observer’sposition is at theintersection of these circles. Although this method successfully solves the problem, in practice itis more normal (Huffer and Marasso 1967, Minnaert 1969) first of all to assume one’s dead reckoning position, then for agiven time precalculatetheheights of twostars.Measured deviations from the calculated heights then can be converted to deviations between the assumed and true position, thusgiving the true position. Both of the major steps in these methods involve the use of the astronomical spherical triangle (Smart 1960) and we havefoundthatmanystudents stumble at this step and lose sight of the processes involved.The use of the stereographic projection allows the concepts to remain clear and the calculations and measurements to be completed rapidly, which more than compensates in the learning situation for the limitationin accuracy to& 0.5”.

Plotting circleson the stereographic projection The stereographic projection is a very useful aid to P h y s c s EducarNon Mav 1 9 7 7

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