Res Sci Educ (2008) 38:545564DOI 10.1007/s11165-007-9061-x

Three Conceptions of Thermodynamics: TechnicalMatrices in Science and Engineering

Frederik V. Christiansen Camilla Rump

Published online: 13 October 2007 Springer Science + Business Media B.V. 2007

Abstract Introductory thermodynamics is a topic which is covered in a wide varietyof science and engineering educations. However, very different teaching traditionshave evolved within different scientific specialties. In this study we examine threecourses in introductory thermodynamics within three different scientific specialties:physics, chemical engineering and mechanical engineering. Based on a generalizationof Kuhns theory of disciplinary matrix, and the idea of boundary objects we analysehow basic thermodynamics theory is conceived in the different scientific specialties.The study is based on interviews with teachers and analysis of the different textbooktraditions. It is concluded that teachers need to take into account how subjectmatter is conceived in other related scientific specialties when designing courses. Twoexamples demonstrating how this may be done are given.

Keywords Thermodynamics Physical chemistry Engineering thermodynamics Disciplinary matrix Problem of transfer

Many, if not most, science and engineering programmes have an educationalstructure which may be described as a stem and branch-structure. At stem level stu-dents are introduced to a range of basic science subjects (typically math, physics andchemistry), and only encounter the scientific specialty of their choice (the branches)after a relatively long time typically 12 years. Many different justifications bothideological and pragmatic can be, and often are, given for this structure.

F. V. Christiansen (B)Department for Medicinal Chemistry, Faculty of the Pharmaceutical Sciences,University of Copenhagen, Universitetsparken 2, 2100 Copenhagen, Denmarke-mail: fvc@farma.ku.dk

C. RumpDepartment for Science Education, University of Copenhagen,Universitetsparken 15, building 12, 2100 Copenhagen, Denmarke-mail: cr@ind.ku.dk

546 Res Sci Educ (2008) 38:545564

Whatever the justifications might be, it is clear that the structure is not unprob-lematic from a learning perspective. Teachers at introductory courses at the branchlevel often experience that large groups of students can not apply the fundamentalrelations they were supposed to have learned at the stem level in spite of the factthat they have passed the exams (Rump et al. 1998). Many explanations can be givenfor this phenomenon:

The basic science teaching has not been good or effective enough (Loverudeet al. 2002; McDermott and Redish 1999).

The students are lazy or do not have the intellectual prerequisites or both.The issue of the increasing diversity of students and their reaction to universityteaching is a major issue of discussion see e.g. Prosser and Trigwell (1999),Biggs (1999).

The subject-matter abundance has prevented the students from understandingthe fundamentals (Prosser and Trigwell 1999).

Assessment is a prime vehicle for controlling student behavior and learning, anddominant forms of assessment direct students in the wrong direction, as discussedby Biggs (1999).

Each of these explanations may have degrees of truth to them when consideringa specific case. In this study we shall consider a different factor contributing to theproblem. Suppose a situation where the students have learned everything that theyhave been taught at stem level. Moreover, the teachers at branch level have studiedthe syllabi of the stem level courses, and agreed that the material is indeed relevant.We claim that, even in this situation, the students may very well fail to apply theirknowledge in the new context.

We shall argue that there are important differences in the epistemological frame-works in which the subject-matter is embedded at stem and branch levels which makeit difficult to apply the methods and tools acquired outside the context in which theywere adopted.

To give an example, take the operation of differentiation as it is often presentedin secondary education. The concept is encountered in two different situations: Inthe maths class and in the physics class. In maths, you are introduced to a functionf (x) and its derivative f (x), in physics you are met with the differential notation dydx .Operations are allowed and encouraged in physics, which are regarded with suspicionin mathematics (e.g., multiplying by dx on both sides of an equation). Furthermore,the connotations of the concept in math and physics contexts are very different:What gives meaning to the operation in physics is considering relations betweenphysical concepts such as time, position, velocity and acceleration, and differentiationprovides a binding link between these different physical concepts. In mathematicsdifferentiation is presented as an general operation relating two abstract functionswith certain properties. Emphasis is laid on the conditions and rules of the game.Physical concepts are rarely mentioned, if at all. It is not strange that many fail to seethe connections when changing from the maths to the physics context.

Somewhat to our surprise there is little or no literature which specifically addressthe issue of conceptual difficulties due to transition problems from stem levelto branch level. The literature on teaching and learning thermodynamics almostexclusively address difficulties in learning concepts within one of the specialties,

Res Sci Educ (2008) 38:545564 547

physical chemistry, engineering thermodynamics, and thermal physics, with far themost studies within physics (Loverude et al. 2002; McDermott and Redish 1999).

Aim and Method

The aim of the present study is to compare and discuss three neighboring teachingtraditions for thermodynamics teaching on the basis of a Kuhnian theoretical frame-work, with a specific focus on the teachers conceptions of subject-matter. By teachersconceptions we are not referring to the teachers as individuals, but as representativesof a scientific specialty. We will discuss the educational implications of the findings,and suggest ways to address the educational problems considered. In the followingwe will outline some of the methodological considerations behind the study.

Our focus is on tertiary introductory thermodynamics teaching. Specifically, wewill analyse three different introductory thermodynamics courses held by differentscientific groupings (and departments) at the Technical University of Denmark.The three courses we are considering are given by physicists (Thermodynamics),chemical engineers (Physical Chemistry) and mechanical engineers (Engineeringthermodynamics), respectively.

The courses are held for different kinds of engineering students. Physical Chem-istry and Thermodynamics are both courses on stem level, whereas the mechanicalengineering course is at branch level.

Thermodynamics as Boundary Object

Differentiation is an operation which plays an important part in both physics andmathematics. But even though there is a common understanding of the conceptwhich allows mathematicians and physicist to agree they are indeed using the sameconcept, quite different working understandings of the concept exist in mathematicsand physics. Our idea is to examine whether the same can be said of the introductorythermodynamics elements appearing in the different courses. Star and Griesemerhave described such elements as boundary objects:

This is an analytic concept of those scientific objects which both inhabit severalintersecting social worlds [. . . ] and satisfy the informational requirements ofeach of them. Boundary objects are objects which are both plastic enough toadapt to local needs and the constraints of the several parties employing them,yet robust enough to maintain a common identity across sites. They are weaklystructured in common use, and become strongly structured in individual siteuse. These objects may be abstract or concrete. They have different meanings indifferent social worlds but their structure is common enough to more than oneworld to make them recognisable, a means of translation. (Star and Griesemer1989)

The basic elements of thermodynamic theory, for instance the first law of thermo-dynamics, certainly inhabits several social worlds and is plastic enough to adapt to thelocal needs. The elements also serve as means of communication across communityboundaries, for instance in curriculum descriptions. We therefore hypothesised thatthe First Law of Thermodynamics and immediately related material can be seen as

548 Res Sci Educ (2008) 38:545564

constituting such boundary objects, which are weakly structured in communicationefforts across different scientific specialties and strongly structured within eachspecialty.

Thus, the focus of our analysis has been elements which recur in several scientificspecialties and how these concepts and models are understood within the differentspecialties such concepts as the laws of thermodynamics, heat, work, internalenergy, power cycles etc. Focusing on the recurring elements in different teachingtraditions is of course in some ways a limitation. Some concepts which are givenheavy weight in one tradition are given only scant treatment (if mentioned at all)in the other traditions. This, for instance, is the case for such crucial conceptsas the chemical potential used in physical chemistry, and exergy or availabilityused in mechanical engineering. Such concepts, it might be argued, constitute themost fundamental difference between the way thermodynamics is conceived in thedifferent traditions. This is probably true, but from the educational perspective theseconcepts are less likely to cause confusion for the students precisely because theyare unique to a specific tradition. What is interesting about the common elements isthat the same words are used to designate quite different meanings. Thus, a potentialfor a problem of transfer arises (Royer et al. 2005).

Conceptualising Differences: Technical Matrices

In order to conceptualise in which way the understanding of common elements inthe specialties differ, we will follow the basic line of thought presented in (Hendrickset al. 2000). In this article it is argued, that the idea of the disciplinary matrixdescribed by Kuhn (1970) in Postscript to The Structure of Scientific Revolutions canbe generalised, so that not only physics, but also applied sciences and engineeringsciences may be accounted for. Because of this extension of scope, Hendricks etal. have relabeled the collection of elements a technical matrix. The elementsof a technical matrix are delimitation of objects, methods, values, theory structure,exemplars, epistemic and ontological assumptions, and experimental structure. Thus,what we have looked for when analyzing our material of the three traditions has beendifferences in delimitation of objects, in methods (or, more precisely, methodolo-gies), in values etc. In our analysis, the first four elements are discussed separately.Discussions of epistemic and ontological assumptions and exemplars are includedin the discussions under values and theory structure. The only element described byHendricks et al. on which our analysis shall have no bearing is experimental structure.The reason for this is that none of the courses considered include laboratory work,and that the textbooks are not experimentally oriented.

Analysing Teachers Conceptions of Subject Matter

As described the focus of our study is teachers conceptions of disciplinary subjectmatter, but we will have to elaborate a little bit on what we mean by the term subjectmatter in this context, and how conceptions of subject matter may be analysed.

In the theory of didactic transpositions (an influential theory in the didactics ofmathematics) Chevellard (1985) has emphasized the difference and relationship be-tween scientific knowledge, school knowledge and taught knowledge. The different

Res Sci Educ (2008) 38:545564 549

types of knowledge are related, but not (typically far from) identical. Accordingto Chevellard, scientific knowledge is transposed into school knowledge in what istermed the external didactic transposition. School knowledge is typically representedin curriculum descriptions, teaching manuals, standard textbooks etc. The taughtknowledge in its turn is a transposition of the official school knowledge theteacher decides upon a specific way to fulfill curriculum objectives etc. This is whatChevellard terms the internal didactic transposition.

Likewise, in our case. The teachers conceptions of thermodynamics pertains inpart to their understanding of thermodynamics as a part of their research field, in partfrom their knowledge of (more or less) official ways of organising thermodynamicscurriculum, and in part from their experience teaching the subject. By teachersconceptions of thermodynamics we mean knowledge of all these levels, as well asknowledge of the external and internal didactic transpositions within their specialty.That is what we mean by teachers conceptions of subject matter.

Concerning the more general question of how teachers conceptions of thermody-namics may be analysed, a few methodological remarks follow.

Kuhns theory represents a general structuralist framework, and our study is incontinuation of that approach. The paradigm theory postulates the existence ofcertain general structures in the organisation of science (e.g., paradigms, normalscience, anomalies etc.), and Kuhns subsequent idea of a disciplinary matrix de-scribes general knowledge structures in scientific communities (Kuhn 1970). Thesestructures are constitutive and regulative of the scientific practices within the com-munities. Kuhns approach was mainly historical and sociological, perhaps becausehis main interest were in the dynamics of science. But since the postulated structurespermeate the scientific communities as such, the structures should be discernible atmany levels of investigation, and many other types of investigations (for instanceethnographic studies of contemporary science) could be undertaken with focus onthe same structures.

Similarly, our endeavor is to understand teachers conceptions of thermodynamicsin three different teaching traditions, by discerning the general structures common tothe traditions. It is clear that many different sources of information can be consideredfor analyses of teaching traditions and teachers conceptions of subject matter forinstance class room analyses of teaching, student problems solving, teachers com-munication with each other, textbook analysis, teachers problem solving, interviewswith teachers, interviews with students etc. Each of these approaches will no doubtshed light upon the specifics of the teaching traditions in question. Obviously, avariety of sources pointing in the same direction will strengthen the validity of thefindings. For this reason we have chosen two different sources of information for oursmall study: The analysis of the used textbooks on the one hand, and interviews withteachers from the different courses on the other.

We have chosen to focus on the textbook traditions because in science andengineering (unlike, say, philosophy) education is largely based upon textbookpresentations of subject-matter, particularly at introductory levels. Thus, textbooksreflect what we previously termed the school knowledge; an official codified rep-resentation of the knowledge to be taught. The choice of textbook for a course inthermodynamics typically reflects a consensus among teachers within the communitythat the specific book represents the subject matter in a good way for the particulargroup of students. It is unlikely that a textbook is chosen if the involved teachers feel

550 Res Sci Educ (2008) 38:545564

that it grossly misrepresents the scientific knowledge of the specialty or omits crucialaspects of relevance. Thus, the presentation given in popular textbooks represent ina very concrete manner the result of a generally accepted external didactic transpo-sition within that specialty. However, while the analysis of textbook traditions willtell us something about school knowledge, it will not tell us much about the taughtknowledge, or the internal didactic transpositions. Thus, in addition to analysing thetextbooks, we have made interviews with teachers from each of the different courses.The interviews were semi-structured and based on our reading of the textbooks inthe light of the technical matrix framework (focus on values, exemplars etc). Theteachers conceptions of what is important for students to understand, and whatthey emphasise in their teaching provides us with an insight into specific internaldidactic transpositions of thermodynamic knowledge within each specialty. Althoughthis insight is of course specific for the interviewed teachers and the specific course,general knowledge of the teaching traditions within the specialties may be obtainedby considering the accordance between the textbook presentations of subject matterand the teachers priorities in their teaching. Thus, if a view presented in an interviewis in general accord with the presentation given in the textbook tradition, we haveconsidered it likely that the view is generally accepted within that teaching tradition.In this way, the analysis of textbooks and the interviews mutually support each otherin informing our understanding of the teaching traditions in the three specialties, andstrengthens the reliability of the results.

As a further note on the reliability of the study, the interviewed teachers haveaccepted our analysis of textbook traditions and the presentation of the interviewsgiven in the article. However, it should be noted that this study is not an empiricalstudy in the sense that it sets out to test a falsifiable hypothesis. Rather, we presenta theoretical perspective on teaching traditions and their relation to experiencedstudent problems, drawing on empirical material for illumination.

Three Textbook Traditions for Basic Thermodynamics Teaching

Before we start the analysis proper, we will make a brief outline of the textbooktraditions in the different scientific specialties.

The three varieties of introductory thermodynamics teaching in physics, physicalchemistry and mechanical engineering all have fairly long and, since the middle ofthe 20th century, fairly independent traditions. Before this time several textbookswere addressing all or several of the specialties.1

From an overall perspective, it may be said that there are two different styles forthermodynamics textbook writing, irrespective of which specialty we are referring to.One style, which we will call Euclidian, roughly presents thermodynamics as a setof interconnected axioms and is generally deductive in its approach. For instance,Guggenheim emphasises the logical formulation of the fundamental principles(Guggenheim 1967, p. v), while Callen employs a postulatory formulation of ther-modynamics (Callen 1985, p. 3).

1Thus, for instance, Zemanskys book addressed students of physics, chemistry and engineering,while Guggenheim addresses physicist and chemists (Zemansky 1957; Guggenheim 1967).

Res Sci Educ (2008) 38:545564 551

The other style, which we will call Babylonian, is less focused on axioms, but givesmore emphasis to useful models and systems. Babylonian textbooks are descriptivein their approach and discuss many phenomena and systems which either haveplayed significant roles in the historical development of thermodynamics or whereinthe systems considered can be seen as exemplary applications of thermodynamicaltheory.

The distinction between Euclidian and Babylonian conceptions of theory is in-spired by (Feynman 1967, p. 46), and refers to the Euclidian and Babylonian schoolsof mathematics. Roughly, Babylonian mathematics (practised in Mesopotamiaapproximately 2000600 BC) was characterised by its focus on solving specificpractical problems mathematically (for instance concerning irrigation systems).Often such problem solving relied on tables and approximations rather than proof.In contrast, Euclidian mathematics took as its starting point very general mathemat-ical axioms definitions of points, lines etc. By means of these definitions specifictheorems are proved deductively. In Euclidian mathematics there is no reference tothe specific practical problems which could be solved. Thus, Euclidian mathematicsis focused entirely upon the logical relations between mathematical axioms, whereasBabylonian mathematics is focused on the application of mathematics for practicalproblem solving.

The distinction between Euclidian and Babylonian styles is quite rough, andintermediate positions can be found. Still, most textbooks can easily be seen to fall inone of the two categories.

In the following we will frame the textbooks used in the courses we are consideringwithin the textbook traditions of the different specialties that is, we will relatethe textbooks used in the courses to our analytic distinction between Euclidian andBabylonian textbooks and explain the relation of the used textbooks to the traditiondeveloped in the different specialties.

Thermodynamics Textbooks in Physics

As a good example of a book in the Euclidian style, H. B. Callens widespreadbook Thermodynamics (originally from 1960) could be mentioned (Callen 1985).The standard fat introductory university physics textbooks follow the Babylonianstyle in their (often very brief) treatment of thermodynamics (e.g., Ohanian 1985;Young and Freedman 2003), as do some more advanced textbooks (e.g., Baierlein1999). More advanced books typically treat statistical thermodynamics in addition toclassical thermodynamics. In the basic thermodynamics course we studied, followedby most engineering students at the Technical University, a Danish book is used,which is clearly written in the Babylonian style (Both and Christiansen 2002). This isreflected in the very first paragraph of the book used in the course we are considering:

Thermodynamics is the scientific discipline describing energy and energy trans-formations. The foundation of thermodynamics is four laws, 0th, 1st, 2nd,3rd law. These laws are postulates. The laws cannot be proved, but theyare posited as natural laws on the basis of experience. Thermodynamics canbe presented in a strict mathematical way, when the four laws are consid-ered as axioms, from which a coherent theory is developed, see for instanceH. B. Callen: Thermodynamics. In this book we will, in contrast to this, present

552 Res Sci Educ (2008) 38:545564

thermodynamics in a more descriptive way and relate it to familiar phenomena.2

(Both and Christiansen 2002, p. 11)

It is interesting to note, that the book starts by pointing out a more systematic wayof presenting the subject-matter. This shows, arguably, that the Euclidian approachplays an important role in physics. It is our view, that the main reason that mostintroductory textbooks in physics are Babylonian is that these are generally morepedagogical in virtue of their overall inductive approach. Although it is hard to verify,it is our impression that in much physics education Babylonian thermodynamicstextbooks are used at undergraduate levels, whereas more Euclidian books are usedat graduate levels.

Textbooks in Physical Chemistry

The picture is a bit clearer for the case of Physical Chemistry. In 1950, the first editionof Moores classic Physical Chemistry appeared (Moore 1972), and this book (withits subsequent editions) became the prototype for introductory textbooks within thefield. This book is clearly Babylonian in its approach: Phenomenologically orientedwith focus on the chemically relevant elements of thermodynamics, statistical me-chanics and quantum physics. As regards the exposition of thermodynamics it isstated that:

Instead of trying to achieve a completely logical presentation of the subject, weshall follow quite closely the historical development of the subject, since moreknowledge can be gained by watching the construction of something than byinspecting the polished final product. (Moore 1972, p. 2)

In recent years a host of Physical Chemistry books have appeared3 which all basicallyretain the approach and content of Moores book. In fact, it is not unfair to saythat Babylonian Physical Chemistry books are in total dominance on the market,while more Euclidian textbooks (e.g., Guggenheim 1967) have gradually lost ground.The course we studied used Laidler et al. (2003), a book clearly following Mooresapproach.

Textbooks in Engineering Thermodynamics

In engineering thermodynamics, the introductory textbook which has shaped thefield most is probably the book Fundamentals of Engineering Thermodynamics(Reynolds and Perkins 1977). However, several previous books had already laid theground for the approach (Keenan 1941; Shapiro 1953; Mooney 1953; Reynolds 1968).Its overall approach is Babylonian rather than Euclidian, and as is the case withMoores book in Physical Chemistry, this book in particular has set the standard fora number of subsequent textbooks, for instance (Moran and Shapiro 1998; Jones andDugan 1996). The engineering thermodynamics course we have looked at used thetextbook Fundamentals of Engineering Thermodynamics (Moran and Shapiro 1998).

2Our translation of the Danish text.3Some of the most influential are Atkins (1994), Levine (1995) and Laidler et al. (2003).

Res Sci Educ (2008) 38:545564 553

Development of Distinct Traditions

We conclude that the only tradition in which the Euclidian presentation of subjectmatter still plays a prominent role is in physics. However, even in physics theBabylonian approach is dominant at introductory level.

In addition to this development the three traditions have moved in differentdirections, so that today it is the exception rather than the norm to find books thatspecifically address two or more of the three specialties.

It is striking that even though the number of textbooks within each of thetraditions has grown tremendously over the last decades, there is in many waysless diversity today with respect to approaches and general layout of the subjectmatter than 50 years ago. There are a lot of Physical Chemistry books, a lot ofEngineering Thermodynamics books, and a lot of University Physics books. Butwithin each tradition the books are surprisingly similar to each other. This is a reasonto consider the teaching traditions as relatively independent of each other, but eachbeing relatively homogenous.

Technical Matrices in the Specialties

In the following we will analyse the textbooks and interviews with respect to theelements in the technical matrices.

Differences in Delimitation of Objects

The textbooks are quite specific on what kinds of systems are (mainly) considered inthe presentation. The physics textbook states this clearly in the introduction:

In this book we consider almost exclusively systems with constant mass, forinstance gas in a cylinder supplied with a piston. (Both and Christiansen 2002,p. 12)

That is, almost only systems where there is no flow of mass in and out of the systemare considered. This is in accord with the systems considered in the book on physicalchemistry however, with the modification that one particular type of closed systemare given special emphasis in the treatment:

In most chemical systems we are concerned with processes occurring in openvessels, which means that they occur at constant pressure rather than at constantvolume. (Laidler et al. 2003, p. 59)

This special emphasis on open vessels is seen among other places in the treatmentof the concept of enthalpy, which is a crucial concept for the treatment of constantpressure systems. In the Physical Chemistry text the applications of enthalpy con-siderations are developed and expanded upon over 30 pages (under the headingThermochemistry), whereas the concept is discussed only very briefly in the physicstextbook.

554 Res Sci Educ (2008) 38:545564

Table 1 Objects of study

Thermodynamics Physicists Closed systems CMPhysical Chemistry Chemical Engineers Open Vessels CM, constant

pressureEngineering Thermodynamics Mechanical Engineers Closed and open systems CM and CV

In contrast to the two other textbook presentations, the engineering thermody-namics textbook does not confine itself to the investigation of closed systems:

The scientist is normally interested in gaining a fundamental understandingof the physical and chemical behavior of fixed, quiescent quantities of matterand uses the principles of thermodynamics to relate the properties of matter.Engineers are generally interested in studying systems and how they interactwith their surroundings. To facilitate this, engineers extend the subject ofthermodynamics to the study of systems through which matter flows. (Moranand Shapiro 1998, p. 1)

Thus, in engineering thermodynamics also open systems, or control volumes (CV),are considered in addition to the closed systems, or control masses (CM).4 In Table 1the different kinds of objects of study in the different thermodynamic traditions aresummarised.

But how do these differences in the kinds of systems considered express them-selves with respect to the basic understanding of the theory? In the interviews,the subjects were asked to express what the first law of thermodynamics says, inwords and symbolically, and give examples of systems which describe its use. Allthe interviewed subjects used the same overall expression to designate the First Lawof Thermodynamics: The principle of conservation of energy. The physicist and thechemical engineer were in general agreement on an elaboration of the meaning ofthis principle: When you consider a closed system the change in internal energy isequal to the transferred heat and work (U = q + w). The mechanical engineer, onthe other hand, starts by saying, that you have to distinguish between control massand control volume systems. While for control mass systems, there is a relation as justmentioned, for control volume systems there is a more complex relation betweenchange in the total energy per time of the control volume and the heat (QCV) andwork (WCV) which is transferred in or out of the control volume and the enthalpy(h), kinetic energy (KE) and potential energy (PE) of the mass entering and leavingthe control volume:

dECVdt

= QCV + WCV + mi (hi + KEi + PEi)me (he + KEe + PEe) (1)

4The terminology of control mass/volume is standard in mechanical engineering, and is of Germanorigin. Vincenti points out, that the German word Kontroll means auditing (as in bookkeeping)as well as regulation, and it is the former meaning in particular which is aimed at with the term(Vincenti 1990, p. 284, n. 2).

Res Sci Educ (2008) 38:545564 555

Thus, the difference in the systems considered actually lead to quite differentconceptions of what is understood by default by the principle of conservation ofenergy a difference which is also reflected in the textbooks.

In physical chemistry and engineering thermodynamics it is clear, that the de-limitation of objects has to do with the kinds of systems typically encountered inthe practice of the two fields. In the physics tradition the picture is less clear. Theprototype system with a piston-fitted cylinder is certainly a useful system to describethe workings of motors etc., but this system can hardly be said to describe systemswith which physicists normally work. Thus, it is most likely the exemplary value ofthis system in describing fundamental relations, concepts and structures that havemade these systems the focus of attention in the physics tradition.

Differences in Methodologies

The differences in the systems considered lead to different methodologies, mostobvious perhaps between engineering thermodynamics and the two other traditions.Specifically, the book on engineering thermodynamics relies heavily on so-calledcontrol volume analysis. The methodology of control volume analysis, as a systematicmethod, has a long history in engineering going back to the 1910s. It was developedfor the study of fluid mechanics problems5 a field which is also drawn upon inengineering thermodynamics. The basic principle of control volume analysis is todelineate a certain spatial region, and keep track of the momentum, mass, energy orentropy rate balances crossing the volume. The chosen volume is normally markedwith a dotted line (as done in every figure in Moran and Shapiro 1998). Controlvolume analysis provides a convenient way to gain insight into fundamental relationsbetween relevant parameters, without having to deal with the full complexity of whatgoes on inside the system.

Choosing the right control volume is of crucial importance, as the choice of volumeoften determines the difficulty (or even solvability) of the problem:

It is essential for the boundary to be delineated carefully before proceedingwith any thermodynamic analysis. However, since physical phenomena canoften be analysed in terms of alternative choices of the system boundary, andsurroundings, the choice of a particular boundary defining a particular system isgoverned by the convenience it allows in the subsequent analysis. (Moran andShapiro 1998, p. 2)

This process of carefully delineating the boundary of the system makes littlesense if considering only control masses, or rather, it is self-evident: The boundarysimply coincides with the container. Therefore system delineation is not given weightin Thermodynamics and in Physical Chemistry.

In Physical Chemistry the object of study is likewise reflected in specific method-ologies. As mentioned earlier, the concept of enthalpy (change) plays a very impor-tant role in physical chemistry. This is due to the fact that enthalpy is a state functionof relevance to the open vessel systems normally considered. However, the potential

5Vincenti has given a thorough description of the principles and history of the methodology (Vincenti1990, Chapter 4).

556 Res Sci Educ (2008) 38:545564

of the concept comes into play only with other principles, concepts and methods suchas the stoichiometric principles, the concepts of standard states, extent of reaction,and the methods of direct and indirect caliometry.

A standard state is defined as the state of the chemical substance at 1 bar (normallyat 25.00C), and it possible to define a number of different standard enthalpy changesfor different physical transformations based on the notions of standard states andenthalpy. Two examples are the standard enthalpy of formation ( f H) and thestandard enthalpy of reaction (r H). Standard enthalpies of formation have beentabulated for a vast number of substances, and may be used to calculate standardenthalpies of reaction for unknown reactions, given that all the reactants andproducts f H values are known. This method for calculating enthalpies of reactionthus, in addition to the conservation of energy and fact that enthalpy is a statefunction, relies on certain specific conventions (standard states) and stoichiometricand caliometric knowledge.

Differences in Values

In the interviews made, subjects were asked to describe what they understood byan engine. The physicist stated, that the engine was introduced as shown in Fig. 1a,where you have a hot reservoir (at temperature Th) and a cold reservoir (Tl), andsome sort of contraption which receives heat from the warm reservoir and deliversto the cold reservoir, while performing a work (W). The contraption may signifydifferent kinds of power cycles which may be represented in different ways, forinstance in a PV-diagram (Fig. 1b).

a An engine b A hypothetical power cycleFig. 1 An engine and accompanying power cycle as presented by the physicist

Res Sci Educ (2008) 38:545564 557

This rather theoretical conception of what an engine is, stands in contrast to thedescription given by the mechanical engineer:

. . . an engine could typically be a gas or steam turbine. . . and that means, that is, acollection of components which operates a thermodynamical power cycle...Themechanical components needed for a power cycle to take place in the real world.

Certainly, one should not place too much emphasis on such differences of under-standing of a single concept, as the definitions is this way cannot be considered to beexhaustive in any way, but it is worth noting that the mechanical engineer, in contrastto the physicist, immediately focuses on the realisability of the engine. He continues:

. . . thats important, not least for mechanical engineers the physicists mighthave a more abstract understanding. But. . . a lot of people have wanted to makea Carnot engine, but the thing is, first making an isotherm and then an isentropiccompression. . . The compression decides for itself what it wants to be, and therenot a lot you can do to influence that.

In the respective following discussions the subjects were asked about what kinds ofpower cycles were given emphasis in the courses. The physicist argued, that becauseof the limited time available only the Carnot cycle is given a substantial treatment.The reason is that the Carnot cycle has the highest efficiency of all power cycles, and:

It is on the basis of the Carnot engine that you, by arguments, derive the absolutethermodynamical temperature. And entropy, for that matter.

Thus, special emphasis is laid on the Carnot cycle because it is particularly wellsuited to illustrate aspects of the theoretical structure. The mechanical engineeron the other hand lays little emphasis on the Carnot cycle, as indicated above.What is considered important for the students to know about the Carnot cycle isthe efficiency. This is in accordance with the presentations given in the textbooktraditions. The mechanical engineer certainly appeared to be less interested in thetheoretical heuristics of the Carnot cycle, and the fact that it is not realizable placesit in a less central position than for the physicist. However, many other power cyclesare treated in the mechanical engineering course:

We consider in detail vapor power, gas turbines, motors, cooling devices plussome more exotic stuff, right? And the existing possibilities for improvement,because a vapor power system is not just a boiler, a turbine, a condenser and apump, is it? Theres also. . . we go through that you can extract steam to preheatthe feedwater, and you can divide the turbine into a high-pressure and a low-pressure turbine, and you can take out steam and regenerate it and therebyimprove the efficiency, and then you can calculate and see that it improves [. . . ]Concepts such as superheating and subcooling for refrigeration systems, thatssomething which isnt considered in the theoretical process, but in reality youhave to increase the temperature a little bit after the evaporator in order to besure there is no vapor in the refrigerant before it enters the compressor, becauseotherwise it might [. . . ] be destroyed. [. . . ] They should know what a power plantis, and a gas turbine and a motor and such things.

558 Res Sci Educ (2008) 38:545564

This quote shows clearly the emphasis on realisability in the mechanical engineer-ing tradition something which is not an issue of the such importance in physics.

The chemical engineer held an intermediate position on this particular point,arguing that from a pedagogical perspective it was important for the students, inaddition to understanding the Carnot cycle, to see examples of cycles that werephysically realisable.

Different power cycles are good examples of what Kuhn denoted exemplars.It appears from this case that different importance is assigned to different powercycles in the different communities, and different emphasis is placed on variousaspects of the individual exemplars. Specifically, it appears that emphasis is placed onrealisability of power cycles in mechanical engineering, while this is not consideredof great importance in physics.

Differences in Conception of Theory Structure

As mentioned, textbooks in university thermodynamics can roughly be described aseither Babylonian or Euclidian in style, but the Babylonian textbooks are dominantin all three traditions. From a pedagogical perspective this is perhaps understandable,as inductive approaches to teaching are better in terms of student learning thandeductive approaches. We have argued, however, that in physics the Euclidiantextbooks still play a prominent role, while this is infinitely less so in Physical Chem-istry and Engineering Thermodynamics. Does this mark a fundamental differencein the conceptions of thermodynamics held by physicists, chemical engineers andmechanical engineers?

In our interview we asked the physicist about the difference between the threeteaching traditions, and what made the physicists tradition special. The answer wasthat physicists like when it is:

. . . like in mechanics . . . we like to focus on the basics Newtons laws that is,the thermodynamical laws and what is in the vicinity of them. Those who wantto apply it for something, are free to do so.

When asked if thermodynamics was to be conceived as a discipline distinct fromother physical disciplines, the answer was a decided yes:

Yes! It is the only one thats purely empirical...it is an empirical science whichdoesnt presuppose anything about [the constitution of] matter. It presupposesnothing! You have three laws, you have some matter that you may be able toform an equation of state from you need that as well. The rest is formalism.And you can connect the different properties by means of functions of multiplevariables, and maybe thats what a physicist will say: Thats beautiful.

What is expressed here is the view that thermodynamics is basically a system ofaxioms with its own inner mathematical structure and distinct from other physical dis-ciplines a clear expression of a Euclidian conception of theory structure. Moreover,this very structure is what provides the theory with its beauty. Finally, it is considereda value that the theory does not presuppose anything about the specific nature ofmatter if it was found out that atoms and molecules did not exist, thermodynamicswould stand. This should not be taken as an ontological claim, rather as a kind ofontological indifference, because when viewed from inside the theory, the question

Res Sci Educ (2008) 38:545564 559

of molecules is irrelevant. These views are challenged by both the chemical engineerand the mechanical engineer. The chemical engineer argued strongly against thosepeople who would like to make thermodynamics into a completely elevated axiom,without referring to molecules. This was not just a matter of taste or pedagogicalconcern, but also a fundamental disagreement with the purely macroscopic view:

[. . . ] it is a fact that they [molecules] exist, and if systems are very small youdget some fluctuations in pressure, for instance. When you say pressure, it meansmolecular impact it is just that theres something like 1023 per second per cm3,thats why we measure an average. [. . . ] It doesnt really make sense to say,that we start by defining something called pressure. Sure, it can be done, but itdoesnt make sense, and the view collapses for very small systems in contrast tothe other view.

As for the exposition of the beauty of the inner mathematical structure of thetheory, this is not something which is given great weight in the course held by thechemical engineers:

Really, it doesnt appeal to first year students and I dont think it should either,and I think the basic position is wrong . . .

As for the view that thermodynamics is as a discipline distinct from other physicaldisciplines, the mechanical engineer argues that there is no sharp distinction betweenone discipline and another. When asked about the relationship between the principleof conservation of energy and the conservation of mass, the physicist argued that thequestion was irrelevant because for the systems considered in the course, no mass islost. The mechanical engineer says:

Well, thats the two conservation principles we use as soon as we have controlvolumes. In the physicists world you dont need conservation of mass, becauseyou concentrate on control masses, but here we need to look at conservation ofmass because we have a number of equations which describes our system andwe need to know how much mass there is in the different sub-volumes we areconsidering. So thats why we need an equation for conservation of mass, but inprinciple its the same thing: A conservation principle, just for mass.

To the question of whether the principle of conservation of mass should beconceived of as a mechanical principle rather than a thermodynamical principle, themechanical engineer responded:

Well, generally I dont really see it as separate things. There is this huge areadescribing the sciences, and then you can make rough divisions, and say thisconglomeration is called thermodynamics and this is called mechanics and soforth, and there are vast overlaps really a lot. So I dont think mechanics hasgreater claim to it [conservation of mass] than thermodynamics.

What can be seen from this is that there is a relatively clear difference betweenthe conception of theory structure in physics and in the engineering traditions, andthat the difference between Babylonian and Euclidian writing styles goes beyondthe purely pedagogical concerns. In physics, the inner structure and consistency ofthe thermodynamic theory is considered an intrinsic value of the theory. On theother hand, the correspondence of theory to nature is of secondary importance (as

560 Res Sci Educ (2008) 38:545564

can be seen from the example with the Carnot engine). In chemical engineeringand mechanical engineering, the inner structure of the theory is considered of lessimportance than the theorys ability describe empirical phenomena, be it machinesor molecular phenomena. Making a strong claim, different conceptions of truth areinvolved in the different traditions. Consistency is stressed in physics, while corre-spondence is stressed in chemical and mechanical engineering. Unlike in physics, theuse of thermodynamics in chemical and mechanical engineering is a means to an end the description of empirical phenomena. In physics, thermodynamic theory is (also)an end in itself.

Discussion

Most studies of paradigms or epistemic cultures in science and engineering focusmainly on the research and development efforts of the involved members of the sci-entific communities6. In contrast, this study has focused on paradigmatic differenceswhich can be discerned by studying basic science teaching.

It is clear, that education plays a vital role in establishing the common knowledgeand assumptions held by a specific scientific (or engineering) community. As Kuhnargues, the members of a scientific community have typically have absorbed thesame technical literature and drawn many of the same lessons from it (Kuhn1970, p. 177). In science and engineering, the technical matrix of the specialty isadopted by newcomers through education, and the ground for valued researchand development (as well as professional) competencies are laid in the studentseducation.

From the educational perspective, it is noteworthy that even such commongoods as introductory thermodynamics are framed so differently within the differentscientific teaching traditions. However, there is no reason to assume that the conceptsof thermodynamics are unique in this respect. Rather, this is a completely generaleducational problem. Other examples, each of which would be worth studying, arecalculus in traditions of mathematics, physics and chemistry, statistics in mathemat-ics, biology, engineering, logic in mathematics, computer science and philosophy.Bucciarelli (2003) gives the examples of mechatronics in mechanical and electricalengineering, and strength of materials in mechanical, civil, and aerospace engineering.Bucciarelli notes that different varieties and versions of different sciences form thecore of different departments and these differences are defended when proposalsare made by Deans anxious to avoid duplication of effort and to lower costs ofdelivery. The note about the anxious Deans is important, because it points toan important feature of stem and branch structures: There are strong economicalincitements for establishing such structures. This is probably the primary reason suchstructures are abundant. Given this, it becomes all the more important to be aware ofto which degree subject matter can be said to be the same across different traditions.

The use of the same concepts to describe subject matter in the different traditionsis by no means a guarantee of the identity of the meanings these concepts (andthe associated practices). This is particularly unfortunate with respect to education,

6To mention just a few of these see Kuhn (1970), Knorr Cetina (1999), Vincenti (1990) and Latour(1988).

Res Sci Educ (2008) 38:545564 561

because a dominant way of communicating about content in education is by meansof syllabus descriptions descriptions which describe only the concepts not themeanings and practices.

It is, seen in the light of the present study, not surprising that students often failto apply the knowledge they have learned at stem level when coming to the branchlevel. This is because knowledge is embedded within an epistemic framework encom-passing different goals, methods, values, exemplars and views of theory structure.What the good student has learned to find important and useful in one context, maybe considered less important or even irrelevant in the next.

The differences in meanings of concepts between scientific specialties are rarelyexplicitly addressed in teaching, perhaps because it is more the exception than therule that teachers have more than vague ideas about of the conceptions of theneighboring specialties. This is an unfortunate consequence of the high degree ofspecialization in science and engineering subjects. That means that it is often leftentirely to the students to deal with these problems. The problems experienced inthe educational system with respect to the transitions from stem to branch (andelsewhere) shows that this situation is far from being ideal.

How should the problem be addressed? The most obvious reply is to try tosolve the problem by disposing of it. This may be done by removing the stem andbranch structures e.g., by letting mechanical engineers teach engineering thermo-dynamics for mechanical engineering students, and likewise in chemical engineering,and physics. Depending on the specific financial and institutional structures, suchsolutions may be possible. But in general they are probably not. The stem and branchstructure is there to stay. It is not there for a pedagogical reason, so it is unlikely thatit will be disposed of for pedagogical reasons.

From a normative perspective it can also be argued that the above solutiononly solves the problem by not considering it. And the problem is actually worthconsidering for most, if not all, students.

The ability to recognise that there are different possible perspectives on the samesubject matter lies, in our view, at the heart of being an academic. Moreover, thereare strong societal demands for students who are able to work in multidisciplinarygroups. In order to do this efficiently there is a need for understanding and respectfor different views on a matter.

When viewed from this perspective, the stem and branch structures may have animportant role to play namely, that of increasing student awareness that scientificspecialties are different from each other, not only in content, but also in adoptedmethods, objects, values etc. But in order to fulfill this function, there is a needfor increased awareness among teachers of the approaches and understandings ofsubject-matter adopted in nearby scientific fields of relevance for the students edu-cation. Moreover, such increased awareness must be made an issue in teaching. Suchmetacognitive elements in the teaching would serve the double purpose of helpingthe students to deal with transition problems and increasing their understanding ofthe nature of multidisciplinary work.7

As to the question of how such increased awareness among teachers may comeabout, we shall give two examples where slightly different approaches have beenused.

7A good discussion of this can be found in Bucciarelli (1996).

562 Res Sci Educ (2008) 38:545564

The first example is an introductory calculus course at the University of Copen-hagen. The course is aimed at students in chemistry, nano-science, bio-chemistry,and physics. The course is planned and lectured by mathematicians, but the problem-solving classes are undertaken by teachers from the other specialties. The specialtyteachers may tone the problems and discusses the relevant applications of mathemat-ics in the specialties. This is important, since one of the decisive factors in transferbetween one learning context (mathematics course) and another (specialty course)is the degree of similarity of contexts (Royer et al. 2005). When students are led tosee the relevance and use of mathematics in their own specialty right from thebeginning, the odds are better that they will able to apply the mathematics in theirspecialty later on.

The second example is an introductory physics course given at the TechnicalUniversity of Denmark (DTU), where the findings of this study were used as a basiswhen the course underwent a major revision. The course covers Newtonian me-chanics, electromagnetism, and thermodynamics, and is compulsory to all studentsat DTU. The teachers responsible for the course are all physicists and 90% of thestudents are engineering students aiming at different engineering specialties, rangingfrom software engineering to civil and mechanical engineering. Approximately 500students follow the course which comprises lectures, problem-solving classes, self-study, and so-called in-depth modules. There are two potential transition problemsin this course. One is from high school physics to university physics, and one is fromthe basic physics in the course to the applied physics in the specialties. The transitionproblem from high school physics is facilitated by having experienced high schoolteachers teach the problem-solving classes. The transition problem to the specialtiesis facilitated by letting the students apply the basic physics concepts to (relatively)authentic engineering problems in the in-depth modules. Here the students work inpairs on an open problems over a period of two weeks, and deliver a report of theirresult. An example of a project theme in thermodynamics is a heat pump, wherethe students among other things get the opportunity to study engineering relevantpower cycles like the reversed Otto cycle and compare this with the Carnot cycle or an opportunity to deal with open systems and control volume analysis.

Neither of the courses explicitly address the metacognitive of the differencesbetween the specialties, but the courses are recognitions of the existence of differentconceptions of subject matter, and we believe that students can benefit tremendouslyby thus becoming aware of and getting experience with subject matter in a context ofrelevance to the field they are studying.

Conclusion

We have argued how students difficulties in applying basic science concepts inthe applied specialties may be attributed to differences in teachers paradigmaticconception of subject-matter. By adopting a comparative Kuhnian approach we haveanalysed three different teaching traditions in thermodynamics. The study is basedon interviews with teachers and analysis of the different textbook traditions, andpoints to differences in all elements of the technical matrices considered, includingdifferences in delimitation of objects, methods, values, ontological assumptions andexemplars.

Res Sci Educ (2008) 38:545564 563

We conclude that educators should take into account how subject matter isconceived in related scientific specialties when designing courses. We have givenexamples of how this can be done either by organising multidisciplinary teaching,or by letting the students work on open-ended problems relevant for the otherspecialties.

As a final conclusion, we would like to stress the fruitfulness of the compar-ative Kuhnian approach to studying teaching traditions and conceptions of subjectmatter not least because it allows for critical analysis of programme and coursedesign in higher education.

References

Atkins, P. W. (1994). Physical chemistry (4th ed.). Oxford, UK: Oxford University Press.Baierlein, R. (1999). Thermal physics. Cambridge, UK: Press Syndicate of the University of

Cambridge.Biggs, J. (1999). Teaching for quality learning at university. Buckingham, UK: Society for Reaserch

into Higher Education.Both, E., & Christiansen, G. (2002). Termodynamik (4th ed.). Lyngby, Denmark: Den private

Ingenirfond.Bucciarelli, L. L. (1996). Designing engineers. Cambridge, MA: The MIT Press.Bucciarelli, L. L. (2003). Designing and learning: A disjunction in contexts. Design Studies, 24(3),

295311.Callen, H. B. (1985). Thermodynamics and an introduction to thermostatistics (2nd ed.). New York,

NY: Wiley (Revised edition of: Thermodynamics, 1960).Chevellard, Y. (1985). La transposition didactique. Du savoir savant au savoir enseign (The didacti-

cal transposition. From scientific knowledge to taught knowledge). Grenoble, France: La PenseSauvage.

Feynman, R. (1967). The character of physical law. Cambridge, MA: The MIT Press.Guggenheim, E. A. (1967). Thermodynamics an advanced treatment for chemists and physicists (5th

revised ed.). Amsterdam, The Netherlands: North-Holland. (First edition 1949).Hendricks, V., Jakobsen, A., & Pedersen, S. (2000). Identification of matrices in science and engi-

neering. Journal for General Philosophy of Science, 31, 277305.Jones, J. B., & Dugan, R. E. (1996). Engineering thermodynamics. Englewood Cliffs, NJ:

Prentice-Hall.Keenan, J. H. (1941). Thermodynamics. New York: Wiley.Knorr Cetina, K. (1999). Epistemic cultures. Cambridge, MA: Harvard University Press.Kuhn, T. S. (1970). The structure of scientific revolutions (2nd ed.). Chicago: University of Chicago.Laidler, K., Meiser, J. H., & Sanctuary, B. C. (2003). Physical chemistry (4th ed.). Boston: Houghton

Mifflin.Latour, B. (1988). Science in action. Cambridge, MA: Harvard University Press.Levine, I. N. (1995). Physical chemistry. New York: McGraw-Hill.Loverude, M. E., Kautz, C. H., & Heron, P. R. L. (2002). Student understanding of the first law of

thermodynamics: Relating work to the adiabatic compression of an ideal gas. American Journalof Physics, 70(2), 137148.

McDermott, L. C., & Redish, E. F. (1999). Resource letter: Per1: Physics education research.American Journal of Physics, 67, 755767.

Mooney, D. A. (1953). Mechanical engineering thermodynamics. New York: Prentice-Hall.Moore, W. J. (1972). Physical chemistry (5th ed.). London: Longman House. (First edition published

1950).Moran, M. J., & Shapiro, H. N. (1998). Fundamentals of engineering thermodynamics (3rd ed.).

London: Wiley.Ohanian, H. C. (1985). Physics (2nd expanded ed.). New York, NY: W. W. Norton.Prosser, M., & Trigwell, K. (1999). Understanding learning and teaching. The experience in higher

education. Buckingham, UK: Society for Reaserch into Higher Education.Reynolds, W. C. (1968). Thermodynamics (2nd ed.). New York: McGraw-Hill.

564 Res Sci Educ (2008) 38:545564

Reynolds, W. C., & Perkins, H. C. (1977). Engineering thermodynamics (2nd ed.). New York:McGraw-Hill Science/Engineering/Math.

Royer, J. M., Mestre, J. P., & Defresne, R. J. (2005). Introduction: Framing the transfer problem. InJ. P. Mestre (Ed.), Transfer of leaning from a modern multidisciplinary perspective (pp. viixxvi).Greenwich, CT: Information Age Publishing.

Rump, C., Jakobsen, A., & Clemmensen, T. (1998). Improving conceptual understanding and usingqualitative tests. In C. Rust (Ed.), 6 improving student learning outcomes (pp. 298308). Oxford,UK: Oxford Centre for Staff & Learning Development.

Shapiro, A. H. (1953). The dynamics and thermodynamics of compressible fluid flow (Vol. 1).New York: Ronald Press.

Star, S. L., & Griesemer, J. R. (1989). Institutional ecology, translations and boundary objects:Amateurs and professionals in Berkeleys Museum of Vertebrate Zoology, 190737. SocialStudies of Science, 19(3), 387420 (August).

Vincenti, W. (1990). What engineers know and how they know it. Baltimore, MD: Johns HopkinsUniversity Press.

Young, H. D., & Freedman, R. A. (2003). Sears and Zemanskys university physics with modernphysics (11th ed.). San Francisco, CA (First edition by Sears and Zemansky, 1949).

Zemansky, M. W. (1957). Heat and thermodynamics an intermediate textbook for students ofphysics, chemistry and engineering (4th ed.). New York: McGraw-Hill (First edition 1937).

Three Conceptions of Thermodynamics: Technical Matrices in Science and EngineeringAbstractAim and MethodThermodynamics as Boundary ObjectConceptualising Differences: Technical MatricesAnalysing Teachers' Conceptions of Subject Matter

Three Textbook Traditions for Basic Thermodynamics TeachingThermodynamics Textbooks in PhysicsTextbooks in Physical ChemistryTextbooks in Engineering ThermodynamicsDevelopment of Distinct Traditions

Technical Matrices in the SpecialtiesDifferences in Delimitation of ObjectsDifferences in MethodologiesDifferences in ValuesDifferences in Conception of Theory Structure

DiscussionConclusionReferences

/ColorImageDict > /JPEG2000ColorACSImageDict > /JPEG2000ColorImageDict > /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 150 /GrayImageMinResolutionPolicy /Warning /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 150 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict > /GrayImageDict > /JPEG2000GrayACSImageDict > /JPEG2000GrayImageDict > /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 600 /MonoImageMinResolutionPolicy /Warning /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 600 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict > /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile (None) /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False

/Description >>> setdistillerparams> setpagedevice