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Studentunderstandingofthefirstlawofthermodynamics:RelatingworktotheadiabaticcompressionofanidealgasARTICLEinAMERICANJOURNALOFPHYSICSJANUARY2002ImpactFactor:0.8DOI:10.1119/1.1417532

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enricments of the effectiveness of instruction have been pub-lished. Our experience suggests that a similar approach tocurriculum development on other topics is necessary.6 Wehave found that the level of detail needed for developingeffective instructional materials requires in-depth probing ofstudent understanding with a variety of questions involvingdifferent contexts and administered in different formats. Inthis paper, we report on the results from such a study inthermal physics and discuss some implications forinstruction.7 The emphasis is on the first law of thermody-namics, and, in particular, on the change in the internal en-ergy of an ideal gas through thermodynamic work.

II. OVERVIEW OF INVESTIGATION

We were interested in whether university students whohave studied thermal physics are able to apply the first law ofthermodynamics to a simple physical phenomenon. Specifi-cally, we wanted to examine the extent to which students,given a familiar situation, could ~1! recognize that the firstlaw is relevant to predicting or explaining an observation, ~2!

dynamic work.

B. Instructional context of the study

Most of the investigation was carried out at the Universityof Washington ~UW! among students in the introductoryalgebra-based course and a second-year course in thermalphysics. Both courses have a standard lecture format. Thealgebra-based course devotes about two weeks to thermalphysics. The number of students in each lecture section ofthis course ranges from fewer than 100 to more than 200students. About half of these enroll in an accompanyinglaboratory course. Enrollment in the second-year course typi-cally varies between 25 and 50 students. Physics majorscomprise about 30% of the students in this course. Almost allof the students in the second-year course have taken intro-ductory calculus-based physics ~which does not include ther-mal physics at UW!. Students from a junior-level statisticalphysics course also participated in the study. Additional datawere obtained from introductory calculus-based physicscourses at other large research institutions in which thermalphysics is part of the first-year curriculum.

137 137Am. J. Phys. 70 ~2!, February 2002 http://ojps.aip.org/ajp/ 2002 American Association of Physics TeachersRelating work to the adiabatic compreMichael E. Loverude,a) Christian H. Kautz,b) andDepartment of Physics, Box 351560, University of Washing~Received 23 July 2001; accepted 14 September 200

We report on an investigation of student understandstudents involved were drawn from first-year universiphysics course. The emphasis was on the ability of thecompression of an ideal gas. Although they had studrelevance. Fewer still were able to apply the concept oin an adiabatic process. Instead most of the studentsmisinterpretation of the ideal gas law. Even when idestudents were unable to give a correct analysis. Theyof heat, temperature, work, and internal energy. Somethe concept of work in a thermal process seemed tofindings also suggest that a misinterpretation of simstudent ability to understand macroscopic phenomphysics and in mechanics are discussed. 2002 Ame@DOI: 10.1119/1.1417532#

I. INTRODUCTION

Articles on the teaching of thermal physics have addresseda number of important issues, such as the proper presentationof relevant concepts and principles, the order in which topicsshould be treated, and the merits of a macroscopic or micro-scopic approach.1 However, for the most part, the discus-sions have not been informed by a detailed understanding ofhow students learn this body of material. Research hashelped identify a number of specific difficulties.2,3 In particu-lar, the tendency to confuse the concepts of heat, tempera-ture, and internal energy has been well documented.4 How-ever, these insights have had little impact on how thermalphysics is typically presented in a standard introductorycourse.

In mechanics, the situation is different. The teaching ofkinematics and dynamics in recent years has been stronglyinfluenced by findings from research.5 Reports from assess-sion of an ideal gasaula R. L. Heronc)n, Seattle, Washington 98195-1560

g of the first law of thermodynamics. Thephysics courses and a second-year thermal

tudents to relate the first law to the adiabaticd the first law, few students recognized itswork to account for a change in temperaturesed their predictions and explanations on aof energy and work were suggested, many

equently failed to differentiate the conceptsthe difficulties that students had in applyingrelated to difficulties with mechanics. Our

le microscopic models may interfere witha. Implications for instruction in thermalan Association of Physics Teachers.

decide whether there is heat transfer or work done and, if so,determine the sign~s!, and ~3! relate these quantities to achange in the internal energy of the system.

A. Previous research

Much of the previous research has involved processes inwhich heat is the only means of energy transfer. Several ofthese studies indicate that students tend to treat heat as asubstance residing in a body.8 Although most of the studieshave been at the precollege level, experienced instructorshave noted that many university students have similardifficulties.9 Studies in physics and chemistry courses haverevealed the failure of many university students to distin-guish between state and process quantities ~for example,temperature and heat transfer!, as well as to apply the idealgas law correctly.10,11 There has been little or no previousresearch on student ability to apply the concept of thermo-

The first law of thermodynamics was expressed differentlyin the two courses at UW in order to be consistent with the

respective textbooks. In the second-year course, it was ex-pressed as DU5Q1W , where U is the internal energy of asystem, Q is the heat transferred to the system, and W is thework done on the system.12 In the algebra-based course, thefirst law was expressed in terms of the work done by thesystem, that is, as DU5Q W .13,14 In both courses, the ap-plication of the first law was limited to ideal gas systems andmostly to quasi-static processes.

All of the students had been taught a general definition forthe work done on a system (Won) by an agent that exerts aforce on that system (Fon). Those in second-year thermalphysics had previous experience with the definition Won5*Fonds in a course on mechanics. This definition wasused in the thermal physics course to derive an expressionfor the work done on ~or by! a gas in terms of its pressureand a change in its volume (Won52*P dV).15 In thealgebra-based course, in which the scalar product was notused, work was defined as the product of a displacement andthe component of the force parallel to that displacement. Anonintegral expression for the work done by a gas (Wby5PDV) was derived for isobaric processes only.

C. Methods

As in most of our research, we used two primary methods.We have found that the focus on real objects and events in anindividual demonstration interview is effective for probingthe ability of students to relate the concepts of physics to thephysical world.16 Written questions that are administered tolarge groups of students allow us to estimate the prevalenceof specific student difficulties. In interviews, students areasked for details or clarification. On written questions, theyare asked for explanations. In the discussion of the results forboth written and interview questions, we quote specific stu-dents. For every case, however, the quotes are representativeand not idiosyncratic.

We began our investigation with individual demonstrationinterviews with students from the two courses at the Univer-sity of Washington. The interviews were designed to elicitideas that students have about thermal phenomena and, morespecifically, to probe their ability to apply the first law to theadiabatic compression of air, considered as an ideal gas. Wedeliberately chose an adiabatic process because we wanted tofocus on the concept of work. During the interviews, thestudents were shown a plastic bicycle pump and were told toimagine that the open end would be sealed while the handleof the pump was rapidly pushed inward. They were asked topredict what would happen to the temperature of the air in-side the pump and to explain their reasoning.

A correct explanation includes the following elements. ~1!Because the compression of the air in the pump is carried outquickly, the process is approximately adiabatic and, there-fore, Q0.17 ~2! Because the force that the piston exerts onthe gas and the displacement of its point of application areparallel, the work done on the gas is positive. ~Alternatively,the expression Won52*P dV could be used, which alsoyields a positive result.! Therefore, according to the first law,DU is positive and the temperature of the ~ideal! gas willincrease.18,19 In this paper, we include students explanationsin which heat transfer is not explicitly mentioned among

138 Am. J. Phys., Vol. 70, No. 2, February 2002those considered correct, provided a correct link betweenthe change in temperature and the work done was made.

We intentionally chose a task that could not be solvedwithout the first law. The ideal gas law (PV5nRT), whichrelates the temperature T of a sample of n moles of dilute gasto the product of the pressure P and the volume V for equi-librium states, is insufficient. The force applied to the pistonincreases the pressure on the gas and decreases the volume.However, the first law is needed ~directly or indirectly! todetermine if the product of these two variables ~and hencethe temperature! increases, decreases, or remains the same.

Written problems were administered either on course ex-aminations or as ungraded quizzes. Unless otherwise noted,all were given after the relevant instruction was completed.

The bicycle pump problem is a written version of the in-terview task described above. In version A, students areasked to predict what will happen to the temperature of thegas when the piston is pushed inward rapidly and to justifytheir prediction @see Fig. 1~a!#. In version B, the text statesthat the temperature of the gas increases, and students areasked to account for this change @see Fig. 1~b!#. A slightlydifferent context is used in the written insulated cylinderproblem, in which the compression is accomplished by add-ing masses to a piston that seals an insulated cylinder ~seeFig. 2!.

Fig. 2. The insulated cylinder problem. Students were asked to predict whatwould happen to the pressure, temperature, and volume of the gas whenmasses are added to a movable piston that seals an insulated cylinder.

Fig. 1. Versions A and B of the bicycle pump problem. ~a! In version A, theproblem states that the pump is insulated and students are asked to predictwhat will happen to the temperature. ~b! In version B, the problem statesthat the temperature increases and students are asked to account for thechange in internal energy.

138Loverude, Kautz, and Heron

Student comments on the concept of work during the in-terviews prompted the design of additional written questionsabout the work done on ~or by! an ideal gas during a specificprocess. Two of these are illustrated in Figs. 3 and 4. Be-cause some of the difficulties we found seemed to reflectdifficulties with mechanics, we posed analogous problems inthat context for the purpose of comparison. An example isshown in Fig. 5.

III. INABILITY TO RECOGNIZE THE RELEVANCEOF THE FIRST LAW OF THERMODYNAMICS

As mentioned, one objective of our investigation was todetermine whether students could recognize the relevance ofthe first law to the analysis of a physical situation, specifi-cally the adiabatic compression of a gas. We worked towardthis objective by conducting individual demonstration inter-views based on the bicycle pump task.

Two rounds of interviews were conducted. They differedwith respect to the follow-up questions that were posed afterthe initial bicycle pump task. The first round involved 22students: 7 from the algebra-based course and 15 from thesecond-year course. In the second round, 14 students partici-pated: 9 from the algebra-based course and 5 from thesecond-year course. The students, who were all volunteers,were drawn from several sections of each course that weretaught by different instructors. Almost all of the students hadfinal grades at or above the mean in their respective classes.All instruction in thermal physics had been completed at thetime of the interviews.

In total, about 75% of the students who were interviewedstated correctly that the temperature of the air in the bicyclepump would increase. Assessing student ability to predict the

Fig. 3. An example of a problem in which students are asked about the workdone on a sample of ideal gas undergoing different processes.

Fig. 4. An example of a problem in which students are asked about the workdone on a sample of ideal gas undergoing a cyclic process.

139 Am. J. Phys., Vol. 70, No. 2, February 2002outcome of this experiment was not the only goal. We wereinterested in what the students explanations revealed abouttheir understanding of the role of work in changing the tem-perature of a gas. Their ability to recognize and to weigh therelevance of the various concepts and principles that theyhad studied was of particular interest. The pattern thatemerged had two major, interdependent features: ~1! failureto consider the concept of work and ~2! misapplication ofideal gas concepts. In the following discussion, the quotesare from dialogues between the interviewer ~I! and indi-vidual students ~S!. The data and quotes from the interviewsare supplemented with information from responses to thewritten questions described above.

A. Failure to consider the work done

The degree to which students deliberated during the inter-views before stating a prediction or giving an explanationvaried widely. At one extreme were students ~about 30% ofthe total! who responded almost immediately that the tem-perature would increase and had to be prompted for an ex-planation by the interviewer. This category includes somestudents who recalled the result from a similar lecture dem-onstration and others who acknowledged that their answerswere based on instinct or experience and not on formal rea-soning. For instance, one student said I made that predic-tion without thinking because it just feels right. At the otherextreme were students ~about 25% of the total! who dis-cussed the first law and/or the ideal gas law ~sometimes forseveral minutes! before giving an answer. In some cases,they could not arrive at an answer in spite of prolonged de-liberation.

A characteristic feature of the first set of interviews wasthat few students spontaneously invoked the concept ofwork. We concluded that if we wanted them to discuss theconcept, we needed to be more direct. This observationprompted a change for the second round of interviews. Theseinterviews started the same way as those in the first round.However, students who did not spontaneously mention workwere given an increasing amount of guidance as the inter-view progressed.

To encourage students who had not mentioned work to doso, we first asked whether the term energy could be related tothe bicycle pump process. Several stated that they could not

Fig. 5. The mechanical work problem. In some courses, students were onlyasked about case 1. In other courses, students were only asked about thework done by the hand in case 2 and a third case was also considered.

139Loverude, Kautz, and Heron

~that is, DU5Q1W), was provided.20 The students were difficulties with general principles are often intermingledwith difficulties related to the specific system to which the

Table I. Student responses to the written versions of the bicycle pump problem ~see Fig. 1!. In version B of the problem, the text states that the temperatureof the gas increases. Therefore, only student explanations are reported. In the two cases in which results were obtained from multiple sections of the same

ctind

base

01tio

aexplicitly asked whether this equation could help in analyz-ing the problem. Only 4 of the 16 students from the algebra-based course and 6 of the 20 from the second-year coursegave correct explanations based on the concept of work, withor without prompting from the interviewer. The dialoguesdemonstrated that the failure of students to mention workspontaneously reflected serious difficulty in understandingboth when and how to apply the concept, not merely a failureto remember it. The specific difficulties that arose when stu-dents tried to apply the concept of work will be discussedlater.

The written versions of the same task were administered atthe University of Washington in the algebra-based andsecond-year courses and in the junior-level course in statis-tical physics and in introductory calculus-based courses atthe University of Maryland, College Park ~UMCP! and theUniversity of Illinois, Urbana/Champaign ~UIUC!. Alto-gether, more than 500 students were involved. In most cases,the question was administered after all relevant instruction

principles are applied. Thus student understanding of the firstlaw of thermodynamics cannot be discussed without somediscussion of student understanding of the ideal gas law. Inthe interviews and written problems, we found that misinter-pretation of the ideal gas law was common. Our observationsare consistent with those of Rozier and Viennot, who de-scribed student difficulties with the ideal gas law at bothmacroscopic and microscopic levels.24

1. Incorrect reasoning at the macroscopic levelIn both the interviews and on the written problems, most

students cited the ideal gas law and argued that changes inpressure and/or volume resulting from the compressionwould lead to an increase in the gas temperature. ~As notedearlier, there is not enough information to reach such a con-clusion.! We observed several distinct types of incorrect ar-guments that are similar to those reported by Rozier andViennot, who attributed some of these difficulties to faulty

140 140Am. J. Phys., Vol. 70, No. 2, February 2002 Loverude, Kautz, and Heronsee how it could be helpful. Others hesitated, and whenpressed by the interviewer, turned to potential energy. Forexample, one student said:

S: I guess...could it be that the potential energy isincreasing? I mean that the air can create aforce when its let go, so the potential energyincreases.

In all cases, students who were asked about energy wereunable to proceed further, and were subsequently askedwhether they could apply the concept of work to the process.All of the students indicated that they recalled that work wasrelevant. However, some acknowledged a lack of under-standing of the connection between work and the tempera-ture of the gas, as illustrated by the following exchange:

I: If I do work on a gas, why is that important?S: If I do work on a pencil, I dont increase its

temperature. But with a gas...it seems, well, itis related somehow.

Finally, if questions about work did not prompt students toapply the concept, the algebraic statement of the first law

course ~some before and some after instruction! the results from individual sebeen combined. For clarity, results reported are expressed as percentages, rou

Algebra-basedcourse

Algebra-cour

UW UWN5114 N51

One section One sec

Version A BInstruction Post Pre

Correct response ~T increases! 67% n/aCorrect explanation based on:

work 10% 9%microscopic work 0% 0%adiabatic equation (PVg5const) 0% 0%

Incorrect explanation 57% 91%Incorrect responses 33% n/aBlank 0% n/had been completed. In a few cases, however, it was admin-istered before instruction began. The amount of instructiondid not seem to affect the results.21,22 In all classes, a major-ity of the students predicted that the temperature of the gaswould increase. Correct explanations were given by fewerthan 10% of the students in the introductory courses and byabout 50% in the more advanced courses. The results aresummarized in Table I.23

The insulated cylinder problem was administered in onesection of the UW algebra-based course (N5179) after allinstruction was completed. In contrast to the bicycle pumpproblem, only about 10% of the students correctly predictedthat the temperature of the gas would increase. The differ-ences between these questions that could account for thisapparent discrepancy are discussed later.

B. Misinterpretation of the ideal gas law

The failure of students to analyze the problems in terms ofwork and the first law of thermodynamics was prevalent andpersistent. As with many other topics, we found that student

ons all were within 5% of the mean value for the course, and therefore haveed to the nearest 1%.

sed Calculus-basedcourse

Thermal physicscourse

Statistical physicscourse

UMCP UW UWN5262 N599 N57

n Three sections Four sections One section

A A APre and post Pre and post Post

58% 86% 100%

3% 25% 14%0% 13% 43%0% 10% 0%

55% 35% 43%36% 14% 0%6% 0% 0%

reasoning with multi-variable relationships. However, as inother research by our group, we found that general reasoning

interactions with its surroundings to make judgments aboutheat transfer, work done, and internal energy. The failure ofdifficulties could not be completely separated from difficul-ties with specific concepts.25

Some students focused on only two macroscopic gas vari-ables at a time and assumed ~implicitly! an invalid relation-ship between them. Several stated that the volume decreaseof the gas in the cylinder would cause a pressure increase~implicitly holding the temperature constant! and that thepressure increase would then cause a temperature increase~implicitly holding the volume constant!. One student wrote:Decreasing the volume increases the pressure, which in-creases the temperature. PV5nRT .

Other students appeared to ignore one variable entirely.For example, on the written problems, about 10% referredonly to the fact that the pressure increases when the piston ispressed inward. One such student wrote: There was a quickchange in pressure. The pressure went up and so did thetemperature. The direct relationship between P and T that isimplied may be an inappropriate generalization of the case ofconstant volume processes.

About 10% of the students made a related but more sur-prising error by treating temperature as inversely propor-tional to volume. For example, one student wrote: In theideal gas law, if we change the volume to a smaller amount,the temperature will rise. Even under the assumption ofconstant pressure ~or if pressure is neglected altogether!, itdoes not follow from the ideal gas law that T varies inverselywith V. The evidence presented below suggests that argu-ments of this nature may be related to incorrect microscopicideas.

2. Incorrect reasoning at the microscopic level

During the interviews, students were often quick to intro-duce ideas related to particles or molecules. Often they madean inappropriate connection between volume and tempera-ture, apparently assuming a relationship between the numberdensity of gas particles and their average speed or energy,and thus the temperature. Some students made vague state-ments to this effect, such as: The smaller volume forces themolecules of gas to increase in speed, therefore increasingthe temperature, or The molecules of gas are closer to-gether, making the energy higher.26

Some students were more explicit about the connectionbetween number density and gas temperature. They proposeda causal mechanism based on an increased frequency of col-lisions between gas particles. For example, one student said:The molecules are getting compressed, and they have lessspace to move around, so they are bumping into each other alot more, and the temperature increases. Often students sug-gested that the collisions would produce or release heat:...more collisions per unit time equals more heat gener-ated.

In their lectures and textbooks, the students had beengiven a simple microscopic model in which gas moleculesinteract only through elastic collisions. The molecules them-selves are assumed to have no internal energy. Moreover,there is no potential energy associated with the distancesbetween molecules. In this model, the temperature of the gasis related to the average molecular kinetic energy, which canbe changed through heat transfer or collisions with a movingpiston.27 Therefore it is necessary to examine the systems

141 Am. J. Phys., Vol. 70, No. 2, February 2002students to do so was widespread.In particular, in the collision mechanism proposed by the

students, a change in internal energy is achieved throughinteractions internal to the system, rather than interactionsbetween the system and its environment. Students who re-ferred to intermolecular collisions were unaware ~or uncon-cerned! that the process they proposed could not increase thetemperature without violating the principle of energy conser-vation. Moreover, they failed to consider the implications forgases in equilibrium states.

It is interesting to note that microscopic arguments wereused by about 30% of the students in interviews, whereas asfew as 10% expressed such ideas on the written problemseven though the questions asked were essentially the same.The difference in format may help account for this apparentdiscrepancy. During the interviews, some students who ini-tially referred to macroscopic quantities very quickly intro-duced microscopic ideas to support their assertions whenasked for further details. Consequently, we believe that somestudents arguments that involve macroscopic quantities arein fact tightly linked to microscopic ideas.28 An underlyingmicroscopic picture could account for the otherwise surpris-ing tendency of students to assume an inverse relationshipbetween V and T on written problems. Of course, answers toa single question administered in a single format do not cap-ture the complexity of student thinking.29

IV. INABILITY TO APPLY THE CONCEPTOF WORK IN THERMAL PHYSICS

During the interviews, it quickly became apparent thatmany students did not treat the first law of thermodynamicsas a causeeffect relationship in which work can bring abouta change in the internal energy of a physical system. In anearlier study of student understanding of the work-energyand impulse-momentum theorems, we had encountered asimilar inclination to view an equation in physics solely as amathematical relation.30 There was a strong tendency to treatthe theorems as formulas, not as mathematical models ofimportant physical principles.

We were able to identify a number of specific difficultiesrelated to the first law. These can be grouped into two broad,overlapping categories: ~a! difficulties in discriminatingamong related concepts ~heat, work, temperature, and inter-nal energy! and ~b! difficulties in applying the definition ofwork to an ideal gas undergoing a specific process. The fol-lowing examples are taken from both the interviews andwritten problems.

A. Difficulty in discriminating among related conceptsheat, work, temperature, and internal energy

Many students seemed to confuse quantities associatedwith processes ~such as heat transfer and work! with thoseassociated with states ~such as temperature and internal en-ergy!. For some, this confusion was reflected in a tendency torefer to the change in heat or the change in work. Inwriting, many used the symbol for a given quantity ~for ex-ample, P! and the symbol denoting a change in that quantity~for example, DP! interchangeably. There is evidence pre-sented below that the inability to distinguish between two

141Loverude, Kautz, and Heron

seemingly similar concepts was often at a sufficiently deeplevel that it precluded students from correctly applying the

2. Confusion among work, heat, and internal energy

first law.

1. Confusion among heat, temperature, and internalenergy

We found that many students had difficulties with the con-cept of heat similar to those reported among precollege stu-dents, notably a tendency to confuse heat, temperature, andinternal energy.31 Some students admitted confusion on thispoint, even wondering why both DU and Q are present in thealgebraic form of the first law, because both seem to describethe heat in an object. Some of the responses reported heremight be seen as primarily reflecting careless use, or mis-interpretation, of admittedly confusing terminology. Severalarticles on the teaching of thermal physics note that eveninstructors and textbook authors, who presumably have mas-tered the concepts, often use technical terms impre-cisely.32 Therefore, an analysis of the language used by stu-dents is not sufficient for making judgments about under-standing. To help distinguish conceptual and linguistic is-sues, it is useful to examine the ability of students to makecorrect predictions concerning physical phenomena.

An excerpt from an interview serves as an example. In thiscase, the student spontaneously used the first law in attempt-ing to analyze the compression of the air in the bicyclepump:

S: The internal energy is equal to the energy ofthe system minus the work. So @writes# U5Q W@sic#.

The interviewer questioned the student on the distinction,if any, between internal energy and energy of the sys-tem. The student responded by acknowledging confusion.

S: Im getting confused with how to apply thething.

I: How are you getting confused?S: First of all, if the heat of the system is the

same as internal energy, or the temperature, orif its related to Q.

The student continued to struggle but was unable to arriveat a prediction. Her inability to distinguish the quantities re-lated by the first law prevented her from applying it even inthis relatively simple case.

Results from the written insulated cylinder problem,which was administered in the algebra-based course, providea further illustration. In contrast to the written bicycle pumpproblem, the majority of students answered incorrectly.Some incorrect responses reflected a failure to recognize ei-ther that work had been done or that work can change thetemperature of the gas. Both of these difficulties are dis-cussed in greater detail below. The most common incorrectanswer, however, was that the temperature of the gas wouldremain the same when the volume decreases because thecylinder is insulated. For example, one student stated that... an insulating jacket will hold all the heat in. About halfof the students explicitly stated that the insulation wouldeither prevent a change in temperature or in internalenergy.33 It seems that many students used the concepts ofheat and internal energy, and not just the words, interchange-ably.

142 Am. J. Phys., Vol. 70, No. 2, February 2002Although some students treated heat transfer as a processthat can produce a change in internal energy, many otherstreated heat as essentially the same thing as internal energy.In both cases, heat may be associated so closely withchanges in temperature that the concept of work may seemsuperfluous. Therefore, it is not surprising that a number ofstudents admitted that they did not see how work is con-nected to the temperature of a gas. Many others, in attempt-ing to connect the concept of work with temperature change,seemed to associate work with heat. During the interviews,several students used the word heat rather than work torefer to the mechanical energy transfer in the process inwhich the piston is pressed inward. In their responses towritten problems, students expressed many similar ideas. Forexample, one wrote: The heat caused by pressing the pistoninward is gained by the gas, so the temperature increased.

Our discussions with students during the interviews sug-gested that such statements do not simply represent carelessor confused use of language. In some cases, there was agenuine confusion between the mechanical energy transferthat physicists refer to as work and the nonmechanicalenergy transfer that physicists refer to as heat.34 This con-fusion prevented many students from correctly applying thefirst law. In particular, students who failed to recognize heatand work as independent means of energy transfer often in-dicated that any process that involves work must also involvea heat transfer.

When this issue arose during the interviews, we askedstudents explicitly whether it was possible for a process toinvolve work but no heat transfer. One student, who had usedthe concept of work to make her initial prediction concerningthe bicycle pump, responded as follows:

I: Coming back to work and heat, is it possible tohave work being done on the environment butno heat transfer?

S: Oh, well, what he @the instructor# was saying isthat work equals PdV. So change in volume@pauses# no, there has to be heat transfer.

This statement suggests that work and heat are not inde-pendent. The student continued by invoking the ideal gaslaw:

S: Since work is related to P and V, thats going torelate to temperature.

The student went on to state that no work is done in anisothermal process, essentially arguing that because the tem-perature does not change, no heat is transferred, and if noheat is transferred, then no work is done. The tendency tomake an inappropriate connection between work and heattransfer has also been reported in studies of chemistrystudents.35

B. Difficulties in applying the definition of work to anideal gas undergoing a specific process

During the interviews, some students were asked directlyabout the sign of the work done on the gas during the bicyclepump compression. Although most answered correctly thatthe work is positive, few applied the definition that they hadbeen taught. The responses revealed a failure to recognizethat the sign of the work has a physical significance in terms

142Loverude, Kautz, and Heron

of the change in internal energy of a system. References tothe sign of work being a matter of convention were com-

system, then W will be negative.36 The textbook used in thesecond-year course, which uses DU5Q1W , states thatmon. The following exchange is illustrative.I: How can you find the sign of work?S: Isnt it a convention? It is. I think its negative,

but I cant remember why that was. If the vol-ume is decreasing that means that there is workbeing done on that, so the DV would be nega-tive but the work will be positive.

I: What is the sign of the work done by the pistonon the gas @in this process#?

S: That work is...I dont know. Im guessing itwould be positive. I dont know the correlationbetween the positive and the negative part.

The incomplete or incorrect responses of the students in-dicated the presence of underlying difficulties related to thedefinition of work. In a number of cases, we broadened thescope of the interviews to pursue specific issues that hadarisen. We also developed written questions that involvednonadiabatic processes, as described below.

1. Failure to recognize that the sign of work is independentof the coordinate system

Some students seemed to apply a simplified definition ofwork, in which they considered either the direction of a forceor the direction of the displacement of the point of applica-tion of the force. For example, one student said:

S: @the sign of work# is not completely arbitrary.The distance is negative, so that means...thework done on the piston is negative. You usethe distance the piston is traveling.

Some students spoke of the direction of work, asthough it were a vector quantity. Others explicitly related thesign of the work done to the choice of coordinate system. Forexample, when one student referred to negative work, theinterviewer asked:

I: Whats negative work?S: I dont know. In the opposite direction.I: Opposite to what?S: Against your coordinate axes.

2. Failure to recognize that work done on and by asystem in a given process have the same absolute value

Several students made comments during the interviewsthat suggested incorrect ideas about the absolute value of thework done on or by a gas in a given process. In some cases,dialogues led the interviewer to ask about the work done onthe gas if it expands while the interviewers hand is stillpressed against the handle of the bicycle pump. Several stu-dents responded that there is no such work.

The students comments were consistent with the beliefthat no work is done by a gas in a compression or on a gas inan expansion. Their statements were also reminiscent ofthose in most textbooks, in which thermodynamic work isdescribed as being done on a system in a compression and bya system in an expansion. This practice necessitates theadoption of a sign convention for work. The convention de-pends on whether the first law is written in terms of Q1W orQ W . For example, the textbook used in the UW introduc-tory algebra-based course, which adopts the DU5Q Wform for the first law, states that If work is done on the

143 Am. J. Phys., Vol. 70, No. 2, February 2002work done on a system is positive.37 ~Variations of thesestatements appear in other textbooks.!

In contrast, in most treatments of mechanics, work that isdone on a system by an agent exerting a force on that systemcan be either positive or negative. The sign depends only onthe relative directions of the force and the displacement ofthe point of application of the force ~or the displacement ofthe system itself if it is a point particle!. The change in ki-netic energy of a system is usually analyzed through thework-kinetic energy theorem exclusively in terms of thework done on the system. The choice of whether to considerthe work done on or by the system does not depend on thespecific circumstances.

In order to apply the first law correctly, the students mustbe able to apply consistently a correct criterion for decidingwhether work is done on or by the gas in a given process.Therefore we were interested in how students would makethis choice in specific situations. We gained some insightfrom some students claims, mentioned above, that no workis done on a gas in an expansion. ~The situation they hadbeen asked about was not a free expansion.! The studentstypically argued that the gas is causing the motion, as illus-trated by the following excerpt:

S: If the gas were to expand, the work done by thegas would be positive.

I: Would there be work done on the gas in thatcase?

S: No.I: Why not?S: Because the work is being done on the piston

in that case.Another student, referring to the compression of the air in

the bicycle pump, said:S: Im causing the movement, not the system, so

the work is being done by me, not by this @theair in the pump#.

Other students claimed that work is done on and by anobject in the same process, but that the absolute values willbe different. For example, referring to the compression of thegas in the bicycle pump, one student said:

S: Theres some kind of force in the opposite @out-ward# direction. There is work done by the gas,but the work I do is greater. The net force is inthis @inward# direction.

Another seemed to associate the motion of the piston withan imbalance between the forces exerted on and by it:

S: In this case, you did work on the system, itkind of lost the war...Your hand was obviouslya whole lot stronger than the gas inside, youdid positive work on the system. Thats how Igot the sign convention of it.

The arguments made are consistent with the belief that apassive object ~the gas! does no work, or does less work thanan active object ~the hand!. Either the piston or the gas isthought of as active ~and the other as passive!, depending onthe direction of motion.38

Several interpretations of the dialogues with students arepossible. They may reflect a misunderstanding of discussionsof sign conventions. The students comments may also reflect

143Loverude, Kautz, and Heron

underlying difficulties with concepts and principles from me-chanics and their relation to thermodynamics. These interpre-

no change in volume overall, there was no work done on thesystem.tations are not mutually exclusive; both may reflect the dif-ferent ways in which the concept of work is usually treatedin mechanics and thermodynamics. This inconsistency maymake it more difficult for students to transfer a concept ini-tially learned in one context to the other.

3. Failure to recognize that work is path dependent in thegeneral case

During interviews and informal conversations, a few stu-dents made comments that suggested they were relating thework done on a system to the net change in volume. ~Thisprocedure is valid if the process is adiabatic, but not other-wise.! To probe student understanding of the path depen-dence of work, we designed several problems in which twodifferent paths between an initial state ~X) and a final state~Z! are depicted on a PV diagram. Thus at least one of thepaths is nonadiabatic.

The problem in Fig. 3 was given on an examination in asection of the UW second-year course (N542) and in theUIUC calculus-based course (N5392).39 The students wereasked ~1! to determine the sign of the work done on the gasin process X-1-Z and ~2! to compare the absolute values ofthe work done on the gas in processes X-1-Z and X-2-Z .The work done on the gas during process X-1-Z is negative.A comparison of the areas under the paths shows that it issmaller in absolute value than that done in process X-2-Z .

About 45% of the students in the second-year course and40% of the students in the UIUC calculus-based course an-swered correctly that the work done on the gas in processX-1-Z is negative. The tendency to focus on the initial andfinal states, rather than on the paths taken, was common. Inboth classes, the most common incorrect answer was that thework done on the gas is zero. In comparing the work done onthe gas in the two processes, about 25% of the students in thesecond-year course and about 45% of the students in thecalculus-based course answered that the absolute valueswould be the same. One student explained that ...the initialand final states are the same for both processes. Severalstudents explicitly stated that The work is independent ofthe path taken. It is possible that these students were over-generalizing their experience with conservative forces intheir mechanics courses.

Students were especially likely to neglect the path depen-dence of work in cyclic processes, such as the one shown inthe PV diagram in Fig. 4. This problem was administered inthe UW algebra-based course (N5112). The students wereasked whether the net work done on the gas in the cycle ispositive, negative, or zero. About half of the students saidthat the net work done on the gas was zero, typically point-ing out that there was no net change in volume. For example,one student wrote:

No net work was done because the cyclestarted and ended at the same place. Sincethere is no displacement, then no work wasdone.

For some students, the belief that the work done would bezero took precedence over other considerations. For ex-ample, one student wrote W5area under curve and shadedthe appropriate area, but finally answered: Since there was

144 Am. J. Phys., Vol. 70, No. 2, February 2002Another category of incorrect responses to questions basedon PV diagrams seems to stem from a failure to recognizethat the absolute value of the work done on and by the gasmust be the same. For example, in reference to the processdepicted in Fig. 3, one student said: From 1-Z work isbeing done on the environment, so the work done on the gasfrom 1-Z is zero. As mentioned earlier, similar ideas wereexpressed by students during the bicycle pump interviews. Itseems that difficulties of this nature can interfere with stu-dent ability to use PV diagrams to determine the work donein a specific process.

V. INABILITY TO APPLY THE CONCEPT OFWORK IN MECHANICS

In both the interviews and on written questions, many stu-dents comments about work were reminiscent of incorrectideas about forces that had been documented.40 Previous re-search has demonstrated the tendency of students to ignoreforces exerted by passive objectsboth in static and dy-namic situations. In the former case, many students neglectthe force by the passive object altogether ~such as the forceexerted on a book by a table!, arguing that the passive objectis simply in the way.41 In the latter case, many studentsassume that a force exerted in the direction of motion isgreater than the corresponding reaction force.42 It seemedthat some of the difficulties encountered by students in ap-plying the concept of work to ideal gas processes wererooted in difficulties with mechanics. We decided to probestudent understanding of work in situations free from thecomplications of thermal physics.

A. Extension of the investigation in thermal physics tomechanics

We designed some written questions about the work doneon objects that can be treated as point particles. The ques-tions were administered on ungraded quizzes in the UW in-troductory algebra-based and second-year courses and in theUMCP introductory calculus-based course.43 The studentshad previously studied mechanics. Instruction on the first lawof thermodynamics had also taken place.

1. Mechanical work problemThe mechanical work problem involves two or more situ-

ations in which a hand pushes on a block that is moving onan inclined plane. The students are asked to determine thesign of the work done: ~1! on the block by the hand, ~2! onthe block by the earth, and ~3! on the hand by the block ~orto state explicitly if there is no such work!.44

In cases 1 and 2, the force exerted by the hand is directedupward along the incline but the motion of the block is dif-ferent ~see Fig. 5!. In case 1, the block is moving up theincline with increasing speed. In case 2, the block is movingdown the incline with decreasing speed. Some versions ofthe quiz included a third case, in which the hand pushesdown the incline as the block moves down with decreasingspeed ~the presence of friction is noted in this case!. In allcases, the sign of the work done on the block by the hand canbe determined by comparing the direction of the force ex-erted by the hand to that of the blocks displacement over ashort time interval. Newtons third law can be used to find

144Loverude, Kautz, and Heron

3. IdentificationSome specific

mirror those fountion of the sign ofand ~b! difficultiesystem. Both refldefinition of worthermal contexts,not appear in resp

References to aabout 10% of theand about 25% ocourse. ~None ofdid so.! One studenegative work sinpends on whereaxis. Other stud

made even by students who demonstrated some understand-student from theork done by theis# no such work,rce on the hand,k. Another stu-ck ...would bes not responsible

Table II. Student responses on the mechanical work problem ~see Fig. 5!. The students had all completed aprevious course on mechanics.

ou

nt

al work problem.

145 145Am. J. P d Heronof specific difficultiesdifficulties with mechanical work closelyd in thermodynamic contexts: ~a! associa-work with the choice of coordinate systems in relating the work done on and by aect a failure to apply correctly a generalk. Some of the issues that had arisen insuch as references to sign conventions, didonses to the mechanical work problem.particular coordinate system were made bystudents in the UW algebra-based course

f the students in the UMCP calculus-basedthe students in the UW second-year coursent wrote, There really is no such thing asce the distance used to calculate work de-a person chooses to place the coordinateents were less explicit but nonetheless de-

ing of Newtons third law. For example, oneUW algebra-based class, referring to the wblock on the hand in case 1, wrote, @Therethe block may have an equal and opposite fobut the block is not actually doing any wordent wrote that the work done by the blozero...because it exerts a force but its force ifor traveling a certain distance.

Fig. 6. A typical student response to the mechanic

hys., Vol. 70, No. 2, February 2002 Loverude, Kautz, anthat the corresponding work done on the hand by the block isof opposite sign. The sign of the work done on the block bythe earth can be found by comparing the directions of thedisplacement of the block and the gravitational force exertedon the block.

2. Results from the mechanical work problemAlmost all of the students gave the correct answer for the

sign of the work done on the block by the hand in case 1.However, correct explanations were given by only about10% in the UW algebra-based course, about 20% in theUMCP calculus-based course, and about 45% in the UWsecond-year thermal physics course. An additional 5% to15% in each class referred to work as the product of forceand displacement, but failed to take into account the vectornature of these quantities. One such student wrote that thework done on the block by the hand is positive, becausework5~force!~distance! and since the block moves work isdone. The percentage of students who answered all partscorrectly ~with or without correct explanations! was about25% in the algebra-based course, about 40% in the calculus-based course, and about 50% in the thermal physics course.The results are summarized in Table II.

Algebra-based cUW

N5101One section

Correct sign of work done on blockby hand in case I

93%

Correct explanation 10%Incomplete explanationa 16%Incorrect explanation:

based on coordinate system 11%based on cause of motion 13%other incorrect 15%

No explanation 28%

Correct sign of work for all parts 23%

aThese students mentioned both force and displacemevector nature of these quantities.scribed a specific coordinate system. For example, onewrote, The work done @on the block by the hand# is posi-tive, because I defined my coordinate system to be positivein the up direction. Students who drew and/or referred tocoordinate systems based their answers on a variety of quan-tities ~for example, the directions of the applied force, dis-placement, velocity, and acceleration!. Shown in Fig. 6 is theresponse of one of these students.

Explanations for the sign of the work done on the block bythe hand in which the hand is considered the cause of themotion were made by between about 5% and 15% of thestudents in each course. In the UW algebra-based course,about 10% of the students stated that the correspondingwork done on the hand by the block would be zero. Anadditional 20% answered that there would be no suchwork.45 Many incorrect responses were consistent with thebelief that the block does no work because it is not the agentcausing the motion: The work done by the block on anyobject is zero because it doesnt make anything move. Oth-ers indicated that the work done by the block on the handwas nonzero, but smaller in absolute value than that done bythe hand, ...the work done on block by hand is more thanvice versa.

It is important to note that statements such as these were

rse Calculus-based course Thermal physics courseUMCP UWN5177 N523

Two sections One section

91% 100%

20% 43%7% 13%

26% 0%5% 13%

19% 22%14% 9%

40% 52%

in their responses, but did not take into account the

B. Comparison of student performance on problemsin mechanics and thermal physics

the first law of thermodynamics. Even references to the con-cept of work, whether by the interviewer or by statements inThe mechanical work problem and a version of the bicyclepump problem were administered as part of the same un-graded quiz in the three courses mentioned above. ~The re-sults for the individual questions are included in Tables I andII.! Both the overall success rates and the distribution oftypes of explanations on the bicycle pump problem wereessentially the same as in those cases in which there hadbeen no questions on mechanical work. Apparently, the pres-ence of the mechanical work problem did not suggest tostudents that they apply the concept of work to the thermalphysics problem.46

We compared the responses of individual students on thetwo problems. For the purpose of these comparisons, a re-sponse to the bicycle pump problem had to include correctreasoning to be considered correct; all parts of the mechani-cal work problem had to be answered correctly. In the UWalgebra-based and UMCP calculus-based courses, we foundno noticeable difference in the success rates on the bicyclepump problem of the students who had answered the me-chanical work problem correctly and those who had not. Inthe UW second-year course, students who answered the me-chanical work problem correctly had a slightly higher suc-cess rate on the bicycle pump problem than those who hadnot done so. However, in all of the classes, the numbers ofstudents who were successful in either of these tasks weresmall. Overall academic strength may also be a factor. There-fore no definitive conclusion can be drawn.

There is another significant aspect to the comparison ofperformance on the mechanics and thermal physics prob-lems. We interpret correct answers on all parts of the me-chanical work problem as evidence of the ability of a studentto apply the concept of work in a situation involving a pointparticle in which the directions of both the relevant force anddisplacement are either explicitly stated or can be easily in-ferred. This ability would seem to be necessary for applyingthe concept of work in more complex situations involvingdeformation and internal energy. However, in the mechanicalwork problem students do not need to recognize the rel-evance of the concept of work in a given situation. To dem-onstrate functional understanding of work, students must beable to apply the concept, but first they must recognize whenthey need to do so.

VI. CONCLUSION

Results from a number of studies in the context of me-chanics have demonstrated that students often ignore generalprinciples in their attempts to solve problems.47 In earlierresearch, our group identified several difficulties that stu-dents have in applying the work-energy and impulse-momentum theorems in mechanics.48 The failure to applygeneral principles to thermal physics problems was evidentthroughout the present study. Students frequently did not se-lect, or even consider, the first law of thermodynamics as therelevant principle.

When presented with the questions described in this paper,most students, like many physicists, first attempted to use theideal gas law. Physicists, however, quickly recognized thelack of information and turned to the first law.49 In contrast,we found that students typically did not recognize that theiruse of the ideal gas law was not valid. Their confidence inthis law seemed to be a significant barrier to consideration of

146 Am. J. Phys., Vol. 70, No. 2, February 2002the written problems, did not seem to trigger application ofthe first law. When directly asked to use the first law, stu-dents revealed many difficulties that precluded correct appli-cation. The results were similar among first-year and second-year students. The courses in which they were enrolleddiffered in the amount of time spent on thermal physics, therange of topics covered, and the depth and mathematicalcomplexity with which topics were treated. The courses alsodiffered greatly in class size and in the background and in-terests of the students. However, student difficulties were thesame in character and surprisingly similar in prevalence.

Although considerable emphasis is placed upon the firstlaw in typical treatments of thermal physics, the importanceof this general principle is lost on many students. It wasevident throughout this investigation that many students hadnot developed an understanding of the relative importance ofthe concepts and principles they had studied. For many stu-dents, the ideal gas law was the most significant equation inthe course.

Throughout this study, many students confirmed their in-correct macroscopic arguments with reference to an incorrectmicroscopic model. On the basis of experience in this andother investigations, we question the desirability of introduc-ing the study of a macroscopic quantity or process ~for ex-ample, gases or electric current! by first presenting studentswith an already developed visual microscopic model ~for ex-ample, molecules or electrons!.50 Although a microscopicmodel may provide a causal explanation that may be appeal-ing to students, we have found that conceptual and reasoningdifficulties with such a model may undo the benefit to stu-dents of a visual explanatory mechanism. We are also con-cerned that the early introduction of a microscopic model,when not necessary to account for the phenomena or whennot strongly suggested by the evidence, may give students afalse impression about the nature of science. In particular, theearly introduction of the kinetic theory of gases may rein-force the notion that such a microscopic model proves theideal gas law. Students may consequently fail to recognizethat the model is designed to agree with experimental obser-vations of macroscopic phenomena. In much of the curricu-lum developed by our group, including materials on thermalphysics, students are provided with opportunities to becomefamiliar with macroscopic phenomena and to use their obser-vations as the basis for developing models with predictivepower. Inferences about the existence of processes that arenot directly observable are drawn only when necessary toaccount for experimental evidence. An example is providedby a series of tutorials by our group on optics in which phe-nomena that defy interpretation in terms of a ray model, suchas interference fringes, provide the motivation for the devel-opment of a simple wave model for light.51

Difficulties with the concept of work precluded correctapplication of the first law for many students. In many intro-ductory physics courses, students encounter thermal physicsshortly after studying the concept of work in mechanics. Inother courses, especially in chemistry, the study of thermo-dynamic work is not typically preceded by consideration ofmechanical work. Our results suggest that we should ensurethat students can apply the concept of work in simple me-chanical contexts before introducing the complexities ofthermal physics.

Linguistic complications have often been blamed for con-

146Loverude, Kautz, and Heron

ceptual confusion experienced by students. It has long beennoted that in everyday usage, heat is strongly associated

the second law of thermodynamicsan interpretive study, J. Res. Sci.Teach. 30, 85106 ~1993!; M. Linn and N. Songer, Teaching thermody-with temperature. The term heat is even used ambiguouslyin some textbooks. Appeals to instructors and authors to useterminology carefully appear frequently in the literature onteaching thermal physics.52 Certainly, precise use of techni-cal terms is to be strongly encouraged. However, for manystudents the problem goes beyond incorrect or inexact use ofterminology and reflects genuine inability to distinguishamong closely related concepts. In such cases, a linguisticremedy is unlikely to be sufficient.

Although the student difficulties described in this articleare serious and numerous, we believe they can be addressed.A concerted effort must be made to help students integratethe concepts and principles they have studied into a coherentconceptual framework that they can use to account forsimple thermal phenomena. We have begun to develop tuto-rials for this purpose.53 As described elsewhere, the develop-ment of instructional materials by our group takes place in aniterative cycle of research, curriculum development, and in-struction, with assessment playing a critical role.54 Prelimi-nary versions of a tutorial on the first law have been testedand appear to be successful in our classes. Our experiencethus far suggests that the effectiveness of the tutorial is in-creased if it is preceded by others that explicitly addressdifficulties with mechanical work and the ideal gas law.However, before we can feel confident about the replicabilityof the results, more cycles in the development process arenecessary. In this as in other cases, ongoing research is nec-essary to ensure that instruction is well matched to the needsof students.

ACKNOWLEDGMENTS

The authors are indebted to Lillian C. McDermott for hermany contributions to the preparation of this paper and to theinvestigation it describes. Thanks are also due to other mem-bers of the Physics Education Group, especially to Peter S.Shaffer for his help throughout the project. Also deeply ap-preciated has been the cooperation of the instructors at theUniversity of Washington, the University of Illinois, Urbana/Champaign, and the University of Maryland, College Park,in whose physics classes the written problems were admin-istered. The authors gratefully acknowledge the ongoing sup-port of the National Science Foundation through Grant Nos.DUE 9354501 and DUE 9727648.

a!Now at: Department of Physics, California State University Fullerton,Fullerton, CA 92834.

b!Now: Department of Physics, Syracuse University, Syracuse, NY 13210.c!Electronic mail: pheron@dirac.phys.washington.edu1See, for example, the following articles in the theme issue on thermal andstatistical physics in Am. J. Phys.: R. W. Chabay and B. A. Sherwood,Bringing atoms into first-year physics, 10451050; F. Reif, Thermalphysics in the introductory physics course, ibid. 67, 10511052 ~1999!;A. B. Arons, Development of energy concepts in introductory physicscourses, ibid. 67, 10631067 ~1999!.

2In addition to the specific references below, see the summary in the chapterby G. Erickson and A. Tiberghien in Childrens Ideas in Science, edited byR. Driver ~Open University Press, Philadelphia, 1985!.

3A list of additional research articles related to student understanding ofheat and temperature can be found in L. C. McDermott and E. F. Redish,Resource Letter: PER-1: Physics Education Research, Am. J. Phys. 67,755767 ~1999!.

4See, for example, R. Stavy and B. Berkovitz, Cognitive conflict as a basisfor teaching quantitative aspects of the concept of temperature, Sci. Educ.64, 679692 ~1980!; S. Kesidou and R. Duit, Students conceptions of

147 Am. J. Phys., Vol. 70, No. 2, February 2002namics to middle school students: What are appropriate cognitive de-mands? ibid. 28, 835918 ~1991!; E. Engel, E. Clough, and R. Driver,A study of consistency in the use of students conceptual frameworksacross different task contexts, Sci. Educ. 70, 473496 ~1986!.

5 The article mentioned in Ref. 3 contains an extensive list of articles onresearch on student understanding in introductory mechanics and on thedevelopment and assessment of curriculum based on research.

6For examples of the development and assessment of curriculum by thePhysics Education Group in topics other than mechanics ~for example,electricity and magnetism, geometrical and physical optics, and modernphysics! see Ref. 25 and articles in Ref. 3 by members of the PhysicsEducation Group.

7The research reported in this paper is described in greater detail in M. E.Loverude, Investigation of student understanding of hydrostatics andthermal physics and of the underlying concepts from mechanics, and inC. H. Kautz, Investigation of student understanding of the ideal gas law,Ph.D. dissertations, Department of Physics, University of Washington,1999 ~unpublished!.

8See, for example, G. Erickson, Childrens conceptions of heat and tem-perature, Sci. Educ. 63, 221230 ~1979!; Childrens viewpoints of heat:A second look, 64, 323336 ~1980!; M. Reiner, J. Slotta, M. Chi, and L.Resnick, Nave physics reasoning: A commitment to substance-basedconceptions, Cognit. Instruct. 18, 134 ~2000!.

9See, for example, A. B. Arons, A Guide to Introductory Physics Teaching~Wiley, New York, 1997!, Part III, pp. 118121.

10See, for example, P. H. van Roon, H. F. van Sprang, and A. H. Verdonk, Work and Heat: On a road towards thermodynamics, Int. J. Sci.Educ. 16, 131144 ~1994!.

11See, for example, S. Rozier and L. Viennot, Students reasoning in ther-modynamics, Int. J. Sci. Educ. 13, 159170 ~1992!.

12R. Resnick, D. Halliday, and K. S. Krane, Physics ~Wiley, New York,1992!, 4th ed.

13D. C. Giancoli, Physics ~PrenticeHall, Englewood Cliffs, NJ, 1995!, 4thed.

14In the courses included in this study, students typically apply the first lawof thermodynamics to closed systems, so there is no term for the chemicalpotential.

15For a discussion of important conceptual issues that need to be addressedin teaching this material, see A. B. Arons, Teaching Introductory Physics~Wiley, New York, 1997!, Part III, pp. 8082, 124129.

16A description of the use of the individual demonstration interview by thePhysics Education Group can be found in R. A. Lawson and L. C. Mc-Dermott, Student understanding of the work-energy and impulse-momentum theorems, Am. J. Phys. 55, 811817 ~1987! and in otherarticles in Ref. 3 that report on research by the group. Since 1994, most ofthe interviews have been both videotaped and audiotaped.

17None of the students raised questions about the insulating capabilities ofthe pump or the speed with which the handle was pushed inward. If anyhad done so, they would have been told to assume the pump is perfectlyinsulating.

18In both interviews and on written problems, a small number of studentsgave other explanations that were acceptable. For example, some studentsin the more advanced courses gave a microscopic work argument. Typi-cally, these students argued that the speed of the gas particles would in-crease as a result of collisions with the moving piston and that the tem-perature would therefore increase. A handful of students in these coursesalso correctly applied the equation PVg5constant for adiabatic processesto predict that the temperature would increase. During interviews, suchstudents were asked to try to account for this relationship between P andV.

19All the students assumed ~explicitly or implicitly! that they could treat theair in the pump as an ideal gas. If this issue had been raised, the studentswould have been told to do so.

20The version of the first law that was used in that particular students coursewas provided.

21Results from three sections of the calculus-based course at the Universityof Maryland serve as an example of the similarity of student performancebefore and after instruction. In the two classes in which the questionwas administered after instruction, a correct prediction concerning thetemperature was made by 61% (N566) and 54% (N583), respectively.In the class in which the question was given before any instruction, 59%

147Loverude, Kautz, and Heron

(N5113) of the students made a correct prediction. The variation in thepercentages of students giving correct explanations was similarly small.

22Additional evidence that student performance on certain types of questionsis essentially the same before and after instruction can be found in severalof the articles in Ref. 3 that report on research by the Physics EducationGroup. Other evidence is reported in R. R. Hake, Interactive engagementversus traditional methods, Am. J. Phys. 66, 6474 ~1998!.

23At UIUC, the question was posed in multiple-choice format with no ex-planations required. Therefore, we have not included this data in Table I.About 65% of the students answered correctly (N5189), a figure consis-tent with that obtained in other introductory courses.

24See Ref. 11.25See, for example, L. C. McDermott and P. S. Shaffer, Research as a guide

for curriculum development: An example from introductory electricity. I.Investigation of student understanding, Am. J. Phys. 60, 9941003~1992!, and printers erratum to Part I, ibid. 61, 81 ~1993!; P. S. Shaffer

cylinder is placed inside an insulating box with some ice water. Case II isidentical in every respect to case I except that the cylinders piston islocked in place. The students were asked to predict how the amounts of icemelted would compare after both systems are allowed to reach thermalequilibrium. In case I, positive work is done on the gas as the pistonlowers at constant pressure. In case II the piston does not move so no workis done. It follows that, in case I, greater heat transfer is required to lowerthe temperature of the gas by the same amount and therefore more ice ismelted. Only two of the five students interviewed took into account thework done in case I, despite having covered in their course the differencebetween heat capacity at constant volume (Cv) and at constant pressure(Cp). It is possible that students failed to regard the piston as doing workbecause it was not active.

39The version given at UIUC was multiple choice. No explanations wererequired.

40For a discussion of some of the relevant research, see, in addition to

and L. C. McDermott, Research as a guide for curriculum development:An example from introductory electricity. II. Design of instructional strat-egies, ibid. 60, 10031013 ~1992!.

26For a description of similar difficulties, see the article in Ref. 11.27In some classes at the second-year level the instructor discussed in detail

collisions between gas molecules and a moving piston. However, a com-plete microscopic treatment of heat transfer is not typically presented inthe courses involved in this study.

28We have also seen students use the fact that expressions for both pressureand temperature involve the mean square particle velocity to back up theirclaims that P and T are directly proportional.

29For other examples, see T. OBrien Pride, S. Vokos, and L. C. McDermott,The challenge of matching teaching assessments to teaching goals: Anexample from the work-energy and impulse-momentum theorems, Am. J.Phys. 66, 147157 ~1998!; R. N. Steinberg and M. S. Sabella, Perfor-mance on multiple-choice diagnostics and complementary exam prob-lems, Phys. Teach. 35, 150155 ~1997!.

30See the article mentioned in Ref. 16 and the first article in Ref. 29.31See Refs. 2, 3, 4, and 11.32See, for example, M. Zemansky, Phys. Teach. 8, 294300 ~1970!; J. W.

Warren, Phys. Educ. 7, 4144 ~1972!; R. Bauman, Phys. Teach. 30, 353356 ~1992!; R. H. Romer, Editorial: Heat is not a noun, Am. J. Phys. 69,107109 ~2001!.

33Failure to understand the role of insulation has also been documentedamong younger students. For example, some studies have found that chil-dren often say that materials like wool will make objects hot, rather thanpreventing heat transfer. See Refs. 2, 4, and 8.

34For a discussion of the confusion between heat and work in the context offrictional processes see the last article in Ref. 1 and Ref. 9, Part III, pp.137142.

35See Ref. 10.36Reference 13, p. 425.37Reference 12, p. 557. The fifth edition of this text, which was not yet in

print at the time of the study described in this article, defines the workdone on the gas as 2*p dV and states that ...if the gas expands, dV ispositive and W is negative, p being a scalar quantity having only positivevalues. Conversely, if the gas is compressed, dV is negative and the workdone on the gas is positive. R. Resnick, D. Halliday, and K. S. Krane,Physics ~Wiley, New York, 2002!, 5th ed., pp. 526527.

38We found similar results in a different set of interviews with a smallnumber of students. In the physical situation on which the interviews werebased, no object was readily identifiable as responsible for the motion.We asked students to consider the following two cases. In case I, a sampleof gas is enclosed in a cylinder with a piston that is free to move. The

148 Am. J. Phys., Vol. 70, No. 2, February 2002articles listed in Ref. 3, L. C. McDermott, Research on conceptual un-derstanding of mechanics, Phys. Today 37 ~7!, 2432 ~1984!.

41See, for example, J. Minstrell, Explaining the at rest condition of anobject, Phys. Teach. 20, 1014 ~1982!.

42See, for example, D. P. Maloney, Rule-governed approaches to physics:Newtons third law, Phys. Educ. 19, 3742 ~1984!.

43In this and other cases we have found little or no systematic variationbetween responses on graded and ungraded versions of the same question.

44We found that many students did not treat work done50 and there isno such work as equivalent statements. Therefore we explicitly allowedfor both possibilities.

45See Ref. 44.46In one version, the students were asked explicitly about the relationship

between the two pages.47For articles in which the failure to use energy principles in mechanics is

documented and discussed, see the section in Ref. 3 on problem-solvingperformance.

48See the article mentioned in Ref. 16 and the first article in Ref. 29.49We have posed the bicycle pump task in informal situations to a number of

friends and colleagues who are physicists.50There have been several articles that support the introduction of micro-

scopic models during the study of topics in classical physics. For examplesin the context of thermal physics, see the first two articles in Ref. 1. For anexample in the context of electric circuits, see B. A. Thacker, U. Ganiel,and D. Boys, Macroscopic phenomena and microscopic processes: Stu-dent understanding of transients in direct current electric circuits, Am. J.Phys. 67, S25S31 ~1999!. In the article, data are presented that indicatethat students who had been given a microscopic model outperformed oth-ers who had not. However, there is additional evidence that students whohad developed a sound macroscopic model performed as well on the ques-tions posed in this study as those who had been given a microscopicmodel.

51K. Wosilait, P. R. L. Heron, P. S. Shaffer, and L. C. McDermott, Address-ing student difficulties in applying a wave model to the interference anddiffraction of light, Am. J. Phys. 67, S5S15 ~1999!.

52See Ref. 32.53For other tutorials developed by the Physics Education Group, see L. C.

McDermott, P. S. Shaffer, and the Physics Education Group at the Univer-sity of Washington, Tutorials in Introductory Physics ~PrenticeHall, Up-per Saddle River, NJ, 2002!.

54For illustrations of the iterative process used by the Physics EducationGroup in the development of curriculum, see the second article in Ref. 25,the first article mentioned in Ref. 29, and articles in Ref. 3 by the PhysicsEducation Group.

148Loverude, Kautz, and Heron