Improvements of Student Understanding of Heat and Temperature

Improvements of Student Understanding of Heat and

Temperature

Gina QuanUniversity of Washington Research Experience for Undergraduates 2011

and the Physics Education GroupAdvisors: Paula Heron, Peter Shaffer, and Lillian McDermott

August 19, 2011

Abstract

This paper reports on an investigation of student understanding of heat transfer. Extensiveresearch has shown that students using the Physics by Inquiry[1] curriculum have demonstrateda solid understanding of topics and tasks directly covered within the module. However, sincethe design of this module, research on the learning and teaching of physics has revealed otherdifficulties not explicitly addressed in the curriculum. In this paper we will examine the ef-fectiveness of the Heat and Temperature unit of the Physics by Inquiry curriculum and usespecific student difficulties to suggest future modifications and areas of research.

I Introduction

Use of traditional lecture based instruction hasproven to be an ineffective way for many stu-dents to gain a solid understanding of phys-ical concepts. Research has shown that sig-nificant misconceptions in physics as well as alack of scientific reasoning skills often persistafter instruction. [3] Many physics educationresearchers attribute this deficiency in part tothe failure of lectures to take into account stu-dents’ existing beliefs and misconceptions[4].

The Physics Education Group (PEG) atthe University of Washington has created asystematic method of developing and improv-ing curriculum to help students build a coher-ent understanding of physical concepts. Stu-dent difficulties are identified in the analysisof pretests, past exams, and interviews. Withthis information, PEG continually refines cur-ricula designed to improve student understand-ing of these difficulties. One such curriculum,Physics by Inquiry (PbI), is designed specifi-cally for K-12 teachers. Physics by Inquiry con-

sists of a self-paced module in which studentsdesign and conduct experiments and then buildan understanding of the physics through obser-vation. This curriculum teaches physics in amanner similar to the practice of real science;students work in small groups to answer ques-tions through experimentation and applicationof knowledge cultivated earlier in the curricu-lum. At the end of each section, students talkthrough the material in a “check-out” with aninstructor before moving on.

The Physics by Inquiry curriculum is imple-mented during PEG’s NSF Summer Institutein Physics and Physical Science for Inservice K-12 Teachers. This year’s Summer Institute con-sisted of 32 inservice K-12 teachers. The pro-gram ran from late June to late July for a totalof five weeks. From 9:00AM to 11:45PM, teach-ers worked on a single morning topic through-out the institute. From 12:30PM to 3:45PM,teachers worked on two afternoon topics, eachlasting half of the institute. The second after-noon topic, Heat and Temperature, will serve

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Figure 1: The original calorimetry problem that was administered by Cochran (2005)[2].

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as the basis for the research described in thispaper.

II Description of Research

This research examines several specific diffi-culties that students have regarding thermo-dynamics. A considerable amount of researchhas been conducted on student understand-ing of heat and temperature. In 2001, Yeoand Zadnik developed a thermal concept inven-tory to probe student understanding of thermalconcepts[4]. This instrument guided several ofthe problems that we administered. At theUniversity of Washington, a 2005 doctoral the-sis by Matthew Cochran [2] also found that stu-dents in the algebra-based physics course havedifficulty distinguishing the quantities heat andtemperature. This leads to difficulties under-standing concepts such as thermal equilibriumand conservation of energy. Cochran also foundthat students with a weak understanding ofheat and temperature also struggle with apply-ing relevant equations[2].

This investigation explores if these studentdifficulties are present among K-12 teachersand the extent to which they persist after tak-ing Physics by Inquiry. We began by adminis-tering a pretest on the second day of instructionto the 32 students (for this paper, we will referto the K-12 teachers as students) in the Sum-mer Institute. At the end of the unit the stu-dents were given an exam after they had com-pleted 26 hours of the Heat and Temperaturemodule. Exams were evaluated on their cor-rectness of their responses as well as the qualityof their reasoning.

We found that students in the Summer In-stitute did considerably better than the stu-dents in the algebra-based physics sequence.In this paper we will discuss two of the ques-tions that were administered: one related tocalorimetry and the other to thermal equilib-rium and thermal conductivity. Both are spe-

cific concepts that were emphasized in the Sum-mer Institute.

III Student Understandingof Calorimetry

In 2005, Cochran administered variouscalorimetry problems to students in severalalgebra-based physics classes at the Universityof Washington. At the end of instruction, twodifferent classes were given the question inFigure 1 on an exam. In one version, the heatcapacities were given in calories and in theother the heat capacities were given in joules.

To solve Part 1, one must understand thatthe blocks begin and end in thermal equilib-rium so the change in temperature should bethe same. To answer Part 2, students neededto recognize that the copper block has a greaterheat capacity than the aluminum block so itshould transfer more heat. In Part 3, to find thefinal temperature one must understand thatthe heat lost by the blocks is equal to the heatgained. By using the equation Q = mc∆T forthe blocks and the water one can find a finaltemperature of about 40 ◦C.

Cochran found that only 60% of studentswere able to answer both of the first two partscorrectly, demonstrating a lack of understand-ing about thermal equilibrium and heat capac-ity. In Part 3, 15% of students who took thejoule version were able to calculate the finaltemperature correctly while 30% of studentswho took the calorie version were were able tocalculate the final temperature. He identifiedthat the most common difficulty was misappli-cation of the equation Q = mc∆T [2]. To com-pare, we gave a similar problem on an exam inthe Summer Institute.

III.A Curriculum Related toCalorimetry

As with the rest of the Physics by Inquiry cur-riculum, the Heat and Temperature module is

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far more conceptual than most traditional ther-modynamics curricula. First, students build afoundational knowledge of heat and tempera-ture through experimentation. These terms areoperationally defined by students only after theneed for the concepts are motivated.

Throughout the curriculum, students cre-ate a model for thermal interaction based ontheir observations, and the model is continu-ously revised. In one part of the model, theytreat thermal interactions between two objectsas successive transfers of heat between the twobodies until they reach the same temperature.An example of this method is in Figure 2 whichshows the interaction of aluminum, nickel andwater for the problem that will be discussedin III.B. In each step, one body transfers anamount of heat to another until equilibrium isreached. Although this method is somewhattedious and may allow for calculation errors,the model makes explicit how the tempera-ture of each body changes. Toward the endof the module, students arrive at the equationQ = C∆T .

III.B Analysis of Post Test

As a post-test, we administered a problem (Fig-ure 3) similar to Cochran’s. For this question,we asked the students to use a table of suc-cessive heat transfers to arrive at the equilib-rium temperature of the system. The first partwas modified because students had spent sometime working on mass and density in the mod-ule. The exam was open-book and open-noteand students were given a table of specific heatsand densities.

To solve Part A, one must first calculate theheat capacities. To find the heat capacities,one would multiply the specific heat, densityand volume. To solve Part B one would createa table of heat transfers, exchanging differentamounts of heat between objects until all ob-jects are in thermal equilibrium. In Figure 2, acorrect solution is found using successive heat

Table 1: Comparison of student performanceon calorimetry problem

SummerInstitute(N=32)

UW 115-calorie(N=42)

UW 115-joule(N=69)

%Correct 56% 30% 15%

transfers. A complete solution including stu-dent reasoning can be found in Appendix A.

Students in the Summer Institute did wellcompared to the algebra-based course. 78% ofstudents were able to calculate the heat capaci-ties (students in the algebra-based course werenot asked to do this part). Most of the in-correct responses for Part A were simple cal-culation errors as well as errors reading thetable. In Part B, 56% of students correctlycalculated the equilibrium temperature, alongwith 9% of students who calculated an equi-librium temperature consistent with incorrectheat capacities in Part A. This is significantlybetter than in the algebra-based course, whichsuggests that the Physics by Inquiry moduleconsiderably improved student ability to solvecalorimetry problems. A comparison of theseclasses can be found in Table 1.

IV Student Understanding

of Thermal Equilibrium

A common source of confusion among stu-dents is how two objects that feel different tothe touch can be in thermal equilibrium. Toprobe this confusion, Cochran (2005) admin-istered the following question to an algebra-based physics class post-lecture but beforehomework was assigned:

“A block of wood and a block of aluminum,both of identical size, have been in a coolerwith a bag of ice for a long time. Thetemperature of each block is measured witha thermometer. Is the temperature of thewood block greater than, less than, or equalto the temperature of the aluminum?”

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Figure 2: An example of how to use successive heat transfers to determine an equilibrium as insection III.A.

Figure 3: The new calorimetry problem as referenced in section III.B.

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To answer this problem, students need tounderstand that if the blocks have been in thecooler for a long time, they are in thermal equi-librium and therefore must be the same tem-perature. Cochran found that only 45% of stu-dents answered correctly with 25% answeringthat the wood block had a higher tempera-ture and 30% answering that the wood blockhad a lower temperature. Cochran noted thatincorrect responses demonstrated a confusionbetween temperature, total heat transfer andconductivity[2]. We administered similar ques-tions to the Summer Institute both early andlater in instruction to see if the Physics by In-quiry module helped students understand thisconcept.

IV.A Curriculum Related toThermal Equilibrium

The difference between temperature and thefeeling of hot or cold is addressed in severalparts in the curriculum. In Section 1 of thePhysics by Inquiry curriculum, students explic-itly reason that two objects that feel differentlymay have the same temperature. After measur-ing a block of wood and a block of aluminumat room temperature the module asks, “Doesthe feeling of hotness or coldness give a reliableindication of the temperature of the object? [1].After students have found that all objects in aroom have the same temperature as measuredby the thermometer, the curriculum also de-fines thermal equilibrium: “In most thermalinteractions between two objects, the temper-ature of the hotter one decreases and that ofthe colder one increases. Eventually the twointeracting objects arrive at the same interme-diate temperature.”[1]. Two concepts empha-sized in these exercises are that that objectswill eventually reach equilibrium with their sur-roundings and that sense of touch is not a goodindication of temperature. These observationsform an empircal foundation for the introduc-tion of heat transfer in the subsequent sections.

IV.B Analysis of First Summer In-stitute Research Task

In our first research task in the Summer Insti-tute, we asked a modified verson of problemdeveloped by Yeo and Zadnik[4]:

“A student takes a metal ruler and awooden ruler from his pencil case. He no-tices that the metal one feels colder thanthe wooden one. Explain why.”

Students answered this problem on the sec-ond day of instruction after most had com-pleted Section 1. All students had completedthe exercise in which they measure the temper-ature of objects in a room with a thermometer.This question served as a post-test for the ex-ercises in Section 1 as well as a pretest for theconductivity section later in the module.

Unsurprisingly, no student indicated thatthe temperature of the wooden ruler waswarmer than the metal ruler.

Although most students answered correctly,their reasoning was not always correct. Moststudents, in their responses to this problem, at-tributed the observation that the metal rulerfeels colder than the wooden ruler to someproperty of the materials. For example, 59% ofstudents specifically mentioned the conductiv-ity of the metal and 3% mentioned the specificheat of metal. Other responses did not referto specific concepts but said metal “pulls moreheat” or that “change in temp... is more easilyfelt” in metal.

We considered a correct reponse to includethat the rulers are the same temperature be-cause they are in thermal equilibrium with theroom and that sense of touch does not indicatetemperature. Of the responses, 31% of studentsexplicitly stated that the rulers are in thermalequilibrium with the room and 59% stated thatsense of touch is not a good indication of tem-perature. Other responses revealed misappli-cation or confusion of physics concepts. Forexample,

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“The surface area in contact with anygiven section of your skin is greater,more energy is transferred to themetal. It is a better conductor.”

Overall, the responses were somewhat tersewith incomplete reasoning. As is usual in theSummer Institute, reasoning improved dramat-ically after instruction. An example of a typicalfirst and second research task can be found inAppendix B.

IV.C Analysis of Second SummerInstitute Research Task

We then administered a similar question, alsoadapted from Yeo and Zadnik[4], for the finalexam of the Institute to see if students’ difficul-ties persisted after instruction. This problemwas the third part of the Heat and Tempera-ture section of the final.

“A student takes a Popsicle out of a freezer,where he had placed it the day before. Henotices that the Popsicle feels colder thanthe stick and concludes that the stick mustbe at a higher temperature than the Popsi-cle. Do you agree with him? Explain yourreasoning.”

Overall, students did well on this problem.While evaluating responses, we looked for threemain criteria- the understanding that the pop-sicle and the stick are the same temperature,the understanding that sense of touch does notindicate temperature, and the clarity and rea-soning of explanation. We found that 84% ofthe responses indicated that the popsicle andstick were in thermal equilibrium, 69% saidthat sense of touch does not indicate tempera-ture and 56% used both in their reasoning. Atypical response can be found in Appendix B.

As with the first research task, some stu-dents attributed the difference in feeling to con-ductivity, although to a much lesser extent onthe second research task. They did so although

thermal conductivity does not make an appear-ance in the curriculum until the last section.Only two students had started on the conduc-tivity section by the end of the class. Onthe exams and throughout Physics by Inquiry,students are instructed to forget any outsideknowledge they have and to base their answersonly on observations they have made in class.This experience not only helps them in deep-ening their understanding of the concepts andprocess of science, it also gives them the back-ground needed to guide their own students toan understanding of the ideas without skippingsteps in the reasoning.

Although the responses were generallygood, many students attributed the differencein sense of touch to a difference in specificheats. This could be due to the fact that nearlyall students had just completed the section onspecific heat. These types of responses are dis-cussed in the next section.

IV.D Student Misconceptions ofSpecific Heat and Conductiv-ity

A significant number of student responses usedspecific heat to account for the difference in feelof the popsicle and the stick. About 25% ofstudents related the specific heat to the rateof heat transfer, demonstrating some confu-sion between specific heat capacity and thermalconductivity. For example,

“The popsicle feels colder because ithas a lower specific heat than thestick– meaning it takes less caloriesper gram to raise the temp by 1�.It is absorbing heat from the handfaster than the stick and thereforefeels colder. (The change in temp isgreater for the popsicle than the stickfor the same amount of time.)”

The rest of this response, as well as theother responses in this section can be found

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in Appendix C. It seems as though the stu-dent arrived at this response by realizing thatthe popsicle must be absorbing heat from thestudent at a faster rate than the wood, andassuming that the popsicle is more responsiveto additions of heat. The popsicle’s abilityto absorb heat more readily could have beenconfused with having a heat capacity that ismore responsive to additions of heat. This re-sponse demonstrates that the student under-stands that the rate of heat transfer is a fac-tor in how we perceive hot and cold; however,there is a gap in understanding about the heattransfer.

In contrast, other students argued that thespecific heat of the popsicle is greater thanwood.

“What the student may be noticingis a difference in specific heat be-tween the ice and wood. Specificheat reflects how many calories a sub-stance needs to raise 1g of it 1�. Itsounds like the wood needed fewercalories/gram to raise its temperaturewhich is why it felt warm. (Lessheat left his fingers in his thermal ex-change). Ice probably felt colder be-cause more heat is needed to raise itstemp.”

This response illustrates a difficulty under-standing that the rate of heat transfer is a fac-tor in how hot or cold an object feels. It seemsas though the student was reasoning that ifthe wood feels warmer, it must have taken lessheat from the student and would have reachedequilibrium with the hand with less heat trans-ferred. Here the student seems to be thinkingin terms of a total quantity of heat rather thanthe rate of heat transfer.

These confusions regarding conductivityand specific heat suggest future directions ofresearch. This and other ideas for the futurewill be discussed later in this paper.

IV.E Student Misconceptions ofSpecific Heat and Phases

Of the students who used specific heat to ac-count for the difference in sense of touch, halftreated the specific heat of the popsicle to bethe same as that for liquid water. They arguedthat the popsicle had a greater specific heatthan the stick.

“The popsicle feels colder than thestick because the water in the popsi-cle requires more calories per gram toraise its temperature ( 1cal

g ◦C) than the

wood does (0.42calg ◦C ).

A table of specific heats was included in atable as an Appendix to the curriculum. Nei-ther the table nor the curriculum state that thespecific heat of liquid water is different thanwater ice. Interestingly, the specific heat of iceis about 0.5cal

g ◦C , which is very nearly the spe-cific heat of wood. Had we explicitly statedthis on the exam, some students may have re-alized that a small difference in specific heatalone could not account for observation.

There are a few reasons why students mayhave used the specific heat of water to refer tothe specific heat of ice. The table of specificheats given on the exam did not include ice,only water. Furthermore, in the module thereis no mention that specific heat changes as ma-terials change phase. There is a somewhat mis-leading portion of the curriculum that statesthat the specific heat of an object is nearly con-stant at all temperatures. It includes a table ofthe specific heat of water from the tempera-tures 0 ◦C to 100 ◦C and shows that it remainsnearly constant (a copy of the table is includedin Appendix D). Since students know that wa-ter freezes at 0 ◦C, they may have been assumedthat water ice has the same specific heat as well.These confusions may give way to future areasof research and curriculum development.

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V Future Research

There is not currently a pretest for the Conduc-tion section of the Heat and Temperature mod-ule but one would be useful to further probestudent understanding of conduction. This re-search has revealed that students’ preconcep-tions regarding conduction of heat are complexand varied. In their responses they related con-ductivity to properties such as density, surfacearea and kinetic energy of the atoms. It wouldbe interesting to see how and if other studentsare relating these properties to conductivity.

Because 25% of students demonstratedsome confusion regarding specific heat capac-ity and conductivity, it may be useful to ad-dress this issue in the curriculum. A pretestor check-out question regarding the differencebetween heat capacity and conductivity couldlead to interesting research. Though one mayargue that students would have learned con-ductivity had they gotten to that section, oneof the two students who worked through con-ductivity still attributed the feeling of coldnessto specific heat. At the present time, it may beuseful to emphasize in the module that heat ca-pacity is not the only property that is a factorin how warm or cold an object will feel. Thiscould be done in an experiment similar to thepopsicle problem, in which students comparethe specific heat and feel of two objects of sim-ilar specific heat. A problem like this could bea good transition into the conduction unit.

The confusion regarding specific heat of wa-ter and ice reveals a weakness in the curriculumto address how specific heat changes as phasechanges. It may be worthwhile for future revi-sions to include experiments which measure theheat capacity of water ice to illustrate this con-cept. The specific heat of water ice should alsobe added to the Appendix in future versions.

VI Conclusion

The process of physics education research is on-going. In the Heat and Temperature section of

the Physics by Inquiry curriculum, it seems asthough this year’s Summer Institute studentshad resolved nearly all of the commonly iden-tified misconceptions. However, the researchthat was conducted this year revealed othermore complex difficulties that had not beenpreviously known. It is the hope of physics edu-cation research that we can continue to identifythese difficulties in order address them by help-ing students build a coherent understanding ofthe physics.

VI.A Acknowledgements

I would like to thank my research advisor PaulaHeron as well as Peter Shaffer and Lillian Mc-Dermott for their endless guidance this sum-mer. I also thank the rest of the membersof PEG for their support, especially DonnaMessina, Timothy Major, Brian Stephanik,Brittany Johnson and Nina Tosti. Finally,thank you to everyone involved in the REU-coordinators Subhadeep Gupta and AlejandroGarcia, Janine and Linda, as well as Megan,Emilie, Charlie, Arman and Micah. Thisproject was made possible by the National Sci-ence Foundation.

References

[1] McDermott, Lillian C., et al., Physics byInquiry, Seattle: University of Washing-ton, 2011.

[2] Cochran, Matthew, Student Understand-ing of the Second Law of Thermodynam-ics and the Underlying Concepts of Heat,Temperature, and Thermal Equilibrium.PhD thesis. University of Washington,2005.

[3] McDermott, Lillian C., “Oersted MedalLecture 2001: ‘Physics EducationResearch— The Key to Student Learn-ing.’” Am. J. Phys. 69.11 (2001):1127–1137.

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[4] Yeo, Shelley and Marjan Zadnik. ”In-troductory Thermal Concept Evaluation:Assessing Students’ Understanding.” ThePhysics Teacher 39 (2001): 496–504

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A Sample Student Response to Calorimetry Problem

Figure 4: This is a typical student response to the calorimetry problem in section III.B.

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B Student Response to Thermal Equilibrium Problem: Firstand Second Research Tasks

Figure 5: This is a typical set of one student’s responses for the thermal equilibrium problems.The top response is from the first research task and the lower response is from the exam.

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C Student Response to Thermal Equilibrium Problem UsingSpecific Heat

Figure 6: This is the full response of the specific heat example in section IV.D

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Figure 7: This is the full response of the specific heat example in section IV.D

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D Specific Heat of Water

Figure 8: This graph in the curriculum may have mislead students to believe that the specificheat of water is constant in any phase IV.E

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