detecting and addressing students’ reasoning difficulties in thermal physics david e. meltzer...

Detecting and Addressing Students Reasoning Difficulties in Thermal Physics

David E. MeltzerDepartment of PhysicsUniversity of WashingtonSeattle, Washington, USA

Supported in part by U.S. National Science FoundationGrant Nos. DUE 9981140, PHY 0406724, and PHY 0604703

CollaboratorsTom Greenbowe (ISU Chemistry)John Thompson (U. Maine Physics)

StudentsNgoc-Loan Nguyen (ISU M.S. 2003)Warren Christensen (Ph.D. student)Tom Stroman (ISU graduate student)

FundingNSF Division of Undergraduate EducationNSF Division of Physics

Research on the Teaching and Learning of Thermal Physics Investigate student learning of statistical thermodynamicsProbe evolution of students thinking from introductory through advanced-level courseDevelop research-based curricular materialsIn collaboration with John Thompson, University of Maine

BackgroundResearch on learning of thermal physics in introductory courses: algebra-based introductory physics (Loverude, Kautz, and Heron, Am. J. Phys. 70, 137, 2002)sophomore-level thermal physics (Loverude, Kautz, and Heron, Am. J. Phys. 70, 137, 2002)calculus-based introductory physics (DEM, Am. J. Phys. 72, 1432, 2004; also some data from LKH, 2002)Focus of current work: research and curriculum development for upper-level (junior-senior) thermal physics course

Student Learning of ThermodynamicsStudies of university students in general physics courses have revealed substantial learning difficulties with fundamental concepts, including heat, work, and the first and second laws of thermodynamics:USAM. E. Loverude, C. H. Kautz, and P. R. L. Heron (2002);D. E. Meltzer (2004); M. Cochran and P. R. L. Heron (2006).GermanyR. Berger and H. Wiesner (1997)FranceS. Rozier and L. Viennot (1991)UKJ. W. Warren (1972)

Previous Phase of Current Project: Student Learning of Thermodynamics in Introductory Physics Investigation of second-semester calculus-based physics course (mostly engineering students) at Iowa State University.Written diagnostic questions administered last week of class in 1999, 2000, and 2001 (Ntotal = 653). Detailed interviews (avg. duration one hour) carried out with 32 volunteers during 2002 (total class enrollment: 424). interviews carried out after all thermodynamics instruction completedfinal grades of interview sample far above class average[two course instructors, 20 recitation instructors]

Primary Findings, Introductory Course

Even after instruction, many students (40-80%):believe that heat and/or work are state functions independent of processbelieve that net work done and net heat absorbed by a system undergoing a cyclic process must be zeroare unable to apply the First Law of Thermodynamics in problem solving

Thermal Physics: Course and StudentsTopics: Approximately equal balance between classical macroscopic thermodynamics, and statistical thermodynamics (Texts: Sears and Salinger; Schroeder)Students enrolled (Ninitial = 20): all but three were physics majors or physics/engineering double majorsall but one were juniors or aboveall had studied thermodynamicsone dropped out, two more stopped attending

Thermal Physics: Course and StudentsTopics: Approximately equal balance between classical macroscopic thermodynamics, and statistical thermodynamics (Texts: Sears and Salinger; Schroeder)Students enrolled [Ninitial = 14 (2003) and 20 (2004)] 90% were physics majors or physics/engineering double majors 90% were juniors or aboveall had studied thermodynamics (some at advanced level)


Course taught by DEM using lecture + interactive-engagement

Performance Comparison: Upper-level vs. Introductory StudentsDiagnostic questions given to students in introductory calculus-based course after instruction was complete:1999-2001: 653 students responded to written questions2002: 32 self-selected, high-performing students participated in one-on-one interviewsWritten pre-test questions given to Thermal Physics students on first day of class

Interview Sample:34% above 91st percentile; 50% above 81st percentileGrade Distributions: Interview Sample vs. Full Class

Chart1

1.65094339620

0.70754716980

0.94339622640

2.12264150940

5.42452830196.25

14.15094339620

17.924528301925

16.27358490579.375

13.91509433969.375

14.150943396212.5

6.60377358496.25

4.245283018918.75

1.415094339612.5

0.47169811320

Full Class, N = 424, median grade = 261

Interview Sample, N = 32, median grade = 305

Total Grade Points

Percentage of Sample

Sheet1

Sheet1

1.65094339620

0.70754716980

0.94339622640

2.12264150940

5.42452830196.25

14.15094339620

17.924528301925

16.27358490579.375

13.91509433969.375

14.150943396212.5

6.60377358496.25

4.245283018918.75

1.415094339612.5

0.47169811320

Full Class, N = 424, median grade = 261

Interview Sample, N = 32, median grade = 305

Total Class Points

Percentage of Sample

Grade Distributions

Sheet2

Sheet3

This P-V diagram represents a system consisting of a fixed amount of ideal gas that undergoes two different processes in going from state A to state B:


[In these questions, W represents the work done by the system during a process; Q represents the heat absorbed by the system during a process.] 1. Is W for Process #1 greater than, less than, or equal to that for Process #2? Explain.2. Is Q for Process #1 greater than, less than, or equal to that for Process #2?


[In these questions, W represents the work done by the system during a process; Q represents the heat absorbed by the system during a process.] 1. Is W for Process #1 greater than, less than, or equal to that for Process #2? Explain.2. Is Q for Process #1 greater than, less than, or equal to that for Process #2? W1 > W2



W1 > W2

Responses to Diagnostic Question #1 (Work question)

1999-2001Introductory Physics (Post-test)Written Sample(N=653)2002Introductory Physics(Post-test)Interview Sample (N=32)2004Thermal Physics(Pretest) (N=19)

W1 > W2

W1 = W2

W1 < W2



W1 = W230%22%24%



W1 = W230%22%20%

Responses to Diagnostic Question #1 (Work question)About one-fifth of Thermal Physics students believe work done is equal in both processes


W1 = W230%22%20%

Explanations Given by Thermal Physics Students to Justify W1 = W2Equal, path independent.Equal, the work is the same regardless of path taken.Some students come to associate work with phrases only used in connection with state functions.Explanations similar to those offered by introductory students

Explanations Given by Thermal Physics Students to Justify W1 = W2Equal, path independent.Equal, the work is the same regardless of path taken.Some students come to associate work with phrases only used in connection with state functions.Confusion with mechanical work done by conservative forces?



Change in internal energy is the same for Process #1 and Process #2.



Change in internal energy is the same for Process #1 and Process #2.

The system does more work in Process #1, so it must absorb more heat to reach same final value of internal energy: Q1 > Q2

Responses to Diagnostic Question #2 (Heat question)


Q1 > Q2

Q1 = Q2

Q1 < Q2


Q1 = Q2


1999-2001Introductory Physics (Post-test)Written Sample(N=653)

Q1 = Q238%


1999-2001Introductory Physics (Post-test)Written Sample(N=653)2002Introductory Physics(Post-test)Interview Sample (N=32)

Q1 = Q238%47%


1999-2001Introductory Physics (Post-test)Written Sample(N=653)2002Introductory Physics(Post-test)Interview Sample (N=32)2003-4Thermal Physics(Pretest) (N=33)

Q1 = Q238%47%30%

Explanations Given by Thermal Physics Students to Justify Q1 = Q2Equal. They both start at the same place and end at the same place.The heat transfer is the same because they are starting and ending on the same isotherm.Many Thermal Physics students stated or implied that heat transfer is independent of process, similar to claims made by introductory students.



Q1 > Q2

Q1 = Q2

Q1 < Q2



Q1 > Q245%34%33%[Correct answer] 11%19%33%



Q1 > Q245%34%33%Correct or partially correct explanation 11%19%33%

Responses to Diagnostic Question #2 (Heat question)Performance of upper-level students significantly better than introductory students in written sample



[From Loverude, Kautz, and Heron (2002)]

An ideal gas is contained in a cylinder with a tightly fitting piston. Several small masses are on the piston. (See diagram above.)

(Neglect friction between the piston and the cylinder walls.)




The cylinder is placed in an insulating jacket. A large number of masses are added to the piston.




The cylinder is placed in an insulating jacket. A large number of masses are added to the piston.

Tell whether the pressure, temperature, and volume of the gas will increase, decrease, or remain the same. Explain.


Correct response regarding temperature (2003 student):Work is done on the gas, but no heat transferred out, so T increases. Thermal Physics (Pre-instruction)Correct responses regarding temperature:2003: 20% (N = 14)2004: 20% (N = 19)

Incorrect responses regarding temperature:

The temperature will remain the same because there is no heat transfer. [2003]Temperature should stay the same due to insulating jacket . [2004]PV=nRT; T will stay the same as a drop in V will trigger an equal rise in pressure. [2004]

[University of Maine question]

A system consisting of one mole of a monatomic ideal gas goes through three different processes as shown below. The initial values of volume (Vo), pressure (Po), and temperature (To) are the same for each process. Also note that the final volume (Vf) is the same for each process, and that Processes #1 and #2 occur very slowly.

#1: Isothermal Expansion #2: Adiabatic Expansion #3: Free Expansion into a Vacuum

EMBED Word.Picture.8


InitialState:




FinalState:


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[University of Maine question]Is the change in internal energy positive, negative, or zero?





InitialState:




FinalState:


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[University of Maine question]Is the change in internal energy positive, negative, or zero?No heat transfer to the system, but the system loses energy by doing work on surroundings change in internal energy is negative





InitialState:




FinalState:


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2004 Thermal Physics, N = 17*

Adiabatic-expansion problem correct on final examAdiabatic-expansion problem incorrect on final examInsulated-piston problem correct on pretestInsulated-piston problem incorrect on pretest

2004 Thermal Physics, N = 17**two students failed to show up for final

Adiabatic-expansion problem correct on final examAdiabatic-expansion problem incorrect on final examInsulated-piston problem correct on pretestInsulated-piston problem incorrect on pretest

2004 Thermal Physics, N = 17

Adiabatic-expansion problem correct on final examAdiabatic-expansion problem incorrect on final examInsulated-piston problem correct on pretest 24%0% Insulated-piston problem incorrect on pretest


Adiabatic-expansion problem correct on final examAdiabatic-expansion problem incorrect on final examInsulated-piston problem correct on pretest 24%0% Insulated-piston problem incorrect on pretest59%


Adiabatic-expansion problem correct on final examAdiabatic-expansion problem incorrect on final examInsulated-piston problem correct on pretest 24%0% Insulated-piston problem incorrect on pretest59% 18%

2004 Thermal Physics, N = 17Is the insulated-piston problem more difficult?

Adiabatic-expansion problem correct on final examAdiabatic-expansion problem incorrect on final examInsulated-piston problem correct on pretest 24%0% Insulated-piston problem incorrect on pretest59% 18%

A Special Difficulty: Free Expansion

[University of Maine question]





InitialState:




FinalState:


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[University of Maine question]Students were asked to rank magnitudes of Q, W, U, and S for #1 and #3(initial and final states are the same for both)





InitialState:




FinalState:


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A Special Difficulty: Free ExpansionDiscussed extensively in class in context of entropys state-function propertygroup work using worksheetshomework assignmentPoor performance on 2004 final-exam question in advanced course (< 50% correct)frequent errors: belief that temperature or internal energy must change, work is done, etc.difficulties with first-law concepts prevented students from realizing that T does not change

Consistent with U. Maine results

Cyclic Process QuestionsA fixed quantity of ideal gas is contained within a metal cylinder that is sealed with a movable, frictionless, insulating piston. The cylinder is surrounded by a large container of water with high walls as shown. We are going to describe two separate processes, Process #1 and Process #2.

Time AEntire system at room temperature.At initial time A, the gas, cylinder, and water have all been sitting in a room for a long period of time, and all of them are at room temperature

[This diagram was not shown to students]

[This diagram was not shown to students]initial state

Beginning at time A, the water container is gradually heated, and the piston very slowly moves upward.

At time B the heating of the water stops, and the piston stops moving

Question #1: During the process that occurs from time A to time B, which of the following is true: (a) positive work is done on the gas by the environment, (b) positive work is done by the gas on the environment, (c) no net work is done on or by the gas.

Failure to Recognize Work as a Mechanism of Energy TransferBasic notion of thermodynamics: if part or all of system boundary is displaced during quasistatic process, energy is transferred between system and surroundings in the form of work.Study of Loverude et al. (2002) showed that few students could spontaneously invoke concept of work in case of adiabatic compression.Present investigation probed student reasoning regarding work in case of isobaric expansion and isothermal compression.

Failure to Recognize Work as a Mechanism of Energy TransferBasic notion of thermodynamics: if part or all of system boundary is displaced during quasistatic process, energy is transferred between system and surroundings in the form of work.Study of Loverude, Kautz, and Heron (2002) showed that few students could spontaneously invoke concept of work in case of adiabatic compression.Present investigation probed student reasoning regarding work in case of isobaric expansion and isothermal compression.

Question #1: During the process that occurs from time A to time B, which of the following is true: (a) positive work is done on the gas by the environment, (b) positive work is done by the gas on the environment, (c) no net work is done on or by the gas.

Results on Question #1positive work done on gas by environment: Interview Sample: 31%; Thermal Physics students: 38%positive work done by gas on environment [correct]: Interview Sample: 69%; Thermal Physics students: 62%Sample explanations for (a) answer:The water transferred heat to the gas and expanded it, so work was being done to the gas to expand it.The environment did work on the gas, since it made the gas expand and the piston moved up . . . water was heating up, doing work on the gas, making it expand.

Results on Question #1positive work done on gas by environment: Interview Sample: 31%; Thermal Physics students: 38%positive work done by gas on environment [correct]: Interview Sample: 69%; Thermal Physics students: 62%Sample explanations for (a) answer:The water transferred heat to the gas and expanded it, so work was being done to the gas to expand it.The environment did work on the gas, since it made the gas expand and the piston moved up . . . water was heating up, doing work on the gas, making it expand.Many students employ the term work to describe a heating process.

Results on Question #1positive work done on gas by environment: Interview Sample: 31%; Thermal Physics students: 38%positive work done by gas on environment [correct]: Interview Sample: 69%; Thermal Physics students: 62%Sample explanations for (a) answer:The water transferred heat to the gas and expanded it, so work was being done to the gas to expand it.The environment did work on the gas, since it made the gas expand and the piston moved up . . . water was heating up, doing work on the gas, making it expand.Nearly one third of the interview sample believe that environment does positive work on gas during expansion.

Results on Question #1positive work done on gas by environment: Interview Sample: 31%; Thermal Physics students: 38%positive work done by gas on environment [correct]: Interview Sample: 69%; Thermal Physics students: 62%Sample explanations for (a) answer:The water transferred heat to the gas and expanded it, so work was being done to the gas to expand it.The environment did work on the gas, since it made the gas expand and the piston moved up . . . water was heating up, doing work on the gas, making it expand.Additional questions showed that half the sample did not know that some energy was transferred away from gas during expansion .

Beginning at time A, the water container is gradually heated, and the piston very slowly moves upward.

At time B the heating of the water stops, and the piston stops moving

Now, empty containers are placed on top of the piston as shown.

Small lead weights are gradually placed in the containers, one by one, and the piston is observed to move down slowly.

While this happens the temperature of the water is nearly unchanged, and the gas temperature remains practically constant.

At time C we stop adding lead weights to the container and the piston stops moving. The piston is now at exactly the same position it was at time A .

[This diagram was not shown to students]TBC = 0

Question #4: During the process that occurs from time B to time C, is there any net energy flow between the gas and the water? If no, explain why not. If yes, is there a net flow of energy from gas to water, or from water to gas?

[This diagram was not shown to students]TBC = 0

[This diagram was not shown to students]Internal energy is unchanged.

[This diagram was not shown to students]Internal energy is unchanged.Work done on system transfers energy to system.

[This diagram was not shown to students]Internal energy is unchanged.Work done on system transfers energy to system.Energy must flow out of gas system as heat transfer to water.

Question #4: During the process that occurs from time B to time C, is there any net energy flow between the gas and the water? If no, explain why not. If yes, is there a net flow of energy from gas to water, or from water to gas?

Results on Question #4

Yes, from gas to water: [correct]Interview sample [post-test, N = 32]: 38%2004 Thermal Physics [pre-test, N = 17]: 30%No [Q = 0]: Interview sample [post-test, N = 32]: 59%2004 Thermal Physics [pre-test, N = 16]: 60%

Typical Explanation for Q = 0:

Misunderstanding of thermal reservoir concept, in which heat may be transferred to or from an entity that has practically unchanging temperatureNo [energy flow], because the temperature of the water does not change.

Thermal Physics Students Shared Difficulties Manifested by Introductory StudentsFailed to recognize that total kinetic energy of ideal gas molecules does not change when temperature is held constant:Interview sample: 44%2004 Thermal Physics students: 45%Failed to recognize that gas transfers energy to surroundings via work during expansion process:Interview sample: 59%2004 Thermal Physics students: 45%

Now, the piston is locked into place so it cannot move, and the weights are removed from the piston.

The system is left to sit in the room for many hours.

Eventually the entire system cools back down to the same room temperature it had at time A.

After cooling is complete, it is time D.

Question #6: Consider the entire process from time A to time D.

(i) Is the net work done by the gas on the environment during that process (a) greater than zero, (b) equal to zero, or (c) less than zero?

(ii) Is the total heat transfer to the gas during that process (a) greater than zero, (b) equal to zero, or (c) less than zero?

[This diagram was not shown to students]|WBC| > |WAB|

[This diagram was not shown to students]|WBC| > |WAB|WBC < 0

[This diagram was not shown to students]|WBC| > |WAB|WBC < 0 Wnet < 0

Results on Question #6 (i)

(c) Wnet < 0: [correct]Interview sample [post-test, N = 32]: 19%2004 Thermal Physics [pre-test, N = 16]: 10%(b) Wnet = 0: Interview sample [post-test, N = 32]: 63%2004 Thermal Physics [pre-test, N = 16]: 45%

[This diagram was not shown to students]U = Q W U = 0 Qnet = Wnet

[This diagram was not shown to students]U = Q W U = 0 Qnet = WnetWnet < 0 Qnet < 0

Results on Question #6 (ii)

(c) Qnet < 0: [correct]Interview sample [post-test, N = 32]: 16%2004 Thermal Physics [pre-test, N = 16]: 20%(b) Qnet = 0: Interview sample [post-test, N = 32]: 69%2004 Thermal Physics [pre-test, N = 16]: 80%

Most students thought that Qnet and/or Wnet must be equal to zero50% of the 2004 Thermal Physics students initially believed that both the net work done and the total heat transferred would be zero.Only one out of 16 Thermal Physics students answered both parts of Question #6 correctly on the pre-test.

Some Strategies for InstructionLoverude et al.: Solidify students concept of work in mechanics context (e.g., positive and negative work);Develop and emphasize concept of work as an energy-transfer mechanism in thermodynamics context.

Some Strategies for InstructionFocus on meaning of heat as transfer of energy, not quantity of energy residing in a system;Emphasize contrast between heat and work as energy-transfer mechanisms.

Some Strategies for InstructionGuide students to make increased use of PV-diagrams and similar representations.Practice converting between a diagrammatic representation and a physical description of a given process, especially in the context of cyclic processes.

Some Strategies for InstructionCertain common idealizations are very troublesome for many students (e.g., the relation between temperature and kinetic energy of an ideal gas; the meaning of thermal reservoir). The persistence of these difficulties suggests that it might be useful to guide students to provide their own justifications for commonly used idealizations.

Cyclic Process Worksheet(adapted from interview questions)

Worksheet StrategyFirst, allow students to read description of entire process and answer questions regarding work and heat.Then, prompt students for step-by-step responses.Finally, compare results of the two chains of reasoning.

Time ASystem heated, piston goes up.

Time BSystem heated, piston goes up.

Time BWeights added, piston goes down.

Time CWeights added, piston goes down.

Time CWeights added, piston goes down.[[[Temperature remains constant]]

Temperature CTime CPiston locked, temperature goes down.

Temperature DTime DPiston locked, temperature goes down.

Time A

Time B

Time BFor the process A B, is the work done by the system (WAB) positive, negative, or zero?

Explain your answer.

Time B

Time C

Time C2) For the process B C, is the work done by the system (WBC) positive, negative, or zero?3) For the process C D, is the work done by the system (WCD) positive, negative, or zero?

Temperature CTime C

Temperature DTime D3) For the process C D, is the work done by the system (WCD) positive, negative, or zero?

1) For the process A B, is the work done by the system (WAB) positive, negative, or zero?2) For the process B C, is the work done by the system (WBC) positive, negative, or zero?3) For the process C D, is the work done by the system (WCD) positive, negative, or zero?

4) Rank the absolute values WAB, WBC, andWCD from largest to smallest; if two or more are equal, use the = sign:

largest _________________________ smallest

Explain your reasoning.

1) For the process A B, is the work done by the system (WAB) positive, negative, or zero?2) For the process B C, is the work done by the system (WBC) positive, negative, or zero?3) For the process C D, is the work done by the system (WCD) positive, negative, or zero?

4) Rank the absolute values WAB, WBC, andWCD from largest to smallest; if two or more are equal, use the = sign:

largest WBC> WAB > WCD = 0 smallest

Explain your reasoning.

Consider the net work done by the system during the complete process A ( D, where

Wnet = WAB + WBC + WCD

i) Is this quantity greater than zero, equal to zero, or less than zero?

ii) Is your answer consistent with the answer you gave for #6 (i)? Explain.

Entropy and Second-Law QuestionsHeat-engine questionsSpontaneous-process question

Heat Engines and Second-Law IssuesAfter extensive study and review of first law of thermodynamics, cyclic processes, Carnot heat engines, efficiencies, etc., students were given pretest regarding various possible (or impossible) versions of two-temperature heat engines.

Heat-engines and Second-Law IssuesMost advanced students are initially able to recognize that perfect heat engines (i.e., 100% conversion of heat into work) violate second law;Most are initially unable to recognize that engines with greater than ideal (Carnot) efficiency also violate second law (consistent with result of Cochran and Heron, 2006);After (special) instruction, most students recognize impossibility of super-efficient engines, but still have difficulties understanding cyclic-process requirement of S = 0; many also still confused about U = 0.

Heat-engines and Second-Law Issues

Heat Engines Pretest

Consider a system composed of a fixed quantity of gas (not necessarily ideal) that undergoes a cyclic process in which the final state is the same as the initial state. During one particular cyclic process, there is heat transfer to or from the system at only two fixed temperatures: Thigh and Tlow

For the following processes, state whether they are possible according to the laws of thermodynamics. Justify your reasoning for each question:

heat transfer of 100 J to the system at Thigh heat transfer of 60 J away from the system at Tlownet work of 20 J done by the system on its surroundings.ThighTlowWNET = 20 JQ = 100 JQ = 60 JSystem(violation of first law of thermodynamics)70% correct (N = 17)(diagram not given)

heat transfer of 100 J to the system at Thigh heat transfer of 60 J away from the system at Tlownet work of 20 J done by the system on its surroundings.

ThighTlowWNET = 100 JQ = 100 JQ = 0 JSystemheat transfer of 100 J to the system at Thigh heat transfer of 0 J away from the system at Tlownet work of 100 J done by the system on its surroundings.(Perfect heat engine: violation of second law of thermodynamics)60% correct (N = 17)(diagram not given)

During one particular cyclic process, there is heat transfer to or from the system at only two fixed temperatures: Thigh and Tlow. Assume that this process is reversible:

heat transfer of 100 J to the system at Thigh heat transfer of 60 J away from the system at Tlownet work of 40 J done by the system on its surroundings.Not given

Now consider a set of processes in which Thigh and Tlow have exactly the same numerical values as in the example above, but these processes are not necessarily reversible. For the following process, state whether it is possible according to the laws of thermodynamics. Justify your reasoning for each question.

ThighTlowWNET = 60 JQ = 100 JQ = 40 JSystemheat transfer of 100 J to the system at Thigh heat transfer of 40 J away from the system at Tlownet work of 60 J done by the system on its surroundings.(violation of second law)0% correct (N = 15)Consistent with results reported by Cochran and Heron (Am. J. Phys., 2006)(diagram not given)

Heat Engines: Post-InstructionFollowing extensive instruction on second-law and implications regarding heat engines, graded quiz given as post-test

Consider the following cyclic processes which are being evaluated for possible use as heat engines.

For each process, there is heat transfer to the system at T = 400 K, and heat transfer away from the system at T = 100 K. There is no heat transfer at any other temperatures.

For each cyclic process, answer the following questions:Is the process a reversible process, a process that is possible but irreversible, or a process that is impossible? Explain. (You might want to consider efficiencies.)

Consider the following cyclic processes which are being evaluated for possible use as heat engines.

For each process, there is heat transfer to the system at T = 400 K, and heat transfer away from the system at T = 100 K. There is no heat transfer at any other temperatures.

For each cyclic process, answer the following questions:Is the process a reversible process, a process that is possible but irreversible, or a process that is impossible? Explain. (You might want to consider efficiencies.)

Not given

Cycle 1: heat transfer at high temperature is 300 J;heat transfer at low temperature is 100 J

Cycle 2: heat transfer at high temperature is 300 J; heat transfer at low temperature is 60 J



Process is impossible60% correct with correct explanation (N = 15)




Process is possible but irreversible55% correct with correct explanation (N = 15)




At the end of the process, is the entropy of the system larger than, smaller than, or equal to its value at the beginning of the process?




At the end of the process, is the entropy of the system larger than, smaller than, or equal to its value at the beginning of the process?Answer: Ssystem = 0 since process is cyclic, and S is a state function




At the end of the process, is the entropy of the system larger than, smaller than, or equal to its value at the beginning of the process?Answer: Ssystem = 0 since process is cyclic, and S is a state function40% correct with correct explanation (N = 15)




At the end of the process, is the entropy of the system larger than, smaller than, or equal to its value at the beginning of the process?Most common error: Assume

(forgetting that this equation requires Qreversible and this is not a reversible process)

Heat-engines and Second-Law IssuesMost advanced students are initially able to recognize that perfect heat engines (i.e., 100% conversion of heat into work) violate second law;Most are initially unable to recognize that engines with greater than ideal (Carnot) efficiency also violate second law (consistent with result of Cochran and Heron, 2006);After (special) instruction, most students recognize impossibility of super-efficient engines, but still have difficulties understanding cyclic-process requirement of S = 0; many also still confused about U = 0.

Entropy and Second-Law QuestionsHeat-engine questionsSpontaneous-process question

For each of the following questions consider a system undergoing a naturally occurring (spontaneous) process. The system can exchange energy with its surroundings.During this process, does the entropy of the system [Ssystem] increase, decrease, or remain the same, or is this not determinable with the given information? Explain your answer.During this process, does the entropy of the surroundings [Ssurroundings] increase, decrease, or remain the same, or is this not determinable with the given information? Explain your answer.During this process, does the entropy of the system plus the entropy of the surroundings [Ssystem + Ssurroundings] increase, decrease, or remain the same, or is this not determinable with the given information? Explain your answer.Spontaneous Process Question[Introductory-Course Version]

Responses to Spontaneous-Process QuestionsIntroductory Students Less than 40% correct on each question

Chart1

404000

413900

193000

Intro Physics, Pretest

Intro Physics, Posttest

Thermal Physics, Pretest

Thermal Physics, Posttest

Correct responses (%)

Sheet1

S(system)40405065

S(surroundings)41395075

S(total)193090100

Sheet1

0000

0000

0000






Sheet2

Sheet3

Introductory Physics Students Thinking on Spontaneous Processes

Tendency to assume that system entropy must always increaseSlow to accept the idea that entropy of system plus surroundings increases

Most students give incorrect answers to all three questions

Responses to Spontaneous-Process QuestionsThermal Physics Posttest: Interactive Engagement, no focused tutorialAdvanced Students

Chart1

005065

005075

0090100






Sheet1

S(system)40405065

S(surroundings)41395075

S(total)193090100

Sheet1






Sheet2

Sheet3

Thermal Physics Students Thinking on Spontaneous Processes

Readily accept that entropy of system plus surroundings increases in contrast to introductory studentsTendency to assume that system entropy must always increasesimilar to thinking of introductory students

Entropy Tutorial(draft by W. Christensen and DEM, undergoing class testing) Consider slow heat transfer process between two thermal reservoirs (insulated metal cubes connected by thin metal pipe)Does total energy change during process?Does total entropy change during process?

Entropy Tutorial(draft by W. Christensen and DEM, undergoing class testing)Guide students to find that: and that definitions of system and surroundings are arbitrary

Preliminary results are promising

You overhear a group of students discussing the above problem. Carefully read what each student is saying.

Student A: Well, the second law says that the entropy of the system is always increasing. Entropy always increases no matter what.

Student B: But how do you know which one is the system? Couldnt we just pick whatever we want to be the system and count everything else as the surroundings?

Student C: I dont think it matters which we call the system or the surroundings, and because of that we cant say that the system always increases. The second law states that the entropy of the system plus the surroundings will always increase. Analyze each statement and discuss with your group the extent to which it is correct or incorrect. How do the students ideas compare with your own discussion [about the insulated cubes] on the previous page?

Fictional Student Discussion for Analysis

Entropy Tutorial(draft by W. Christensen and DEM, undergoing class testing)Guide students to find that: and that definitions of system and surroundings are arbitrary

Preliminary results are promising

Responses to Spontaneous-Process Questions Introductory Students

Chart2

0.18665540540.29803921570.67932489450.060.060.040.040.020.02

0.04391891890.07058823530.5569620253

Pre-instruction (N = 1184)

Post-instruction, no tutorial (N = 255)

Post-instruction, with tutorial (N = 237)

Sheet1

Concrete context question

Fall 2005 Pre

IncDecSameNDIncDecSameNDIncDecSameNDIncDecSameNDcorrect

207314128935620159922111468194152147

15%20%14%45%27%10%7%48%11%5%71%4%9%2%73%7%3%

Spring 2005 Pre


15530254833913147527110573619599

19%16%3%54%25%8%9%48%17%1%68%5%23%1%61%6%6%

Spring 2005 Post

IncDecSameNDIncDecSameNDIncDecSameNDIncDecSameNDCorrectlook at obj + air correct that didn't get all correct

249525111135692322135595171155941721229and how does that compare to spr 2006

21%20%4%54%28%9%9%54%24%2%69%6%24%2%69%5%12%

0.02706529370.0205936006

Spring 2006 Pre


223384761166223711234916463211611812

17%21%3%52%28%10%3%50%15%4%74%3%14%0%72%8%5%

Spring 2006 Post

IncDecSameNDIncDecSameNDIncDecSameNDIncDecSameNDCorrect

23131261171351831711584551110111231124

13%11%0%74%15%8%1%74%68%2%24%5%44%0%53%0%54%

0.030.03

Spring 2006 Pre (Kent State)


21260126201220190401422

10%29%0%57%29%10%0%57%10%0%90%0%19%0%67%10%10%

Spring 2006 Post (Kent State)


1344055125506220822

31%31%0%38%38%8%15%38%38%0%46%15%15%0%62%15%15%

5858328

14%5%

0.010.01

General Process Question

Fall 2004 Pre

IncDecSameNDIncDecSameNDIncDecSameNDCorrect

406122783615810466501707782743219

30%19%9%39%26%16%12%42%19%2%67%8%5%

Fall 2005 Pre

IncDecSameNDIncDecSameNDIncDecSameNDConserv??=Correct

36087894812711350411355710248261113814

24%25%13%35%31%14%11%38%16%3%69%7%31%11%4%

Tot Consv

Spring 2005 Pre41%


1714424985441816803921032128426

26%14%5%50%26%11%9%47%23%1%60%12%16%25%4%

Tot Consv

Spring 2005 Post41%


2558746191027549269976414427682918

34%18%7%40%29%19%10%39%30%2%56%11%27%11%7%

0.0286972022Tot Cons0.0159779259

Spring 2006 Pre38%


24760453210570342710348417611613213

24%18%13%43%28%14%11%42%19%2%71%4%25%13%5%

Tot Consv

Spring 2006 Post38%


237292641783813618016145417132

12%11%2%75%16%5%3%76%68%2%23%7%56%

3%3%



22332143241300156460

14%14%9%64%14%9%18%59%0%0%68%27%18%27%0%

Tot Consv

Spring 2006 Post (Kent State)45%

IncDecSameNDIncDecSameNDIncDecSameNDcorr

134207230760341

31%15%0%54%15%23%0%54%46%0%23%31%8%

118422152

19%4%

0.0110.006

New Free Expansion Question

Spring 2006 Post


2391432145872611749119116970

6%1%90%2%36%11%49%2%38%8%49%4%29%

Entropy sys/env Ques -

> Spring 2006 61.1% correct

Fall 2004 - 30% correct

Spring 2005 - 27% correct

Delta(S) PV diagram Ques -

> #16 Delta(S) and pV diagram 65.0% correct

Spring 2004 - 67%

Sheet1

0000

0000

0000

0000

Spring 2005

Fall 2005

Spring 2006

Spr 2006 Kent State

Pre-Instructions ReponsesEntropy of Object

Sheet2

000

000

000

000

Spring 2005

Fall 2005

Spring 2006

Pre-Instructions ReponsesEntropy of Air in Room

Sheet3

0.17419354840.10628019320.15246636770.0952380952

0.00645161290.05314009660.04035874440

0.67741935480.70531400970.7354260090.9047619048

0.04516129030.0386473430.02690582960

Spring 2005

Fall 2005

Spring 2006

Spr 2006 Kent State

Pre-Instructions ReponsesEntropy of Obj + Air

0.23225806450.09178743960.14349775780.1904761905

0.00645161290.01932367150.00448430490

0.61290322580.73429951690.72197309420.6666666667

0.05806451610.06763285020.08071748880.0952380952

Spring 2005

Fall 2005

Spring 2006

Spr 2006 Kent State

Pre-Instructions ReponsesEntropy of Universe

0.20883534140.13419913420.3076923077

0.20481927710.11255411260.3076923077

0.04417670680.00432900430

0.54216867470.74025974030.3846153846

Spring 2005

Spring 2006

Kent

Post-Instructions ReponsesEntropy of Object

0.27710843370.15151515150.3846153846

0.09236947790.07792207790.0769230769

0.08835341370.0129870130.1538461538

0.54216867470.74025974030.3846153846

Spring 2005

Spring 2006

Kent

Post-Instructions ReponsesEntropy of Air in Room

0.23694779120.6839826840.3846153846

0.02008032130.01731601730

0.6867469880.23809523810.4615384615

0.06024096390.04761904760.1538461538

Spring 2005

Spring 2006

Kent

Post-Instructions ReponsesEntropy of Obj + Air

0.23694779120.43722943720.1538461538

0.0160642570.00432900430

0.69076305220.53246753250.6153846154

0.04819277110.00432900430.1538461538

Spring 2005

Spring 2006

Kent


0.30049261080.24166666670.25730994150.34117647060.24291497980.12236286920.13636363640.3076923077

0.19211822660.24722222220.14035087720.18039215690.18218623480.10970464140.13636363640.1538461538

0.08866995070.13333333330.05263157890.07450980390.12955465590.01687763710.09090909090

0.38916256160.35277777780.49707602340.40.42510121460.75105485230.63636363640.5384615385

Fall 2004 Pre N = 406

Fall 2005 Pre N = 360

Spring 2005 Pre N = 171

Spring 2005 Post, N = 255



Kent State Pre

Kent State Post

Entropy of system

0.18965517240.15833333330.22807017540.29803921570.19433198380.679324894500.4615384615

0.01970443350.02777777780.01169590640.01568627450.0161943320.016877637100

0.67487684730.68888888890.60233918130.56470588240.71255060730.22784810130.68181818180.2307692308

0.0788177340.07222222220.12280701750.10588235290.0445344130.07172995780.27272727270.3076923077

Fall 2004 Pre N = 406

Fall 2005 Pre N = 360





Kent State Pre

Kent State Post

Entropy of system + surroundings

0.25615763550.31388888890.25730994150.29411764710.28340080970.16033755270.13636363640.1538461538

0.16256157640.13888888890.10526315790.19215686270.13765182190.05485232070.09090909090.2307692308

0.12315270940.11388888890.09356725150.10196078430.10931174090.02531645570.18181818180

0.41871921180.3750.46783625730.38823529410.41700404860.75949367090.59090909090.5384615385

Fall 2004 Pre N = 406

Fall 2005 Pre N = 360





Kent State Pre

Kent State Post

Entropy of surroundings

0.04679802960.03888888890.03508771930.07058823530.05263157890.556962025300.0769230769

Fall 2004 Pre N = 406

Fall 2005 Pre N = 360





Kent Stat Pre

Kent State Post

0.05857740590.01255230130.89539748950.0209205021

0.36401673640.10878661090.4895397490.0167364017

0.38075313810.07949790790.48535564850.0376569038

Increases

Decreases

Same

Not determinable

0000

0000

0000

0000

Spring 2005

Fall 2005

Spring 2006

Spr 2006 Kent State


0.14188034190.23694779120.6839826840.060.060.020.020.050.05

0.04786324790.11553784860.5367965368


Post-instruction, No tutorial (N= 249)

Post-instruction, With tutorial (N = 231)

0.18665540540.29803921570.67932489450.060.060.040.040.020.02

0.04391891890.07058823530.5569620253


Post-instruction, No tutorial (N = 255)


Responses to Spontaneous-Process Questions Intermediate Students (N = 32, Matched)

Chart2

0.340.720.160.160.140.13

0.130.63

Pre-instruction

Post-instruction, with tutorial

Sheet1

Concrete context question

Fall 2005 Pre


207314128935620159922111468194152147

15%20%14%45%27%10%7%48%11%5%71%4%9%2%73%7%3%

Spring 2005 Pre


15530254833913147527110573619599

19%16%3%54%25%8%9%48%17%1%68%5%23%1%61%6%6%

Spring 2005 Post

IncDecSameNDIncDecSameNDIncDecSameNDIncDecSameNDCorrectlook at obj + air correct that didn't get all correct

249525111135692322135595171155941721229and how does that compare to spr 2006

21%20%4%54%28%9%9%54%24%2%69%6%24%2%69%5%12%

0.02706529370.0205936006

Spring 2006 Pre


223384761166223711234916463211611812

17%21%3%52%28%10%3%50%15%4%74%3%14%0%72%8%5%

Spring 2006 Post


23131261171351831711584551110111231124

13%11%0%74%15%8%1%74%68%2%24%5%44%0%53%0%54%

0.030.03



21260126201220190401422

10%29%0%57%29%10%0%57%10%0%90%0%19%0%67%10%10%

Spring 2006 Post (Kent State)


1344055125506220822

31%31%0%38%38%8%15%38%38%0%46%15%15%0%62%15%15%

5858328

14%5%

0.010.01

General Process Question

Fall 2004 Pre


406122783615810466501707782743219

30%19%9%39%26%16%12%42%19%2%67%8%5%

Fall 2005 Pre


36087894812711350411355710248261113814

24%25%13%35%31%14%11%38%16%3%69%7%31%11%4%

Tot Consv

Spring 2005 Pre41%


1714424985441816803921032128426

26%14%5%50%26%11%9%47%23%1%60%12%16%25%4%

Tot Consv

Spring 2005 Post41%


2558746191027549269976414427682918

34%18%7%40%29%19%10%39%30%2%56%11%27%11%7%

0.0286972022Tot Cons0.0159779259

Spring 2006 Pre38%


24760453210570342710348417611613213

24%18%13%43%28%14%11%42%19%2%71%4%25%13%5%

Tot Consv

Spring 2006 Post38%


237292641783813618016145417132

12%11%2%75%16%5%3%76%68%2%23%7%56%

3%3%



22332143241300156460

14%14%9%64%14%9%18%59%0%0%68%27%18%27%0%

Tot Consv

Spring 2006 Post (Kent State)45%

IncDecSameNDIncDecSameNDIncDecSameNDcorr

134207230760341

31%15%0%54%15%23%0%54%46%0%23%31%8%

118422152

19%4%

0.0110.006

New Free Expansion Question

Spring 2006 Post


2391432145872611749119116970

6%1%90%2%36%11%49%2%38%8%49%4%29%

Entropy sys/env Ques -

> Spring 2006 61.1% correct

Fall 2004 - 30% correct

Spring 2005 - 27% correct

Delta(S) PV diagram Ques -

> #16 Delta(S) and pV diagram 65.0% correct

Spring 2004 - 67%

Sheet1

0000

0000

0000

0000

Spring 2005

Fall 2005

Spring 2006

Spr 2006 Kent State

Pre-Instructions ReponsesEntropy of Object

Sheet2

000

000

000

000

Spring 2005

Fall 2005

Spring 2006


Sheet3

0000

0000

0000

0000

Spring 2005

Fall 2005

Spring 2006

Spr 2006 Kent State

Pre-Instructions ReponsesEntropy of Obj + Air

0.23225806450.09178743960.14349775780.1904761905

0.00645161290.01932367150.00448430490

0.61290322580.73429951690.72197309420.6666666667

0.05806451610.06763285020.08071748880.0952380952

Spring 2005

Fall 2005

Spring 2006

Spr 2006 Kent State


000

000

000

000

Spring 2005

Spring 2006

Kent

Post-Instructions ReponsesEntropy of Object

000

000

000

000

Spring 2005

Spring 2006

Kent

Post-Instructions ReponsesEntropy of Air in Room

000

000

000

000

Spring 2005

Spring 2006

Kent

Post-Instructions ReponsesEntropy of Obj + Air

0.23694779120.43722943720.1538461538

0.0160642570.00432900430

0.69076305220.53246753250.6153846154

0.04819277110.00432900430.1538461538

Spring 2005

Spring 2006

Kent


00000000

00000000

00000000

00000000

Fall 2004 Pre N = 406

Fall 2005 Pre N = 360





Kent State Pre

Kent State Post

Entropy of system

00000000

00000000

00000000

00000000

Fall 2004 Pre N = 406

Fall 2005 Pre N = 360





Kent State Pre

Kent State Post

Entropy of system + surroundings

00000000

00000000

00000000

00000000

Fall 2004 Pre N = 406

Fall 2005 Pre N = 360





Kent State Pre

Kent State Post

Entropy of surroundings

00000000

Fall 2004 Pre N = 406

Fall 2005 Pre N = 360





Kent Stat Pre

Kent State Post

0000

0000

0000

Increases

Decreases

Same

Not determinable

0000

0000

0000

0000

Spring 2005

Fall 2005

Spring 2006

Spr 2006 Kent State


0000.060.060.020.020.050.05

000


Post-instruction, No tutorial (N= 249)


0000.060.060.040.040.020.02

000


Post-instruction, No tutorial (N = 255)


SummaryDifficulties with fundamental concepts found among introductory physics students persist for many students beginning upper-level thermal physics course.Intensive study incorporating active-learning methods yields only slow progress for many students.Large variations in performance among different students persist throughout course.

detecting and addressing students’ reasoning difficulties in thermal physics david e. meltzer...

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