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Student Learning in Thermodynamics: Exploring the Chemistry/Physics Connection

Student Learning in Thermodynamics: Exploring the Chemistry/Physics Connection. David E. Meltzer Department of Physics and Astronomy Iowa State University Ames, Iowa Supported in part by National Science Foundation grant DUE #9981140. Collaborator Thomas J. Greenbowe

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Student Learning in Thermodynamics: Exploring the Chemistry/Physics Connection

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  1. Student Learning in Thermodynamics: Exploring the Chemistry/Physics Connection David E. Meltzer Department of Physics and Astronomy Iowa State University Ames, Iowa Supported in part by National Science Foundation grant DUE #9981140

  2. Collaborator Thomas J. Greenbowe Department of Chemistry Iowa State University

  3. Our Goal: Investigate learning difficulties in thermodynamics in both chemistry and physics courses • First focus on students’ initial exposure to thermodynamics (i.e., in chemistry courses), then follow up with their next exposure (in physics courses). • Investigate learning of same or similar topics in two different contexts (often using different forms of representation). • Devise methods to directly address these learning difficulties. • Test materials with students in both courses; use insights gained in one field to inform instruction in the other.

  4. Outline 1. The physics/chemistry connection 2. First-semester chemistry: • state functions • heat, work, first law of thermodynamics 3. Second-semester physics: • heat, work, first law of thermodynamics • cyclic process 4. Second-semester chemistry: • second law of thermodynamics • Gibbs free energy

  5. Initial Hurdle:Different approaches to thermodynamics in physics and chemistry • For physicists: • Primary (?) unifying concept is transformation of internal energy U of a system through heat absorbed and work done; • Second Law analysis focuses on entropy concept, and analysis of cyclical processes. • For chemists: • Primary (?) unifying concept is enthalpy H [H = U + PV] (H = heat absorbed in constant-pressure process) • Second law analysis focuses on free energy (e.g., Gibbs free energy G = H – TS)

  6. Our Goal: Investigate learning difficulties in thermodynamics in both chemistry and physics courses • First focus on students’ initial exposure to thermodynamics (i.e., in chemistry courses), then follow up with their next exposure (in physics courses). • Investigate learning of same or similar topics in two different contexts.

  7. Initial Hurdle:Different approaches to thermodynamics in physics and chemistry • For physicists: • Primary (?) unifying concept is transformation of internal energy U of a system through heat absorbed and work done; • For chemists: • Primary (?) unifying concept is enthalpy H [H = U + PV] (H = heat absorbed in constant-pressure process)

  8. How might this affect physics instruction? • For many physics students, initial ideas about thermodynamics are formed during chemistry courses. • In chemistry courses, a particular state function (enthalpy) comes to be identified -- in students’ minds -- with heatin general, which is not a state function.

  9. Initial Objectives: Students’ understanding of “state functions” and First Law of Thermodynamics Diagnostic Strategy: Examine two different processes leading from state “A” to state “B”:

  10. Sample PopulationsIntroductory courses for science majors • First-semester Chemistry • Fall 1999: N = 426 • Fall 2000: N = 532 • Second-semester Physics • Fall 1999: N = 186 • Fall 2000: N = 188 • Second-semester Chemistry • Spring 2000: N = 47 • Spring 2000, Interview subjects: N = 8

  11. Results of Chemistry Diagnostic: Is the net change in [(a) temperature T; (b) internal energy E] of the system during Process #1 greater than, less than, or equal to that for Process #2? (Answer: Equal to) [Second version results in brackets] T during Process #1 is: greater than: …….61% [48%] less than:…………..3% [3%] T for Process #2. equal to:…………..34% [47%] E during Process #1 is: greater than: …….51% [30%] less than:…………..2% [2%] E for Process #2. equal to:…………..43% [66%] Students answering correctly that bothT and E are equal: 20% [33%]

  12. Physics Diagnostic • Given in second semester of calculus-based introductory course. • Traditional course; thermal physics comprised 18% of course coverage. • Diagnostic administered in last week of course: • Fall 1999: practice quiz during last recitation; N = 186 • Fall 2000: practice quiz during final lecture; N = 188

  13. Samples of Students’ Answers(All considered correct) “U = Q – W. For the same U, the system with more work done must have more Q input so process #1 is greater.” “Q is greater for process 1 since Q = U + W and W is greater for process 1.” “Q is greater for process one because it does more work, the energy to do this work comes from the Qin.” “U = Q – W, Q = U + W, if U is the same and W is greater then Q is greater for Process #1.”

  14. W1 < W2 2% W1 = W2 25% W1 > W2 73% Q1=Q2 21% Q1>Q2 40% Q1<Q2 11% ? 0% Q1>Q2 15% Q1<Q2 2% Q1=Q2 10% [incorrect] 26% U = Q-W 14% Results, Fall 1999[N = 186]

  15. W1 < W2 4% W1 = W2 26% W1 > W2 70% Q1=Q2 29% Q1>Q2 27% Q1<Q2 11% ? 4% Q1>Q2 11% Q1>Q2 3% Q1=Q2 13% [incorrect] 17% U = Q-W 10% Results, Fall 2000[N = 188]

  16. Students’ Reasoning on Work Question [Fall 2000: N = 188] • Correct or partially correct . . . . . . . . . . . . 56% • Incorrect or missing explanation . . . . . . . 14% • Work is independent of path . . . . . . . . . . 26% (majority explicitly assert path independence) • Other responses . . . . . . . . . . . . . . . . . . . . 4%

  17. Of the students who correctly answer that W1 > W2 : [Fall 2000: 70% of total student sample] • 38% correctly state that Q1 > Q2 • 41% state that Q1 = Q2 • 16% state that Q1 < Q2

  18. Of the students who assert that W1 = W2 : [Fall 2000: 26% of total student sample] • 43% correctly state that Q1 > Q2 • 51% state that Q1 = Q2 • 4% state that Q1 < Q2

  19. Relation Between Answers on Work and Heat Questions • Probability of answering Q1 > Q2 is almost independent of answer to Work question. [However, correct explanations are only given by those who answer Work question correctly.] • Probability of claiming Q1 = Q2 is slightly greater for those who answer W1 = W2. • Probability of justifying Q1 = Q2 by asserting that “Q is path-independent” is higher for those who answer Work question correctly. • Correct on Work question and state Q1 = Q2 : 61% claim “Q is path-independent” • Incorrect on Work question and state Q1 = Q2 : 37% claim “Q is path-independent”

  20. Reasoning for Q1 = Q2[Fall 2000: 43% of total student sample] • Q is independent of path . . . . . . . . . . 23% • “same start and end point” • “same end point” • “path independent” • Other explanations . . . . . . . . . . . . . . . . 5% • No explanation offered . . . . . . . . . . . . 15% Note: Students who answered Work question correctly were more likely to assert path-independence of Q

  21. Reasoning for Q1 = Q2[Fall 2000: 43% of total student sample] Student Response Proportion of sub-sample • Q is independent of path 53% • “same start and end point” • “same end point” • “path independent” • Other explanations 12% • No explanation offered 35% Note: Students who answered Work question correctly were more likely to assert path-independence of Q

  22. Reasoning for Q1 > Q2[Fall 2000: 40% of total student sample] • U1 = U2  Q1 > Q2[correct] . . . . . . . 10% • Q higher because pressure is higher . . . 7% • Q = W (and W1 > W2 ) . . . . . . . . . . . . . . . . 4% • Other explanations . . . . . . . . . . . . . . . . . 8% • No explanation offered . . . . . . . . . . . . . 12% Note: Only students who answered Work question correctly gave correct explanation for Q1 > Q2

  23. Reasoning for Q1 > Q2[Fall 2000: 40% of total student sample] Student Response Proportion of sub-sample • U1 = U2  Q1 > Q2[correct] 24% • Q higher because pressure is higher 18% • Q = W (and W1 > W2 ) 9% • Other explanations 20% • No explanation offered 29% Note: Only students who answered Work question correctly gave correct explanation for Q1 > Q2

  24. Reasoning for Q1 < Q2[Fall 2000: 12% of total student sample] • Essentially correct, but sign error. . . . . 4% • Other explanations . . . . . . . . . . . . . . . . 5% • No explanation offered . . . . . . . . . . . . . 3%

  25. Students’ Reasoning on Heat Question [Fall 2000: N = 188] • Correct or partially correct . . . . . . . . . . . . 15% • Q is independent of path . . . . . . . . . . . . . 23% • Q is higher because pressure is higher . . . 7% • Other explanations . . . . . . . . . . . . . . . . . . 18% Q1 > Q2 : 8% Q1 = Q2 : 5% Q1 < Q2 : 5% • No response/no explanation . . . . . . . . . . . 36% Note: Only students who answered Work question correctly gave correct explanation for Q1 > Q2

  26. Of the students who correctly answer that Q1 > Q2 : [Fall 2000: 40% of total student sample] • 66% correctly state that W1 > W2 • 28% state that W1 = W2 • 7% state that W1 < W2

  27. Of the students who assert that Q1 = Q2 : [Fall 2000: 43% of total student sample] • 67% correctly state that W1 > W2 • 31% state that W1 = W2 • 1% state that W1 < W2

  28. Responses, Fall 1999 (N = 186)

  29. Responses, Fall 2000 (N = 180)

  30. Responses, 1999-2000 combined (N = 366)

  31. Conclusions from Physics Diagnostic •  25% believe that Work is independent of process. • Of those who realize that Work is process-dependent, 30-40% appear to believe that Heat is independent of process. •  25% of all students explicitly state belief that Heat is independent of process. • There is only a partial overlap between those who believe that Q is process-independent, and those who believe that W is process-independent. •  15% of students appear to have adequate understanding of First Law of Thermodynamics.

  32. Conjectures from Physics Diagnostic • Belief that Heat is process-independent may not be strongly affected by realization that Work is not process-independent. • Understanding the process-dependence of Work may strengthen belief that Heat is independent of process.

  33. Results from Chemistry Diagnostic [Given in general chemistry course for science majors, Fall 2000, N =532] • 65% of students recognized that change in internal energy was same for both processes. • 11% of students were able to use First Law of Thermodynamics to correctly compare Work done in different processes.

  34. Summary Fewer than one in six students in both chemistry and physics introductory courses demonstrated clear understanding of First Law of Thermodynamics.

  35. Student Understanding of Entropy and the Second Law of Thermodynamics in the Context of Chemistry • Second-semester course; covered standard topics in chemical thermodynamics: • Entropy and disorder • Second Law of Thermodynamics: Suniverse [= Ssystem+Ssurroundings] 0 • Gibbs free energy: G = H - TS • Spontaneous processes: GT,P < 0 • Standard free-energy changes • Written diagnostic administered to 47 students (11% of class) last day of class. • In-depth interviews with eight student volunteers

  36. Difficulties Interpreting Meaning of “G” • Students seem unaware or unclear about the definition of G (i.e., G = Gfinal – Ginitial) • Students often do not interpret “G < 0” as meaning “G is decreasing” • The expression “G” is frequently confused with “G” • “G < 0” is interpreted as “G is negative,” therefore, conclusion is that “G must be negative for a spontaneous process”

  37. Previous Investigations of Learning in Chemical Thermodynamics(upper-level courses) • A. C. Banerjee, “Teaching chemical equilibrium and thermodynamics in undergraduate general chemistry classes,” J. Chem. Ed. 72, 879-881 (1995). • M. F. Granville, “Student misconceptions in thermodynamics,” J. Chem. Ed. 62, 847-848 (1985). • P. L. Thomas, and R. W. Schwenz, “College physical chemistry students’ conceptions of equilibrium and fundamental thermodynamics,” J. Res. Sci. Teach. 35, 1151-1160 (1998).

  38. Student Interviews • Eight student volunteers were interviewed within three days of taking their final exam. • The average course grade of the eight students was above the class-average grade. • Interviews lasted 40-60 minutes, and were videotaped. • Each interview centered on students “talking through” a six-part problem sheet. • Responses of the eight students were generally quite consistent with each other.

  39. Students’ Guiding Conceptions(what they “know”) • H is equal to the heat absorbed by the system. • “Entropy” is synonymous with “disorder” • Spontaneous processes are characterized by increasing entropy • G = H - TS • G must be negative for a spontaneous process.

  40. Examples from Interviews Q: Tell me again the relationship between G and “spontaneous”? Student #7:I guess I don’t know, necessarily, about G; I know G. Q: Tell me what you remember about G. Student #7: I remember calculating it, and then if it was negative then it was spontaneous, if it was positive, being nonspontaneous. Q: What does that tell you about G itself. Suppose G is negative, what would be happening to G itself? Student #7:I don’t know because I don’t remember the relationship.

  41. Student Conception: If the process is spontaneous, G must be negative. Student #1:If it’s spontaneous, G would be negative . . . But if it wasn’t going to happen spontaneously, G would be positive. At equilibrium, G would be zero . . . if G doesn’t become negative, then it’s not spontaneous. As long as it stays in positive values, it can decrease, but [still be spontaneous]. Student #4: Say that the Gibbs free energy for the system before this process happened . . . was a negative number . . . [then] it can still increase and be spontaneous because it’s still going to be a negative number as long as it’s increasing until it gets to zero.

  42. Students’ confusion: apparently conflicting criteria for spontaneity • GT,P < 0 criterion, and equation G = H - TS, refer only to properties of thesystem; • Suniverse > 0 refers to properties outside the system; Consequently, students are continually confused as to what is the “system” and what is the “universe,” and which one determines the criteria for spontaneity.

  43. Student #2: I assume that S [in the equation G = H - TS] is the total entropy of the system and the surroundings. Student #3: “ . . . I was just trying to recall whether or not the surroundings have an effect on whether or not it’s spontaneous.” Student #6: “I don’t remember if both the system and surroundings have to be going generally up . . . I don’t know what effect the surroundings have on it.”

  44. Difficulties related to mathematical representations • There is confusion regarding the fact that in the equation G = H - TS, all of the variables refer to properties of the system (and not the surroundings). • Students seem unaware or unclear about the definition of G (i.e., G = Gfinal – Ginitial) • There is great confusion introduced by the definition of standard free-energy change of a process: G  = n Gf(products) - m Gf(reactants)

  45. Lack of awareness of constraints and conditions • There is little recognition thatH equals heat absorbed only for constant-pressure processes • There appears to be no awareness that the requirement that G < 0 for a spontaneous process only holds for constant-pressure, constant-temperature processes.

  46. Overall Conceptual Gaps • There is no recognition of the fact that change in G of the system is directly related to change in S of the universe (= system + surroundings) • There is uncertainty as to whether a spontaneous process requires entropy of the system or entropy of the universe to increase. • There is uncertainty as to whether G < 0 implies that entropy of the system or entropy of the universe will increase.

  47. Curriculum Development and Testing: An Iterative Process • Initial draft of materials subject to review and discussion by both physics and chemistry education research groups; • Revised draft tested in lab or recitation section; • New draft prepared based on problems identified during initial test; • Additional rounds of testing in lab/recitation sections; further revisions; • Analysis of student exam performance (“treated” vs. “untreated” groups);  Entire cycle repeats

  48. Learning Difficulty: Weak Understanding of “State Function” Concept Instructional Strategy: Examine two different processes leading from state “A” to state “B”: • What is the same about the two processes? • What is different about the two processes? • Elicit common misconception that different heat absorption must lead to different final temperatures (i.e., ignoring work done) • Guide students to identify temperature as a prototypical state function • Strengthen conceptual distinction between changes in state functions (same for any processes connecting states A and B), and process-dependent quantities (e.g., heat and work)

  49. Learning Difficulty: Failure to recognize that entropy increase of “universe” (not system) determines whether process occurs spontaneously Instructional Strategy: Present several different processes with varying signs of DSsystem and DSsurroundings (Present DSsurroundings information both explicitly, and in form of DG or DH data) Ask students to decide: • Which processes lead to increasing disorder of system? • Which processes occur spontaneously? Etc.

  50. Learning Difficulty: Not distinguishing clearly between heat and temperature Instructional Strategy I: Confront students with objects that have equal temperature changes but different values of energy loss. Instructional Strategy II: Guide students through analysis of equilibration in systems with objects of same initial temperature but different heat capacities.

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