Teaching Thermodynamics: How do Mismatches between Chemistry and Physics Affect Student Learning?

1
Teaching Thermodynamics How do Mismatches
between Chemistry and Physics Affect Student
Learning?

• David E. Meltzer
• Department of Physics and Astronomy
• Iowa State University
• Ames, Iowa
• Supported in part by National Science Foundation
  grant DUE 9981140

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

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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.

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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

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Students Evolving Concepts of Thermodynamics

• Most students study thermodynamics in chemistry
  courses before they see it in physics
• at Iowa State ? 90 of engineering students
• Ideas acquired in chemistry may impact learning
  in physics
• Certain specific misconceptions are widespread
  among chemistry students

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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)

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Conceptual Minefields Created in Chemistry

• The state function enthalpy H comes to be
  identified in students minds with heat in
  general, which is not a state function.
• H E PV ?H heat absorbed in
  constant-pressure process
• Contributions to ?E due to work usually
  neglected gas phase reactions de-emphasized
• The distinction between H and internal energy E
  is explicitly downplayed (due to small
  proportional difference)
• Sign convention different from that most often
  used in physics ?E Q W (vs. ?E Q - W )

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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 heat in general, which is not a
  state function.

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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

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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

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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

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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.
• Only 47 of students recognized that change in
  temperature must be the same for both processes
  (since initial and final states are identical).

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Detailed Analysis of Sub-sample (N 325)

• 11 gave correct or partially correct answer to
  work question based on first law
  of thermodynamics.
• (10 had correct answer with incorrect
  explanation)
• 16 stated (about half because
  initial and final states are same).
• 62 stated (almost half because
  internal energy is greater).

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Physics Diagnostic

• Given in second semester of calculus-based
  introductory course.
• Traditional course thermal physics comprised
  ? 20 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
• Spring 2001 practice quiz during last
  recitation N 279

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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.

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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

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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 gt Q2 8
• Q1 Q2 5
• Q1 lt Q2 5
• No response/no explanation . . . . . . . . . . .
  36
• Note Only students who answered Work question
  correctly gave correct explanation for Q1 gt
  Q2

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Of the students who correctly answer that W1 gt W2

• Fall 2000 70 of total student
  sample
• 38 correctly state that Q1 gt Q2
• 41 state that Q1 Q2
• 16 state that Q1 lt Q2

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Of the students who assert that W1 W2

• Fall 2000 26 of total student
  sample
• 43 correctly state that Q1 gt Q2
• 51 state that Q1 Q2
• 4 state that Q1 lt Q2

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Relation Between Answers on Work and Heat
Questions

• Probability of answering Q1 gt 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

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Conceptual Difficulties with Work

• Difficulty interpreting work as area under the
  curve on a p-V diagram
• Only ? 50 able to give correct explanation for
  W1 gt W2
• Belief that work done is independent of process
• About 15-25 are under impression that work is
  (or behaves as) a state function.

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Conceptual Difficulties with Heat

• Belief that heat absorbed is independent of
  process
• About 20-25 of all students explicitly state
  belief that heat is path independent
• Association of greater heat absorption with
  higher pressure (independent of complete process)
• Use of compensation argument, i.e., more work
  implies less heat and vice versa.
• Some students use opposite sign convention, ?E
  Q W
• Others use correct sign convention, but make
  mathematical sign error

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Difficulty with First Law of Thermodynamics

• Only about 15 of all 645 students were able to
  give correct answer with correct (or partially
  correct) explanation based on first law of
  thermodynamics
• very little variation semester to semester
• Proportion of correct answers virtually identical
  to that found in chemistry course

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Patterns Underlying Responses

• Of students who answer W1 W2, about 50
  incorrectly assert Q1 Q2
• Of students who correctly answer Work question
  (W1 gt W2), about 35 also assert Q1 Q2

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Justifications Given by Students Who Incorrectly
Assert Q1 Q2

• Students who answered Work question correctly
  usually claim heat is independent of path
• Students who answered Work question incorrectly
  usually do not claim heat is independent of path

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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.

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Conjectures Regarding Dynamics of Student
Reasoning

• Belief that heat is process-independent may not
  be strongly affected by realization that work is
  not process-independent.
• Understanding process-dependence of work may
  strengthen mistaken belief that heat is
  independent of process.

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Interviews with Physics Students

• 32 student volunteers from class of 424
• Grades earned by interview group much higher than
  class average
• Students prompted to explain reasoning as they
  worked through question sequence
• Interviews recorded on audiotape, average length
  around 1 hr

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Results of Interviews

• Very consistent with results of written
  diagnostics
• Additional conceptual difficulties revealed
• Yielded additional clues to explain students
  learning difficulties

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New Findings from Interviews

• Many students clearly unaware that macroscopic
  work can alter systems internal energy
• Inability to distinguish work and heat is very
  common
• Most students unable to recognize heat transfer
  in isothermal process
• Strong belief that Qnet and Wnet in cyclic
  processes are equal to zero

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Summary of Results on First Law

• No more than ??15 of students are able to make
  effective use of first law of thermodynamics
  after introductory chemistry or introductory
  physics course.
• Although similar errors regarding thermodynamics
  appear in thinking of both chemistry and physics
  students, possible linking of incorrect thinking
  needs further study.

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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).

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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 lt 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

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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.

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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.

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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 lt 0 as
  meaning G is decreasing
• The expression ?G is frequently confused with
  G
• ?G lt 0 is interpreted as G is negative,
  therefore, conclusion is that G must be negative
  for a spontaneous process

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Examples from Interviews

• Q Tell me again the relationship between G and
  spontaneous?
• Student 7 I guess I dont 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 dont know because I dont remember
  the relationship.

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Student Conception If the process is
spontaneous, G must be negative.

• Student 1 If its spontaneous, G would be
  negative . . . But if it wasnt going to happen
  spontaneously, G would be positive. At
  equilibrium, G would be zero . . . if G doesnt
  become negative, then its 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 its still
  going to be a negative number as long as its
  increasing until it gets to zero.

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Students confusion apparently conflicting
criteria for spontaneity

• ?GT,P lt 0 criterion, and equation ?G ?H - T?S,
  refer only to properties of the system
• ?Suniverse gt 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.

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• 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 its spontaneous.
• Student 6 I dont remember if both the system
  and surroundings have to be going generally up .
  . . I dont know what effect the surroundings
  have on it.

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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 ?G f?(products) - ?m ?G f?(reactants)

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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 lt 0 for a spontaneous process
  only holds for constant-pressure,
  constant-temperature processes.

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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 lt 0 implies
  that entropy of the system or entropy of the
  universe will increase.

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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

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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)

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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.

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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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Summary

• In our sample, most introductory students in both
  chemistry and physics courses had inadequate
  understanding of fundamental thermodynamic
  concepts.
• Curriculum development will probably need to
  target very elementary concepts in order to be
  effective.
• Interaction between chemistry and physics
  instruction on development of understanding of
  thermodynamics merits additional study.