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

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Title: 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

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
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

6
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)

7
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 )

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 heat in 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 Populations Introductory 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
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).

13
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).

14
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

15
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.

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
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

18
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

19
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

20
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

21
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.

22
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

23
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

24
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

25
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

26
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.

27
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.

28
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

29
Results of Interviews
  • Very consistent with results of written
    diagnostics
  • Additional conceptual difficulties revealed
  • Yielded additional clues to explain students
    learning difficulties

30
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

31
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.

32
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).

33
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

34
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.

35
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.

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 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

37
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.

38
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.

39
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.

40
  • 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.

41
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)

42
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.

43
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.

44
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

45
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)

46
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.

47
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.

48
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.
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