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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 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
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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