Student Learning in Thermodynamics: Exploring the Chemistry/Physics Connection

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 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
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
Results, Fall 1999N 186
15
Results, Fall 2000N 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 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

18
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

19
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

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
Proportion of sub-sample
Student Response

• 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 gt Q2 Fall 2000 40 of total
student sample

• ?U1 ?U2 ? Q1 gt Q2 correct . . . . . . . 10
• Q higher because pressure is higher . . . 7
• Q W (and W1 gt W2 ) . . . . . . . . . . . . . .
  . . 4
• Other explanations . . . . . . . . . . . . . . .
  . . 8
• No explanation offered . . . . . . . . . . . . .
  12
• Note Only students who answered Work question
  correctly gave correct explanation for Q1 gt
  Q2

23
Reasoning for Q1 gt Q2 Fall 2000 40 of total
student sample
Proportion of sub-sample
Student Response

• ?U1 ?U2 ? Q1 gt Q2 correct 24
• Q higher because pressure is higher 18
• Q W (and W1 gt W2 ) 9
• Other explanations 20
• No explanation offered 29
• Note Only students who answered Work question
  correctly gave correct explanation for Q1
  gt Q2

24
Reasoning for Q1 lt 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 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

26
Of the students who correctly answer that Q1 gt Q2

• Fall 2000 40 of total student
  sample
• 66 correctly state that W1 gt W2
• 28 state that W1 W2
• 7 state that W1 lt W2

27
Of the students who assert that Q1 Q2

• Fall 2000 43 of total student
  sample
• 67 correctly state that W1 gt W2
• 31 state that W1 W2
• 1 state that W1 lt W2

28
Responses, Fall 1999 (N 186)
W1 gt W2 W1 W2 W1 lt W2
Q1 gt Q2 75 28 1
Q1 Q2 39 18 0
Q1 lt Q2 21 1 3
29
Responses, Fall 2000 (N 180)
W1 gt W2 W1 W2 W1 lt W2
Q1 gt Q2 50 21 5
Q1 Q2 54 25 2
Q1 lt Q2 21 2 0
30
Responses, 1999-2000 combined (N 366)
W1 gt W2 W1 W2 W1 lt W2
Q1 gt Q2 125 49 6
Q1 Q2 93 43 2
Q1 lt Q2 42 3 3
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 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

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
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 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.

41
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.

42
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.

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 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.

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 ?G f?(products) - ?m ?G f?(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 lt 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 lt 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.

51
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.
• U Q W, Q U W, if U is the same
  and W is greater then Q is greater for Process
  1.

52
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.

53
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.