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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

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

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.

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

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

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)

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 )

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.

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

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

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

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).

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).

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

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.

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

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

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

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

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

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.

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

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

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

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

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.

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.

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

Results of Interviews

- Very consistent with results of written

diagnostics - Additional conceptual difficulties revealed
- Yielded additional clues to explain students

learning difficulties

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

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.

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).

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

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.

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.

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

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.

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.

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.

- 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.

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)

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.

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.

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

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)

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.

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.

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.