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0b`bzr___PPT9Tz@(NStudent Learning in Thermodynamics: Exploring the Chemistry/Physics Connection ON((David E. Meltzer
Department of Physics and Astronomy
Iowa State University
Ames, Iowa
Supported in part by National Science Foundation grant DUE #99811404VF ( EF ++
V Collaborator
Thomas J. Greenbowe
Department of Chemistry
Iowa State University
j!`((E!(!
%%01,,cOur Goal: Investigate learning difficulties in thermodynamics in both chemistry and physics courses d "["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.
\pZ(ZSNOutline1. The physics/chemistry connection
2. Firstsemester chemistry:
state functions
heat, work, first law of thermodynamics
3. Secondsemester physics:
heat, work, first law of thermodynamics
cyclic process
4. Secondsemester chemistry:
second law of thermodynamics
Gibbs free energy$!PZ<!Z8 Z!0Z<7 Z!0Z</ Z$76/..PInitial Hurdle: Different approaches to thermodynamics in physics and chemistryQ@"J
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]
(DH = heat absorbed in constantpressure process)
Second law analysis focuses on free energy (e.g., Gibbs free energy G = H TS)
Z 0ZuZT0Z2Z 0Z8Z3ZP0Z2Z2P &cOur Goal: Investigate learning difficulties in thermodynamics in both chemistry and physics courses d $[$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.
N`(Sk%%PInitial Hurdle: Different approaches to thermodynamics in physics and chemistryQ@"&
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]
(DH = heat absorbed in constantpressure process)
<Z 0ZuZZ 0Z,ZSZ21 * *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.lP

!!Initial Objectives: Students understanding of state functions and First Law of Thermodynamics6d!!!"!O Diagnostic Strategy: Examine two different processes leading from state A to state B :
[!" !
/11:Sample PopulationsIntroductory courses for science majors;(Firstsemester Chemistry
Fall 1999: N = 426
Fall 2000: N = 532
Secondsemester Physics
Fall 1999: N = 186
Fall 2000: N = 188
Secondsemester Chemistry
Spring 2000: N = 47
Spring 2000, Interview subjects: N = 8
,Z&Z0ZF&Z0ZF;ZZ
$22!Results of Chemistry Diagnostic: "!""f Is the net change in [(a) temperature DT; (b) internal energy DE] of the system during Process #1 greater than, less than, or equal to that for Process #2? (Answer: Equal to)
[Second version results in brackets]
DT during Process #1 is:
greater than: & & .61% [48%]
less than:& & & & ..3% [3%] DT for Process #2.
equal to:& & & & ..34% [47%]
DE during Process #1 is:
greater than: & & .51% [30%]
less than:& & & & ..2% [2%] DE for Process #2.
equal to:& & & & ..43% [66%]
Students answering correctly that both DT and DE are equal: 20% [33%]!n!0Z<!0ZN!Z!0ZF!0ZN!ZG!0}Z&< "1(1("Physics Diagnostic+Given in second semester of calculusbased introductory course.
Traditional course; thermal physics comprised 18% of course coverage.
Diagnostic administered in last week of course:
Fall 1999: practice quiz during last recitation; N = 186
Fall 2000: practice quiz during final lecture; N = 188
@<0t023&&jSamples of Students Answers(All considered correct)6, DU = Q W. For the same DU, the system with more work done must have more Q input so process #1 is greater.
Q is greater for process 1 since Q = U + W and W is greater for process 1.
Q is greater for process one because it does more work, the energy to do this work comes from the Qin.
U = Q W, Q = U + W, if U is the same and W is greater then Q is greater for Process #1.
/!PZZa!PZ2!PZZ!PZ2PZ2Z&h)kResults, Fall 1999[N = 186] Results, Fall 2000[N = 188]
tStudents Reasoning on Work Question [Fall 2000: N = 188] ;&$Correct or partially correct . . . . . . . . . . . . 56%
Incorrect or missing explanation . . . . . . . 14%
Work is independent of path . . . . . . . . . . 26%
(majority explicitly assert path independence)
Other responses . . . . . . . . . . . . . . . . . . . . 4%
mPZ(4PZ
/!pZ(;PZ(ZO4/;
5Of the students who correctly answer that W1 > W2 :L6+ [Fall 2000: 70% of total student sample]
38% correctly state that Q1 > Q2
41% state that Q1 = Q2
16% state that Q1 < Q2
6!@("`UA@A@(@(5,Of the students who assert that W1 = W2 :L" [Fall 2000: 26% of total student sample]
43% correctly state that Q1 > Q2
51% state that Q1 = Q2
4% state that Q1 < Q2 5!@("`<A@A@(44Relation Between Answers on Work and Heat QuestionsZProbability of answering Q1 > 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 pathindependent is higher for those who answer Work question correctly.
Correct on Work question and state Q1 = Q2 : 61% claim Q is pathindependent
Incorrect on Work question and state Q1 = Q2 : 37% claim Q is pathindependent SZ]!0ZRpZPPZT0Z2TZ
3\
/$
Q
'@Reasoning for Q1 = Q2 [Fall 2000: 43% of total student sample]BA*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 pathindependence of Q
1Z?Zq0Z7sZ1 ?5 3 m @Reasoning for Q1 = Q2 [Fall 2000: 43% of total student sample]JA*
**
** 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 pathindependence of Q
!Z?ZA0Z7ZjZZ ?Ai?Reasoning for Q1 > Q2 [Fall 2000: 40% of total student sample]B@)DU1 = DU2 Q1 > Q2 [correct] . . . . . . . 10%
Q higher because pressure is higher . . . 7%
Q = W (and W1 > W2 ) . . . . . . . . . . . . . . . . 4%
Other explanations . . . . . . . . . . . . . . . . . 8%
No explanation offered . . . . . . . . . . . . . 12%
Note: Only students who answered Work question correctly gave correct explanation for Q1 > Q2
PZ(5ZlZ
3
\5X
@Reasoning for Q1 > Q2 [Fall 2000: 40% of total student sample]JA*
**
**>DU1 = DU2 Q1 > Q2 [correct] 24%
Q higher because pressure is higher 18%
Q = W (and W1 > W2 ) 9%
Other explanations 20%
No explanation offered 29%
Note: Only students who answered Work question correctly gave correct explanation for Q1 > Q2
%pZ#(PZ(i0Z(Z
+
CX
j@Reasoning for Q1 < Q2 [Fall 2000: 12% of total student sample]BA*Essentially correct, but sign error. . . . . 4%
Other explanations . . . . . . . . . . . . . . . . 5%
No explanation offered . . . . . . . . . . . . . 3%
b0r 7 05 4
tStudents 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 > Q2 : 8%
Q1 = Q2 : 5%
Q1 < Q2 : 5%
No response/no explanation . . . . . . . . . . . 36%
Note: Only students who answered Work question correctly gave correct explanation for Q1 > Q2
PZ(;PZ"!0Z!pZ(5ZlZS0;
5X
5Of the students who correctly answer that Q1 > Q2 :L6+ [Fall 2000: 40% of total student sample]
66% correctly state that W1 > W2
28% state that W1 = W2
7% state that W1 < W2 5!@("`<A@A@(4,Of the students who assert that Q1 = Q2 :L" [Fall 2000: 43% of total student sample]
67% correctly state that W1 > W2
31% state that W1 = W2
1% state that W1 < W2 5!@("`<A@A@(4Responses, Fall 1999 (N = 186)2Responses, Fall 2000 (N = 180)2'Responses, 19992000 combined (N = 366)2(
#Conclusions from Physics Diagnostic 25% believe that Work is independent of process.
Of those who realize that Work is processdependent, 3040% 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 processindependent, and those who believe that W is processindependent.
15% of students appear to have adequate understanding of First Law of Thermodynamics.ZPZ<XZ"#Conjectures from Physics DiagnosticBelief that Heat is processindependent may not be strongly affected by realization that Work is not processindependent.
Understanding the processdependence of Work may strengthen belief that Heat is independent of process. X{@Pj@<af##!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.PL!XZZWPZstZJ$$Summary Fewer than one in six students in both chemistry and physics introductory courses demonstrated clear understanding of First Law of Thermodynamics."!//aStudent Understanding of Entropy and the Second Law of Thermodynamics in the Context of Chemistrybb"DSecondsemester course; covered standard topics in chemical thermodynamics:
Entropy and disorder
Second Law of Thermodynamics: DSuniverse [= DSsystem+ DSsurroundings] 0
Gibbs free energy: G = H  TS
Spontaneous processes: DGT,P < 0
Standard freeenergy changes
Written diagnostic administered to 47 students (11% of class) last day of class.
Indepth interviews with eight student volunteers
M0Z<Z?Z0Z<ZMI
>
00RDifficulties Interpreting Meaning of DG $*&Students seem unaware or unclear about the definition of DG (i.e., DG = Gfinal Ginitial)
Students often do not interpret DG < 0 as meaning G is decreasing
The expression DG is frequently confused with G
DG < 0 is interpreted as G is negative, therefore, conclusion is that G must be negative for a spontaneous process ,PZU4ZyZ94J,G 44UPrevious Investigations of Learning in Chemical Thermodynamics(upperlevel courses)0V?@A. C. Banerjee, Teaching chemical equilibrium and thermodynamics in undergraduate general chemistry classes, J. Chem. Ed. 72, 879881 (1995).
M. F. Granville, Student misconceptions in thermodynamics, J. Chem. Ed. 62, 847848 (1985).
P. L. Thomas, and R. W. Schwenz, College physical chemistry students conceptions of equilibrium and fundamental thermodynamics, J. Res. Sci. Teach. 35, 11511160 (1998). bZ]>o 55Student InterviewsEight student volunteers were interviewed within three days of taking their final exam.
The average course grade of the eight students was above the classaverage grade.
Interviews lasted 4060 minutes, and were videotaped.
Each interview centered on students talking through a sixpart problem sheet.
Responses of the eight students were generally quite consistent with each other.PZ266`Students Guiding Conceptions(what they know )DH is equal to the heat absorbed by the system.
Entropy is synonymous with disorder
Spontaneous processes are characterized by increasing entropy
DG = DH  TDS
DG must be negative for a spontaneous process.
0ZAZ!,!g!!! !!!77Examples from InterviewsQ: Tell me again the relationship between G and spontaneous ?
Student #7: I guess I don t know, necessarily, about G; I know DG.
Q: Tell me what you remember about DG.
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 DG is negative, what would be happening to G itself?
Student #7: I don t know because I don t remember the relationship. b!0Z<<""")"" """"!""
""{""1"4"""9"88FStudent Conception: If the process is spontaneous, G must be negative.@G3"" " ""Student #1: If it s spontaneous, G would be negative . . . But if it wasn t going to happen spontaneously, G would be positive. At equilibrium, G would be zero . . . if G doesn t become negative, then it s 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 it s still going to be a negative number as long as it s increasing until it gets to zero.
C!Z""I""$"""""
"""99Students confusion: apparently conflicting criteria for spontaneityFE#fDGT,P < 0 criterion, and equation DG = DH  TDS, refer only to properties of the system;
DSuniverse > 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.
J0ZA!0ZP0ZAZ
!
)k
*Z ::
6Student #2: I assume that DS [in the equation DG = DH  TDS] 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 it s spontaneous.
Student #6: I don t remember if both the system and surroundings have to be going generally up . . . I don t know what effect the surroundings have on it.
!ZZ
<y;;4Difficulties related to mathematical representations&There is confusion regarding the fact that in the equation DG = DH  TDS, all of the variables refer to properties of the system (and not the surroundings).
Students seem unaware or unclear about the definition of DG (i.e., DG = Gfinal Ginitial)
There is great confusion introduced by the definition of standard freeenergy change of a process:
DG = n DG f(products)  m DG f(reactants)
^Z4ZZ;
2V<+
,<</Lack of awareness of constraints and conditionsThere is little recognition that DH equals heat absorbed only for constantpressure processes
There appears to be no awareness that the requirement that DG < 0 for a spontaneous process only holds for constantpressure, constanttemperature processes. ^.(==Overall Conceptual GapsThere 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 DG < 0 implies that entropy of the system or entropy of the universe will increase.
8pZ7w0Z7Z3! S 1 ''9Curriculum 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
RpZ!pZZ((Learning Difficulty: Weak Understanding of State Function Concept D"0"\ 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 processdependent quantities (e.g., heat and work)
@^!PZ(UZZ0" Z0" Z2Z" Z$
/!
U8)).Learning Difficulty: Failure to recognize that entropy increase of universe (not system) determines whether process occurs spontaneously6"@=h 'BInstructional 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.
!Z\ 0Z20Z2ZZZR
,
a_**MLearning Difficulty: Not distinguishing clearly between heat and temperature N"9"&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.
v'!ZjK
jSamples of Students Answers(All considered correct)6T DU = Q W. For the same DU, 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.
!@Kd!@2@2#""jSamples of Students Answers(All considered correct)6d DU = Q W. For the same DU, 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.
!PZsm!PZ2PZ2Z&)33Summary}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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s* W2 : Of the students who assert that W1 = W2 : 5Relation Between Answers on Work and Heat Questions AReasoning for Q1 = Q2 [Fall 2000: 43% of total student sample]AReasoning for Q1 = Q2 [Fall 2000: 43% of total student sample]@Reasoning for Q1 > Q2 [Fall 2000: 40% of total student sample]AReasoning for Q1 > Q2 [Fall 2000: 40% of total student sample]AReasoning for Q1 < Q2 [Fall 2000: 12% of total student sample]=Students’ Reasoning on Heat Question [Fall 2000: N = 188]6Of the students who correctly answer that Q1 > Q2 : Of the students who assert that Q1 = Q2 : Responses, Fall 1999 (N = 186)Responses, Fall 2000 (N = 180)(Responses, 19992000 combined (N = 366)$Conclusions from Physics Diagnostic$Conjectures from Physics Diagnostic"Results from Chemistry DiagnosticSummarybStudent Understanding of Entropy and the Second Law of Thermodynamics in the Context of Chemistry0Difficulties Interpreting Meaning of “G”VPrevious Investigations of Learning in Chemical Thermodynamics (upperlevel courses) Student Interviews7Students’ Guiding Conceptions (what they “know”)Examples from InterviewsGStudent Conception: If the process is spontaneous, G must be negative.HStudents’ confusion: apparently conflicting criteria for spontaneityPowerPoint Presentation5Difficulties related to mathematical representations0Lack of awareness of constraints and conditionsOverall Conceptual Gaps:Curriculum Development and Testing: An Iterative ProcessHLearning Difficulty: Weak Understanding of “State Function” ConceptLearning Difficulty: Failure to recognize that entropy increase of “universe” (not system) determines whether process occurs spontaneously NLearning Difficulty: Not distinguishing clearly between heat and temperature 8Samples of Students’ Answers (All considered correct)8Samples of Students’ Answers (All consider/00DTimes New Romanlv0(
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0LXzr___PPT9Tz@(?%NStudent Learning in Thermodynamics: Exploring the Chemistry/Physics Connection ON((David E. Meltzer
Department of Physics and Astronomy
Iowa State University
Ames, Iowa
Supported in part by National Science Foundation grant DUE #99811404VF (EF++
V Collaborator
Thomas J. Greenbowe
Department of Chemistry
Iowa State University
j!`((E!(!
##01,,cOur Goal: Investigate learning difficulties in thermodynamics in both chemistry and physics courses d "["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.
\pZ(ZSNOutline1. The physics/chemistry connection
2. Firstsemester chemistry:
state functions
heat, work, first law of thermodynamics
3. Secondsemester physics:
heat, work, first law of thermodynamics
cyclic process
4. Secondsemester chemistry:
second law of thermodynamics
Gibbs free energy$!PZ<!Z8 Z!0Z<7 Z!0Z</ Z$76/..PInitial Hurdle: Different approaches to thermodynamics in physics and chemistryQ@"J
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]
(DH = heat absorbed in constantpressure process)
Second law analysis focuses on free energy (e.g., Gibbs free energy G = H TS)
Z 0ZuZT0Z2Z 0Z8Z3ZP0Z2Z2P &cOur Goal: Investigate learning difficulties in thermodynamics in both chemistry and physics courses d $[$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.
N`(Sk%%PInitial Hurd
!"#$%&'()*+,./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{}~le: Different approaches to thermodynamics in physics and chemistryQ@"&
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]
(DH = heat absorbed in constantpressure process)
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0b`bzr___PPT9Tz@(NStudent Learning in Thermodynamics: Exploring the Chemistry/Physics Connection ON((David E. Meltzer
Department of Physics and Astronomy
Iowa State University
Ames, Iowa
Supported in part by National Science Foundation grant DUE #99811404VF ( EF ++
V Collaborator
Thomas J. Greenbowe
Department of Chemistry
Iowa State University
j!`((E!(!
%%01,,cOur Goal: Investigate learning difficulties in thermodynamics in both chemistry and physics courses d "["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.
\pZ(ZSNOutline1. The physics/chemistry connection
2. Firstsemester chemistry:
state functions
heat, work, first law of thermodynamics
3. Secondsemester physics:
heat, work, first law of thermodynamics
cyclic process
4. Secondsemester chemistry:
second law of thermodynamics
Gibbs free energy$!PZ<!Z8 Z!0Z<7 Z!0Z</ Z$76/..PInitial Hurdle: Different approaches to thermodynam*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 ics in physics and chemistryQ@"J
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]
(DH = heat absorbed in constantpressure process)
Second law analysis focuses on free energy (e.g., Gibbs free energy G = H TS)
Z 0ZuZT0Z2Z 0Z8Z3ZP0Z2Z2P &cOur Goal: Investigate learning difficulties in thermodynamics in both chemistry and physics courses d $[$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.
N`(Sk%%PInitial Hurdle: Different approaches to thermodynamics in physics and chemistryQ@"&
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]
(DH = heat absorbed in constantpressure process)
<Z 0ZuZZ 0Z,ZSZ21 * *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.lP

!!Initial Objectives: Students understanding of state functions and First Law of Thermodynamics6d!!!"!O Diagnostic Strategy: Examine two different processes leading from state A to state B :
[!" !
/11:Sample PopulationsIntroductory courses for science majors;(Firstsemester Chemistry
Fall 1999: N = 426
Fall 2000: N = 532
Secondsemester Physics
Fall 1999: N = 186
Fall 2000: N = 188
Secondsemester Chemistry
Spring 2000: N = 47
Spring 2000, Interview subjects: N = 8
,Z&Z0ZF&Z0ZF;ZZ
$22!Results of Chemistry Diagnostic: "!""f Is the net change in [(a) temperature DT; (b) internal energy DE] of the system during Process #1 greater than, less than, or equal to that for Process #2? (Answer: Equal to)
[Second version results in brackets]
DT during Process #1 is:
greater than: & & .61% [48%]
less than:& & & & ..3% [3%] DT for Process #2.
equal to:& & & & ..34% [47%]
DE during Process #1 is:
greater than: & & .51% [30%]
less than:& & & & ..2% [2%] DE for Process #2.
equal to:& & & & ..43% [66%]
Students answering correctly that both DT and DE are equal: 20% [33%]!n!0Z<!0ZN!Z!0ZF!0ZN!ZG!0}Z&< "1(1("Physics Diagnostic+Given in second semester of calculusbased introductory course.
Traditional course; thermal physics comprised 18% of course coverage.
Diagnostic administered in last week of course:
Fall 1999: practice quiz during last recitation; N = 186
Fall 2000: practice quiz during final lecture; N = 188
@<0t023&&jSamples of Students Answers(All considered correct)6, DU = Q W. For the same DU, the system with more work done must have more Q input so process #1 is greater.
Q is greater for process 1 since Q = U + W and W is greater for process 1.
Q is greater for process one because it does more work, the energy to do this work comes from the Qin.
U = Q W, Q = U + W, if U is the same and W is greater then Q is greater for Process #1.
/!PZZa!PZ2!PZZ!PZ2PZ2Z&h)kResults, Fall 1999[N = 186] Results, Fall 2000[N = 188]
tStudents Reasoning on Work Question [Fall 2000: N = 188] ;&$Correct or partially correct . . . . . . . . . . . . 56%
Incorrect or missing explanation . . . . . . . 14%
Work is independent of path . . . . . . . . . . 26%
(majority explicitly assert path independence)
Other responses . . . . . . . . . . . . . . . . . . . . 4%
mPZ(4PZ
/!pZ(;PZ(ZO4/;
5Of the students who correctly answer that W1 > W2 :L6+ [Fall 2000: 70% of total student sample]
38% correctly state that Q1 > Q2
41% state that Q1 = Q2
16% state that Q1 < Q2
6!@("`UA@A@(@(5,Of the students who assert that W1 = W2 :L" [Fall 2000: 26% of total student sample]
43% correctly state that Q1 > Q2
51% state that Q1 = Q2
4% state that Q1 < Q2 5!@("`<A@A@(44Relation Between Answers on Work and Heat QuestionsZProbability of answering Q1 > 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 pathindependent is higher for those who answer Work question correctly.
Correct on Work question and state Q1 = Q2 : 61% claim Q is pathindependent
Incorrect on Work question and state Q1 = Q2 : 37% claim Q is pathindependent SZ]!0ZRpZPPZT0Z2TZ
3\
/$
Q
'@Reasoning for Q1 = Q2 [Fall 2000: 43% of total student sample]BA*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 pathindependence of Q
1Z?Zq0Z7sZ1 ?5 3 m @Reasoning for Q1 = Q2 [Fall 2000: 43% of total student sample]JA*
**
** 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 pathindependence of Q
!Z?ZA0Z7ZjZZ ?Ai?Reasoning for Q1 > Q2 [Fall 2000: 40% of total student sample]B@)DU1 = DU2 Q1 > Q2 [correct] . . . . . . . 10%
Q higher because pressure is higher . . . 7%
Q = W (and W1 > W2 ) . . . . . . . . . . . . . . . . 4%
Other explanations . . . . . . . . . . . . . . . . . 8%
No explanation offered . . . . . . . . . . . . . 12%
Note: Only students who answered Work question correctly gave correct explanation for Q1 > Q2
PZ(5ZlZ
3
\5X
@Reasoning for Q1 > Q2 [Fall 2000: 40% of total student sample]JA*
**
**>DU1 = DU2 Q1 > Q2 [correct] 24%
Q higher because pressure is higher 18%
Q = W (and W1 > W2 ) 9%
Other explanations 20%
No explanation offered 29%
Note: Only students who answered Work question correctly gave correct explanation for Q1 > Q2
%pZ#(PZ(i0Z(Z
+
CX
j@Reasoning for Q1 < Q2 [Fall 2000: 12% of total student sample]BA*Essentially correct, but sign error. . . . . 4%
Other explanations . . . . . . . . . . . . . . . . 5%
No explanation offered . . . . . . . . . . . . . 3%
b0r 7 05 4
tStudents 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 > Q2 : 8%
Q1 = Q2 : 5%
Q1 < Q2 : 5%
No response/no explanation . . . . . . . . . . . 36%
Note: Only students who answered Work question correctly gave correct explanation for Q1 > Q2
PZ(;PZ"!0Z!pZ(5ZlZS0;
5X
5Of the students who correctly answer that Q1 > Q2 :L6+ [Fall 2000: 40% of total student sample]
66% correctly state that W1 > W2
28% state that W1 = W2
7% state that W1 < W2 5!@("`<A@A@(4,Of the students who assert that Q1 = Q2 :L" [Fall 2000: 43% of total student sample]
67% correctly state that W1 > W2
31% state that W1 = W2
1% state that W1 < W2 5!@("`<A@A@(4Responses, Fall 1999 (N = 186)2Responses, Fall 2000 (N = 180)2'Responses, 19992000 combined (N = 366)2(
#Conclusions from Physics Diagnostic 25% believe that Work is independent of process.
Of those who realize that Work is processdependent, 3040% 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 processindependent, and those who believe that W is processindependent.
15% of students appear to have adequate understanding of First Law of Thermodynamics.ZPZ<XZ"#Conjectures from Physics DiagnosticBelief that Heat is processindependent may not be strongly affected by realization that Work is not processindependent.
Understanding the processdependence of Work may strengthen belief that Heat is independent of process. X{@Pj@<af##!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.PL!XZZWPZstZJ$$Summary Fewer than one in six students in both chemistry and physics introductory courses demonstrated clear understanding of First Law of Thermodynamics."!//aStudent Understanding of Entropy and the Second Law of Thermodynamics in the Context of Chemistrybb"DSecondsemester course; covered standard topics in chemical thermodynamics:
Entropy and disorder
Second Law of Thermodynamics: DSuniverse [= DSsystem+ DSsurroundings] 0
Gibbs free energy: G = H  TS
Spontaneous processes: DGT,P < 0
Standard freeenergy changes
Written diagnostic administered to 47 students (11% of class) last day of class.
Indepth interviews with eight student volunteers
M0Z<Z?Z0Z<ZMI
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00RDifficulties Interpreting Meaning of DG $*&Students seem unaware or unclear about the definition of DG (i.e., DG = Gfinal Ginitial)
Students often do not interpret DG < 0 as meaning G is decreasing
The expression DG is frequently confused with G
DG < 0 is interpreted as G is negative, therefore, conclusion is that G must be negative for a spontaneous process ,PZU4ZyZ94J,G 44UPrevious Investigations of Learning in Chemical Thermodynamics(upperlevel courses)0V?@A. C. Banerjee, Teaching chemical equilibrium and thermodynamics in undergraduate general chemistry classes, J. Chem. Ed. 72, 879881 (1995).
M. F. Granville, Student misconceptions in thermodynamics, J. Chem. Ed. 62, 847848 (1985).
P. L. Thomas, and R. W. Schwenz, College physical chemistry students conceptions of equilibrium and fundamental thermodynamics, J. Res. Sci. Teach. 35, 11511160 (1998). bZ]>o 55Student InterviewsEight student volunteers were interviewed within three days of taking their final exam.
The average course grade of the eight students was above the classaverage grade.
Interviews lasted 4060 minutes, and were videotaped.
Each interview centered on students talking through a sixpart problem sheet.
Responses of the eight students were generally quite consistent with each other.PZ266`Students Guiding Conceptions(what they know )DH is equal to the heat absorbed by the system.
Entropy is synonymous with disorder
Spontaneous processes are characterized by increasing entropy
DG = DH  TDS
DG must be negative for a spontaneous process.
0ZAZ!,!g!!! !!!77Examples from InterviewsQ: Tell me again the relationship between G and spontaneous ?
Student #7: I guess I don t know, necessarily, about G; I know DG.
Q: Tell me what you remember about DG.
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 DG is negative, what would be happening to G itself?
Student #7: I don t know because I don t remember the relationship. b!0Z<<""")"" """"!""
""{""1"4"""9"88FStudent Conception: If the process is spontaneous, G must be negative.@G3"" " ""Student #1: If it s spontaneous, G would be negative . . . But if it wasn t going to happen spontaneously, G would be positive. At equilibrium, G would be zero . . . if G doesn t become negative, then it s 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 it s still going to be a negative number as long as it s increasing until it gets to zero.
C!Z""I""$"""""
"""99Students confusion: apparently conflicting criteria for spontaneityFE#fDGT,P < 0 criterion, and equation DG = DH  TDS, refer only to properties of the system;
DSuniverse > 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.
J0ZA!0ZP0ZAZ
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6Student #2: I assume that DS [in the equation DG = DH  TDS] 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 it s spontaneous.
Student #6: I don t remember if both the system and surroundings have to be going generally up . . . I don t know what effect the surroundings have on it.
!ZZ
<y;;4Difficulties related to mathematical representations&There is confusion regarding the fact that in the equation DG = DH  TDS, all of the variables refer to properties of the system (and not the surroundings).
Students seem unaware or unclear about the definition of DG (i.e., DG = Gfinal Ginitial)
There is great confusion introduced by the definition of standard freeenergy change of a process:
DG = n DG f(products)  m DG f(reactants)
^Z4ZZ;
2V<+
,<</Lack of awareness of constraints and conditionsThere is little recognition that DH equals heat absorbed only for constantpressure processes
There appears to be no awareness that the requirement that DG < 0 for a spontaneous process only holds for constantpressure, constanttemperature processes. ^.(==Overall Conceptual GapsThere 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 DG < 0 implies that entropy of the system or entropy of the universe will increase.
8pZ7w0Z7Z3! S 1 ''9Curriculum 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
RpZ!pZZ((Learning Difficulty: Weak Understanding of State Function Concept D"0"\ 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 processdependent quantities (e.g., heat and work)
@^!PZ(UZZ0" Z0" Z2Z" Z$
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U8)).Learning Difficulty: Failure to recognize that entropy increase of universe (not system) determines whether process occurs spontaneously6"@=h 'BInstructional 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.
!Z\ 0Z20Z2ZZZR
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a_**MLearning Difficulty: Not distinguishing clearly between heat and temperature N"9"&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.
v'!ZjK
jSamples of Students Answers(All considered correct)6T DU = Q W. For the same DU, 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.
!@Kd!@2@2#""jSamples of Students Answers(All considered correct)6d DU = Q W. For the same DU, 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.
!PZsm!PZ2PZ2Z&)33Summary}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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heat in general, which is not a state function.ZP

!!Initial Objectives: Students understanding of state functions and First Law of Thermodynamics6d!!!"!Oh+'0hp
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WingdingsDO Diagnostic Strategy: Examine two different processes leading from state A to state B :
[!" !
/11:Sample PopulationsIntroductory courses for science majors;(Firstsemester Chemistry
Fall 1999: N = 426
Fall 2000: N = 532
Secondsemester Physics
Fall 1999: N = 186
Fall 2000: N = 188
Secondsemester Chemistry
Spring 2000: N = 47
Spring 2000, Interview subjects: N = 8
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$22!Results of Chemistry Diagnostic: "!""f Is the net change in [(a) temperature DT; (b) internal energy DE] of the system during Process #1 greater than, less than, or equal to that for Process #2? (Answer: Equal to)
[Second version results in brackets]
DT during Process #1 is:
greater than: & & .61% [48%]
less than:& & & & ..3% [3%] DT for Process #2.
equal to:& & & & ..34% [47%]
DE during Process #1 is:
greater than: & & .51% [30%]
less than:& & & & ..2% [2%] DE for Process #2.
equal to:& & & & ..43% [66%]
Students answering correctly that both DT and DE are equal: 20% [33%]!n!0Z<!0ZN!Z!0ZF!0ZN!ZG!0}Z&< "1(1("Physics Diagnostic+Given in second semester of calculusbased introductory course.
Traditional course; thermal physics comprised 18% of course coverage.
Diagnostic administered in last week of course:
Fall 1999: practice quiz during last recitation; N = 186
Fall 2000: practice quiz during final lecture; N = 188
@<0t023&&jSamples of Students Answers(All considered correct)6, DU = Q W. For the same DU, the system with more work done must have more Q input so process #1 is greater.
Q is greater for process 1 since Q = U + W and W is greater for process 1.
Q is greater for process one because it does more work, the energy to do this work comes from the Qin.
U = Q W, Q = U + W, if U is the same and W is greater then Q is greater for Process #1.
/!PZZa!PZ2!PZZ!PZ2PZ2Z&h)kResults, Fall 1999[N = 186] Results, Fall 2000[N = 188]
tStudents Reasoning on Work Question [Fall 2000: N = 188] ;&$Correct or partially correct . . . . . . . . . . . . 56%
Incorrect or missing explanation . . . . . . . 14%
Work is independent of path . . . . . . . . . . 26%
(majority explicitly assert path independence)
Other responses . . . . . . . . . . . . . . . . . . . . 4%
m@(4@
/!`(;@(O4/;
5Of the students who correctly answer that W1 > W2 :L6+ [Fall 2000: 70% of total student sample]
38% correctly state that Q1 > Q2
41% state that Q1 = Q2
16% state that Q1 < Q2
6!@("`UA@A@(@(5,Of the students who assert that W1 = W2 :L" [Fall 2000: 26% of total student sample]
43% correctly state that Q1 > Q2
51% state that Q1 = Q2
4% state that Q1 < Q2 5!@("`<A@A@(44Relation Between Answers on Work and Heat QuestionsZProbability of answering Q1 > 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 pathindependent is higher for those who answer Work question correctly.
Correct on Work question and state Q1 = Q2 : 61% claim Q is pathindependent
Incorrect on Work question and state Q1 = Q2 : 37% claim Q is pathindependent SZ]!0ZRpZPPZT0Z2TZ
3\
/$
Q
'@Reasoning for Q1 = Q2 [Fall 2000: 43% of total student sample]BA*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 pathindependence of Q
1Z?Zq0Z7sZ1?5 3 m @Reasoning for Q1 = Q2 [Fall 2000: 43% of total student sample]JA*
**
** 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 pathindependence of Q
!Z?ZA0Z7ZjZZ ?Ai?Reasoning for Q1 > Q2 [Fall 2000: 40% of total student sample]B@)DU1 = DU2 Q1 > Q2 [correct] . . . . . . . 10%
Q higher because pressure is higher . . . 7%
Q = W (and W1 > W2 ) . . . . . . . . . . . . . . . . 4%
Other explanations . . . . . . . . . . . . . . . . . 8%
No explanation offered . . . . . . . . . . . . . 12%
Note: Only students who answered Work question correctly gave correct explanation for Q1 > Q2
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@Reasoning for Q1 > Q2 [Fall 2000: 40% of total student sample]JA*
**
**>DU1 = DU2 Q1 > Q2 [correct] 24%
Q higher because pressure is higher 18%
Q = W (and W1 > W2 ) 9%
Other explanations 20%
No explanation offered 29%
Note: Only students who answered Work question correctly gave correct explanation for Q1 > Q2
%pZ#(PZ(i0Z(Z
+
CX
j@Reasoning for Q1 < Q2 [Fall 2000: 12% of total student sample]BA*Essentially correct, but sign error. . . . . 4%
Other explanations . . . . . . . . . . . . . . . . 5%
No explanation offered . . . . . . . . . . . . . 3%
b0r 7 05 4
tStudents 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 > Q2 : 8%
Q1 = Q2 : 5%
Q1 < Q2 : 5%
No response/no explanation . . . . . . . . . . . 36%
Note: Only students who answered Work question correctly gave correct explanation for Q1 > Q2
PZ(;PZ"!0Z!pZ(5ZlZS0;
5X
5Of the students who correctly answer that Q1 > Q2 :L6+ [Fall 2000: 40% of total student sample]
66% correctly state that W1 > W2
28% state that W1 = W2
7% state that W1 < W2 5!@("`<A@A@(4,Of the students who assert that Q1 = Q2 :L" [Fall 2000: 43% of total student sample]
67% correctly state that W1 > W2
31% state that W1 = W2
1% state that W1 < W2 5!@("`<A@A@(4Responses, Fall 1999 (N = 186)2Responses, Fall 2000 (N = 180)2'Responses, 19992000 combined (N = 366)2(
#Conclusions from Physics Diagnostic 25% believe that Work is independent of process.
Of those who realize that Work is processdependent, 3040% 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 processindependent, and those who believe that W is processindependent.
15% of students appear to have adequate understanding of First Law of Thermodynamics.ZPZ<XZ"#Conjectures from Physics DiagnosticBelief that Heat is processindependent may not be strongly affected by realization that Work is not processindependent.
Understanding the processdependence of Work may strengthen belief that Heat is independent of process. X{@Pj@<af##!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.JL!HZW@stJ$$Summary Fewer than one in six students in both chemistry and physics introductory courses demonstrated clear understanding of First Law of Thermodynamics."!//aStudent Understanding of Entropy and the Second Law of Thermodynamics in the Context of Chemistrybb"DSecondsemester course; covered standard topics in chemical thermodynamics:
Entropy and disorder
Second Law of Thermodynamics: DSuniverse [= DSsystem+ DSsurroundings] 0
Gibbs free energy: G = H  TS
Spontaneous processes: DGT,P < 0
Standard freeenergy changes
Written diagnostic administered to 47 students (11% of class) last day of class.
Indepth interviews with eight student volunteers
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00RDifficulties Interpreting Meaning of DG $*&Students seem unaware or unclear about the definition of DG (i.e., DG = Gfinal Ginitial)
Students often do not interpret DG < 0 as meaning G is decreasing
The expression DG is frequently confused with G
DG < 0 is interpreted as G is negative, therefore, conclusion is that G must be negative for a spontaneous process &@U4y94J,G 44UPrevious Investigations of Learning in Chemical Thermodynamics(upperlevel courses)0V?@A. C. Banerjee, Teaching chemical equilibrium and thermodynamics in undergraduate general chemistry classes, J. Chem. Ed. 72, 879881 (1995).
M. F. Granville, Student misconceptions in thermodynamics, J. Chem. Ed. 62, 847848 (1985).
P. L. Thomas, and R. W. Schwenz, College physical chemistry students conceptions of equilibrium and fundamental thermodynamics, J. Res. Sci. Teach. 35, 11511160 (1998). bZ]>o 55Student InterviewsEight student volunteers were interviewed within three days of taking their final exam.
The average course grade of the eight students was above the classaverage grade.
Interviews lasted 4060 minutes, and were videotaped.
Each interview centered on students talking through a sixpart problem sheet.
Responses of the eight students were generally quite consistent with each other.PZ266`Students Guiding Conceptions(what they know )DH is equal to the heat absorbed by the system.
Entropy is synonymous with disorder
Spontaneous processes are characterized by increasing entropy
DG = DH  TDS
DG must be negative for a spontaneous process.
0ZAZ,g 77Examples from InterviewsQ: Tell me again the relationship between G and spontaneous ?
Student #7: I guess I don t know, necessarily, about G; I know DG.
Q: Tell me what you remember about DG.
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 DG is negative, what would be happening to G itself?
Student #7: I don t know because I don t remember the relationship. b!0Z<<""")"" """"!""
""{""1"4"""9"88FStudent Conception: If the process is spontaneous, G must be negative.@G3"" " ""Student #1: If it s spontaneous, G would be negative . . . But if it wasn t going to happen spontaneously, G would be positive. At equilibrium, G would be zero . . . if G doesn t become negative, then it s 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 it s still going to be a negative number as long as it s increasing until it gets to zero.
C!Z""I""$"""""
"""99Students confusion: apparently conflicting criteria for spontaneityFE#fDGT,P < 0 criterion, and equation DG = DH  TDS, refer only to properties of the system;
DSuniverse > 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.
J0ZA!0ZP0ZAZ
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6Student #2: I assume that DS [in the equation DG = DH  TDS] 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 it s spontaneous.
Student #6: I don t remember if both the system and surroundings have to be going generally up . . . I don t know what effect the surroundings have on it.
!ZZ
<y;;4Difficulties related to mathematical representations&There is confusion regarding the fact that in the equation DG = DH  TDS, all of the variables refer to properties of the system (and not the surroundings).
Students seem unaware or unclear about the definition of DG (i.e., DG = Gfinal Ginitial)
There is great confusion introduced by the definition of standard freeenergy change of a process:
DG = n DG f(products)  m DG f(reactants)
^Z4ZZ;
2V<+
,<</Lack of awareness of constraints and conditionsThere is little recognition that DH equals heat absorbed only for constantpressure processes
There appears to be no awareness that the requirement that DG < 0 for a spontaneous process only holds for constantpressure, constanttemperature processes.Z ^.(==Overall Conceptual GapsThere 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 DG < 0 implies that entropy of the system or entropy of the universe will increase.
8pZ7w0Z7Z3! S 1 ''9Curriculum 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
RpZ!pZZ((Learning Difficulty: Weak Understanding of State Function Concept D"0"\ 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 processdependent quantities (e.g., heat and work)
@^!PZ(UZZ0" Z0" Z2Z" Z$
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U8)).Learning Difficulty: Failure to recognize that entropy increase of universe (not system) determines whether process occurs spontaneously6"@=h 'BInstructional 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.
!Z\ 0Z20Z2ZZZR
,
a_**MLearning Difficulty: Not distinguishing clearly between heat and temperature N"9"&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.
v'!ZjK
jSamples of Students Answers(All considered correct)6T DU = Q W. For the same DU, 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.
!@Kd!@2@2#""jSamples of Students Answers(All considered correct)6d DU = Q W. For the same DU, 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.
!@sm!@2@2&)33Summary}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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