Transcript Slide 1

Students’ Ideas About the State-Function Property of Entropy*
Warren M. Christensen, David E. Meltzer, Thomas A. Stroman
Iowa State University
*Supported in part by NSF grants #DUE-9981140 and #PHY-0406724
Previous Results
A fundamental concept of thermodynamics is that a system in a
particular state has a set of properties that is unique to that state.
When a system changes from some initial state to some final state,
the change of a given state function is the same regardless of how
the system gets from the initial to the final state. Heat transfer, Q,
is not a state function and its value depends on the process that the
system undergoes. Student thinking regarding these quantities
have been studied by Loverude, et al., [AJP, 2002] and Meltzer,
[AJP, 2004] in the context of the first law of thermodynamics.
Which would produce the largest change in the total energy of all the atoms in the
system: Process #1, Process #2, or both processes produce the same change?
In 2001, 73% of students taking a second-semester calculus-based
physics course (N = 279) determined correctly that the change in
total energy would be the same for both processes.
Is Q for Process #1 greater than, less than, or equal to that for Process #2?
From Meltzer 2004
1999
2000
2001
Incorrect
N = 186
N = 188
N = 279
Q1 = Q2
31%
43%
41%
Heat transfer is not a state
function but ~40% of students give
answers consistent with that idea.
P-V Diagram
Cyclic Process
The P-V diagram question was administered to all students in first-semester algebra-based and a
calculus-based physics courses after all instruction was completed during the Spring 2005.
The cyclic process question was administered to second-semester calculus-based
physics students in Spring 2005 after all instruction on thermodynamics was complete.
This P-V diagram represents a system consisting of a fixed amount of ideal
gas that undergoes three different processes in going from state A to state B:
Consider a heat engine that uses a fixed quantity of ideal gas. This gas
undergoes a cyclic process which consists of a series of changes in
pressure and temperature. The process is called “cyclic” because the gas
system repeatedly returns to its original state (that is, same value of
temperature, pressure, and volume) once per cycle.
Consider one complete cycle; the system begins in a certain state and
returns to that same state, so the initial state and the final state are the
same.
a) Is the change in temperature (DT) of the gas at the completion of one
complete cycle always equal to zero for any cyclic process or not always
equal to zero for any cyclic process? Explain.
DT always = 0
b) Is the change in internal energy (DU) of the gas at the completion of one
complete cycle always equal to zero for any cyclic process or not always
equal to zero for any cyclic process? Explain.
Rank the change in entropy of the system for each process.
NOTE: DS1 represents the change in entropy of the system for Process #1,
etc.
a. DS3 < DS2 < DS1
b. DS1 < DS2 < DS3
c. DS1 = DS2 < DS3
d. DS1 = DS2 = DS3
e. Not enough information
Solution: The entropy of a system is
unique to its thermodynamic state;
therefore, regardless of the process
details, the change in entropy is the
same for all three processes since they
have the same initial and final states.
Algebra-based Course (N = 232)
A
B
C
D
E
6%
19%
9%
62%
4%
Calculus-Based Course (N = 341)
A
B
C
D
E
5%
23%
2%
67%
3%
65% of students were able to successfully answer this question. Since overgeneralization of the state
function property has been seen in previous work in thermodynamics (see above), the high number of correct
responses may not reflect a meaningful association between entropy and the state of a system. The most
common incorrect answer is “b. DS1 < DS2 < DS3”, which is consistent with the idea that greater area under
the curve means greater entropy change and is probed further in one-on-one student interviews.
Student Interviews (N = 7):
After receiving modified instruction on the
state-function property of entropy, students were given the above problem.
Interview Data (N = 7)
DS is the same for all processes
5
Initially responded “DS is path-dependent” but
switched to “DS is the same for all processes” 3 of 5
DS is proportional to the area under the curve
2
Five out of the seven students asserted that the
change in entropy would be greater for the process
with the larger area under the curve. About half
offered explicit reasoning using DS ~ Q/T to justify
that answer. After thinking about the problem further,
three students changed to the correct answer, stating
that they had just remembered it, and were confident
they now had the correct answer.
DU always = 0
c) Is the change in entropy (DS) of the gas at the completion of one
complete cycle always equal to zero for any cyclic process or not always
equal to zero for any cyclic process? Explain.
DS always = 0
d) Is the net heat transfer to the gas during one complete cycle always equal
to zero for any cyclic process or not always equal to zero for any cyclic
process? Explain.
QNET not always = 0
Cyclic Process Post-Instruction (N = 191)
a. Temperature
b. Internal Energy
c. Entropy
d. Heat transfer
=0
≠0
=0
≠0
=0
≠0
=0
≠0
89%
11%
74%
26%
54%
46%
40%
60%
Response rates on this question are nearly identical to those reported by Meltzer on a similar question
(above) for both internal energy always equal to zero [correct], 74% to 73%, and heat transfer always
equal to zero [incorrect], 40% to 38%. However, students answer question (c) correctly [DS always equal
to zero] only 54% of the time, which is significantly different (p < 0.01) from the correct response rate
(67%) in the question employing a P-V diagram.
Conclusions:
• Student responses concerning the state-function property of entropy are
significantly different when problems are posed using different representations.
• Students’ tendency to ascribe state-function properties to path-dependent
quantities may mask their thinking about the state-function property of entropy.