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Research-Based Curriculum Development in Thermodynamics
David E. Meltzer (Department of Physics and Astronomy) and Thomas J. Greenbowe (Department of Chemistry)
Iowa State University
Supported by NSF DUE-#9981140
Phase I: Investigation of Students’ Reasoning
Thermodynamics
Calorimetry
Physics Students’ Reasoning in
Thermodynamics
Thermochemistry
Pretest Question
Written pretest given after lecture instruction completed
• Investigation of second-semester calculus-based
physics course (mostly engineering students).
The specific heat of water is greater than that of copper.
A piece of copper metal is put into an insulated calorimeter
which is nearly filled with water. The mass of the copper is the
same as the mass of the water, but the initial temperature of
the copper is lower than the initial temperature of the water.
The calorimeter is left alone for several hours.
During the time it takes for the system to reach equilibrium,
will the temperature change (number of degrees Celsius) of
the copper be more than, less than, or equal to the
temperature change of the water? Please explain your
answer.
Reasoning Difficulties in
Thermodynamics
• Written diagnostic questions administered last week
of class in 1999, 2000, and 2001 (Ntotal = 653).
• Detailed interviews (with additional questions)
carried out with 32 volunteers during 2002.
•
– interviews carried out after all thermodynamics instruction
completed
– final grades of interview sample far above class average
•
Diagnostic Question
This P-V diagram represents a system consisting of a fixed amount
of ideal gas that undergoes two different processes in going from
state A to state B:
•
[In these questions, W represents the work done by the system during a process; Q
represents the heat absorbed by the system during a process.]
Student Learning of
Thermochemical Concepts
Many students incorrectly
attribute state-function
properties to processdependent quantities such
as heat and work.
Most students interviewed
believed incorrectly that net
work done and net heat
absorbed by a system
undergoing a cyclic process
are zero.
T. J. Greenbowe and D. E. Meltzer,
Int. J. Sci. Educ. 25, 779 (2003)
• Investigated students’
misunderstanding of role of
bond breaking and forming in
determining heats of reaction
– student belief that heat flows from one
reactant to the other
• Uncovered students’
misinterpretation of role of
mass in relationship Q = mcT
Answer: More than.
Reasoning Difficulties in Calorimetry
More than 80% of students
are unable to apply the first
law of thermodynamics after
completion of study.
•
Nearly half (45%) of all students (N = 311) were
unable to give correct answer with correct
explanation to pretest question.
•
Nearly one-quarter (22%) of all students gave
explanations reflecting substantial
misunderstanding of key concepts
1. Is W for Process #1 greater than, less than, or equal to that for Process #2?
Explain.
2. Is Q for Process #1 greater than, less than, or equal to that for Process #2?
–
–
–
3. 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?
– strong tendency to associate “m” with
reactants only, instead of with total
mass undergoing temperature change
“temperature changes equal since energy transfers equal”
“temperature changes equal since system goes to equilibrium”
“specific heat is directly proportional to temperature change”
Phase II: Development of Curricular Materials
Thermodynamics
Calorimetry
Thermodynamics Worksheet Strategy
Calorimetry Worksheet Strategy
• Focus on meaning of heat as transfer of energy, not
quantity of energy residing in a system.
3
2
monatomic ideal gas, the relationship is given by U =
P
i
C
Thermochemistry Worksheet
Calorimetry Worksheet
f
Process #2
0
V
8. Rank the temperature of the gas at the six points i, A, B, C, D, and f.
9. Consider all sub-processes represented by straight-line segments. For each one, state
whether the work done by the gas is positive, negative, or zero. In the second column, rank
all six processes according to their U. (Pay attention to the sign of U.) If two segments
have the same U, give them the same rank. In the last column, state whether heat is
transferred to the gas, transferred away from the gas, or is zero (i.e., no heat transfer).
Process
iA
AB
Bf
iC
CD
Df
P
Is W +, –, or 0?
rank according to U
heat transferred to, transferred away, or zero?
State A
0
3. If a system starts with an initial internal energy of Uinitial and ends up with Ufinal some time
later, we symbolize the change in the system’s internal energy by U and define it as
follows: U = Ufinal – Uinitial.
A
The textbook describes an experiment in which Silver Nitrate (AgNO3) solution is mixed
with hydrochloric acid (HCl) solution in a constant-pressure calorimeter. (We assume
that the calorimeter loses only a negligible quantity of heat.) The temperature of the
resulting solution is observed to increase, due to the following reaction:
AgNO3(aq) + HCl(aq)  AgCl(s) + HNO3(aq)
1. During this reaction, does energy flow into the resulting solution (if so, where did
the energy come from?), out of the solution (if so, where did it go?), or is there no
net flow of energy into or out of the solution (if so, how do you know?).
10 kJ
8. Experiment A. Let’s suppose that 2 liters of 1.0 M silver nitrate solution reacts
with 2 liters of 1.0 M hydrochloric acid solution, and the temperature of the resulting
4 liter solution rises by 8C. Suppose that during this process x joules of energy flow
either into or out of the system. (Your answer to #7 should have decided whether it’s
into or out of, or if instead x is really just 0 joules. Which is it?)
Experiment B. Suppose that again we have 2 liters of each reactant solution.
Now, though, let’s suppose that the concentration of each solution is four times
greater than before (so, e.g., instead of a 1.0 M solution, we have a 4.0 M solution).
Remember that the total volume of solution is still just 4 liters.
a) Will the temperature of the resulting 4 liter solution rise, fall, or not
change at all? Explain.
8 kJ
6 kJ
2. Three students are discussing this experiment. Here is part of their discussion:
4 kJ
2 kJ
insulation
10. Consider only the sub-processes that have W = 0. Of these, which has the greatest
absolute value of heat transfer Q? Which has the smallest absolute value of Q?
V
Internal Energy
0
State B
0
Find the absolute temperature of sample A at
time zero (the initial time), and plot it on the
chart. Complete the bar charts by finding the
“Long After” values for temperature and
internal energy. Explain your reasoning.
Suppose we have two samples, A and B, of an
ideal gas placed in a partitioned insulated
container which neither absorbs energy nor
allows it to pass in or out. The gas in sample A
is the same gas that is in Sample B. Sample A
has the same mass as sample B and each side
of the partition has the same volume. Energy
but no material can pass through the conducting
partition; the partition is rigid and cannot move.
D
0
Figure 1
• Make more extensive use of P-V diagrams so students can develop alternate routes for
Process #1
moles of gas, and R is the universal gas constant.
2. Suppose that m moles of an ideal gas are contained inside a cylinder with a movable
piston (so the volume can vary). At some initial time, the gas is in state A as shown on the
PV-diagram in Figure 1. A thermodynamic process is carried out and the gas eventually
ends up in State B. Is the internal energy of the gas in State B greater than, less than, or
equal to its internal energy in State A? (That is, how does UB compare to UA?) Explain.
• Guide students to resolve discrepancies by using concept of bond
forming and breaking.
B
nRT, where n is the number of
1. Find a relationship between the internal energy U, pressure P and volume V of an ideal
gas. Does the relationship depend on the number of moles n or the temperature T?
• Allow students to grapple with common misconception that heat
of reaction arises through heat flow from one reactant to another.
• Practice proportional reasoning and algebraic skills by varying
system parameters, gradually increasing problem complexity.
Figure 2
For an ideal gas, the internal energy U is directly proportional to the temperature T. (This
is because the internal energy is just the total kinetic energy of all of the gas molecules,
and the temperature is defined to be equal to the average molecular kinetic energy.) For a
• Elicit students’ explanations for source of heats of reaction.
• Explore meaning of specific heat by finding temperature
changes of different objects in thermal contact with each other
• Develop concept of work as energy transfer mechanism.
• Make more extensive use of P-V diagrams so students can
A
Thermochemistry Worksheet Strategy
• Guide students to confront distinction between temperature of
a system, and its internal energy
• Build on students’ understanding of state-function concept.
Thermodynamics Worksheet
Thermochemistry
A
B
A
Time Zero
Mary: The silver nitrate was originally a solid. When it’s put into solution
along with the HCl, I think that heat flows out from the AgNO3 and into the HCl
solution, and that’s why the temperature increases.
B
Long After
Bob: Well, the hydrochloric acid is the more powerful reactant; it’s a
strong acid, so it must be the one that reacts most strongly. I think that the heat
must come out of the HCl.
Absolute Temperature
B
11. Rank the six segments in the table above according to the absolute value of their W.
Hint: For processes at constant pressure, W = P V.
Lisa: I don’t really think that the heat flows into either of those two. I
think heat flows out of both the silver nitrate and the hydrochloric acid solution,
and that’s why the temperature rises.
12. Using your answers to #9 and #11, explain whether W1 is greater than, less than,
or equal to W2. [Refer to definitions, page 3.] Is there also a way to answer this
question using an “area” argument?
Mary: But how could heat flow out of both of the reactants? Where is it
coming from then? Doesn’t that violate conservation of energy?
a. For the process described in #2 (where the system goes from State A to State B),
is U for the gas system greater than zero, equal to zero, or less than zero?
13. Is Q1 greater than, less than, or equal to Q2? Explain. Hint: Compare the
magnitude of U1 and U2, and make use of the answer to #6.
b. During this process, was there any energy transfer between the gas system and its
0
surrounding environment? Explain.
A
B
A
Time Zero
b) If you said that the temperature will change, will the temperature change
in this case be equal to, greater than, or less than 8C? Explain your
answer.
Comment on the students’ statements. Do you agree with one of them
more than the others? If so, explain why. If you don’t think that any of them are
completely correct, give your own opinion.
B
Long After
Check with one of the instructors before proceeding. ________
Experiment C. Suppose now that we react 4 liters of silver nitrate solution with 4
liters of hydrochloric acid solution, and assume that the concentration of the
solutions in this case is the same as it was when we only used 2 liters of each. The
amount of energy that flows is now y joules.
Is y going to be equal to: (i) 2x, (ii) 0.5x, (iii) x (but not zero), or (iv) equal to x
because x = y = 0? Explain your answer.
Phase III: Preliminary Assessment of Curricular Materials
Example: Classroom Testing
of Calorimetry Worksheets
• Use worksheets in randomly chosen recitation
sections.
• Compare exam performance of students in
experimental sections to those in control
sections.
Pretest Question
Suppose we have two separate containers: One container holds Liquid A, and
another contains Liquid B. The mass and initial temperature of the two liquids are
the same, but the specific heat of Liquid A is two times that of Liquid B. Each
container is placed on a heating plate that delivers the same rate of heating in
joules per second to each liquid beginning at initial time t0.
On the grid below, graph the temperature as a function of time for each liquid, A
and B. Use a separate line for each liquid, even if they overlap. Make sure to
clearly label your lines, and use proper graphing techniques.
• Modify worksheets based on student response
and input from recitation instructors.
Preliminary Assessment Results
Posttest Question
Suppose that a mass of aluminum (Al) is heated to a high initial
temperature. At time t0 it is placed in an insulated container of water that is at a
lower initial temperature. The mass of the aluminum is the same as the mass of the
water. (Note: The specific heat of water is higher than that of aluminum.)
On the grid below, graph the temperature as a function of time of the aluminum
and water separately. Make sure to clearly label your graphs. (Note: t1 represents a
time shortly after the initial time, before equilibrium is reached.)
Temperature
Insulation
Temperature
Liquid A
Liquid B
Aluminum
Liquid B
Second-semester calculus-based course
• Experimental group (45%, N = 129) had lower pretest
scores than control group (57%, N = 182), but higher
posttest scores (49% vs. 41%).
– posttest problem more challenging than pretest problem
• Results favor experimental group (although posttestscore difference not statistically significant).
• No difference between groups on multiple-choice
questions
Water
Slope of
Al = –1
Liquid A
Slope of
H20 = 1/4
Water
Heating Plate
t0
t0
[Solution to problem is shown]
Time
The specific heat of A is greater than the
specific heat of B.
t1
Al
Preliminary conclusion: Worksheet should be more
concise and focused for use in introductory course.
Time
Thermal
Equilibrium
[Approximate solution shown: similar solutions were accepted]
Materials Development Team
Warren M. Christensen
Thomas J. Greenbowe
David E. Meltzer
Ngoc-Loan Nguyen