We introduce a series of activities to help students understand the partial derivatives that arise in thermodynamics. Students construct thought experiments that would allow them to measure given partial derivatives. These activities are constructed with a number of learning goals in mind, beginning with helping students to learn to think of thermodynamic quantities in terms of how one can measure or change them. A second learning goal is for students to understand the importance of the quantities held fixed in either a partial derivative or an experiment. Students additionally are given an experimental perspective—particularly when this activity is combined with real laboratory experiments—on the meaning of either fixing or changing entropy. In this paper, we introduce the activities and explain their learning goals. We also include examples of student work from classroom video and follow-up interviews.

1.
Ana
Raquel Pereira de Ataíde
and
Ileana
Maria Greca
, “
Epistemic views of the relationship between physics and mathematics: Its influence on the approach of undergraduate students to problem solving
,”
Sci. Educ.
22
,
1405
1421
(
2012
).
2.
Brandon R.
Bucy
,
John R.
Thompson
, and
Donald B.
Mountcastle
, “
Student (mis) application of partial differentiation to material properties
,” AIP Conf. Proc.
883
,
157
160
(
2007
).
3.
W.
Christensen
and
J.
Thompson
, “
Investigating student understanding of physics concepts and the underlying calculus concepts in thermodynamics
,” in
Proceedings of the 13th Annual Conference on Research in Undergraduate Mathematics Education
(
Mathematical Association of America
,
2010)
, <http://sigmaa.maa.org/rume/crume2010/Archive/Thompson\%20\&\%20Christensen.pdf>.
4.
Christian H.
Kautz
,
Paula R. L.
Heron
,
Michael E.
Loverude
, and
Lillian C.
McDermott
, “
Student understanding of the ideal gas law, Part I: A macroscopic perspective
,”
Am. J. Phys.
73
,
1055
1063
(
2005a
).
5.
David E.
Meltzer
, “
Observations of general learning patterns in an upper-level thermal physics course
,”
AIP Conf. Proc.
1179
,
31
34
(
2009
).
6.
Evan B.
Pollock
,
John R.
Thompson
, and
Donald B.
Mountcastle
, “
Student understanding of the physics and mathematics of process variables in P- V diagrams
,”
AIP Conf. Proc.
951
,
168
171
(
2007
).
7.
John R.
Thompson
,
Brandon R.
Bucy
, and
Donald B.
Mountcastle
, “
Assessing student understanding of partial derivatives in thermodynamics
,”
AIP Conf. Proc.
818
,
77
80
(
2006
).
8.
John R.
Thompson
,
Corinne A.
Manogue
,
David J.
Roundy
, and
Donald B.
Mountcastle
, “
Representations of partial derivatives in thermodynamics
,”
AIP Conf. Proc
1413
,
85
88
(
2012
).
9.
Webpage of the Paradigms in Physics project
,” <http://physics.oregonstate.edu/portfolioswiki>, contains a description of the Energy and Entropy course, a summary of the course content, and detailed descriptions of the activities used in the course.
10.
David
Roundy
and
Michael
Rogers
, “
Exploring the thermodynamics of a rubber band
,”
Am. J. Phys.
81
,
20
23
(
2013
).
11.
Fredrik
Jeppsson
,
Jesper
Haglund
,
Tamer G.
Amin
, and
Helge
Strömdahl
, “
Exploring the use of conceptual metaphors in solving problems on entropy
,”
J. Learn. Sci.
22
,
70
120
(
2013
).
12.
R. H.
Romer
, “
Heat is not a noun
,”
Am. J. Phys.
69
,
107
109
(
2001
).
13.
J. W.
Jewett
, Jr.
, “
Energy and the confused student III: Language
,”
Phys. Teach.
46
,
149
153
(
2008
).
14.
R.
Newburgh
and
H. S.
Leff
, “
The Mayer-Joule Principle: The foundation of the First Law of Thermodynamics
,”
Phys. Teach.
49
,
484
487
(
2011
).
15.
Michael E.
Loverude
,
Christian H.
Kautz
, and
Paula R. L.
Heron
, “
Student understanding of the first law of thermodynamics: Relating work to the adiabatic compression of an ideal gas
,”
Am. J. Phys.
70
,
137
148
(
2002
).
16.
Richard
Alan Duschl
,
Heidi A.
Schweingruber
, and
Andrew W.
Shouse
,
Taking science to school: Learning and teaching science in grades K-8
(
National Academy Press
,
2007
).
17.
Mary
Bridget Kustusch
,
David
Roundy
,
Tevian
Dray
, and
Corinne
Manogue
, “
An expert path through a thermo maze
,”
AIP Conf. Proc.
1513
,
234
237
(
2013
).
18.

See the “Ice calorimetry lab” on the Paradigms in Physics Activities wiki, Ref. 9.

AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.