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```Name the Experiment
www.physics.oregonstate.edu/portfolioswiki
Corinne A. Manogue
David Roundy
Emily van Zee
Abstract
We introduce a series of activities to help students
understand the partial derivatives that arise in
thermodynamics. Students are asked to construct thought
experiments which would allow them to measure given
partial derivatives. These activities are constructed with
several learning goals in mind, e.g. to help students to see
 A 
that the quantity held constant—the C in  B  —is an

C
experimental control or constraint, and to see how
Maxwell relations can be useful. We are analyzing
classroom video to find out what kinds of reasonings
students are actually employing during these activities.
Draw and describe an experiment
represented by this partial derivative.
 p 


 T  S
This experiment is much easier to imagine if we
turn the derivative upside-down. In this case, we
change the pressure on an insulated piston, for
instance by putting weights on it, and measure
how much its temperature changes with a
thermometer.
Student Learning Opportunities
• Understanding derivatives as experiments.
• Since entropy is being held fixed, this corresponds to an
adiabatic process, in which the system is thermally
insulated from its environment. We are changing the
temperature, which students often find confusing, since
we are intentionally not heating the system.
• Students are surprisingly persistent in believing that the
quantity held constant need not be specified. We
(hopefully) help them to see this as the controlled variable
in an experiment.
• Recognizing that the inverse of a derivative is just the
derivative with top and bottom inverted
Draw and describe an experiment
represented by this partial derivative.
 U 
 p 

S
This is another adiabatic process, so imagine an insulated piston
system. Change the pressure by placing weights on the piston.
However, we don't have a way to directly measure the change in
internal energy, and must work this out using the First Law. Since
the change is adiabatic, there is no heating (Q=0), and the change
in internal energy is equal to the quantity of work done, dU = pdV, from which we can conclude mathematically that
 U 
 V 
 p    p  p 

S

S
Now we can design a much easier experiment to measure the
change in volume as we change the pressure adiabatically.
Student Learning Opportunities
• Uses of the First Law
• Our students seldom recognize the form of the
work done mathematically, but they are able to
express that they measure the work by seeing
how the volume changes.
Draw and describe an experiment
represented by this partial derivative.
 S 


 V T
This example is more challenging, since we don't have a
direct way to measure entropy itself. The key to these
derivatives is recognizing the thermodynamic definition
of entropy
dQ
S  
T
We need to change the volume at fixed temperature,
and measure the energy transferred between the system
and environment by heating. Arrange a thermally
insulated system with a thermometer and heater (a
resistor), and measure how much energy is needed to
keep its temperature from dropping as it is expanded.
This would require that the temperature change slightly,
such that the thermostat could respond.
Student Learning Opportunities
• Exploring what it means to change the entropy.
• This experiment is particularly tricky because
temperature is held fixed: when temperature is
being changed, the experiment can be reduced to
one of calorimetry, and since we begin the course
with a simple calorimetry experiment, our students
find those examples reasonably easy.
• This example highlights the student assumption
that fixed temperature will mean fixed entropy—i.e.
no heating is going on.
Draw and describe an experiment
represented by this partial derivative.
 S 


 V T
We can construct a Maxwell relation involving this
derivative from the Helmholtz free energy:
dA   SdT  pdV
 A
 S   p 
 
 

T V
 V T  T  S
2
From this, we can see that this “hard” derivative is
just the same as the “simple‘” derivative we have
already done, so we can do a far easier experiment
to measure this derivative.
Student Learning Opportunities
• Immediately after introducing Maxwell relations,
we have a final name-the-experiment activity in
which students use a Maxwell relation to find a
second (ideally easier) experiment to measure a
given partial derivative. We actually ask students
to find two experiments for their derivative.
Narratives
We are developing a narrative interpretation of videos of class
sessions on Name the Experiment. The intent is to help
interested instructors envision an interactive classroom culture,
one in which students learn by talking with one another about
what they think as well as by listening to and conversing with
their instructor. This approach to documenting and interpreting
learning experiences draws on the power of narrative to convey
cultural values and practices. These narratives are written in the
tradition of ethnography of communication (Philipsen &
Coutu, 2004; van Zee & Minstrell, 1997). Ethnographers of
communication examine cultural practices by interpreting what
is said, where, when, by whom, for what purpose, in what way,
and in what context. See a short paper about how/why to write
narratives: van Zee & Manogue, Documenting and Interpreting
Ways to Engage Students in ‘Thinking Like a Physicist’, PERC,
2010.
```