Thermal Expansion
Perry A. Tompkins
Physics Department
Samford University
Instructor’s Portion
Most all introductory physics classes are accompanied by instructional
laboratories. In thermodynamics, there are two common experiments
performed, the specific heat of solids and the thermal expansion of solids.
Thermal expansion is an important, fundamental concept in physics,
however an instrumented apparatus for the measurement of thermal
expansion is difficult to locate. This experiment was designed to take
advantage of an existing experimental apparatus, combined with easy
modifications, to form a completely instrumented laboratory experiment in
thermal expansion. During expansion, the temperature and the length of
the rod are continuously measurable, yet because of the slow timescales of
thermal effects, these measurements do not stress the most basic of DAQ
systems. Through the design of this experiment, the strength of authentic
instrumentation is well represented in a fundamental experiment.
The basic premise of this experiment is in a first-year physics laboratory,
but it also introduces an elementary solution to the measurement of length
change, which could easily have uses in mechanical or structural
Equipment List
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Pasco Thermal Expansion Apparatus, TD-8558A, Modified as
described below. www.pasco.com.
Pasco Steam Generator, TD-8556A, www.pasco.com.
Omega, Miniature Linear Displacement Potentiometer, LP804-1/2,
Computer with LabVIEW Full Development system. See
http://www.ni.com/labview/lv_sysreq.htm for computer requirements.
Additionally, it must be compatible with the DAQ board described next.
Any DAQ analog input system. Our preferred is a PCI-MIO16-E4
with a Connector Block CB-68LPR inside of a CA-1000 enclosure
with an internal power supply. This allows easy connection using the
BNC panelletts.
Any 5-VDC power supply (less that a mA is sourced for both devices.)
BNC to Banana cable to connect the thermistor input.
Eye dropper bulb.
Safety Glasses.
Glass Beaker
Note on modifications of apparatus: While most modified apparatus is
discouraged, I believe that these simple modifications allow the design
of an outstanding experiment. I was not able to find a comparable
setup from any manufacturer. Combined with the NI DAQ paradigm,
this experiment is one of the most satisfying experiments that we hold
during first-year physics laboratories. The following modifications
were accomplished by a couple advanced undergraduate students on
all of our set-ups.
Modifications of apparatus (One time only):
The linear expansion shall be measured using the Linear Displacement
Potentiometer instead of the dial depth gauge that comes with the
Thermal Expansion Apparatus. Loosen the holding clamp and remove
the depth gauge. If Pasco will sell the Thermal Expansion Apparatus at
a lower price without the gauge, buy them this way. We did not think
to ask and had to discard ours. If you have them, remove them and use
them for something else.
The linear expansion potentiometer is slightly larger than the depth gauge,
slightly ream out the hole in the holding clamp. Use a ½ “ drill bit. Do
not over drill the hole or the clamp will not hold the potentiometer.
Mount the linear potentiometer into the clamp (possibly after wiring as
described below.)
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The expansion tubes all need an added hole to grab the potentiometer
with. Remove the angle bracket from the sides of the expansion tubes.
Drill a small hole, slightly larger than the size of the potentiometer
shaft in the center. Re-install the bracket onto the expansion tube. See
Figure 1 for the final results of this procedure.
Add three nuts to the shaft of the linear potentiometer. Two should be
placed as far on the shaft as possible and tightened together. Do not
bend the shaft while tightening these! The third is used by the student
during the experiment. Figure 5 in the set-up shows final assembly.
Wiring of the Linear displacement potentiometer and the thermistor (part
of the Thermal Expansion Apparatus) can be accomplished either
permanently by the instructor of each time by the student. Wiring of
the potentiometer is shown in Figure 2. By using 5 Volts, the
expansion rod converts into 2.54 mm per volt (12.7 mm/5Volts). The
resolution spec of the potentiometer is 0.0127 mm which translates to
5 mV. If the DAQ system is unipolar with a gain of 2 (5 V effective
range) and a 12-bit card, the LSB is 1.22mV or ~1/4 the resolution of
the potentiometer. Therefore the measurement is limited by the
resolution of the potentiometer. Most expansions are 0.6-1.2 mm total,
therefore the systematic error due to resolution is around 5% or less.
Figure 1, Expansion tube modification.
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Figure 2, Wiring diagram for Omega’s Linear Displacement
The wiring diagram for the Thermistor is shown in Figure 3. This is a
simple way to measure the resistance of the thermistor. More accurate
ways are available, but the look-up table that does the conversion in
the software corresponds to Figure 3.
This completes the modifications to be able to use this experiment and this
Figure 3, Wiring diagram for the thermistor in the Pasco Thermal
Expansion Apparatus.
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Normal Set-up is shown in Figure 5. This set-up should be completed by
the student and is included in that section.
Configure your data acquisition computer hardware as per the installations
instructions provided by National Instruments.
Load LabVIEW Full Development system as per the installations
instructions provided by National Instruments.
Place the library Expansion.llb on the desktop, or place a shortcut pointing
to the file on the desktop.
Run through the experiment and verify each component’s functionality.
Figure 4 shows a screen capture of the software with data from an
Figure 4, Thermal Expansion.vi software allows simple measurement of
L and T .
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National Instruments, www.NI.com .
College Physics, 5th Edition, Serway & Faughn, 1999,Harcourt Brace
& Company, Orlando Florida.
Student’s Portion
Figure 5, Full Set-up of Thermal Expansion Apparatus. This interface is
set for a customized CA-1000 Enclosure.
When the temperature of an object increases, the object undergoes
fundamental changes at the molecular level. The size of a solid or liquid
sample is defined in part by the volume of the atoms contained within, and
also by the spacing between those atoms. The atoms vibrate about their
equilibrium positions as if the bonds between neighboring atoms were
little springs. The kinetic energy of these vibrations is directly related to
the temperature. An increase in the temperature of a substance increases
the kinetic energy of the molecular vibrations of the atoms within. This
increase in the amplitude of the molecular vibrations, increases the
average separation between atoms.
The object literally “swells up” with the addition of heat and temperature.
This swelling of materials with temperature is called “thermal expansion.”
Just like the specific heat, the amount of thermal expansion that occurs for
a given temperature change is dependent upon the material of interest.
This experiment measures the thermal expansion of different materials,
and by comparing the experimental data to tabular data, the identity of the
materials can be determined.
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The objective for this experiment is to explore the concepts of thermal
expansion, and use these principles as a way to identify materials.
When an object expands, it expands in every direction. Every linear
dimension expands. Figure 6 shows a two dimensional object that
undergoes an increase in temperature. This Figure is an exaggeration in
the amount of possible expansion for most normal materials. The diameter
of the hole in the object increases, not decreases as is commonly thought.
For this experiment we are only going to measure the expansion in one
dimension of a long skinny object. If an object of original length L0 is
brought through a temperature change of T it will change its length by:
L  L0 T ,
where  is called the “coefficient of linear expansion.” If T is negative,
then L will be negative and if T is positive, then L will be positive.
 is an intrinsic property of a material. If I measure the expansion of a
material, and determine  , I can look the measurement up in a table to
determine the material’s identity.
Figure 6, Object originally at temperature, T, expands in every linear
dimension, as the temperature increases.
Pre-Lab Preparation
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Review the theory of Thermal Expansion from any fundamental
Physics Textbook.
Identify a table of the coefficients of linear expansion of common
Bring the table/book to the laboratory for this experiment.
Modified Pasco Thermal Expansion Apparatus.
Pasco Steam Generator.
Computer Data Acquisition interface. Computer with National
Instruments’ LabVIEW Full Development System and the file
Connectors as needed between the DAQ and the experimental
5-VDC power supply, if needed.
Eye dropper bulb.
Safety Glasses. USE THEM!!!!
Glass Beaker
Workstation Details
The tube in the beaker can be easily knocked out and can make a hot
Be careful when operating this system, hot steam will be generated and
can be dangerous.
Please drain the water from the expansion tubes before returning for
Lab Procedure
1. Setup apparatus as shown in Figure 5. For each measurement,
select any of the three different “room temperature” tubes to be
measured. Measure the length of the tube from the cross-pin
support to the screw that attaches the bracket on the tube for the
linear potentiometer. Place the tube in the cradle and attach the
potentiometer to the bracket on the tube. Hand tighten a third nut
to the end of the potentiometer as shown in Figure 7.
2. Connect a tube for the steam generator to either end of the
measurement tube. Do not connect the other end to the generator,
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yet. Connect tubing to the other end of the measurement tube and
feed it to a beaker.
The tube in the beaker can be easily knocked out and can make a hot
mess. Do not connect the tube to the steam generator until you have
started data collection. To increase steam output for the measurement,
place the rubber stopper over the open tube on the steam generator. Be
careful when operating this system, hot steam will be generated and
can be dangerous.
3. Connect the green thermistor outputs to ACH1 as per your
instructor’s directions. Tighten the thermistor lug to the thumb
screw on the side of the measurement tube.
4. Connect the Linear displacement potentiometer to ACH0 and the
5-V power supply as per your instructor’s directions.
Figure 7, Close-up of thermal expansion apparatus showing connection of
expansion tube to linear potentiometer.
5. Fill the steam generator half full of water and turn it on and allow
it to start generating steam. Do not connect it to the tube yet.
6. When set-up is complete, start the program by double-clicking
Expansion.llb on the desktop.
During this time the temperature and the length should not have started
changing. If you start taking data as soon as you start the steam
generator, you will be taking “flat” data for about 15 minutes. If you
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start taking data too late, you could miss the onset of the change, and
miss some important Keep the steam generator disconnected until just
after it is making steam, and connect it to the tube after starting data
7. Press :”Start” on the Expansion program.
8. After a few seconds, connect the open tube to the steam generator.
Use the eye dropper bulb to plug the other hole on the steam
generator. This will allow the expansion to occur very quickly.
9. Allow the data to level out before ceasing data collection.
10. Press Stop to cease data collection. The live data is plotted on the
graphs. One shows the temperature as a function of time, and the
other shows the length as a function of time.
11. Use the cursors to determine L and T for your experiment.
12. Use Equation 1 to determine the coefficient of linear expansion 
for your tube.
13. Use a table in your Physics textbook or in a materials handbook to
identify the material of your tube.
14. Use the tabular data and your measurement to calculate a percent
error for your experiment.
ExperimentalMagnitude  TheoreticalMagnitude
100  %error
15. Repeat steps 7 to 14 with one of the other tubes in the expansion
apparatus. Careful things are probably still hot!
Please drain the water from the expansion tubes before returning for
If a spreadsheet compatible data file is desired, Press “Save to
Spreadsheet” after each measurement is completed. Alternately, Select
“Print Screen” Under the file menu.
16. Press Exit when finished.
Lab Report
Your lab report should be as required by your instructor and include at least the
1. Normal laboratory write-up. Include purpose, diagram, procedure, and sample
2. Print-outs of your two measurements.
3. Your data table as described below.
4. Answers to the questions, conclusions and three sources of error.
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Data Sheet
Original Length
Delta Length
Delta Temperature
Measured 
Material of Tube
Instructor's Approval
Theoretical 
Percent Error
Tube 1
Tube 2
1. Why do we only measure part of the tube and not the whole end to end length?
2. Does the outside radius of the tube also expand during this experiment? If so does this
expansion have an effect on the experiment? _____________________________
3. Could we take a more accurate measurement if the program collected the data more
frequently? ___________________________________________________________
4. If you look at the data for both the length and the temperature on the same graph (as
in the strip chart), you will see that the two transitions do not occur at the same time.
Why is this happening?__________________________________________________
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