Perry A. Tompkins
Physics Department
Samford University
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 engineering.
 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, www.omega.com
.
Submitting an Experiment 1

Submitting an Experiment
 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-68LP R 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.)
2

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.
Submitting an Experiment
Figure 1, Expansion tube modification.
3

Figure 2, Wiring diagram for Omega’s Linear Displacement
Potentiometer.
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 software.
Submitting an Experiment
Figure 3, Wiring diagram for the thermistor in the Pasco Thermal
Expansion Apparatus.
4

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 experiment.
Figure 4, Thermal Expansion.vi software allows simple measurement of

L
and 
T
.

National Instruments, www.NI.com
.

College Physics, 5th Edition, Serway & Faughn, 1999,Harcourt Brace
& Company, Orlando Florida.
Submitting an Experiment 5

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.
Submitting an Experiment 6

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
L
is
0 brought through a temperature change of 
T it will change its length by:

L
 then

L
0 where


L

T
,
is called the “coefficient of linear expansion.” If
will be negative and if 
T material, and determine 
is positive, then 
L

T
[Equation-1]
is negative,
, I can look the measurement up in a table to determine the material’s identity.
will be positive.
 is an intrinsic property of a material. If I measure the expansion of a
Figure 6, Object originally at temperature, T, expands in every linear dimension, as the temperature increases.
 Review the theory of Thermal Expansion from any fundamental
Physics Textbook.
Submitting an Experiment 7

 Identify a table of the coefficients of linear expansion of common materials.
 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
Expansion.LLB.
 Connectors as needed between the DAQ and the experimental apparatus.
 5-VDC power supply, if needed.
 Eye dropper bulb.
 Safety Glasses. USE THEM!!!!
 Glass Beaker
The tube in the beaker can be easily knocked out and can make a hot mess.
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 storage.
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,
Submitting an Experiment 8

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.
Submitting an Experiment
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 collection.
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
11.
other shows the length as a function of time.
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.
Experiment alMagnitud e

Theoretica lMagnitude

100

% error
Theoretica lMagnitude
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 storage.
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.
Your lab report should be as required by your instructor and include at least the following:
1.
Normal laboratory write-up. Include purpose, diagram, procedure, and sample calculations.
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.
Submitting an Experiment 10



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?__________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
Submitting an Experiment 11