FAST-NU Research Journal (FRJ), Volume 1, Issue 1, January 2015
Alternate Method to Experimentally Determine
the Coefficient of Thermal Expansion for Metals
1,2
Saman Shahid1, Afifa Sadaqat2, Hasnain Abbas3
National University of Computer & Emerging Sciences, Lahore, Pakistan; saman.shahid@nu.edu.pk
3
Center of High Energy Physics, University of the Punjab, Lahore, Pakistan;
α = ΔL/(L x ΔT)
Abstract—The
thermal
expansion
coefficient of different metals can be
experimentally determined for three metals,
namely, Aluminum, Brass and Copper,
(called ABC metals in this paper) using the
standard PASCO experimental setup. This
paper describes and compares two alternate
methods to experimentally determine the
coefficients of the same metals. The benefits
and shortcomings of the two methods have
been discussed in this paper. Observed
results have been reported in the form of
graphs and tables. It was concluded that
our proposed methods are not as good as
the already available method. However, the
proposed methods provide us with a cleaner
experimental set-up. They also allow us to
use additional metals and alloys for
experimentation.
where ΔL is the increase in length, L is the
original length of the material, and ΔT is the
increase in temperature[4].
A number of methods, including ‘computerbased’ techniques, are available for the
evaluation of the thermal expansion coefficient
of a given metal or alloy. Examples include:
‘mechanical dilatometry’, ‘optical imaging’,
and ‘X-ray diffraction’ [2-4]. An “Infrared
Image Correlation” method has been reported
by [5], a “Non-contact optical” method has
been reported by [6], and the use of a
Thermo-mechanical Analyzer (TMA) to
measure coefficient of thermal expansion of
several materials through linear position
sensors has been reported by [7].
Keywords--- thermal coefficients, thermal
expansion.
II. STANDARD PASCO SETUP
The PASCO Science Workshop 500 Interface
[8] was used to experimentally determine the
thermal expansion coefficient of the ABC
metals in the lab. A bi-directional digital
‘Rotary Motion Sensor’ or RMS, part number
CI-6538, was used to measure the change in
length. It can measure ‘linear position’ with a
resolution of 0.055 mm or ‘rotary motion’
with a resolution of 0.25°. A ‘thermistor
sensor’, part number CI-6527A, was used to
measure the change in temperature. The
thermistor sensor can read the resistance of a
thermistor connected to the metal rod under
observation, and can convert it to temperature.
These sensors connect to the computer system
through the Science Workshop 500 Interface,
CI-6400, as shown in Figure 1. The “DataStudio” software is provided by PASCO to
enable the students to acquire data during the
experiment, and perform various analyses
tasks on the collected data.
I. INTRODUCTION
Thermal expansion is a property of matter
because of which a change in volume occurs
as a result of changes in the temperature [1].
Thermal expansion has applications in many
areas, for example, in bimetallic strips used for
the construction of digital thermometers [2].
An understanding of thermal expansion is also
important. As an example, in the microelectronics industry, it is often required to
assess the mechanical and thermal properties
of the semi-conductor material used in the
fabrication of integrated circuits [3].
The thermal expansion “coefficient” has
importance in the structural and mechanical
design of materials. The “coefficient of linear
thermal expansion”, α, indicates the extent to
which the material will expand upon heating.
It is defined to be a fractional increase in
length per unit rise in temperature, i.e.,
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FAST-NU Research Journal (FRJ), Volume 1, Issue 1, January 2015
TABLE I.
Material
Aluminum
Brass
Copper
TABLE II.
Material
Aluminum
Brass
Copper
Fig. 1: Standard PASCO experimental setup using
steam heating of the metal rod under test.
TABLE III.
III. USING ALTERNATE HEATING
METHODS
Material
Figure 2 shows the experimental setup used to
measure the coefficient of thermal expansion
using a soldering iron to heat the ABC metal
rods under test. A similar setup was used to
heat the three metal rods using a hair dryer.
Aluminum
Brass
Copper
DATA USING STEAM HEAT
Original
Length
‘L’ (mm)
410
410
410
Change in
length
‘ΔL’ (mm)
0.631
0.481
0.417
ΔT
(℃)
63.371
65.5
66.0
DATA USING SOLDERING IRON
HEAT
Original
Length
‘L’ (mm)
410
410
410
Change in
length
‘ΔL’ (mm)
0.058
0.039
0.031
ΔT
(℃)
9.90
7.91
6.67
DATA USING HAIR DRYER HEAT
Original
Length
‘L’ (mm)
410
410
410
Change in
length
‘ΔL’ (mm)
0.045
0.032
0.020
ΔT
(℃)
8.86
6.68
5.67
TABLE IV. COMPARISON OF THERMAL
COEFFICIENTS (STEAM)
Material
α (per deg. C)
Standard
×10-6
α (per deg. C)
Experimental
×10-6
Percentage
Error
(%)
Aluminum
Brass
Copper
23
19
17
24.2
17.9
15.5
4.3
5.7
8.8
TABLE V.
COMPARISON OF THERMAL
COEFFICIENTS (SOLDERING IRON)
Fig. 2: Experimental setup using soldering iron heating
of the metal rod.
IV. RESULTS AND DISCUSSION
Figures 3, 4 and 5 show the change in length
versus time and change in temperature versus
time for each of the ABC metal rods,
respectively, using standard steam heating.
The initial length of each rod is 410 mm.
Table I gives a summary of these results, while
Table IV compares the calculated value of the
thermal coefficient with the theoretical value,
and tabulates the percentage error.
Material
α (per deg. C)
Standard
×10-6
α (per deg. C)
Experimental
×10-6
Percentage
Error
(%)
Aluminum
Brass
Copper
23
19
17
14.2
11.9
11.3
61.97
59.66
50.4
TABLE VI. COMPARISON OF THERMAL
COEFFICIENTS (HAIRDRYER)
44
Material
α (per deg. C)
Standard
×10-6
α (per deg. C)
Experimental
×10-6
Percentage
Error
(%)
Aluminum
Brass
Copper
23
19
17
12.3
11.6
8.6
86.99
63.79
97.67
FAST-NU Research Journal (FRJ), Volume 1, Issue 1, January 2015
Fig. 3: Change in length and temperature versus time
for an aluminum rod (steam heat)
Fig. 6: Change in length and temperature versus time
for an aluminum rod (soldering iron heat)
Fig. 4: Change in length and temperature versus time
for a brass rod (steam heat)
Fig. 5: Change in length and temperature versus time
for a copper rod (steam heat)
Fig. 7: Change in length and temperature versus time
for an aluminum rod (hair dryer heat)
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FAST-NU Research Journal (FRJ), Volume 1, Issue 1, January 2015
Fig. 8: Change in length and temperature versus time
for a brass rod (soldering iron heat)
Fig. 10: Change in length and temperature versus time
for a copper rod (soldering iron heat)
Fig. 9: Change in length and temperature versus time
for a brass rod (hair dryer heat)
Fig. 11: Change in length and temperature versus time
for a copper rod (hair dryer heat)
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FAST-NU Research Journal (FRJ), Volume 1, Issue 1, January 2015
Figures 6 and 7 show the change in length
versus time and change in temperature versus
time for the aluminum rod, using soldering
iron heating and hair dryer heating,
respectively. Figures 8 and 9 are for the brass
rod, and Figures 10 and 11 are for the copper
rod. Tables II, III, V and VI give a summary of
the results shown in these figures.
be achieved by using a soldering iron or a hair
dryer.
The PASCO setup requires a special metal rod
during the experiment. This means that the
thermal coefficients of only those metal rods
that are provided by PASCO can be
determined.
Simple metal rods can be
employed if the alternate methods of heating
are used. This allows the use of the existing
setup for experimentally determining the
coefficient of thermal expansion of more
metals and alloys.
It can be seen from these results that by using
the two alternate methods, the change in
length and temperature which could be
achieved were much less than the values
obtained using steam heating of the metal
rods. While using steam for heating can raise
the temperature of the sample to about 100
degrees C, the two alternate methods could not
give a maximum temperature of more than 50
degrees C each. As a result, the coefficient of
thermal expansion determined experimentally
is very different from the theoretical value.
One solution to this problem is to use a
soldering iron with more heating capability.
The soldering iron used was rated at 25watts.
Instead, using a 100 watt soldering iron is
expected to provide better results. Both the
above mentioned alternate methods took an
average time of 35 minutes to get the results,
while the standard steam heating method
provided measurements in only 5 minutes.
V.
REFERENCES
[1]
[2]
[3]
CONCLUSIONS
Two alternate heating mechanisms used with
the standard PASCO experimental setup have
been proposed and described in this paper.
Instead of using steam for heating the metal
rods, heating was done by using a soldering
iron in one set of experiments, and a hair dryer
in the second set of experiments. The benefit
is that the experiments can be done by the
students without the risk of getting steamburn. It also provides a cleaner experimental
set-up, as there is no drainage of condensed
water. An additional benefit is that samples
from more metals can be used thereby
enabling the students to find the thermal
coefficients of more metals and alloys.
[4]
[5]
[6]
The proposed alternate methods did not prove
to be better than the one recommended by
PASCO for determining the thermal
coefficients of aluminum, brass and copper.
The reason is that uniform heating could not
47
I. Yamada. K. Tsuchida. K. Ohgushi. N.
Hayashi. J. Kim. N. Tsuji. R. Takahashi. M.
Matsushita. N. Nishiyama. T. Inoue. (2011,
Jul.) .Giant Negative Thermal Expansion in
the Iron. Angewandte Chemie International
Edition. 50(29), pp. 6579–6582.
American Society of Metals (ASM)
International. (2002). Thermal Properties of
Metals
(#06702G).
Available:
http://www.asminternational.org/documents/1
0192/1849770/ACFAAD6.pdf
A. Zimprich. M. Grabowski. F. Asmus. M.
Naumann. D. Berg. M. Bertram. K.
Scheidtmann. P. Kern. J. Winkelmann. B.
Müller-Myhsok. L. Riedel. M. Bauer. T.
Müller. M. Castro. T. Meitinger. T. M. Strom.
T. Gasser. (2001, Aug.). Mutations in the
gene encoding epsilon-sarcoglycan cause
myoclonus-dystonia syndrome. 1(29), pp. 6669.
Avialable:
http://www.nature.com/ng/journal/v29/n1/full
/ng709.html
J. D. James. J. A. Spittle. S. G. R. Brown. R.
W. Evans. (2001, Mar.). A review of
measurement techniques for the thermal
expansion coefficient of metals and alloys at
elevated temperatures. Measurement Science
and Technology 12(3).
R. Montanini. F. Freni. (2012, 11-14 Jun.). A
new method for the determination of the
coefficient of thermal expansion of solid
materials. 11th International Conference on
Quantitative
InfraRed
Thermography,
University of Naples Federico II, Naples
Italy.
R. Montanini. F. Freni. (2013, Dec.). Noncontact measurement of linear thermal
expansion coefficients of solid materials by
infrared image correlation. Measurement
Science and Technology. 25(1).
FAST-NU Research Journal (FRJ), Volume 1, Issue 1, January 2015
[7]
[8]
K. Menard. B. Cassel. (2013). Basics of
Thermo mechanical Analysis with TMA
4000. PerkinElmer Inc. Shelton, CT USA.
Available:
http://www.perkinelmer.com/CH/CMSResour
ces/Images/44-154962TCH_TMA_4000.pdf
PASCO
Scientific,
California,
USA.
Available: http:// www.PASCO.com.
ABOUT THE AUTHORS
Saman Shahid has done her M.S. and M.Phil.
from Government College University (GCU),
Lahore. She teaches Physics at the National
University of Computer and Emerging
Sciences, Lahore, Pakistan.
Hasnain Abbas Khan Sumbal has done his
B.S. (Hons.) and M.Phil. in high energy
physics from the University of the Punjab,
Lahore, Pakistan. His current areas of interest
are quark gluon plasma and finite temperature
and density in quantum chromo dynamics.
Afifa Sadaqat has done her B.S. and M.Phil.
in
microelectronics
engineering
and
semiconductor physics from the University of
the Punjab, Lahore, Pakistan. Her areas of
interest include device fabrication via nanoparticles.
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