On The Properties of Linear Expansion
R.L.Griffith,M.R.Levi,A.Okunyan,A.Okunyan
∗
09/08/2005
Abstract
between the atoms causing the material to expand.
If the temperature change, is such that the material
does not go through a phase change, then it can be
shown that the change in the object’s length, , is given
by the equation
Keywords: Thermodynamics,Solids,Linear Expansion
The linear expansion coefficients were calculated for
three different metals, a linear expansion apparatus
was used to measure the change in length of a metal
pipe. The three metals that were studied were, copper, steel, and aluminum. The temperatures had to be
acquired for the room temperature of the pipe and at
maximum temperature for the pipe (using a thermister). once the change in temperature and the change
in length were calculated the derived equation for linear expansion can be used to solve for the coefficient
of linear expansion and compared to theoretical values. Some of the experimental values were found to
be in agreement with the theoretical values. Some errors were acquired during this experiment.
∆L = αLi ∆T
(1)
where Li , is the initial length of the object before heat
is added, and α is the linear expansion coefficient of
the material. From Equation 1, we see that ∆L, is not
only dependent on ∆T , but also on the initial length
of the object, Li . So, the longer the object, the greater
change in its length. A thermister thermometer was
used to calculate the temperature for the metal rods.
In this experiment we have acquired the ∆L , the ∆T ,
and the Li , so if we rearrange equation one we can
solve for the linear expansion coefficient and compare
it to the theoretical value to calculate a percentage
error for this experiment. we will use equation 2 for
this procedure, which is
Diagram
Metal Rod
L
Stainless steel pin
Bracket on tube
α=
2
∆L
Li ∆T
(2)
Method
Slotted bracket
2.1
Equipment Used
Dial gauge spring arm
Diagram of Thermal Expansion Apparatus
Equipment
Thermal Expansion Apparatus
Steam Generator model TD-8556A
600 ml beaker
Tap water
Digital Multi meter(Fluke)
wooden block
Figure 1: Diagram of thermal expansion apparatus.
1
Introduction
It is found that most solids expand when heated.
When heat is added to most materials, the average
amplitude of the atoms’ vibration within the material increases. This, in turn, increases the separation
2.2
Serial
8558A
n/a
n/a
n/a
n/a
n/a
Procedure
The length of each rod was measured before they
were heated, this is the Li that will be used equation 2, the measurements were made from the inner
∗ The
authors would like to thank Los Angeles City College
for the use of their facilities
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edge of the stainless steel pin on one end, to the inner
edge of the bracket. The metal rod was then mounted
onto the apparatus and the thermistor resistance was
recorded for the initial temperature of the rod. The
steam hose was than connected to one end of the rod,
and the rod was allowed to be heated to maximum
heat. then the ∆L was recorded from the dial gauge.
The final reading that was recorded was the final thermistor reading, which determines the heat of the rod
at that point. the process was repeated for each different metal rod. With these recorded values we can
then calculate the linear expansion coefficient for each
metal. For a more detailed explanation of the procedures used during this experiment please refer to lab:2
in the Los Angeles City College physics lab manual.
3
The experimental values for the linear coefficient were
calculated using equation 2 from the values obtained
in the experiment, the values used for the equation are
found in Table 2. the theoretical values were obtained
from the Physics: for scientist and engineers, Volume
1 text book Table 19.1 pg.588.
4
Conclusion
The purpose of this experiment was to confirm the
accuracy of the linear expansion properties of solids
discussed in the introduction section. The results acquired confirmed that this experiment was prone to
some errors. Possible sources of errors could have
been acquired for the initial temperatures of the metals rods, by not allowing for the thermister to reach
full equilibrium. Another source of error could have
possibly been in the calibration of the gauge scale, by
not setting it to zero initially. Errors were also acquired in the conversion of resistance to temperature
using the thermister. A close approximation was used
for the values of the temperatures using the table provided with the apparatus, which can also be included
in the errors acquired.
Results and Discussion
There are three calculations to make for this report,
The linear coefficients for copper, aluminum, and steel
are calculated using the data that was acquired during
the experiment.
Li = The initial length of each metal rod
Trm = The initial temperature of the rod
5
Thot = The final temperature of the rod
The author would like to thank Roni, Alina, and Arman for their help with conducting this experiment.
∆L = The change in length of the rod, measured with
the gauge scale
References
∆T = the change in temperature Thot − Trm .
[1] Los Angeles City College, Lab Manual, Lab number 2.
with these values we can then calculate the linear expansion of each metal using equation 2.
Metal
Copper
Steel
Aluminum
Li
698
698
698
∆L
0.9
0.63
1.17
Trm
26.0
28.0
25.5
Thot
90.0
90.0
89.5
[2] Serway & Jewet, Physics for scientist and engineers Volume 1, 6th Edition.
∆T
64.0
62.0
64.0
Table 2.1 Values obtained during experiment
The units used for the lengths are in millimeters and
the units used for the temperature are in degrees Celsius.
Metal
αCu
αsteel
αAl
Theory
1.7 × 10−5
1.1 × 10−5
2.4 × 10−5
Exp.
2.01 × 10−5
1.45 × 10−5
2.61 × 10−5
Acknowledgements
Error
18.23%
31.81%
8.75%
Table 2.2 Calculated values obtained from experiment
2