ITU Termodynamics Lab Report

1. PHYSICS ENGINEERING DEPARTMENT
FIZ341E - Statistical Physics and Thermodynamics
Laboratory
Name of Exp. : Thermal Expansion Coefficient of Solids
Date of Exp. : 05.11.2014
BARIŞ ÇAKIR
090100235

2. Introduction
Many substances expand and shrink according to their temperatures.
Telephone wires, and mercury in thermometers.
In this experiment just linear expansion is investigated of a metal. Linear
expansion coefficient is a distinctive feature for solids and liquids. With this
feature, we calculated linear expansion coefficient of an unknown metal rod
with following equation;
∆ =∝ ∆
We need to match experimental coefficient, with the real coefficients in the
following table for assuming experimental metals type.
Material Linear expansion coefficient
Aluminum 24
Copper 17
Glass 9
Steel 11
Lead 29
Table1. Linear expansion coefficients
Experimental Procedure
Tools and devices: A heather set-up, thermometer, a metal rod.
Figure1. Experimental Setup
First initial length of the rod calculated at the initial temperature, after the
temperature was increased of the metal rod and the amount of expansion
calculated for each temperature. Second we plot the amount of elongation per

3. temperature graphic, finally thermal expansion coefficient calculated from plot
of the graphic and equation which was explained in introduction part.
Data Analysis
The initial temperature and length was measured as,
= 20 , = 738
Rod was heated by the heater, difference at length of the metal rod was
calculated for each temperature.
T2 (o
C) ∆L (mm)
25 0.005
30 0,03
40 0,15
50 0,28
60 0,395
70 0,51
80 0,645
Table2. Length difference at several temperatures
Graphic1. ∆L vs Temperature Graphic
If we plug in plot of the graphic to the equation which was given in introduction
part.
∆
∆
= , =
∆
∆
= 0,0118

4. ∝=
0,0118
738
= 16 10
Conclusion
According to founded linear expansion coefficient we can assume our
metal rod is made of copper. We make this assumption from the table which was
given at introduction part; however linear expansion coefficient for copper is
17x10-6
, so we got a experimental error which can be calculated by following
equation;
% =
(17 − 16) 10
17 10
100 = %5.88
Also we got a relative error which depends on measurement devices’ errors and
it can be calculated by following formula we did not calculate this error for each
point we just take best point which compatible to the linear fit;
∆∝
∝
=
∆(∆ )
∆
+
∆
+
∆(∆ )
∆
Where,
∆(∆ ): ∆
∆(∆ ):
∆ :
So, relative error equals to,
∆
=
0.01
0,395
+
0.01
738
+
0.5
60
= 0.034 = %3.4
Resources
 http://mathworld.wolfram.com/RelativeError.html
 http://www.engineeringtoolbox.com/linear-expansion-coefficients-
d_95.html
 Thermodynamics LAB FÖY
 http://iopscience.iop.org/1468-6996/13/1/013001/pdf/1468-
6996_13_1_013001.pdf
 http://books.google.com.tr/books?id=dVIWAAAAQBAJ&pg=PT1202&l
pg=PT1202&dq=why+in+winter+surface+of+lakes+freeze,+but+water+t
emperature+remains+at+4+C+in+the+deep&source=bl&ots=_BOAfU4Jn
u&sig=VazsAU4LfnyNQzDizjmjtQqLJ6w&hl=tr&sa=X&ei=4OFwVIIo
6bvKA7TtgAg&ved=0CB0Q6AEwAA#v=onepage&q&f=false

5. Answers
1- Negative thermal expansion coefficient: For some materials thermal
expansion can not be observed with increasing temperature, even and
even some of them shrinks and shortens. This type of materials can be
used for producing 0 thermal coefficient.
Table3. Negative thermal coefficients of some materials
2- Water has a unique property; it reaches maximum density at 4o
C, with the
density declining as it gets colder. That’s why ice floats appear on the
surface of the water.