Department of

PHYSICS
Experiment 105
Linear Expansion
Name:
Course/Year: ME/1
Subject/Section: PHYS101L/A23
Date of Performance:
Date of Submission:
Criteria Score
Data Sheet with sample computation (40 points)
Guide Questions (GQ) (10 points)
Interpretation of Results (Analysis) (15 points)
Error Analysis (5 points)
Conclusion (15 points)
Application (10 points)
Graph/figure (5 points)

Instructor
Guide Questions

1. What is relationship between the change in length and change in temperature of a body?

Materials that heat was added resulted an increase of its initial temperature
undergone thermal expansion among its dimension. Thermal expansion can exist in linear
i.e. change in length or change in volume. The change in length of the material has a direct
relationship with its temperature change. If the change in temperature of the material
increases, its change in length also increase, otherwise the change in temperature decreases
the length of the material decreases also.

2. List down 2 sources of error in this experiment and your suggested solutions for these.

Source of Error: Uncalibrated and wear instruments and materials.

Analysis

All materials tend to change its dimension such as length, area, and volume due to its
change of temperature. These are composed of individual atoms constantly and randomly in
motion if the material is not equal to absolute zero (0 kelvin). The individual motion of the atoms
in a system yields kinetic energy in each atom. The average kinetic energy of the atoms in a system
measured as temperature in kelvin or Celsius scale. The higher temperature of a system, the faster
the atoms moved, the greater the space it covers. A system’s temperature may change by adding
or subtracting energy in the form of heat. A system experienced heat transfer may contract or
expand. Adding heat increases the temperature of the system and expands it while subtracting heat
decreases the temperature of the system and contracts it. The experiment demonstrated linear
thermal expansion wherein the system’s change in length has a direct relationship to its
temperature change and initial length with a coefficient of linear expansion as a proportionality
constant and determined the coefficient of linear expansion. The direct relationship and
determinant of coefficient of linear expansion is mathematically shown below, respectively:

𝛥𝐿
𝛥𝐿 = 𝐿0 𝑎𝛥𝑇; 𝑎 = 𝐿
0 𝛥𝑇

where 𝛥𝐿 is the difference of the final length of the material from its initial length; 𝐿0 is
initial length of the material; 𝑎 is the coefficient of linear expansion depending on the material;
and 𝛥𝑇 is the difference of the final temperature of the material from its initial temperature. This
is the primary principle used.
 Percent error was used to compare the accepted value and experimental value of the
acquired coefficient of linear expansion ensuring the accuracy and precision of data as shown
below:
|𝐴𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒−𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑉𝑎𝑙𝑢𝑒|
x 100
𝐴𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒

The experiment conducted two trials with different materials such as aluminum and brass.
The different materials used in those trials demonstrated the dependence of the system’s change
in length with respect with the material used. Both materials have an initial length of 700 mm. The
resistance read through the thermistor was transmuted into temperature. Both materials had an
initial resistance ranging 80k Ω transmuted into 30 0C as initial temperature. After the two
materials where heated by steam, the final resistance was 12.048k Ω transmuted into 77 0C. The
change in temperature on both materials were 47 0C. The length of the aluminum tube and copper
tube increased by 1.16 mm and 0.83 mm, respectively. Thus, verifying the direct relationship of
the increased amount of length with the increased of temperature. The experimental coefficient of
linear expansion of aluminum tube and brass tube were 35.26 x 10-6 / Co and 25.23 x 10-6 / Co,
respectively. It was compared to actual value which were 23.80 10-6 / Co and 19.30 10-6 / Co for
aluminum tube and brass tube, respectively. The percent error found was 48 % and 31 % in
aluminum tube and brass tube, respectively.

Error Analysis

High percentage of error was found on both trials. The errors observed in this experiment
can be systematic errors or random errors. For the systematic errors, the calibration of the
instruments such as the thermistor and gauge for providing accurate and precise readings; and
longevity of the materials used. In this experiment the thermistor does not hold a static reading.
The usage frequency of the instrument may cause it to be uncalibrated also its longevity may affect.
The air condition room also affect the temperature of the system. The ideal ambient temperature
was 25 0C due to the air condition ambient temperature must be lowered and heat flows from a
higher temperature to a lower temperature. Thus, the heat from the tubes flow into the surroundings
and its rate varies. Also, heat from the steam generator is not completely transferred into the tubes
due to the pipes used; some heat was transferred into the pipes. Human errors such as reading the
gauge and deciding the resistance to be used were random errors. The setup of the experiment may
cause some errors such as the connectivity of the thermistor to the tubes and the steam generator
tot the tubes.

Conclusion

The experiment exhibited linear thermal expansion among two different kinds of materials.
Thus, verified the dependence of the body’s change in length with the kind of material. The
increase of 47 0C in temperature on both trials increased the aluminum tube by 1.16 mm and the
brass tube by 0.83mm. Hence, verified the direct relationship of the body’s change of length to its
temperature change. The experimental coefficient of linear expansion of aluminum tube and brass
tube were determined which were 35.26 x 10-6 / Co and 25.23 x 10-6 / Co, respectively. The
experimental value was compared to the actual coefficient of linear expansion yielded a percent
error of 48% and 31% for aluminum tube and brass tube, respectively. The errors were generated
mainly on the uncalibrated thermistor and airconditioned room.

Application

The application of thermal expansion can be seen in the construction industry. The change
in temperature can change the dimension of a system such as bridges. The environment can be the
cause of the change of temperature of the bridge which it can expand or contracts. Hence,
expansion joints were added. As a mechanical engineering student, the application of thermal
expansion may take form in a variety of way. The gasoline from underground tank at a gas station
is relatively cool. If a car i.e. driven fueled, the gasoline will warm in the driven car’s tank but if
the car’s tank is filled and not driven the gasoline will expand in volume faster than the fuel tank.
Thus, overflowing onto the pavement. Mechanical engineers deal with the capacity of a gas to do
work as shown in an internal combustion engine. As the gas is being heated its volume increases
thus if contained against a piston the gas will do work.

Graphs/Figures
The graphs below were a visual representation of the direct relationship of the change in
length of a system to its temperature change where its length is a function of temperature. A
positive slope can be seen therefore verifying the direct relationship as temperature increase the
length of the material also increases.

Aluminum Tube Linear

701
700
699
30 77
Temperature

Brass Tube Linear Expansion

700.5

700

699.5
30 77
Temperature