1

The Coefficient of Linear Expansion of Iron

and Brass & Thermal Diffusivity of Solid
P. Bunac, S. Diño, L. Felix, K. Jarantilla, and E. Sabeniano, College of Engineering, National
University Manila Philippines
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ABSTRACT

A material's response to temperature changes is characterized by its thermal diffusivity and

coefficient of linear expansion. The coefficient of linear expansion calculates how much a material's
length changes with each unit change in temperature, whereas the thermal diffusivity evaluates how
quickly heat moves through a substance. By exposing a solid material to control temperature changes,
this experiment seeks to examine both properties. By applying heat to one end of the metal sample
and monitoring the temperature distribution along the material at different time intervals, the
experiment's first section determines the thermal diffusivity of a solid material. The thermal
diffusivity, which provides information on the material's capacity to conduct heat, is then computed
using the rate of temperature change and the heat conduction equation. In the second section, the
change in length of the material as its temperature varies is used to get the coefficient of linear
expansion. The coefficient is computed using the linear expansion equation and exact length and
temperature change observations. The material's expansion or contraction in response to temperature
changes is indicated by this value. With applications in material science, engineering, and thermal
management, these measurements offer a thorough grasp of how materials react to temperature
fluctuations. The findings aid in improving material choice and functionality in systems exposed to
different temperatures.

vibrate more intensely, leading to an increase

I. INTRODUCTION in the material’s length. The extent of this
Heat and temperature play a expansion depends on the material’s specific
fundamental role in determining the physical coefficient of thermal expansion (CTE).
properties of materials, particularly metals. Materials with a high CTE, such as aluminum,
The ability of materials to expand or contract expand more significantly than those with a
due to thermal changes is a crucial factor in low CTE, such as steel or iron. This
various engineering and scientific applications, phenomenon has significant implications in
from construction and transportation to structural engineering, where bridges,
electronics and manufacturing. The study of railways, and pipelines are designed with
thermal expansion and thermal diffusivity expansion joints to accommodate temperature-
provides essential insights into how materials induced expansion and contraction. Failure to
behave under different temperature conditions, account for thermal expansion can lead to
which is critical for ensuring the reliability and structural damage, warping, and even
durability of structures and mechanical catastrophic failures in extreme conditions.
systems. Understanding these properties
In addition to expansion, the rate at
allows engineers and scientists to design
which heat transfers through a solid material is
materials that can withstand temperature
another crucial thermal property, known as
fluctuations, prevent failures caused by
thermal diffusivity. The second experiment,
thermal stress, and improve the efficiency of
"Thermal Diffusivity of Solids," explores how
heat transfer processes.
quickly heat spreads through different metal
One key aspect of thermal behavior is samples. Thermal diffusivity is defined as the
the coefficient of linear expansion, which ratio of thermal conductivity to the product of
quantifies the change in length of a material density and specific heat capacity, indicating
per unit temperature change. This concept is how efficiently a material can distribute heat
explored in the first experiment, "Coefficient energy. Materials with high thermal diffusivity,
of Linear Expansion," which investigates how such as copper and aluminum, conduct heat
different metals expand when subjected to rapidly and are commonly used in heat
heat. Metals, like all solids, are composed of exchangers, cooling systems, and electronics
atoms arranged in a lattice structure. When to dissipate excess heat. Conversely, materials
heated, these atoms gain kinetic energy and with low thermal diffusivity, such as ceramics
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and certain alloys, are effective insulators and second metal rod. The coefficient of linear
are used in applications where heat retention is expansion for each material was then
necessary, such as furnace linings and thermal calculated using the recorded data, and a
protection systems. labeled diagram of the experimental setup was
created.
Understanding thermal diffusivity is
vital for industries that rely on precise heat For the second experiment, the
management, such as aerospace, automotive, thermal diffusivity of solids was determined.
and semiconductor manufacturing. For The dimensions of the metal samples were
example, electronic devices generate measured, and their initial temperatures were
significant amounts of heat during operation, recorded. A beaker was filled with tap water,
and improper heat dissipation can lead to ensuring the metal sample could be fully
overheating, reduced performance, and immersed. The water was heated to 40°C
shortened lifespan of components. Engineers using an electric stove or hot plate. Once the
use thermal diffusivity measurements to desired temperature was reached, the metal
design materials with optimal heat transfer sample was immersed, and thermocouple
properties, ensuring that electronic devices readings were recorded every 10 seconds until
remain operational under varying the temperature of the sample stabilized. The
environmental conditions. Furthermore, sample was then removed, and the procedure
advanced measurement techniques, such as the was repeated using a hot water bath at 80°C.
laser flash method, have been developed to After heating, the metal sample was
accurately determine the thermal diffusivity of immediately placed in an ice bath to stabilize
different materials, aiding in the development its temperature. Temperature readings were
of new materials with improved thermal taken every 10 seconds until no significant
performance. changes were observed. This process was
repeated for the second metal sample to ensure
II. METHODOLOGY
accuracy and consistency in data collection.
The experiments were conducted to
determine the coefficient of linear expansion
and the thermal diffusivity of solid materials.
For the first experiment, the coefficient of
linear expansion was measured using a linear
expansion apparatus. A rubber tube was
connected from a steam generator to the linear
expansion apparatus, while another tube was
attached to allow excess steam to escape into a
sink. The initial lengths of the metal rods,
including brass and iron, were measured using
a meter stick. Each metal rod was then inserted
into the linear expansion apparatus, ensuring
proper contact with the dial-type mechanism
to register initial readings. Water was added to
the steam generator, which was then heated
using a Bunsen burner. After allowing the
steam to flow for two minutes, it was directed
into the jacket holding the metal rod. A
thermometer was inserted to monitor
temperature changes, and after a few minutes
of stabilization, the final readings were
recorded. The procedure was repeated for the
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III. RESULT AND DISSCUSSION

Coefficient of Linear Expansion −5
10
Table 1: Linear Expansion vs. Temperature α Iron =1.18 ×
°C
% of Error:
Meta Lo Lf ∆ L( To ( Tf ( ∆T( α Actual −α Theo.
l rod cm) ° C) %Error Iron=
(cm) (cm) ° C) ° C) α Theo .
Iron 10−5 10−5
52 52.8 0.2 28 92 64 4.535 × −1.18 ×
(1) °C °C
%Error Iron= −5
Iron 10
52.7 52.8 0.1 28 90 62 1.18 ×
(2) °C
%Error Iron=284.32 %
Brass
52.5 52.8 0.3 28 93 65
(1)

Brass
52.7 52.7 0 28 89 61 Brass (1)
(2)
ΔL
Actual: α 2=
( L ₀× ΔT )
Iron (1)
ΔL 0.3 cm
α 1= α 1=
( L ₀× ΔT ) (52.5 cm ×65 ° C )
−5
0.2 cm 10
α 1= α 1=8.79 ×
(52 cm× 64 ° C) °C
−5 Brass (2)
10
α 1=6.01 × ΔL
°C α 2=
( L ₀× ΔT )
Iron (2)
ΔL 0 cm
α 2= α 2=
( L ₀× ΔT ) (52.7 cm ×61 ° C )
0.1 cm α 2=0
α 2= Average of α Brass
(52.7 cm ×62 ° C )
−5
10
α 2=3.06 × α 1+ α 2
°C α=
2
−5 −5
Average of α Iron 10 10
8.79 × +0×
α 1+ α 2 °C °C
α= α=
2 2
−5
10
−5
10
−5 10
6.01× +3.06 × α Brass =4.395 ×
°C °C °C
α=
2
−5 Theoretical:
10 −5
α Iron =4.535 × 10
°C α Brass =1.9×
°C
Theoretical:
% of Error:
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α Actual −α Theo. particularly when temperatures are high. The

%Error Brass = development of temperature gradients where
α Theo.
−5 −5 the temperature isn't constant throughout
10 10
4.395 × −1.9 × occurs while heating a material, particularly
°C °C big samples. Non-uniform expansion may
%Error Brass = −5
10 result from this, making it more difficult to
1.9 ×
°C determine the actual CTE. . The measurement
%Error Brass =131.32 % of the iron's average CTE may be inaccurate if
it is not completely homogeneous since it may
expand differently at different locations.
Micrometers and calipers, which are Higher error rates can also result from timing
used to measure changes in length, may not be errors, misreading equipment, or improperly
accurate enough for tiny expansions, capturing data.
Thermal Diffusivity of Solid Metal Sample 2 (Gram)

Metal Sample 1 (Gram)

Temperature, °C
Time, s (Heating) Temperature,
IV. CONCLUSION
°C (Cooling)
To To
40.0°C 80.0°C Based on the data collected, this
10 26 31 43 experiment aimed to determine the coefficient
20 27 42 34 of linear expansion for iron and brass by
30 28 50 26 measuring how their lengths changed with
40 30 53 22 increasing temperature. The results revealed
50 30 54 18 significant deviations from the theoretical
60 31 57 17 values, with iron exhibiting a percentage error
70 31 58 16 of 284.32% and brass showing an error of
80 31 58 15 131.32%. These high error percentages
90 32 58 14 suggest that various factors influenced the
100 32 58 14 accuracy of the measurements. One of the
110 32 58 13 primary sources of error could be the
120 33 12 limitations of the measuring instruments used.
130 34 10 Micrometers and calipers, while useful for
140 34 9 general measurements, may not provide the
150 34 9 level of precision required to detect the
160 34 9 extremely small expansions that occur in
170 34 9 response to temperature changes. Additionally,
180 9 human error in reading and recording
Time, Temperature, °C measurements could have contributed to
s (Heating) Temperature, inconsistencies in the data.
To To °C (Cooling)
40.0°C 80.0°C Another significant factor affecting the
10 25 28 40 accuracy of the results is the development of
20 26 37 33 temperature gradients within the metal
30 31 39 25 samples. Ideally, the entire metal rod should be
40 32 44 21 heated uniformly, ensuring that every part of
50 32 44 17 the material expands at the same rate.
60 34 48 16 However, in practice, temperature distribution
70 35 49 14 may not be perfectly even, leading to localized
80 35 49 13 expansions that differ from the expected
90 35 53 12
100 36 53 12
110 36 53 12
120 36 53 12
130 36 53 12
140 36
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theoretical behavior. This non-uniform heating have practical applications in engineering,

could be exacerbated in larger samples, where construction, and materials science.
heat transfer occurs more slowly and unevenly.
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