1

Comparative Study of Iron and Brass

Expansion & Solid Thermal Diffusivity

Aldrin John A. Adolfo, Jiane

Bryle O. Andaya,Kurt Romiel L. Balita, Dan Abraham M. Evangelista, Aceyork N. Sibal,

College of Engineering, National University Manila Philippines

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ABSTRACT

A material's reaction to changes in temperature is defined by its thermal diffusivity and linear
expansion coefficient. The linear expansion coefficient determines the extent to which a material's
length alters with each unit temperature change, while thermal diffusivity assesses the speed at which
heat transfers through a substance. This experiment aims to investigate both properties by subjecting a
solid material to controlled temperature variations. In the first part of the experiment, heat is applied
to one end of a metal sample, and the temperature distribution along the material is tracked at various
time intervals to ascertain its thermal diffusivity. The thermal diffusivity is then calculated using the
temperature change rate and the heat conduction equation, which reveals the material’s ability to
conduct heat. During the second part, the change in the material's length as its temperature fluctuates
is utilized to determine the linear expansion coefficient. This coefficient is calculated by using the
linear expansion formula along with precise observations of length and temperature alterations. This
value signifies the material's expansion or contraction in response to temperature shifts. These
measurements are significant in material science, engineering, and thermal management, providing a
comprehensive understanding of how materials behave with temperature changes. The results aid in
enhancing material selection and performance in environments subject to varying temperatures.

"Coefficient of Linear Expansion," which

I. INTRODUCTION studies the expansion of various metals
Heat and temperature are crucial in when heated. Metals, like all solids, are
defining the physical characteristics of made up of atoms arranged in a lattice
materials, especially metals. The capacity pattern. As they are heated, these atoms
of materials to expand or contract in acquire kinetic energy and vibrate more
response to changes in temperature is vital vigorously, resulting in a length increase
in numerous engineering and scientific of the material. The degree of this
fields, including construction, expansion is dictated by the specific
transportation, electronics, and coefficient of thermal expansion (CTE) of
manufacturing. Investigating thermal the material. Materials with a high CTE,
expansion and thermal diffusivity offers such as aluminum, undergo a greater
important understanding of how materials degree of expansion compared to those
react under varying temperature with a low CTE, like steel or iron. This
conditions, which is essential for ensuring behavior has critical ramifications in
the dependability and longevity of structural engineering, where structures
structures and mechanical systems. such as bridges, railways, and pipelines
Gaining insight into these properties incorporate expansion joints to manage
allows engineers and scientists to create temperature-related expansion and
materials capable of enduring temperature contraction. Neglecting thermal expansion
variations, avert failures associated with considerations can result in structural
thermal stress, and enhance the damage, distortion, and even catastrophic
effectiveness of heat transfer processes. failures under extreme conditions.
II. III.
One significant element of thermal Alongside expansion, the speed at which
properties is the coefficient of linear heat is transferred through a solid is
expansion, which measures how much a another significant thermal characteristic,
material's length changes with a unit referred to as thermal diffusivity. The
temperature variation. This idea is second experiment, "Thermal Diffusivity
examined in the initial experiment, of Solids," investigates how quickly heat
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propagates through various metal samples. sink. The initial lengths of the metal rods,
Thermal diffusivity is defined as the ratio including brass and iron, were measured using
of thermal conductivity to the product of a meter stick. Each metal rod was then inserted
density and specific heat capacity, into the linear expansion apparatus, ensuring
reflecting how effectively a material can proper contact with the dial-type mechanism
spread heat energy. Materials with high to register initial readings. Water was added to
thermal diffusivity, such as copper and the steam generator, which was then heated
aluminum, transmit heat swiftly and are using a Bunsen burner. After allowing the
frequently utilized in heat exchangers, steam to flow for two minutes, it was directed
cooling systems, and electronics to release into the jacket holding the metal rod. A
excess heat. In contrast, materials with low thermometer was inserted to monitor
thermal diffusivity, such as ceramics and temperature changes, and after a few minutes
certain alloys, serve as effective insulators of stabilization, the final readings were
and are employed in scenarios requiring recorded. The procedure was repeated for the
heat retention, like furnace linings and second metal rod. The coefficient of linear
thermal protection mechanisms. expansion for each material was then
IV. calculated using the recorded data, and a
Comprehending thermal diffusivity is labeled diagram of the experimental setup was
crucial for industries that depend on created.
precise heat management, including
aerospace, automotive, and semiconductor For the second experiment, the
production. For instance, electronic thermal diffusivity of solids was determined.
devices generate significant heat during The dimensions of the metal samples were
operation, and inadequate heat dispersion measured, and their initial temperatures were
can result in overheating, diminished recorded. A beaker was filled with tap water,
performance, and a reduced lifespan of ensuring the metal sample could be fully
components. Engineers rely on thermal immersed. The water was heated to 40°C
diffusivity measurements to design using an electric stove or hot plate. Once the
materials with optimal heat transfer desired temperature was reached, the metal
abilities, ensuring that electronic devices sample was immersed, and thermocouple
remain functional under varying readings were recorded every 10 seconds until
environmental conditions. Additionally, the temperature of the sample stabilized. The
advanced measurement methods, such as sample was then removed, and the procedure
the laser flash technique, have been was repeated using a hot water bath at 80°C.
created to accurately assess the thermal After heating, the metal sample was
diffusivity of various materials, facilitating immediately placed in an ice bath to stabilize
the development of new materials with its temperature. Temperature readings were
enhanced thermal properties. taken every 10 seconds until no significant
V. changes were observed. This process was
VI. repeated for the second metal sample to ensure
VII. 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
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VIII. RESULT AND DISSCUSSION

Coefficient of Linear Expansion −5 −5
10 10
Table 1: Linear Expansion vs. Temperature 6.01× + 3.06×
°C °C
α=
2
Meta Lo Lf ∆ L( To ( Tf ( ∆T( 10
−5

l rod (cm) (cm) cm) ° C) ° C) ° C) α Iron =4.535 ×

°C
Iron Theoretical:
52 52.8 0.2 28 92 64 10
−5
(1)
α Iron =1.18 ×
°C
Iron % of Error:
52.7 52.8 0.1 28 90 62
(2)
α Actual − α Tℎeo .
%Error Iron=
Brass α Tℎeo.
52.5 52.8 0.3 28 93 65
(1) −5 −5
10 10
4.535 × −1.18 ×
Brass °C °C
52.7 52.7 0 28 89 61 %Error Iron=
(2) 10
−5
1.18 ×
Actual: °C
Iron (1) %Error Iron=284.32 %
ΔL
α 1=
( L ₀× ΔT )
0.2 cm
α 1= Brass (1)
(52 cm× 64 ° C)
ΔL
10
−5
α 2=
α 1=6.01 × ( L ₀× ΔT )
°C
0.3 cm
Iron (2) α 1=
ΔL (52.5 cm ×65 ° C )
α 2= 10
−5
( L ₀× ΔT ) α 1=8.79 ×
0.1 cm °C
α 2= Brass (2)
(52.7 cm ×62 ° C )
ΔL
10
−5
α 2=
α 2=3.06 × ( L ₀× ΔT )
°C
0 cm
α 2=
(52.7 cm ×61 ° C )
Average of α Iron
α 2=0
α 1+ α 2
α= Average of α Brass
2
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α 1+ α 2 %Error Brass =131.32 %

α=
2
−5 −5
10 10
8.79 × +0 × Micrometers and calipers, which are
°C °C
α= used to measure changes in length, may not be
2
−5 accurate enough for tiny expansions,
10 particularly when temperatures are high. The
α Brass =4.395 ×
°C development of temperature gradients where
the temperature isn't constant throughout
Theoretical: occurs while heating a material, particularly
−5
10 big samples. Non-uniform expansion may
α Brass =1.9×
°C result from this, making it more difficult to
% of Error: determine the actual CTE. . The measurement
of the iron's average CTE may be inaccurate if
α Actual − α Tℎeo . it is not completely homogeneous since it may
%Error Brass = expand differently at different locations.
α Tℎeo .
−5 −5 Higher error rates can also result from timing
10 10 errors, misreading equipment, or improperly
4.395 × − 1.9×
°C °C capturing data.
%Error Brass = −5
10
1.9 ×
°C
Time, Diffusivity
Thermal Temperature, °C
of Solid
s (Heating) Temperature, °C
To To
Metal Sample 1 (Gram) (Cooling) IX. CONCLUSION
40.0°C 80.0°C
10 Temperature,
25 28 °C 40 The objective of this experiment was to
Time,
20 s 26(Heating)
37 Temperature,
33 °C ascertain the coefficient of linear expansion for
30 31 39 (Cooling)
25 iron and brass by analyzing the changes in
To To
40 32 44
40.0°C 80.0°C 21 their lengths as the temperature increased. The
50
10 32
26 4431 1743 findings displayed considerable discrepancies
60
20 34
27 4842 1634 from the expected theoretical values, with iron
70
30 35
28 4950 1426 exhibiting a percentage error of 284.32% and
80
40 35
30 4953 1322 brass showing an error of 131.32%. Such
90
50 35
30 5354 1218 substantial error percentages imply that
100
60 36
31 5357 1217 various factors affected the precision of the
110
70 36
31 5358 1216 measurements. One major source of error
120
80 36
31 5358 1215 might be the limitations inherent in the
130
90 36
32 5358 1214 measuring devices utilized. While micrometers
140
100 36
32 58 14 and calipers are beneficial for general
110 32 58 13 measurements, they may lack the necessary
120 33 12 precision to detect the very minute expansions
130 34 10 that occur with temperature variations.
140 34 9 Moreover, human error in interpreting and
150 34 9 documenting measurements could have led to
160 34 9 inaccuracies in the data.
170 34 9
180 9
Another crucial factor impacting the
Metal Sample 2 (Gram) accuracy of the results is the formation of
temperature gradients within the metal
samples. Ideally, the entire metal rod should be
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uniformly heated to ensure that all parts of the instruments, ensuring consistent heating
material expand consistently. However, in methods, and adopting automated data
reality, the distribution of temperature may not collection processes to reduce human error.
be entirely uniform, resulting in localized Managing external factors, such as variations
expansions that deviate from the anticipated in ambient temperature and ensuring steady
theoretical behavior. This uneven heating heat application, could further enhance the
might be intensified in larger samples, where experiment's accuracy. Despite these
heat transfer takes place at a slower and less challenges, the results emphasize the
uniform rate. Consequently, the measured significance of comprehending thermal
expansion may not truly represent the expansion and heat transfer characteristics,
coefficient of linear expansion. Timing errors which have valuable applications in
in recording length variations at specific engineering, construction, and materials
temperature intervals could have also science.
contributed to inaccuracies, alongside potential
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