RESEARCH QUESTION
How does
the rate of
cooling of hot
water depend on
the thermal conductivity of the selected insulating materials?
INTRODUCTION
Insulators are materials that
inhibit the property of resisting electricity and heat. The idea of insulators
sparked in my mind while referring a journal which discusses why a person feels
warm even while wearing a light weight cloth. This discussion was based on the
concept of heat transfer. In the chapter thermal physics, I remember the concept
of heat transfer being discussed. My teacher introduced a
concept called thermal conductivity to give more clarity and understanding
about heat transfer. I decided to choose this topic because the concept of
thermal insulation is very much used in our daily life. The cloths we wear, the
buildings that are built, the mechanical systems that are manufactured, in
automobiles, in electrical systems, mostly everywhere we see the application of
thermal insulation. This sparked a curiosity in me to know how different
materials insulate heat differently.
In order to investigate this, I
decided to conduct an experiment by building an apparatus of my own design to
determine the best thermal insulator among the chosen materials. Four commonly
known materials that most of us have come across were chosen for the experiment.
The materials chosen are cement, mud (which is used in the production clay
tiles), Plaster of Paris
BACKGROUND information
The underlying principle of this experiment is thermal conductivity. by comparing the
thermal conductivity the
effectiveness of different materials as an
insulator can be
compared. The material with the least
thermal conductivity is
considered as a
good insulator and
the material with
higher thermal conductivity is a good
conductor of heat[2]. According
to law of
thermal conductivity, the
thermal conductivity of
a material can
be expressed as:
Here, k represents the thermal conductivity value. from the
equation it can
be said that
the amount of
heat energy (Q)
is directly proportional to the surface area, temperature difference and inversely proportional to the distance between the opposite sides of the
insulator[2]. From the values obtained through the
data collection, a
temperature v/s
time graph will
be plotted for
the analysis. the
obtaining graph is
expected to be
an exponential curve
based on the
principle of Newton’s law of
cooling[3]. By linearizing
the graphs, the curve which
gives the least
slop will be
the best insulator.
HYPOTHESIS
the thermal insulation property increases with decrease in
thermal conductivity
VARIABLES
·
Independent variables: Time(s)
·
Dependent variables: Temperature
(°C)
·
Controlled variables:
1. The distance
between the plastic and metallic container: This parameter was made constant
because according to the law of thermal conductivity, the rate at which the
heat flows through a material is directly proportional to the area through
which it flows[2].
2. The
mass of water taken to heat: The amount of heat released depends on the amount
of water taken based on the concept of specific heat capacity. Mass is directly
proportional to the amount of energy released or absorbed[4].
METHOD
Apparatuses
Required:
1.
Cylindrical plastic container of 5 cm radius
2.
Cylindrical copper container with the same height
that of the plastic container and of radius 2 cm
3.
Plaster of Paris, 500g (Fig. A)
4.
Mud, 500g (Fig. B)
5.
Cement powder, 500g (Fig. C)
6.
Saw dust, 500g (Fig. D)
7.
Temperature probe
8.
Hot water
9.
Bunsen burner
10. Insulating
lid with same radius that of the plastic container.
11. Vernier lab quest Logger Pro (software interface for data-collection)
Experimental set-up
Schematic diagram
Experimental
procedure
1. The
copper container was placed inside the plastic container as shown in Fig. F.
It was placed equidistant from all the sides of the plastic container for
uniform heat distribution.
2. The
remaining gap between the plastic container and the copper container were
filled with the insulating material.
3. The hot
water having a temperature around
4. Both the containers were covered with a thermocol lid which was fit
inside the cap of the plastic container. This was done in order to provide maximum
insulation such that the heat energy is not lost through any air gap and also
such that the plastic lid doesn’t absorb the heat.
5. The temperature probe was fixed in a hole which was provided on the insulating
lid and connected to the vernier lab quest and to the laptop as shown in Fig.
E.
6. A continuous data collection was begun when the temperature reading was
shown as
7. The above procedures were repeated for different insulating materials.
8. The time for every
Precautionary measures
1. It
was made sure that there is enough gap between the plastic and copper
containers such that the plastic container does not conduct the radiated heat
from the copper container.
2. It
was made sure that the gap between the plastic and copper containers is kept constant
for all the trials and with other insulating materials.
3. Packing
of the insulating materials into the gaps was done uniformly for all the
trials. This includes making sure that there is not air gap between the
containers where the insulating materials are packed.
4. The
insulating lid was tightly fit in order to minimize heat loss.
5. It
was made sure that the insulating material after the trial was kept outside for
cooling such that it attains the room temperature.
6. Safety
goggles and gloves were worn since the experiment dealt with hot water and
heater.
DATA collection
DATA PROCESSING
The
table shown below (TABLE 5) gives the average time taken for the hot
water to cool down by a factor of
Error
calculation
The
calculated error values shown in TABLE 6 are for the time taken for
every
Graphs
The TABLE 7 shown below represents the average
time taken for every
Linearization
of the graphs
Since
the obtained graphs are of exponential form as expected, the linearization of
the graphs was done by taking the log value of the y-axis i.e. the log value of
the temperature and the time on x-axis. The TABLE 8 shown below gives
the log values of the temperature. The TABLE 9 shown below is the slop
values of the linearized curves. The curve giving the least slope will be the
best insulator and the curve with the maximum slope will be a good thermal
conductor. The modulus of the slopes is taken in order to remove the negative
sign.
TABLE 8
|
Temperature
( |
80 |
75 |
70 |
65 |
60 |
|
Log
(Temperature) |
1.903 |
1.875 |
1.845 |
1.813 |
1.778 |
CONCLUSION
From the
data collection and data processing it can be concluded saw dust is
comparatively the best insulator and mud is the least insulating material. This
was confirmed using GRAPH 6. The
steepness of the exponential curve can give a qualitative result about the rate
of cooling of the water kept in the copper container with respect to each
insulating material used. Greater the steepness, higher the rate of cooling and
lesser the steepness of the curve, the better insulator it is due to the lesser
cooling rate. The curve produced by mud was very steep compared to curves of
other insulating materials. In the same way the curve of saw dust had the least
steep. Therefore, the saw dust resulted in being a better insulator. To study
the linear relationship between temperatures and time of the respective
insulating material a graph log (temperature) v/s time was plotted for each
material. A linear best fit was inserted into the graph to obtain the slope of
the linearized graph. The slope of the linearized graphs gave an idea about the
rate of cooling and thus determining the best insulator. The graph with the
least slope will be a good insulator and the graph with the highest slope will
be a bad insulator. From TABLE 9 it can be seen that the graph of saw
dust gave the least slope resulting in being a good insulator of heat. The
graph of mud gave the highest slope which results mud being a bad insulator of
heat. Therefore, from TABLE 9 and GRAPH 6, I can also arrange the
selected insulating materials in the order of decreasing thermal conductive property
as:
EVALUATION
This investigation was very successful in determining the best insulating material among the selected ones. I am
very confident with the obtained results. The average percentage uncertainty
values for all the insulating materials were less than 10% except for the
material mud, 18.2%. In TABLE2, all the values obtained for trial 3
& 4 are comparatively very much away from the values obtained for trial 1,
2 & 5. The deviations in the value are due to the experimental error
(random error). From TABLE 5 I observed that the values obtained in each
trial were deviated from the mean value by a factor of 50 to 178 seconds for
certain trials especially with saw dust mud. I assume it to happen due to the
initial temperature of the hot water. According to law of thermal conductivity,
the temperature difference between the system and surrounding affects the rate
of heat transfer. Higher the value of
BIBLIOGRAPHY
[1] Y. Ke and F. Wang, “Warmth without the
weight,” Eng. High-Performance Text., no. 1983, pp. 231–245, 2017.
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thermal conductivity? (article) Khan Academy,” Khan Academy, 2015.
[Online]. Available:
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[Accessed: 27-Feb-2020].
[3] M. Kleiber, “A
New Newton ’ s Law of Cooling ? Author ( s ): Max Kleiber Published by :
American Association for the Advancement of Science Stable URL :
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[9] The Editors of
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