Table of Contents:
Introduction………………………………………………………………………………1
Background and Reviews of Literature……………………………….………………2
Problem Statement……………………………………………………………………...9
Experimental Design…………………………………………………………………..10
Data and Observations………………………………………………………………..17
Data Analysis and Interpretation……………………………………………………..23
Conclusion……………………………………………………………………………...36
Acknowledgements……………………………………………………………………39
Appendix A: Sample Calculations…………………………….……………………..40
Appendix B: Randomization………………...………………………………………..42
Appendix C: LoggerPro……………………...………………………………………..43
Appendix D: Calorimeter Construction……………….……………………………..44
Appendix E: Thermal Expansion Jig……..….………………………………………46
Works Cited…………………………………………………………………………….47
Kirby-Koury 1
Introduction
Metals play a huge role in the day-to-day lives of every human. They are
used to make many products that assist with or allow daily activities to take
place. Metal products used everyday range from things as simple as silverware
to things as complex as bridges. Bridges have to sustain large amounts of weight
constantly and remain stable under harsh, constantly changing conditions such
as weather and traffic. But how do architects keep these structures stable? They
use linear thermal expansion as one of their quantities to assist in the
calculations of the specific measurements of the structure. For instance, an iron
bridge must take into account the linear thermal expansion coefficient of iron to
allow for its expansion and contraction within the bridge.
Another important quality of metal is the specific heat. Specific heat
applies to every metal, and is used to make everything from thermometers to
frying pans to cars. Metals with low specific heat can heat up very quickly,
making these metals ideal for pots and pans. Furthermore, research can be
conducted to determine the linear thermal expansion coefficient and specific heat
value of a metal. On a smaller scale however, similar techniques can be used to
identify an unknown metal or determine if it is the same metal as another known
metal using specific heat and calorimetry, the measure of heat changes (Chang).
With these techniques, the researchers conducted an experiment to identify if an
unknown metal is the same as the known metal, iron, based on linear thermal
expansion and specific heat. The comparison was made after collecting the
values and conducting a statistical test to analyze the data.
Kirby-Koury 2
First, a linear thermal expansion test was conducted by using a linear
thermal expansion jig that measured the change in length. In addition, initial
length of the unknown metal rod and the change in temperature of the rod were
measured. Once the linear thermal expansion coefficient was found, the next
step was to determine its specific heat value. This value is determined by using
calorimeters that allow the researchers to measure the change in temperature of
the metal. The other component in the specific heat calculation is the mass of the
metal rod.
Overall, the data collected from the specific heat and linear thermal
expansion trials was used in a two-sample t-test statistical analysis. The results
from the analysis determined whether the unknown metal was iron or not, which
is the purpose of the following research.
Background and Review of Literature
Background:
While making up more than five percent of the earth’s crust, iron is also
the fourth most abundant element on earth. Iron has been known since ancient
times, and was first manufactured by humans around 2000 BCE, beginning the
Iron Age. The first area of the world to use iron was most likely in south-west or
south-central Asia (Spoerl).
Iron Fe is naturally found as iron ore, due to the affinity of iron to oxygen.
This is the cause for iron ore being classified as an oxide of iron. In order to
separate iron from iron ore the substance must go through a process called
Kirby-Koury 3
smelting. When the iron ore is heated over burning charcoal the oxygen is
released and the iron is left. The chemical reaction to extract the element from its
raw state is (Justusson):
Fe3O4 (s)+CO(s)→Fe(s)+CO2( g)
Iron, having a wide range of uses, is often a part of industrial production. A
few examples of iron’s uses include tongs, furnaces, magnets, and more. Not
only is iron used to form new products, it is used to create steel. Steel production
reached 1,414 million metric tons in 2010, a record high amount, and iron is one
of the main components of steel (“About Steel”).
To determine if the metals are the same, intensive properties will be used.
These are specific to each metal. The density of iron, 7.874 g
cm3 , will be the
same for any sample of iron. It is an intensive property. This can be used to
determine if the metals are the same. When compared to the density of water, 1
gcm3 , iron is very heavy. This means that it has a high mass per unit of volume
(cm3). Next is specific heat, which is an intensive property as well so it can be
used to determine if the two metals are the same. The specific heat of iron is
0.444 J
g ∙℃ (Stretton), and the specific heat of water is 4.184 (Hilliard). There is a
large difference between the two which means that it takes much less energy to
change the temperature of iron by one degree Celsius than it takes to change the
temperature of water by one degree Celsius. Then there is thermal expansion,
which is specific to each metal. When heated, the metals expand and the
expansion value can be used to compare the two metals to see if they are the
Kirby-Koury 4
same. The linear thermal expansion coefficient for iron is 11.8 mm∙10-6 (Lide).
This value is slightly on the high side of the coefficients for other transition
metals, which means it expands and contracts more than most other transition
metals when heated or cooled.
The electronic structure of iron is essential to the property of the metal
because the electrons are what take part in the chemical reaction. Therefore, the
electron interactions determine the chemical reaction. The electronic structure is
relevant to the project because it is what helps determine whether the known and
unknown elements are the same.
1s2
2s2 2p6
3s2 3p6 3d6
4s2
Figure 1. Electron Configuration of Iron
Figure 1 above shows the electron configuration for iron. The written form
of this would be [Ar] 4s2 3d6 (Gagnon).
Specific Heat:
When energy in the form of heat is added to a substance, its atoms or
molecules gain kinetic energy. On a molecular level, this process can be
described as the movement of the molecules from a relaxed and fairly motionless
state to a hectic and rapid moving state. With the additional heat, the metal
increases in temperature, and the change in temperature gives researchers the
Kirby-Koury 5
ability to identify the element. The specific heat of a substance is the heat
required to raise one gram of it by 1°C. It is often measured in J/g∙ ⁰C (Hilliard). In
order to create an experimental design, prior research was reviewed and two
experiments were used to design this research.
The first experiment for finding the specific heat of an element begins with
heating water, massing a boiler cup, and placing a known metal into the boiler
cup and determining its mass. Then, the boiler cup is heated with the metal.
Next, a graduated cylinder is used to fill the calorimeter with about 100 mL of
water and then record the temperature of the metal and the temperature of the
calorimeter water. Once the metal temperature reaches 95℃ quickly put the
metal into the calorimeter and begin recording the temperature until
equilibrium is met. The final step is to calculate the specific heat (Shipman,
Wilson, and Todd). The formula to calculate specific heat uses the heat energy
released or absorbed by the reaction in joules, q, set equal to the specific heat
in J/g∙℃, s, times the mass of the solution in grams, m, times the change in
temperature in degrees Celsius, ∆t (Hilliard).
q=sm∆ t
By substituting these values into the equation, one can calculate the specific heat
of the element.
The second experiment had a similar procedure, but instead of using the
temperature of the water in the calorimeter and the temperature of the metal in
the heated water, the experiment used the temperature of the hot metal bath
before and after the metal was placed into an ice cold calorimeter. The
Kirby-Koury 6
researchers first poured 210 mL of cold water into a calorimeter and measured
and recorded its temperature. Then, the students placed 0.5 kg of iron from a hot
iron bath into the calorimeter and recorded the temperature of the water in the
calorimeter. Next, the iron was removed from the calorimeter and returned to the
bath and the temperatures of both the bath and the water in the calorimeter were
recorded. With this data, the students used the formula where mass of the
solution, m, times the specific heat in cal/g∙℃, c, times the change in
temperature, ∆t, set equal to two times the mass times the specific heat times the
change in temperature(Stephanie & Candace).
mc ∆t=mc∆ t+mc∆ t
These formulas can be used to calculate the specific heat of an element
such as iron. On a molecular level, the molecules inside of the metal rods are
being heated by the water causing the energy in the water to move into the metal
increasing the level of kinetic energy in the metal. This increase is slowed when
the rod is placed into the colder calorimeter. When the metal is decreasing and
reaching equilibrium the metal is losing kinetic energy to the water in the
calorimeter, and the movement of the molecules has slowed as well. The First
Law of Thermodynamics states that there is no creation or loss of energy. The
kinetic energy gained by the metal came from the surrounding water, and the
energy lost by the metal moves into the water in the calorimeter until the
distribution of energy equalizes, reaching the state of equilibrium.
Kirby-Koury 7
Linear Thermal Expansion:
When designing and constructing a bridge linear thermal expansion must
be considered. When the bridge is heated or cooled, it expands or contracts,
causing the bridge to buckle or crack and possible collapse if it is not designed
and built correctly. In order to allow for the expansion and contraction, the
thermal expansion coefficient(s) of its material(s) must be found. This is an
essential step in design and construction of many pieces of equipment as well,
and could save millions of dollars if done correctly. If done incorrectly, or not
considered, the bridge could be destroyed and millions of dollars lost (Wilson).
To determine the linear expansion coefficient of a material, one must understand
what it is and how to find it.
Kinetic molecular theory occurs when the metal is heated and the
molecules inside of the metal receive more energy and move at a faster pace,
causing them to emit force on the molecules and metal in their surroundings. The
force put upon the surroundings causes the metal to expand (Brucat). This
expansion can be measured to help identify the material and is modeled by an
equation that uses the change in length, ∆L, is equal to the thermal expansion
coefficient, a, times the initial length, Li, times the change in temperature, ∆T.
∆ L=a Li∆T
Linear thermal expansion coefficients are measured with the unit m/moC. They
are classified as an intensive property. Therefore, this coefficient can be used to
identify a material, particularly a pure element (Hester).
Kirby-Koury 8
In a previously conducted experiment through the Stony Brook NN Group,
researchers first measured the length and temperature of a rod of pure metal
using a meter stick and a thermometer. Then, steam was passed through a heat
tube containing the rod. The temperature of the rod was measured, again using
the thermometer, and it was recorded once the reading reached a stable value.
The length of the rod was also measured, again using the meter stick, and the
value was recorded. These values of temperature, temperature change, length,
and length change were used to determine the linear thermal expansion
coefficient of the metal rod using the same equation as that shown above
(McGrew).
In a second experiment conducted through Lock Haven University, an
apparatus was assembled to measure the temperature and length of a rod before
and after thermal expansion has taken place. The rod in this experiment began at
60 centimeters long when measured at room temperature using the apparatus.
Then, steam is allowed into a tube containing the rod, and the rod is heated. It
gains thermal energy, causing it to expand. Readings of the temperature and
length of the rod are recorded every few degrees as it increases in temperature
and length. Then, the final and initial temperatures can be used in the formula
shown above to compute the linear thermal expansion coefficient of the metal rod
("Thermal Expansion - Linear").
Overall, one way to identify a metal is through the intensive property of
linear thermal expansion. Essentially, the metal is heated and the initial and final
Kirby-Koury 9
data are used in calculations to determine the total expansion. This value
determines the metal.
Problem Statement
Problem:
Can the researchers determine if an unknown metal rod has the same
composition as an iron rod by using its specific heat and linear thermal
expansion?
Hypothesis:
If the researchers determine the specific heat within 1% error and linear
thermal expansion coefficient within a 3% error, then the unknown metal can be
determined as iron or not iron.
Data:
The researchers will measure specific heat and linear thermal expansion
of the metal rods. The specific heat procedure measures initial temperature,
equilibrium temperature, changes in temperature, and mass. The temperatures
are in degrees Celsius and the masses are measured in grams. The final specific
heat value is measured in J/g∙℃. See Appendix A for a sample calculation. The
linear thermal expansion procedure measures the net change in length, initial
temperature, and the final temperature of the metal. The temperatures are
measured in degrees Celsius and the lengths and changes in length are
Kirby-Koury 10
measured in millimeters. The final value is an alpha coefficient measured in
millimeters. See Appendix A for a sample calculation.
Experimental Design
Specific Heat:
Materials:
(2) Iron Fe pure metal rods
(2) Unknown pure metal rods
Insulated calorimeter
Calorimeter stand
LoggerPro
LoggerPro thermometer probe (0.1°C)
Ti-nspire CX graphing calculator
Thermometer
Safety Concerns:
Iron is not considered hazardous (Flinn).
Wear safety equipment, i.e. goggles, lab coat, and gloves (Flinn).
Procedure:
1. Using randomization function on the Ti-nspire CX graphing calculator,
randomize the order of the fifteen trials (see Appendix B).
2. Tare the Scout Pro electronic scale to calibrate it.
3. Use the scale to determine the mass of the insulated calorimeter.
Scout Pro electronic scale (0.1 g)
Hot plate
Tongs
(2) 20.3 cm x 9.8 cm x 6.3 cm loaf pan
100 ml graduated cylinder
Electronic timer
Insulated glove
Kirby-Koury 11
4. Using the 100 ml graduated cylinder, fill the calorimeter with 50 ml of
water and place cap on calorimeter.
5. Using the 100 ml graduated cylinder again, fill the 20.3 cm x 9.8 cm x 6.3
cm loaf pan with about 200 ml of water, or enough to cover the metal.
6. Place the loaf pan on the hot plate and turn it on.
7. Cover the loaf pan containing the water with the second loaf pan and allow
the water to boil.
8. Using the rod that was determined to be used in the first trial, place it on
the scale and record its mass in the data table.
9. Place the metal rod into the boiling water using tongs.
10. Allow the metal rod to heat for two minutes. Use the electronic timer to
time the trial, and assume that the temperature of the water is equal to the
temperature of the rod.
11. While it heats, turn on the LoggerPro (see Appendix C) and set it to collect
data once every second for 180 seconds.
12. Insert the temperature probe of the LoggerPro into the hole in the cap of
the calorimeter and start data collection.
13. When the electronic timer reaches one minute and fifty seconds, start the
LoggerPro data collection. After ten seconds, remove the cap of the
calorimeter. Make sure that the probe is not removed from the water.
14. Remove the metal rod from the beaker, using tongs, and place it inside
the calorimeter.
15. Place the cap back on the calorimeter.
Kirby-Koury 12
16. Allow the LoggerPro to complete data collection, and remove the
temperature probe from the calorimeter.
17. Remove the cap from the calorimeter, remove the rod, and pour the water
into a sink to discard.
18. Repeat steps one through seventeen for the known and unknown metals,
adjusting data collection time to end after the water temperature reaches
equilibrium.
Diagram:
Figure 2. Calorimeter
Figure 2 shows a model of the calorimeter that was constructed using
Google SketchUp 8. The calorimeters used in the specific heat procedure were
constructed using PVC pipe, insulation, PVC primer, PVC cement, and tape (see
Appendix D).
Cap
Insulation
Stand
Kirby-Koury 13
Figure 3. Specific Heat Materials
Figure 3 shows the materials required to carry out the specific heat
procedure. These include a loaf pan, insulated gloves, metal rods, a hot plate,
calorimeters with stands, an electronic timer, a 100 ml graduated cylinder, a
Scout Pro electronic scale, tongs, a LoggerPro, a LoggerPro thermometer probe.
Linear Thermal Expansion:
Materials:
(2) Iron Fe pure metal rods
(2) Unknown pure metal rods
Ti-nspire CX graphing calculator
Hot plate
Tongs
20.3 cm x 9.8 cm x 6.3 cm loaf pan
Dry-erase marker
Electronic Timer/TI-nspire CX Graphing Calculator
Thermometer Hot Plate
Tongs
Thermometer Probe
LoggerPro
Electronic Scale
Graduated Cylinder
Calorimeters
Metal Rods
Insulated Gloves
Loaf pan
Thermometer (°C)
Thermal Expansion Jig (cm)
Caliper (mm)
Spray Bottle (16 oz)
Electronic Timer
100 ml Graduated Cylinder
Gloves
Kirby-Koury 14
Safety Concerns:
Metal is unknown, so be cautious since dangers are also unknown.
Wear safety equipment, i.e. goggles, lab coat, and gloves (Flinn).
Procedure:
1. Using randomization function on the Ti-nspire CX graphing calculator (see
Appendix B), randomize the order of the fifteen trials.
2. Use the caliper to record the initial length of the pure metal rod.
3. Using the 100 ml graduated cylinder, fill the 20.3 cm x 9.8 cm x 6.3 cm
loaf pan with about 200 ml of water, or enough to cover the metal.
4. Place the loaf pan on the hot plate and turn it on.
5. Cover the loaf pan containing the water with the second loaf pan and allow
the water to boil.
6. Once water is boiling, place the metal rod into the loaf pan using metal
tongs.
7. Allow the metal rod to heat for two minutes. Use the electronic timer to
time the trial.
8. Use the thermometer to measure the temperature of the water, and record
as the initial temperature of the water. Assume that the temperature of the
water is the temperature of the metal rod.
9. Use the gloves to remove the loaf pan, and use the tongs to remove the
rod from the loaf pan after the timer has finished, and quickly place it in
the thermal expansion jig (see Appendix E).
Kirby-Koury 15
10. Move the tab on the thermal expansion jig to the starting position of the
needle, or use a dry-erase marker to mark the initial position.
11. Allow the metal to cool and the needle on the face of the thermal
expansion jig to stop moving. Use the spray bottle to spray the metal rod
twelve times every twenty seconds with cold water.
12. When the dial ceases to move, move the second tab on the thermal
expansion jig to the final location of the needle, or use the dry-erase
marker, and record the net change in length.
13. The final temperature of the rod is assumed to be room temperature.
14. Remove the metal rod from the thermal expansion jig.
15. Repeat steps two through fourteen for the remaining trials.
Diagram:
Figure 4. Linear Thermal Expansion Jig
Dial face
Wooden frame
Rod groove
Measurement prong
Kirby-Koury 16
Figure 4 shows the linear thermal expansion jig that was used to measure
the change in length of the metal. To know how to operate the jig, see Appendix
E.
Figure 5. Linear Thermal Expansion Materials
Figure 5 shown above is an image of the materials used for the linear
thermal expansion experiment. All of the materials were pictured except for the
iron metal rods.
Jig
Thermometer
Loaf PansGraduated CylinderSpray Bottle
TongsUnknown Metal Rods
Insulated Gloves
Dry-erase Marker
Electronic Timer/TI-nspire CX Graphing Calculator
Caliper
Kirby-Koury 17
Data and Observations
Table 1Iron Specific Heat Data
Trial RodInitial
Temperature (⁰C)Equilibrium
Temperature (⁰C)
Change in Temperature
(⁰C)Mass (g) Specific
Heat (J/g∙⁰C)Water Metal Water Metal Water Metal
1 A 22.7 98.1 26.7 4.0 71.4 50 31.7 0.370
2 A 20.4 96.3 24.5 4.1 71.8 50 31.7 0.377
3 B 22.0 96.7 26.4 4.4 70.3 50 31.7 0.413
4 A 20.8 97.2 25.1 4.3 72.1 50 31.7 0.394
5 B 21.6 97.1 25.5 3.9 71.6 50 31.7 0.359
6 A 21.8 98.3 26.0 4.2 72.3 50 31.7 0.383
7 B 18.5 96.9 23.8 5.3 73.1 50 31.7 0.478
8 A 22.4 97.9 25.9 3.5 72.0 50 31.7 0.321
9 B 19.9 97.9 24.3 4.4 73.6 50 31.7 0.395
10 A 18.3 96.0 23.0 4.7 73.0 50 31.7 0.425
11 B 17.6 93.0 21.8 4.2 71.2 50 31.7 0.389
12 A 16.6 99.2 21.7 5.1 77.5 50 31.7 0.434
13 B 17.7 96.1 22.2 4.5 73.9 50 31.7 0.402
14 A 19.8 99.5 24.7 4.9 74.8 50 31.7 0.432
15 B 19.5 98.2 24.3 4.8 73.9 50 31.7 0.429
Average: 20.0 97.2 24.4 4.4 72.8 50.0 31.7 0.400
Table 1 shows the raw data collected from the known metal, iron, in the
trials to determine its specific heat. The values resulted in an average specific
heat of 0.400 J/g·°C. See Appendix A for sample calculation of specific heat.
Table 2Iron Specific Heat Observations
Trial Rod Date Observations1 A 4/15/2013 Used LoggerPro #6 and calorimeter #1
2 A 4/17/2013 Used LoggerPro #1 and calorimeter #4. Probe lifted out of water when inserting metal.
3 B 4/17/2013 Used LoggerPro #1 and calorimeter #1.4 A 4/17/2013 Used LoggerPro #1 and calorimeter #3.5 B 4/17/2013 Used LoggerPro #1 and calorimeter #2.6 A 4/17/2013 Used LoggerPro #1 and calorimeter #4.7 B 4/17/2013 Used LoggerPro #1 and calorimeter #3.
Kirby-Koury 18
Trial Rod Date Observations
9 B 4/17/2013 Used LoggerPro #1 and calorimeter #2. 100 ml of water added to the loaf pan after trial.
10 A 4/17/2013 Used LoggerPro #1 and calorimeter #4.11 B 4/17/2013 Used LoggerPro #1 and calorimeter #1.12 A 4/17/2013 Used LoggerPro #1 and calorimeter #4.13 B 4/17/2013 Used LoggerPro #1 and calorimeter #1.14 A 4/19/2013 Used LoggerPro #3 and calorimeter #3.15 B 4/19/2013 Used LoggerPro #3 and calorimeter #4.
Table 2, which spans from page one to page two, shows the observations
made during specific heat trials of the known metal, iron. Most trials used
LoggerPro #1. The rods were used almost equal amounts, and calorimeter
numbers were randomized. The probe was lifted out of the water in trial two, and
100 ml of water was added to the loaf pan after trial nine.
Table 3Iron Linear Thermal Expansion Data
Trial Rod JigChange
in Length (mm)
Initial Length (mm)
Initial Temperature
(°C)
Final Temperature
(°C)
Alpha Coefficient
(mm)
1 A 7 0.10 129.29 97.1 26.7 1.116E-052 B 11 0.10 129.28 97.1 26.7 1.116E-053 A 7 0.08 129.29 92.3 23.5 8.566E-064 B 11 0.08 129.29 92.3 23.5 8.566E-065 A 7 0.05 129.26 97.9 27.1 5.551E-066 B 11 0.05 129.29 97.9 27.1 5.550E-067 A 7 0.08 129.29 96.2 24.7 8.243E-068 B 11 0.08 129.29 94.4 24.1 8.384E-069 A 11 0.08 129.34 96.9 23.3 8.005E-06
10 B 7 0.08 129.28 96.4 23.3 8.063E-0611 A 11 0.08 129.29 96.8 24.2 8.118E-0612 B 7 0.08 129.28 95.0 24.2 8.325E-0613 A 11 0.05 129.36 96.3 26.5 5.626E-0614 B 7 0.05 129.27 97.2 26.5 5.558E-0615 A 11 0.08 129.24 96.7 25.7 8.304E-06
Average: 0.07 129.29 96.0 25.1 7.944E-06Table 3, on previous page, shows the raw data collected from the trials to
determine the linear thermal expansion coefficient of the known metal, iron. The
Kirby-Koury 19
average linear thermal expansion coefficient of the metal rods is 7.944∙10-6 mm.
See Appendix A for sample calculation of linear thermal expansion.
Table 4Iron Metal Linear Thermal Expansion ObservationsTria
l Rod Date Observations
1 A 4/18/2013 Did not measure time between sprays. Jig not aligned properly.
2 B 4/18/2013 Did not measure time between sprays.
3 A 4/18/2013 Did not measure time between sprays. Jig not aligned properly.
4 B 4/18/2013 Did not measure time between sprays.
5 A 4/18/2013100 ml of water added to loaf pan before this trial. Did not measure time between sprays. Jig not aligned properly.
6 B 4/18/2013 Did not measure time between sprays.
7 A 4/18/2013Re-did because dropped before in jig. Did not measure time between sprays. Jig not aligned properly.
8 B 4/18/2013 Rod sprayed twice upon beginning of measurement and again every 20 seconds for a total of 12 sprays.
9 A 4/18/2013 Rod sprayed twice upon beginning of measurement and again every 20 seconds for a total of 12 sprays.
10 B 4/18/2013Rod sprayed twice upon beginning of measurement and again every 20 seconds for a total of 12 sprays. Jig not aligned properly.
11 A 4/18/2013 Rod sprayed twice upon beginning of measurement and again every 20 seconds for a total of 12 sprays.
12 B 4/18/2013Rod sprayed twice upon beginning of measurement and again every 20 seconds for a total of 12 sprays. Jig not aligned properly.
13 A 4/18/2013 Rod sprayed twice upon beginning of measurement and again every 20 seconds for a total of 12 sprays.
14 B 4/18/2013Rod sprayed twice upon beginning of measurement and again every 20 seconds for a total of 12 sprays. Jig not aligned properly.
15 A 4/18/2013 Rod sprayed twice upon beginning of measurement and again every 20 seconds for a total of 12 sprays.
Table 4, which is shown on the previous page, shows the observations
made during the trials to determine the linear thermal expansion coefficient for
Kirby-Koury 20
the known metal, iron. All of the trials were conducted on April 18, 2013. About
half of the trials used jig #7, which was not aligned properly, and about half used
jig #11.
Table 5Unknown Metal Specific Heat Data
Trial Rod
Initial Temperature
(⁰C)Equilibrium
Temperature (⁰C)
Change in Temperature
(⁰C)Mass (g) Specific
Heat (J/g∙⁰C)Water Metal Water Metal Water Metal
1 A 23.7 100.0 29.2 5.5 70.8 50 46.5 0.349
2 B 18.7 98.7 25.1 6.4 73.6 50 46.5 0.391
3 B 18.6 98.5 24.9 6.3 73.6 50 46.5 0.385
4 A 20.8 101.0 26.8 6.0 74.2 50 46.5 0.364
5 B 22.6 97.3 28.5 5.9 68.8 50 46.5 0.386
6 A 18.3 101.6 25.1 6.8 76.5 50 46.5 0.400
7 B 19.3 98.9 25.5 6.2 73.4 50 46.5 0.380
8 A 20.1 99.6 26.5 6.4 73.1 50 46.5 0.394
9 B 16.3 99.9 23.2 6.9 76.7 50 46.5 0.405
10 A 19.6 102.2 25.9 6.3 76.3 50 46.5 0.371
11 B 19.7 99.5 25.7 6.0 73.8 50 46.5 0.366
12 A 17.9 99.6 25.0 7.1 74.6 50 46.5 0.428
13 B 18.2 98.9 24.2 6.0 74.7 50 46.5 0.361
14 A 20.1 100.3 26.4 6.3 73.9 50 46.5 0.384
15 B 18.0 98.0 24.5 6.5 73.5 50 46.5 0.398
Average: 19.5 99.6 25.8 6.3 73.8 50 46.5 0.384
Table 5 shows the raw data collected from the unknown metal in the trials
to determine its specific heat. The values resulted in an average specific heat of
0.384 J/g·°C.
Table 6Unknown Metal Specific Heat Observations
Trial Rod Date Observations
Kirby-Koury 21
1 A 4/19/2013 Used LoggerPro #3 and calorimeter #1.2 B 4/19/2013 Used LoggerPro #3 and calorimeter #4.3 B 4/19/2013 Used LoggerPro #3 and calorimeter #1.4 A 4/19/2013 Used LoggerPro #3 and calorimeter #3.5 B 4/19/2013 Used LoggerPro #3 and calorimeter #2.
6 A 4/19/2013 Added 100 ml of water after trial. Used LoggerPro #3 and calorimeter #4.
7 B 4/19/2013 Used LoggerPro #3 and calorimeter #3.8 A 4/19/2013 Used LoggerPro #3 and calorimeter #1.9 B 4/19/2013 Used LoggerPro #3 and calorimeter #2.
10 A 4/19/2013 Used LoggerPro #3 and calorimeter #4.11 B 4/19/2013 Used LoggerPro #3 and calorimeter #1.
12 A 4/19/2013 Added 100 ml of water after trial. Used LoggerPro #3 and calorimeter #4.
13 B 4/19/2013 Used LoggerPro #3 and calorimeter #1.14 A 4/19/2013 Used LoggerPro #3 and calorimeter #3.15 B 4/19/2013 Used LoggerPro #3 and calorimeter #4.
Table 6 shows the observations made during the trials to determine the
specific heat of the unknown metal. All trials used LoggerPro #3. 100 ml of water
was added after both trials six and twelve.
Table 7Unknown Metal Linear Thermal Expansion Data
Kirby-Koury 22
Trial Rod JigChange
in Length (mm)
Initial Height (mm)
Initial Temperature
(°C)
Final Temperature
(°C)
Alpha Coefficient
(mm)
1 A 7 0.0508 121.21 99.7 22.5 5.429E-062 B 11 0.0508 121.42 95.1 22.5 5.763E-063 A 7 0.0762 121.37 99.1 24.1 8.371E-064 B 11 0.0762 121.18 90.7 24.1 9.442E-065 A 7 0.0762 120.97 99.7 23.5 8.267E-066 B 11 0.0762 121.06 96.7 23.5 8.599E-067 A 7 0.0762 121.23 100.1 24.0 8.260E-068 B 11 0.0762 121.40 95.2 24.0 8.816E-069 A 11 0.0762 121.26 99.5 23.9 8.312E-06
10 B 7 0.0508 121.29 98.3 23.9 5.629E-0611 A 11 0.0762 121.29 99.7 24.6 8.365E-0612 B 7 0.0508 121.40 98.6 24.6 5.655E-0613 A 11 0.0762 121.33 100.0 23.6 8.220E-0614 B 7 0.0508 121.33 96.8 23.6 5.720E-0615 A 11 0.0762 121.28 99.1 24.6 8.434E-06
Average: 0.0680 121.27 97.9 23.8 7.552E-06
Table 7 shows the raw data collected from the trials to determine the
linear thermal expansion coefficient of the unknown metal. The researchers were
able to calculate that the average linear thermal expansion coefficient of the
unknown metal rods was 7.552 x 10-6 mm.
Table 8Unknown Metal Linear Thermal Expansion ObservationsTrial Rod Date Observations
1 A 4/22/2013
Jig not aligned properly. Rod sprayed twice upon beginning of measurement and again every 20 seconds for a total of 12 sprays.
2 B 4/22/2013
Rod sprayed twice upon beginning of measurement and again every 20 seconds for a total of 12 sprays.
3 A 4/22/2013
Jig not aligned properly. Rod sprayed twice upon beginning of measurement and again every 20 seconds for a total of 12 sprays.
4 B 4/22/2013
Rod sprayed twice upon beginning of measurement and again every 20 seconds for a total of 12 sprays.
Trial Rod Date Observations5 A 4/22/201
3Jig not aligned properly. Added 100 ml of water after trial. Rod sprayed twice upon beginning of
Kirby-Koury 23
measurement and again every 20 seconds for a total of 12 sprays.
6 B 4/22/2013
Rod sprayed twice upon beginning of measurement and again every 20 seconds for a total of 12 sprays.
7 A 4/22/2013
Jig not aligned properly. Trial re-done because it was dropped before being placed into the jig the first time.
8 B 4/22/2013
Rod sprayed twice upon beginning of measurement and again every 20 seconds for a total of 12 sprays.
9 A 4/22/2013
Rod sprayed twice upon beginning of measurement and again every 20 seconds for a total of 12 sprays.
10 B4/22/201
3
Jig not aligned properly. Added 100 ml of water to loaf pan after trial. Rod sprayed twice upon beginning of measurement and again every 20 seconds for a total of 12 sprays.
11 A4/22/201
3Rod sprayed twice upon beginning of measurement and again every 20 seconds for a total of 12 sprays.
13 A4/22/201
3Rod sprayed twice upon beginning of measurement and again every 20 seconds for a total of 12 sprays.
14 B4/22/201
3
Jig not aligned properly. Rod sprayed twice upon beginning of measurement and again every 20 seconds for a total of 12 sprays.
15 A4/22/201
3Rod sprayed twice upon beginning of measurement and again every 20 seconds for a total of 12 sprays.
Table 8 shows the observations made during the trials to determine the
linear thermal expansion coefficient for the unknown metal. All trials were
sprayed twice every twenty seconds for a total of twelve sprays while cooling.
Data Analysis and Interpretation
To determine the success level of the researchers’ hypothesis, a statistical
analysis must be completed. What the researchers are measuring is the
likelihood of the unknown metal being, or not being, iron. In order to test the
hypothesis, samples of metals for the known and unknown trials were chosen
using a simple random sample, SRS. Then the samples were randomly allocated
to trials using the Ti-nspire graphing calculator. The randomization is an
Kirby-Koury 24
important factor because it assists in eliminating bias. The statistical analysis test
that the researchers determined would be the best fit to the data is a two-sample
t-test. A two-sample t-test was chosen because the data collected compares the
means of two different factors, in this case, the known and the unknown metals.
The t-test will be applied to both the linear thermal expansion analysis and
specific heat analysis. In order to conduct the test, the statistical analysis
assumptions must be made prior to the mathematics portion. The assumptions
for this analysis are that the samples are independent, the samples have been
selected using a simple random sample, and that either the sample size is
greater than or equal to thirty or the data is known to be normal. Also, the
population means and population standard deviations are not known, that alpha
(α) is equal to 0.10, and the population’s variances are normal. The validity of this
depends on how accurately the experiment was conducted and the experience
level of the researchers. The null hypothesis sets the first mean of the known
metal, x1, equal to the unknown metal, x2, because the hypothesis is to see if the
metals are the same. The alternative hypothesis is trying to validate if the metals
are different, so the first mean of iron is set as not equal to the second mean of
the unknown metal.
H o : x1=x2
H a : x1≠ x2
Next, the researchers must determine if every assumption is met. First,
the samples can be assumed independent because the metals are two separate
pieces and do not affect each other because they do not interact. The samples
Kirby-Koury 25
have been selected using a simple random sample because the researchers
randomly allocated them to each trial. The assumption of the population means
and population standard deviations being unknown is assumed because not
every pure metal rod can be tested to find such values. Also, the alpha level is
assumed to be 0.10 because this value is the given value for alpha. Lastly, the
assumption that the sample size is greater than or equal to thirty has not been
met. So, a normal probability plot must be created to see if the samples are
normally distributed. The data used in the normal probability plot for linear
thermal expansion can be seen in Table 9 below.
Table 9Iron Linear Thermal Expansion Data
Table 9 shows the raw data collected from the linear thermal expansion
trials conducted on the iron rods. The percent error allows the researchers to
analyze how precise the experiment was. The lower the percent error is, the
Trial RodAlpha
Coefficient (mm)
Percent Error
1 A 1.116E-05 -5%2 B 1.116E-05 -5%3 A 8.566E-06 -27%4 B 8.566E-06 -27%5 A 5.551E-06 -53%6 B 5.550E-06 -53%7 A 8.243E-06 -30%8 B 8.384E-06 -29%9 A 8.005E-06 -32%
10 B 8.063E-06 -32%11 A 8.118E-06 -31%12 B 8.325E-06 -30%13 A 5.626E-06 -52%14 B 5.558E-06 -53%15 A 8.304E-06 -30%
Average: 7.944E-06 -33%
Kirby-Koury 26
better, because it implies a more accurate test and thus a lower chance of
misinterpreting the identity of the metal. The percent error farthest from zero is
relatively high, -53%, implying an inaccurate trial. The value closest to zero is
relatively low, -5%, implying a fairly accurate trial. The range of percent error is
about 48%. This large range shows that the trials were not run precisely the
same. The average percent error was -33%. The average percent error is higher
than the necessary percent error stated in the hypothesis, 3%. This shows that
the trials were not nearly as accurate as they should have been and that the data
collected is not the most accurate and best data.
Table 10Unknown Metal Linear Thermal Expansion Data
Trial RodAlpha
Coefficient (mm)
Percent Error
1 A 5.429E-06 -54%2 B 5.763E-06 -51%3 A 8.371E-06 -29%4 B 9.442E-06 -20%5 A 8.267E-06 -30%6 B 8.599E-06 -27%7 A 8.260E-06 -30%8 B 8.816E-06 -25%9 A 8.312E-06 -30%
10 B 5.629E-06 -52%11 A 8.365E-06 -29%12 B 5.655E-06 -52%13 A 8.220E-06 -30%14 B 5.720E-06 -52%15 A 8.434E-06 -29%
Average: 7.552E-06 -36%
Table 10 shows the raw data collected from the linear thermal expansion
trials conducted on the unknown metal rods. The minimum value was -54%, and
the maximum is -20%. The range of the percent error is 34% showing that these
trials may not have been very precise, but they were more precise than the data
Kirby-Koury 27
in Table 9 above. The average percent error was -36%. The average percent
error is greater than the necessary percent error, 3%. This data is not the most
accurate either.
Table 11Iron Specific Heat Data
Trial RodSpecific
Heat (J/g∙⁰C)
Percent Error
1 A 0.370 17%2 A 0.377 15%3 B 0.413 -7%4 A 0.394 11%5 B 0.359 19%6 A 0.383 14%7 B 0.478 8%8 A 0.321 8%9 B 0.395 11%
10 A 0.425 -4%11 B 0.389 12 %12 A 0.434 -2%13 B 0.402 -9%14 A 0.432 -3%15 B 0.429 -3%Average: 0.400 -10%
Table 11 shows the raw data collected from the specific heat trials
conducted on the iron rods. The value closest to zero is -3%, and the value
farthest from zero is 19%. The range for percent error is 22%, this range is much
smaller than the ranges in previous tables, and this range implies that the trials
were more precise and more accurate than previous data. However, the range is
still fairly large implying that the trials could have been more precise. The
average percent error was -10%. Due to the necessary percent error of 1% and
Kirby-Koury 28
the average percent error being -10%, it is assumed that the trials were not as
accurate as necessary and the data is not the best.
Table 12Unknown Metal Specific Heat Trials
Trial Rod
Specific Heat (J/g∙⁰C)
Percent Error
1 A 0.349 -21%2 B 0.391 -12%3 B 0.385 -13%4 A 0.364 -18%5 B 0.386 -13%6 A 0.400 -10%7 B 0.380 -14%8 A 0.394 -11%9 B 0.405 -9%
10 A 0.371 -16%11 B 0.366 -18%12 A 0.428 -4%13 B 0.361 -19%14 A 0.384 -14%15 B 0.398 -10%
Average: 0.384 -13%
Table 12 shows the raw data collected from the specific heat trials
conducted on the unknown metal rods. The value closest to zero is -4%, and the
value farthest from zero is -21%. The range for percent error is 17%, this range is
smaller than the ranges in previous experiments, and this range implies that the
trials were more precise and more accurate than previous data. However, the
range is still fairly large showing that the trials could have been more accurate.
The average percent error was -13%. The necessary percent error for the
specific heat trials is 1%, however the average percent error for these trials is
Kirby-Koury 29
greater than 1%, -13%, it is assumed that the trials were not as accurate as
necessary and the data is not the best.
Figure 6. Linear Thermal Expansion of Iron Normal Probability Plot
For the known linear thermal expansion experiment, the normal probability
plot can be seen in Figure 6 above. It shows the line of best fit for the values, and
the closer the data points are to forming the line of best fit, the more normal the
data. The graph does not show a very normal distribution since the data does not
follow the line of best fit very closely. Because the data did not appear very
normal, the data was checked for outliers. Outliers can be determined by
multiplying the inner quartile range by 1.5 and subtracting it from quartile two as
well as adding it to quartile three. If a value is outside of this range, it is
considered an outlier. The data does not contain outliers, so the data is not
skewed or affected by outliers that may cause a non-normal distribution.
Kirby-Koury 30
Figure 7. Linear Thermal Expansion of Unknown Metal Normal Probability Plot
Figure 7 shown above is the normal probability plot for the linear thermal
expansion of the unknown metal. The data does not form the line of best fit very
well, so the distribution is not perfectly normal. This implies that the reliability of
the results is not very good. The trials should have been more accurate and more
precise in order to be reliable.
Figure 8. Linear Thermal Expansion Box Plot of Data
Figure 8 shows the box plots for the linear thermal expansion data. The
box plot on top is the Iron data, and the box plot on the bottom is the unknown
metal. Both box plots do not appear symmetrical, and the graphs appear to be
Kirby-Koury 31
skewed left. The box plots overlap for a large majority of their data Over 75% of
the unknown metal data overlaps the iron data. Also, just less than 25% of the
iron data is higher than the values of the unknown metals linear thermal
expansion coefficient. It is seen that there are no outliers in either of the data
collections.
Figure 9. Linear Thermal Expansion Normal Distribution Graph
Figure 9 shown on previous page displays the normal distribution graph
for linear thermal expansion. The t-value was found to be 0.6643, and the p-
value was found to be 0.5122. The t-value is the center of the graph, also named
the mean or occasionally median of the data. The p-value is a probability. It is the
percentage of the time that a value will be found as extreme as this under the
assumption that the null hypothesis is true. Figure 10 below shows all of the
values used to calculate the t-value and the p-value.
Kirby-Koury 32
Figure 10. Two-Sample t-test Calculations
Figure 10 shows the results of the t-test. The formula used has the first
mean of iron, x1, minus the second mean of the unknown metal, x2, all divided by
the square root of the first standard deviation of iron squared, s1, over the number
of iron trials, n1, plus the square root of the second standard deviation of the
unknown metal squared, s2, divided by the number of unknown metal trials, n2.
t=x1−x2
√ s12
n1+s22
n2
For a sample calculation, see Appendix A.
For the linear thermal expansion data, the null hypothesis failed to be
rejected because the p-value of 0.5122 is greater than the alpha level of 0.10.
There is no significant difference between iron and the unknown metal. There is
about a 51.22% chance of getting a difference in the test scores this extreme by
chance alone, if the null hypothesis is true. There is not enough evidence to
show that the unknown metal is not the same as the known metal, iron. However,
Kirby-Koury 33
since the data was found to not be very reliable, the decisions based of this data
should not be fully trusted because they may not be correct.
Figure 11. Specific Heat of Iron Normal Probability Plot
Figure 11 shows a normal probability plot of the specific heat values of the
iron rods. The values appear to fit the trend line, and therefore the data can be
determined to be normal.
Figure 12. Specific Heat of Unknown Metal Probability Plot
Figure 12 shows the normal probability plot of the values determined for
the specific heat of the unknown metal rods. The data values appear to fit the
trend line, and therefore the data can be determined to be normal.
Kirby-Koury 34
Figure 13. Box Plots of the Known and Unknown Specific Heat Data
Figure 13 shows two box plots displaying the distribution of the data
values for the known and unknown metals’ specific heat. One may determine
from the distributions that both data sets appear to be relatively symmetrical and
normally distributed. The top plot represents the iron rods and the bottom plot
represents the unknown metal rods. The top plot has a much greater range than
the bottom plot, and 100% of the bottom plot overlaps it. The top plot’s range
seems to be approximately twice the range of the bottom plot. About 25% of the
iron data has higher values than the unknown metal, and less than 25% of the
iron data has values less than the unknown metal.
To determine if the null hypothesis should be rejected, one should
determine if the p-value of the samples is less than the alpha level. In this case,
the alpha level is 0.10. The p-value can be found with the use of the t-value,
which can be calculated by a specific equation previously stated.
Kirby-Koury 35
Figure 14. T-test
Figure 14 shows the calculation of each value required to conduct the t-
test, as well as the results of the t-test itself. The t-value is 1.4496, which results
in a p-value of 0.1617. The t-value represents the number of standard deviations
away from the mean that the result lies, and can be shown visually on a bell
curve. However, this decision may not be fully trusted due to the unreliability of
the data.
Figure 15. T-Distribution
Kirby-Koury 36
Figure 15 shows the distribution of the t-value determined in the t-test with
a shaded area displaying the p-value. The p-value is not extremely small and
thus relatively close to the population mean. This shows that getting a result this
extreme or more extreme is not very improbable.
Since the p-value of 0.1617 is greater than the alpha level of 0.10, the
researchers have failed to reject the null hypothesis. There is no significant
evidence that the unknown metal, n2, is a different metal than the known metal
(iron,n2). There is a 16.17% chance of getting a result this extreme or more
extreme by chance alone if the null hypothesis is true. Based on specific heat,
the unknown metal is likely to be iron.
Conclusion
The researchers tested the specific heat and linear thermal expansion of
iron and an unknown metal to determine if the unknown metal was iron. The
researcher's hypothesis that an unknown metal's identity could be determined
using only specific heat and linear thermal expansion was accepted since the
researchers were able to determine that iron was the unknown metal using these
attributes. This determination was made using the collected values and the
results of the statistical analysis of the data. Both the iron and unknown metal
were tested for their specific heat value and linear thermal expansion coefficient,
and then statistical test on the collected data values was conducted. The data
analysis of the specific heat value showed that the null hypothesis of the metals
being the same was failed to be rejected, because there was a very high chance,
nearly a 51%, of getting the same result by chance alone. As for linear thermal
Kirby-Koury 37
expansion, the analysis showed over a 16% chance that the computed values
could be as extreme as or more extreme than were calculated by chance alone.
This indicated that there was no significant evidence that the unknown metal rod
was of a different atomic composition than the known iron metal rod. In this way,
the data supports the research.
In addition, the average percent error of the data collected for the known
metal’s specific heat is about -10%, and the unknown percent error is about -
13%. These percentages are very similar, indicating that the experiments were
run with the same accuracy. However, the necessary percent error value for
specific heat is nearly -1% error. The same situation can be seen with linear
thermal expansion, the average percent error of the data collected in for the
known metal’s linear thermal expansion coefficient is -33%, and the unknown
average percent error is -36%. The necessary percent error value is about 3%.
The linear thermal expansion experiment was assumed to have been run
similarly as well. Due to the similar accuracy of the known and unknown
experiments it was assumed that the data collected was acceptable for the
analysis and that their comparisons could be accepted for a conclusion. Also,
there were not any data points that were extremely different or outliers from the
rest, showing that all of the data collected could be used.
The researchers encountered several problems while conducting the tests
and making measurements. During the specific heat trials, the temperature
probe was occasionally lifted out of the water in the calorimeter while inserting
the rod. During some of the linear thermal expansion trials, the researchers
Kirby-Koury 38
failed to measure the number of times the rods were sprayed with water and the
intervals between the sprays, and the intensities of the sprays may have been
different. This may have affected the cooling rate of the metal rods. In addition,
one of the two jigs used to measure the change in length was not aligned
properly, which may have caused the data to be collected inaccurately. Similarly,
occasionally the placement would not be as quick or as accurate as other trials,
which may have led to results that are not as accurate as possible. Also, the
environment of the experimentation was different with each trial, on certain days
windows may have been open causing a cooler room temperature and a more
rapid cooling rate for the metals.
Many steps could be taken in order to improve the procedures and
improve the experimental design to reduce errors and produce more accurate
data. To improve the specific heat procedure, the researchers could acquire a
longer temperature probe, allowing the cap of the calorimeter to be lifted farther
away from the opening and easier insertion preventing loss of heat. During the
linear thermal expansion trials, the researchers should set specific guidelines for
spraying the rods with water while cooling, such as time between sprays and
intensity of sprays. These standards would allow for more uniform cooling
processes among the trials. In addition, the researchers should use a jig that is
properly aligned. This misalignment of the jig may have affected the measured
values of linear thermal expansion, and a properly aligned jig would ensure more
accurate results. A more enclosed and stabilized environment would help ensure
the accuracy of the results. All in all, with each improvement, the results of the
Kirby-Koury 39
experiment would more accurate, more trustworthy, and percent error faults
could be corrected.
This research can be expanded by finding density, another intensive
property. To determine density, the only additional information necessary would
be radius and volume of the metal rods, and no additional equipment would be
needed. Uses for this research include welding. This data could help determine
which metals are which, and could prevent mistakes while welding because each
metal has a different welding technique and not all metals can be welded
together.
Acknowledgements
The researchers wish to acknowledge several people who have aided
them in carrying out their research. Mrs. Jamie Hilliard has helped the
researchers by editing and proofreading sections of this paper and supplying the
known and unknown metal rods, linear thermal expansion jigs, thermometer,
LoggerPro, LoggerPro thermometer probe, hot plate, caliper, dry-erase marker,
tongs, graduated cylinder, and insulated gloves. Mrs. Rose Cybulski has aided
the researchers by educating them about the statistical test used to analyze the
data. The researchers wish to thank Mrs. Christine Kincaid-Dewey for aiding in
the data analysis and editing and proofreading the section. Mr. Mark Supal has
aided the researchers by constructing the linear thermal expansion jigs and
helping with construction of the calorimeters used in this experiment, as well as
proofreading and editing sections of the paper. Mr. Brian Kirby has taken his time
to shop for the materials needed to construct the calorimeters.
Kirby-Koury 40
Appendix A: Sample Calculations
Mathematics is a major part of science. For example, throughout this
research mathematics was used to calculate percent error, t-values, alpha
coefficients, and specific heat values. Without these values much of the research
would be worthless. Below are samples of all of the calculations.
percent error= experimental value−true valuetrue value
∙100
percent error=1.116 ∙10−5mm−1.18 ∙10−5mm1.18 ∙10−5mm
∙100
percent error=−5%
Figure 16. Sample Calculation for Percent Error
Figure 16 shows the sample calculation for percent error. The values used
were from the first trial in Table 3. The percent error found is -5%.
t=x1−x2
√ s12
n2+s12
n2
t= 8.0 ∙10−6mm−8.0 ∙10−6mm
√ 2.0 ∙10−6mm2
15+ 1.0 ∙10
−6mm2
15
t=0.6643
Figure 17. Sample Calculation for Two-Sample t Test
Figure 17 shows the sample calculation for the two-sample t test. The
values used were the linear thermal expansion data. The same process would be
completed for specific heat. The result of this calculation is equal to 0.6643.
Kirby-Koury 41
LTECoefficient= ΔLengthHeight initial ∙¿¿
LTECoefficient= 0.10mm97.1mm∙(26.7℃−97.1℃)
LTECoefficient=1.116 ∙10−5mm
Figure 18. Sample Calculation of Linear Thermal Expansion
Figure 18 shows the sample calculation for linear thermal expansion. The
result is 1.116 ∙10-5 mm. The values seen in Figure 18 can be seen in the first
trial of Table 3.
SpecificHeat=4.184 ∙mass of water g ∙Δtemperature of water℃metalmass g ∙ Δtemperture of metal℃
SpecificHeat=4 .184 ∙50.0g ∙4.0℃31.7g ∙71.4℃
SpecificHeat=0.370
Figure 19. Sample Calculation of Specific Heat
Figure 19 shows the sample calculation for specific heat. The result of the
calculation is 0.370 J/g∙℃. The values used in this calculation were taken from
the first trial in Table 1.
Kirby-Koury 42
Appendix B: Randomization
In order to prevent bias in research, many researchers randomize trials. In
this research, the trials were randomize. Below are the directions on how to
randomize using the TI-nspire graphing calculator software.
Materials:
TI-nspire graphing calculator software
Procedure:
1. Open the TI-nspire graphing calculator software and select a calculator
page.
2. Press Menu Probability Random and Integer.
3. Then, enter the minimum value, 1, the maximum value, 2, and the number
of responses, 15.
4. Click Enter.
5. Use the values to order the trials. Note, the ones represent Rod A, and the
twos represent Rod B.
Kirby-Koury 43
Appendix C: LoggerPro
In order to complete the specific heat section of the research, the
LoggerPro was used to collect the initial and equilibrium temperatures of the
metals and the water inside of the calorimeter. The following appendix is the
directions on how to properly use the LoggerPro.
Materials:
LoggerPro
LoggerPro temperature probe
Procedure:
1. Turn on LoggerPro.
2. Set specific time and rate of measurements by clicking on the values on
the right side of the screen.
3. Enter values.
4. Place temperature probe into water in calorimeter.
5. Click the green arrow to begin recording.
6. Press the red square to finish recording once equilibrium has been met.
7. Save file to flash drive or computer.
8. Start a new file for each trial.
Kirby-Koury 44
Appendix D: Calorimeter Construction
For the specific heat trials, a calorimeter was used to calculate the change
in temperature. Calorimeters are used in order to have sufficient insulation to
prevent heat loss. The following appendix is the directions for the calorimeter
construction.
Materials:
34 inch diameter PVC pipe
34 inch non-threaded PVC cap
1 14 inch diameter threaded PVC pipe
end
1inch diameter threaded PVC cap
Foam PVC pipe insulator
Electrical tape
Oatey PVC primer
Oatey PVC cement
1 14 inch diameter PVC pipe stand
Permanent marker
Procedure:
1. Drill an off center 18 inch diameter hole in the top of the threaded PVC cap.
2. Cut the 34 inch diameter PVC pipe to six inches in length.
3. Using the Oatey PVC primer, prime the ends of the PVC pipe.
4. Then using the Oatey PVC cement, apply cement on top of primer and
attach the non-threaded PVC cap and the threaded PVC pipe end.
5. Cut the PVC insulator to six inches in length, or a length that covers the
body of the PVC pipe.
Kirby-Koury 45
6. Wrap the insulator around the body of the PVC pipe and secure with
electrical tape.
7. Use the permanent marker number the calorimeters and label with
necessary information, such as researchers names.
8. Screw the 1 inch diameter threaded PVC cap onto the threaded PVC pipe
end.
9 Place the calorimeter, non-threaded cap down, into the 114 inch inner
diameter PVC pipe stand.
Kirby-Koury 46
Appendix E: Thermal Expansion Jig
Another important part of this research was the thermal expansion jig
which was used to find the net change in length of the metals. The directions on
how to operate the jig are below.
Materials:
Linear Thermal Expansion Jig
Procedure:
1. Place linear thermal expansion jig on flat surface at a slight angle to
reduce the amount of water resting on the measurement prong.
2. Pull measurement prong up.
3. Once metal is placed in jig release prong and mark initial length. Note,
may require more than one operator.
Kirby-Koury 47
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