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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.


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.


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.






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


4 B 4/22/2013


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


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


9 A 4/22/2013


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


14 B4/22/201

3


15 A4/22/201


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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