Introduction - Weebly · Web viewVanadium’s elemental symbol is V and its atomic number is 23. Vanadium has an atomic weight of 50.942 amu and a density of 6.1g/cm3, which is semi-dense

Identifying a Metal Using Specific Heat and Linear Thermal Expansion

Danny Havern and Andrew Rouditchenko

Macomb Mathematics Science Technology Center

Chemistry – 10B

Mrs. Hilliard, Mr. Supal, Mrs. Dewey

May 20, 2013

Havern – Rouditchenko 2

Table of Contents

Introduction............................................................................................................2

Background............................................................................................................4

Review of Literature: Specific Heat........................................................................6

Review of Literature: Linear Thermal Expansion...................................................8

Problem Statement..............................................................................................10

Experimental Design............................................................................................11

Data and Observations........................................................................................15

Data Analysis and Interpretation..........................................................................25

Conclusion...........................................................................................................39

Appendix A...........................................................................................................42

Appendix B...........................................................................................................43

Appendix C...........................................................................................................44

Appendix D...........................................................................................................46

Appendix E...........................................................................................................48

Works Cited..........................................................................................................51


Introduction

Experimentation on metals is conducted daily to discover new and unique

properties that could be used to benefit society. If two similar metals were mixed

up in a laboratory, how would the scientists determine which metal was which?

Using the procedures from this experiment, the scientists would be able to

confidently identify the metals. The purpose of this experiment was to determine

if an unknown metal was the same or different compared to another metal using

the intensive properties of specific heat and linear thermal expansion. The known

metal was correctly identified from a previous experiment as Vanadium using the

property of density. In this experiment, the researchers correctly observed that

two unknown metal rods were not the same as the Vanadium rods.

The metals were compared by calculating intensive properties, or

properties that do not depend on the sample size, of the metals. The specific

heats and linear thermal expansion coefficients were found using various tools.

The researchers had limited background knowledge on the subject, therefore

extensive research was performed. This knowledge was used to design a

procedure for an experiment that would provide accurate results. The experiment

for specific heat involved observing several changes of temperatures including

for the metals and water while the experiment for linear thermal expansion

involved observing the change in length of the metal rods and the change in

temperature. For specific heat, the researchers used calorimeters that were

designed and built specifically for the dimensions of the metal rods. The

calorimeters were built from PVC piping, which is an excellent insulator.


Computer software was used to analyze the change in temperatures and

calculate the specific heat. The most important tools used for the linear thermal

expansion procedure were the expansion jigs. These jigs were built in previous

years by a skilled professional. These jigs measured the miniscule change of

length of the metal rods as they cooled. The researchers used statistical tools to

analyze the data, including two sample t-tests and percent error. The

experimental averages were compared to the known values for Vanadium. The

data proved to be precise as the researchers made an accurate conclusion.


Vanadium Metal Background

Vanadium, V, is a greyish white metal which is very hard, yet ductile. It

was first discovered in 1801 by Andrés Manuel del Rio, a Mexican chemist. He

later withdrew his claim, but Vanadium was rediscovered in 1830 by the Swedish

chemist Gabriel Sefstrôm. The metal was isolated and made pure in 1867 by Sir

Henry Enfield Roscoe by reducing Vanadium chloride with hydrogen (Gerhartz).

Mining for titanomagnetite ore is the first step in the process of extracting

the element to its pure state. Although this mineral only contains about 1.5

percent Vanadium, it is the most common mineral used for the production of

Vanadium. Vanadium is in such a small amount in the mineral, it is not included

in the formula, as seen below. It yields only 0.24 percent Vanadium from the total

extracted materials (Carlson).

Mg3[Si2O5](OH)4(s)+(MgAlFe)3[Si2O5](OH)4(s)→ (MgFe)2SiO4(s)+2MgOAl2O3(s)+5SiO2(s)

Titanomagnetite ore is reduced in flaming kilns and later melted in a

furnace. Olivine, (Mg,Fe)2SiO4, and Cordierite, 2MgOAl2O3+5SiO2 are produced

along with a slag of titanium and pig iron, the product of smelting iron ore with

high-carbon fuel, with high Vanadium content (Gerhartz). The separated molten

pig iron is then blown with oxygen to form a new compound which contains 12-24

percent Vanadium pentoxide (V2O5) (Processing). Pure Vanadium is produced by

reducing Vanadium pentoxide with aluminum powder.

Vanadium has many practical uses, but 99 percent of all Vanadium

produced worldwide was for use as a metal alloy (Vanadium). Pure Vanadium


and Vanadium oxides are combined with steel and titanium respectively in order

to increase their toughness, ductility, and strength. Vanadium has properties not

unlike most other metals. Vanadium’s elemental symbol is V and its atomic

number is 23. Vanadium has an atomic weight of 50.942 amu and a density of

6.1g/cm3, which is semi-dense. The specific heat of Vanadium is 0.485J/mol and

the thermal expansion coefficient of 8.4 x 10-6 K-1. The boiling point is 3653.15 K

(O’Leary). Vanadium is fairly similar to other metals. Compared to water, the

values for each property are very different and are not within the same range.

Vanadium is shaped just like every atom. Protons and neutrons build the

nucleus while electrons surround it in the electron cloud. Electrons fill each orbital

up to the 3d orbital, as seen below (Greenwood).

Electron structure is relevant to this project because electrons deal with

energy. The electrons shifting between orbitals require energy, which in turn can

affect specific heat, and the size of the orbital directly affects thermal expansion

because a larger atomic radius results in expansion of the material (Greenwood).

Vanadium’s use as an alloy allows materials to increase strength while

decrease weight (Vanadium). Essentially, this characteristic makes Vanadium

useful and practical for making products such as buildings and automobiles.

Figure 1. Vanadium Electron Orbital Diagram


Review of Literature: Specific Heat

Heat is the transfer of thermal energy (“Experiment 2”). At constant

pressure, this transfer is equal to enthalpy, the flow of heat energy (“Enthalpy”).

As heat energy flows in or out of a system to its surroundings, the temperature

changes, which is a measure of thermal energy. According to the kinetic

molecular theory, the kinetic energy of the molecules is directly proportional to

absolute temperature, therefore, as heat energy is added to a substance, the

kinetic energy of the molecules increases (“Kinetic-Molecular Theory”). If the

enthalpy is negative, the reaction is exothermic; heat energy is lost from the

system and is transferred to the surroundings (“Enthalpy”). If the enthalpy is

positive, the reaction is endothermic; heat energy is lost from the surroundings

and is transferred to the system. The relation between the change in heat energy

and the change in temperature is the specific heat. Specific heat is an intensive

property which means that the property is not dependent on sample size.

Specific heat is the heat energy required to raise the temperature of one gram of

a substance by one Kelvin; the unit of measure is J/g*K (Schreck). The

relationship between heat energy and specific heat is that the heat energy (Q) in

J is equal to the mass of the substance (m) in grams times the specific heat (c) in

J/g*K times the change in temperature ∆T in Kelvin (“Experiment 2”).

Q=mc∆T

Specific heat is important in the design of materials and products in

modern industry. Extensive research is done to determine the right metal to use


in products like heat exchangers and piping as they have different specific heats

and some insulate heat better than others (Violeta). Specific heat was a useful

property in this experiment because each element has a unique specific heat

(“Experiment 2”). The specific heats of both metals were determined using

calorimetry, which is the process of measuring the enthalpy change during a

reaction (“Calorimetry”). A calorimeter is a tool that involves an isolated system.

In an isolated system, no energy or mass can be transferred to the surroundings.

One experiment that the researchers found was to find the specific heat of

aluminum using a Styrofoam cup to simulate the calorimeter as it insulates heat

fairly well (“Experiment 2”). The metal was massed and then heated to 100° C in

boiling water. The mass and initial temperature of the water was also recorded.

The metal was placed into the cup full of water and the temperature was

recorded when equilibrium was reached, when the water and the metal reached

the same temperature and the graph of the temperature of the water reached a

stable plateau. According to the First Law of Thermodynamics which states that

energy is neither created nor destroyed but only converted from one form to

another, the heat energy lost by the hotter substance was equal to the energy

gained by the colder substance (“Kinetic-Molecular Theory”). The recorded data

was then manipulated in the specific heat formula to find the specific heat of the

metal. In another experiment, various metals were tested to find their specific

heats (Schreck). The calorimeter was an insulated thermos jar which may

insulate heat better than a cup. The other elements of the experiment were very

similar to others, the specific heat was found by placing the metal into water and

observing the masses and temperatures. Both experiments were simple in

design and easy to replicate.


Review of Literature: Linear Thermal Expansion

The property of linear thermal expansion refers to the tendency of a metal

to expand in length when heated. With small temperature changes, the thermal

expansion of regular linear objects is proportional to the change in temperature

(Furrer). In a system, the thermal energy increase within the atoms results in an

increase in atomic radius of those atoms, and thus a larger distance between the

atoms that is signified by an increase in the dimensions of the material (Sutara).

Thermal energy increase also results in more kinetic energy of the atoms. Larger

volume is a result of the atoms bouncing off of each other at a faster rate. These

materials expand volumetrically, but linear thermal expansion refers to the length.

This intensive property was used to determine the identity of the unknown

metal because each element expands and contracts at different rates, therefore

making linear thermal expansion applicable (Nave). Once the experimenters

compared their experimental linear thermal expansion coefficient to an accepted

value and calculated percent error, they were able to determine the identity of the

metal. The linear coefficient of thermal expansion (α) describes a change in

length of the metal per degree temperature change (Davis). To calculate the

linear thermal expansion coefficient, the experimenters used the equation where

the change in length, ΔL, of the metal rod is equal to the expansion coefficient,

α, times the initial length, Li, times the change in temperature, ∆T (Linear).

∆ L=α ∙ Li ∙∆T


The experimenters calculated the coefficient by manipulating the equation

above and substituting in their values recorded during the experiment. The linear

thermal expansion coefficient is expressed in units defined as the reciprocal

temperature, ºC-1. Another common expression of the numerical coefficient is in

terms of 10-6/℃ (Gale). There are multiple linear thermal expansion labs, but this

experiment was a simple one. Some colleges and universities use steam

generators and a thermal expansion apparatus, but they do have similar parts of

the procedure. The procedure was applied to more than one rod and it was

repeated several times to eliminate outliers (Linear). The length temperature of

the metal rod was recorded. It was then placed in boiling water. Once the rod

reached equilibrium with the temperature of the water, the temperature was

recorded and the rod was taken out and the length was quickly measured

(Sutara). Using this data, the experimenters calculated the linear thermal

expansion coefficient of their metal.

Linear thermal expansion has applications in many fields, but it is most

often used in engineering. Designing bridges, buildings, and aircraft or spacecraft

requires the science of thermal expansion. The expanding and contracting of the

metal that makes these objects may cause some serious problems if not taken

into account. Bridges have expansion joints which allow the bridge to expand and

contract according to the temperature without collapsing (Gale). Rebar used in

buildings sidewalks could expand or contract at a greater rate than the concrete

and result in damage (Sutara). A simple application of linear thermal expansion

would be in the kitchen with a jar. If the lid was on a jar, running it under hot


water allowed the lid to expand, therefore making it easier to remove (Nave).

Essentially, linear thermal expansion is used in a multitude of fields.

Problem Statement

Problem Statement:

Can the material properties of specific heat and linear thermal expansion

be used to correctly identify an unknown metal as Vanadium?

Hypothesis:

The experimental data will provide an approximate value of specific heat

and the linear thermal expansion coefficient with which the experimenters will be

able to correctly identify the unknown metal as Vanadium with one percent error.

Data measured:

Specific Heat was measured in J/g°C. To calculate specific heat,

the mass of the rod and the mass of water was measured in grams, and the

initial and final temperatures of both the rod and water were measured in

degrees Celsius. Also, the specific heat of water, 4.184 J/g°C, was used in the

calculation of the specific heat value.

Linear Thermal Expansion Coefficient was measured in 10-6 °C-1. To

calculate the linear thermal expansion coefficient, the original and final lengths of

the metal rods were measured in millimeters. The initial and final temperatures of

the rods were measured in degrees Celsius.


Specific Heat Experimental Design

Materials:

Logger ProLogger Pro thermometer probe, 0.1ºC Digital thermometer, 0.1ºC TI-nspire CX graphing calculatorElectronic timerCalorimeter (2) Unknown metal rods(2) Vanadium, V, rod

(2) 20.3 cm x 9.8 cm x 6.3 cm loaf panHotplateTongsScout Pro electronic scale, 0.1g100 ml graduated cylinder300 ml BeakerWork Glove

Procedure:

1. Use the TI-nspire CX graphing calculator to randomize the order of the trials and the order of the rods. See Appendix A for directions on how to randomize. Make sure to assign fifteen trials to the known metal and fifteen trials to the unknown metal.

2. Turn on and set up Logger Pro. Plug in Logger Pro thermometer probe and adjust data gathering information. See Appendix B for further instructions.

3. Using the 300 ml beaker, pour 150 ml of water into the loaf pan and set it on the hot plate. Turn the hot plate on and place the second loaf pan on top of the first as a lid.

4. Fill the graduated cylinder with 50 ml of water. Record the mass of the water as 50 g.

5. Pour this amount of water into each calorimeter. See Appendix C for instructions on building the calorimeter.

6. Insert the Logger Pro thermometer probe through the hole in the lid of the calorimeter and place the thermometer in the water of the calorimeter.

7. Mass the metal rod using the scale and record.


8. Lift the lid of the loaf pan with the work glove. Insert the digital thermometer into the beaker. Continue to boil the water until it reaches a temperature of about 100℃.

9. Insert the rod(s) into the boiling water. Make sure the entire rod is submerged in the water and begin the electronic timer.

10. After two and a half minutes, stop the timer. Assume that the temperature of the water is the same as the temperature of the metal. Insert the digital thermometer into the boiling water around the rod or between the two rods. Record this temperature as the initial temperature of the metals.

11. Begin collecting temperature measurements of the water in the calorimeter using the Logger Pro temperature probe.

12. Use the tongs to carefully remove the metal from the boiling water and place it in the calorimeter. Quickly, attach the top of the calorimeter. The Logger Pro temperature probe should be in the calorimeter through the hole in the lid.

11. Data collection should stop after three minutes if the Logger Pro was set up correctly. Save data into the appropriate file and record results into the data table.

12. Remove the cap and empty out the calorimeter. Start a new set of data collection on the Logger Pro by selecting the File Cabinet icon in the top right corner of the screen.

13. Repeat steps 3 through 12 for each trial.

Diagram:TI-nspire Calculator


Figure 2. Specific Heat Materials

Figure 2 above shows most of the materials used in the specific heat

experiment. Not pictured is the graduated cylinder.

Linear Thermal Expansion Experimental Design

Materials:

Digital thermometer 0.1ºC TI-nspire CX graphing calculatorElectronic timerLinear thermal expansion jig(2) Unknown metal rods(2) Vanadium, V, rods

(2) 20.3 cm x 9.8 cm x 6.3 cm loaf pan

HotplateTongs300 ml BeakerThick glovesDigital Calipers 0.1 mm50 ml Spray Bottle

Procedure:

1. Use the TI-nspire CX graphing calculator to randomize the order of the trials and the order of the rods. See Appendix A for directions on how to randomize. Make sure to assign fifteen trials to the known metal and fifteen trials to the unknown metal.

2. Using the 300 ml beaker, pour 150 ml of water into the loaf pan and set it on the hot plate. Turn the hot plate on and set the second loaf pan on top of the

Hot Plate

Work Gloves

Lab QuestMetal Rods

Timer

Scale

Digital Thermometer

Loaf Pans

Tongs

CalorimetersThermometer Probes

Beaker


loaf pan with the boiling water to act as a lid. Boil the water until it reaches a temperature of about 100℃.

3. Measure the length of the metal rod using the digital calipers and record as the initial length.

4. Using the tongs, insert the rod into the boiling water. Make sure the entire rod is submerged in the water and begin the electronic timer.

5. After two and a half minutes, stop the timer. Assume that the temperature of the metal is equal to the temperature of the water. Lift the top loaf pan using the work glove. Insert the digital thermometer into the loaf pan. Record this as the initial temperature.

6. See Appendix D for information on how to use the linear thermal expansion jig. Pull back the pin in the jig to allow the metal to be placed in the jig.

6. Carefully remove the rod from the boiling water using the work glove and tongs and place the rod in the thermal expansion jig. Start the timer and move the needle of the gauge to the starting position.

7. Use the spray bottle filled with water to speed up the cooling process. After three minutes, stop the timer and record the change in length.

8. Use the digital thermometer to measure the temperature of each metal and record it as the final temperature.

9. Repeat steps two through nine for each trial.

Diagram:

Digital Thermometer


Figure 3. Linear Thermal Expansion Materials

Figure 3 above shows the materials used on the linear thermal expansion

experiment. Not included in the picture are the metal rods and the work gloves.

An image of these materials can be seen in Figure 2. The picture contains a

towel that is not included in the materials because it is not mandatory, but it was

used to keep the work area dry during the experiment.

Data and Observations

Data:

Table 1Vanadium Specific Heat Experiment Data

Hot Plate

Expansion Jigs

Timer

Scale

Loaf Pans

Tongs

Spray Bottle

Beaker

Towel


Trial Rod

Initial Temp. (°C ) Equilibrium

Temp. (°C)

Change in Temp. (°C )

Mass(g) Specific

Heat (J/g°C)

Metal Water Metal Water Metal Wate

r1 B 98.0 26.8 31.0 -67.0 4.20 25.50 50 0.5142 B 99.0 22.6 26.3 -72.7 3.70 25.50 50 0.4183 A 99.3 24.6 29.6 -69.7 5.00 25.50 50 0.5894 A 99.5 28.3 33.0 -66.5 4.70 25.50 50 0.5805 B 99.5 30.6 33.9 -65.6 3.30 25.50 50 0.4136 A 98.5 30.7 35.1 -63.4 4.40 25.50 50 0.5697 A 99.3 27.4 31.1 -68.2 3.70 25.50 50 0.4458 B 98.5 28.9 32.7 -65.8 3.80 25.50 50 0.4749 A 99.3 27.8 31.5 -67.8 3.70 25.50 50 0.44810 B 99.3 23.7 27.0 -72.3 3.30 25.50 50 0.37411 B 99.3 31.1 33.8 -65.5 2.70 25.50 50 0.33812 A 100.0 26.0 29.5 -70.5 3.50 25.50 50 0.40713 A 100.0 27.7 34.2 -65.8 6.50 25.50 50 0.81014 B 100.0 20.5 25.2 -74.8 4.70 25.50 50 0.51515 B 100.0 26.2 29.6 -70.4 3.40 25.50 50 0.396

Avg. 99.3 26.9 30.9 -68.4 4.00 25.50 50 0.485

Table 1 above shows the data recorded during the trials for the specific

heat of the Vanadium rods. Most trials were performed two at a time as indicated

in the observations tables. The change in temp represents the change of

temperature for both the metal and the water. All temperature measuring devices

had three significant figures. The mass of the water has only one significant

figure because the measuring device was a graduated cylinder. The specific heat

was calculated with three significant figures after the decimal. For a sample

calculation, see Appendix D.

Table 2Unknown Metal Specific Heat Experiment Data


Trial RodInitial Temp.

(°C ) Equilibrium Temp. (°C)

Change in Temp. (°C )

Mass(g)

Specific Heat

(J/g°C)Metal Water Metal Water Metal Water

1 B 99.0 22.6 26.3 -72.7 3.70 24.50 50 0.4352 A 99.0 22.6 26.1 -72.9 3.50 24.50 50 0.4103 B 99.0 20.4 23.9 -75.1 3.50 24.50 50 0.3984 B 99.3 17.0 20.8 -78.5 3.80 24.50 50 0.4135 A 99.0 19.9 23.8 -75.2 3.90 24.50 50 0.4436 A 99.5 27.7 30.7 -68.8 3.00 24.50 50 0.3727 B 99.5 21.5 25.5 -74.0 4.00 24.60 50 0.4608 B 99.4 26.0 30.4 -69.0 4.40 24.60 50 0.5429 B 99.4 21.2 24.8 -74.6 3.60 24.60 50 0.41010 A 99.5 19.2 23.3 -76.2 4.10 24.50 50 0.45911 A 99.4 26.6 29.9 -69.5 3.30 24.50 50 0.40512 B 99.9 23.7 27.1 -72.8 3.40 24.60 50 0.39713 A 99.4 19.6 23.3 -76.1 3.70 24.50 50 0.41514 A 99.9 18.0 22.0 -77.9 4.00 24.50 50 0.43815 A 99.3 16.8 21.0 -78.3 4.20 24.50 50 0.458

Avg. 99.4 21.5 25.3 -74.1 3.70 24.53 50 0.430

Table 2 above shows the data recorded during the trials for the specific

heat of the unknown metal rods. Most trials were performed two at a time as

indicated in the observations tables. The change in temp represents the change

of temperature for both the metal and the water. All temperature measuring

devices had three significant figures. The mass of the water has only one

significant figure because the measuring device was a graduated cylinder. The

specific heat was calculated with three significant figures after the decimal. For a

sample calculation, see Appendix D.

Table 3Vanadium Linear Thermal Expansion Data


Trial RodOriginal Length (mm)

Change in Length(mm)

Initial Temp. (°C )

Final Temp. (°C )

Change in

Temp. (°C)

Alpha Coefficient (10-6°C-1)


1 B 127.31 0.05 98.7 30.1 68.6 5.7252 A 127.39 0.06 99.3 29.9 69.4 6.2213 B 127.34 0.05 99.3 30.5 68.8 5.7074 A 127.41 0.04 98.3 27.7 70.6 4.4475 B 127.29 0.04 98.9 28.4 70.5 4.4576 B 127.37 0.05 98.9 29.2 69.7 5.6327 A 127.36 0.04 98.9 28.4 70.5 4.4558 B 127.28 0.05 98.6 30.4 68.2 5.7609 B 127.37 0.05 98.6 31.5 67.1 5.85010 A 127.44 0.05 98.9 29.2 69.7 5.62911 A 127.33 0.05 98.6 29.5 69.1 5.68312 A 127.4 0.05 98.6 30.6 68.0 5.77213 B 127.37 0.06 99.0 29.7 69.3 6.23114 A 127.44 0.06 99.0 30.0 69.0 6.25515 A 127.37 0.06 98.7 30.1 68.6 6.295

Avg. 127.36 0.05 98.8 29.7 69.1 5.608

Table 3 above shows the data recorded during the trials for the linear

thermal expansion coefficient of the Vanadium rods. Most trials were performed

two at a time as indicated in the observations tables. The change in length

represents the change of length of the metal as it cooled down in the jig after

being heated. The dial on the jig was accurate to two significant figures. The

linear thermal expansion coefficient was calculated with three significant figures

after the decimal. For a sample calculation, see Appendix D.

Table 4Vanadium Linear Thermal Expansion Data

Trial RodOrigina

l Length

Change in Length(mm)

Initial Temp. (°C )

Final Temp. (°C )

Change in

Temp.

Alpha Coefficient (10-6°C-1)


(mm) (°C)1 A 128.28 0.07 100.2 30.2 70.0 7.7952 B 128.81 0.07 100.2 28.5 71.7 7.5793 B 128.88 0.07 101.0 26.5 74.5 7.2904 A 128.26 0.08 100.4 26.2 74.2 8.4065 B 128.77 0.08 100.4 29.7 70.7 8.7876 A 128.40 0.08 100.4 29.1 71.3 8.7387 A 128.30 0.08 100.8 28.1 72.7 8.5778 B 128.87 0.07 100.8 28.5 72.3 7.5139 B 128.79 0.07 100.4 28.2 72.2 7.52810 A 128.28 0.08 100.4 26.9 73.5 8.48511 B 128.81 0.08 100.5 26.3 74.2 8.37012 A 128.31 0.08 100.5 26.0 74.5 8.36913 B 128.76 0.07 100.2 25.1 75.1 7.23914 A 128.29 0.08 100.2 24.5 75.7 8.23815 A 128.35 0.08 101.0 26.1 74.9 8.322

Avg. 128.54 0.08 100.5 27.3 73.2 8.082

Table 4 above shows the data recorded during the trials for the linear

thermal expansion coefficient of the unknown metal rods. Most trials were

performed two at a time as indicated in the observations tables. The change in

length represents the change of length of the metal as it cooled down in the jig

after being heated. The dial on the jig was accurate to two significant figures. The

linear thermal expansion coefficient was calculated with three significant figures

after the decimal. For a sample calculation, see Appendix D.

Observations

Table 5Vanadium Specific Heat Observations


Trial Rod Date Cal. Observations

1 B 15-Apr 1 First day of experimenting. Pre trials were run and the procedures were adjusted.

2 B 17-Apr 1

Both researchers were present. This trial was run by itself. The window was open, and there was cold air blowing in making the room very chilly. The researchers forgot to mass the metal rod and it was massed after being removed from the calorimeter.

3 A 17-Apr 2

The researchers forgot to mass the rod again. It was once again massed after being removed from the calorimeter. The water from the loaf pan was emptied.

4 A 17-Apr 1

The researches decided to start putting two metals in the loaf pan during the heating process due to time constraints. This trial was done with trial five.

5 B 17-Apr 2 The Vanadium rod was dropped on the floor. The water in the loaf pan was emptied and refilled.

6 A 17-Apr 1This trial was performed along with trial eight. The temperature of the water deviated slightly on the thermometer about 0.1 – 0.3°C.

7 A 17-Apr 1

This trial was performed along with trial 10. The Vanadium rod dropped in and out of the water two times in the loaf pan while attempting to pick it up using the tongs. The temperatures of the water in the calorimeters varied.

8 B 17-Apr 2The water in the loaf pan was emptied and refilled after removing the metal rods from it. The amount was slightly more than 150 ml.

9 A 17-Apr 1This trial was performed with trial 11. The researchers had difficulty placing the metal rod into the calorimeter.

10 B 17-Apr 2 The water in the loaf pan was emptied and refilled after removing the metal rods from it.

11 B 17-Apr 2The researchers began to transfer the metal rods slightly late and this rod spent more time than usual in the loaf pan.

12 A 17-Apr 1This trial was performed with trial 14. The researchers began to transfer the metal right on time.

13 A 17-Apr 1

The metal rod slipped from the tongs while being transferred to the calorimeter and touched one of the researcher's hands. The calorimeter was spilled and this trial had to be redone. The redone trial was performed as usual.


Trial Rod Date Cal. Observations

14 B 17-Apr 2

The transfer of the metal to the calorimeter from the loaf pan was very smooth. The water in the loaf pan was emptied and refilled after removing the metal rods from it.

15 B 17-Apr 2

This was the final trial of the day. The water poured into the calorimeter was slightly more than 50 ml. After this trial the researchers began to clean up.

Table 5 shows the observations recorded during the trials for the specific

heat of the Vanadium rods. The table indicates observations for each trial, the

date, which rod and calorimeter were being used, and which trials were done

together. All trials for the A rod were done with calorimeter 1and all trials for the B

rod were done with calorimeter 2.

Table 6Unknown Metal Specific Heat Observations

Trial Rod Date

Cal. Observations

1 B 18-Apr 2

Both researchers were present during the second day of trials. This trial was performed along with trial two. The water in the loaf pan spent a longer duration of time than usual on the hot plate. The wrong data collection method was set up on logger pro, but the data was still valid. The researches forgot to measure the initial temperature of the metal; however they measured the temperature of the water in the loaf pan after removing the metal rods from it.

2 A 18-Apr 1The metal rod was dropped before being placed in calorimeter. The water in the loaf pan was emptied and refilled after removing the metal rods from it.

3 B 18-Apr 2

This trial was performed with trial five. This trial was redone as the original value gave a large percent error. The metal rods were touching in the loaf pan while being heated.

4 B 18-Apr 2This trial was performed with six. The metal rod touched the side of the calorimeter before being dropped in it.


Trial Rod Date

Cal. Observations

5 A 18-Apr 1The metal wiggled around in the tongs while being transferred from the loaf pan to the calorimeter and the process took more time than usual.

6 A 18-Apr 1 The metal spent a longer time in the loaf pan because the transfer of rod A took longer than usual.

7 B 18-Apr 2

This trial was performed with trial 10. The researcher had difficulty placing the top of the loaf pan on. The metal wobbled in the tongs as it was being transferred.

8 B 18-Apr 2

This trial was performed with trial 11. The metal dropped on the floor before boiling. A few seconds went by as the rods were out of the boiling water and placed into the calorimeters.

9 B 18-Apr 2 This trial was performed with trial 13. The metal was dropped while attempting to put in the calorimeter.

10 A 18-Apr 1 The metal touched the outside edge of the calorimeter while being transferred.

11 A 18-Apr 1 The researcher had difficulty placing the metal in the loaf pan. The position of the rod had to be adjusted.

12 B 18-Apr 2This trial was performed with trial 14. The exteriors of the calorimeters were slightly warm; this may have been from the heat of the hot plate.

13 A 18-Apr 1 The window in the experimenting area was opened.

14 A 18-Apr 1 The metal was removed from the loaf pan right on time.

15 A 18-Apr 1This trial was done along with a redo of trial 3 as well; the original value gave a large percent error. This was the last trial of the day.

Table 6 shows the observations recorded during the trials for the specific

heat of the unknown metal rods. The table indicates observations for each trial,

the date, which rod and calorimeter were being used, and which trials were done

together. All trials for the A rod were done with calorimeter 1and all trials for the B

rod were done with calorimeter 2.

Table 7Vanadium Linear Thermal Expansion Observations


Trial Rod DateJig Observations

1 B 19-Apr S3

Both researchers were present during the third day of trials. The linear thermal expansion jigs S1 and S3 were used and they provided a metric measurement. The heat on the hot plate was turned to 10.

2 A 19-Apr S1 The window was closed and it was slightly humid in the room.

3 B 19-Apr S3

This trial was performed with trial four. The length of the rod was measured on the rag as opposed to the face of the table. The metal was removed from the loaf pan slightly later than usual, at about three minutes.

4 A 19-Apr S1 The cooling time of the metal was cut short to about two minutes. The water in the loaf pan was refilled.

5 B 19-Apr S3

This trial was performed with trial seven. The length of the metal was taken twice as the first measurement was an odd value. The calipers were used on the table.

6 B 19-Apr S3This trial was performed with trial 10. The length was measured on the table. The orientation of the metals was switched when they were placed in loaf pan.

7 A 19-Apr S1

The transfer of the metals began slightly late at about three minutes. The temperature of the spraying water was 29 ºC; cold water was added to drop it to 25 ºC. The water in the loaf pan was emptied and refilled.

8 B 19-Apr S3

This trial was performed with trial 11. The metal was measured on the table. The metals were placed correctly in the center of the loaf pan. The water in the loaf pan seemed hotter to the researcher that placed metal in the water. The metal spent about three minutes in the loaf pan.

9 B 19-Apr S3

This trial was performed with trial 12. It took several attempts to get an accurate measure. The researchers began feel very hot and took a brief break.

10 A 19-Apr S1

The temperature of the water in the loaf pan was measured slightly earlier than usual. More than three minutes passed as the researchers waited for the metal to change length.

11 A 19-Apr S1The temperature reading of the water in the loaf pan started late the metal was placed in the jig after about three minutes.

12 A 19-Apr S1 The length of the metal was measured on the table. The water in the spraying bottle was at 28.7º C.

13 B 19-Apr S3 This trial was performed with trial 13. The rods were


Trial Rod DateJig Observations

touching in the loaf pan.

14 A 19-Apr S1The metal was sprayed with a larger quantity of water than usual to cool it down. The change in length of the metal was greater than usual.

15 A 19-Apr S1

This trial was performed with trial one. The tips of the rods were touching again in the loaf pan. The rods were dropped crooked in the jigs and then straightened. The transfer of the metals began right on time. This was the last trial of the day.

Table 7 shows the observations recorded during the trials for the linear

thermal expansion of the Vanadium rods. The table indicates observations for

each trial, the date, which rod and jig were being used, and which trials were

done together. During these trials, all trials for the A rod were done with jig S1

and all trials for the B rod were done with jig S3.

Table 8Vanadium Linear Thermal Expansion Observations

Trial Rod Date Jig Observations

1 A 22-Apr S1

Both researchers were present during the third day of trials. The trial was performed along with trial two. It was noticed that the both metal rods were magnetic to the hot plate.

2 B 22-Apr S3

The metals were very hard to remove from the loaf pan using the tongs as they were attracted to the surface of the plate. The metal rod was put in the jig late at about three minutes. The rod slipped from the slot while trying to place it in the jig.

3 B 22-Apr B1

The jigs were switched with another group, but one had a faulty dial. The dial was replaced and both jigs provided a metric measurement. The transfer of the metal from the loaf pan to the calorimeter began late.

4 A 22-Apr A1This trial was performed along with trial three. The water in the loaf pan was refilled before the metals were heated.

5 B 22-Apr B1 This trial was performed along with trial six. The loaf pan was adjusted on the hot plate, while the rods stuck to the bottom. The researchers began to indicate the


Trial Rod Date Jig Observationsoriginal length of the metals with a marker as opposed to the previous method because the dial moved if touched.

6 A 22-Apr A1The water in the spray bottle was refilled. The water seemed quite cold. The amount of time that the metal spent in the jig was longer than usual.

7 A 22-Apr A1This trial was performed along with trial eight. The water in loaf pans was refilled. The metals were touching while being heated in the loaf pan.

8 B 22-Apr B1The metal rod was transferred to the jig late and the cooling time was less than usual. The Metals had to be adjusted when placed into the jigs.

9 B 22-Apr B1

This trial was performed along with trial 10. The cooling time was about three and a half minutes as the researchers forgot to pay attention to the stopwatch. The jigs were very wet and the wood was soaked with water.

10 A 22-Apr A1 The water used in the spray bottle was refilled again.

11 B 22-Apr B1This trial was performed along with trial 12. The water in the loaf pan was refilled and slightly exceeded 150 ml.

12 A 22-Apr A1

The metal was dropped back into loaf pan while being transferred into the jig. The metals received a heavy dousing of water from the bottle during the cooling process.

13 B 22-Apr B1Trial performed with trial 14. The water in the loaf pan was refilled. The researcher had some trouble with the timer and the transfer of the metals started late.

14 A 22-Apr A1The water in the spray bottle was refilled with water at approximately room temperature. The metal had to be adjusted when placed into the jig.

15 A 22-Apr A1

This trial was performed along with a redo of trial three. The top of the loaf pan put was put on after about 10 seconds from when the metals were placed in the water. This was the final trial of the day.

Table 8 shows the observations recorded during the trials for the linear

thermal expansion of the unknown metal rods. The table indicates observations

for each trial, the date, which rod and jig were being used, and which trials were

done together.


Data Analysis and Interpretation

Several statistical graphs and tests were used to analyze the data from

the experiment. The data was both quantitative and continuous as the data was

numerical and could take any value in a range. The data measured included

values for specific heat and linear thermal expansion coefficients of the metals.

These values were calculated using data collected from the experiment including

temperatures, masses, and lengths of the metal rods. The two sample t- test was

used for the analysis. This test was appropriate as two different samples were

being compared. The first sample was the data for the Vanadium rods and the

second sample was the data for the unknown metal rods. Two t- tests were

conducted; one for specific heat and the other for linear thermal expansion.

Before the tests were conducted, several assumptions had to be checked.

If these assumptions are not met for a two sample t- test, the validity of the

results of the test is questionable. The first assumption was that both samples

were simple random samples taken from two distinct populations. This condition

was met because the trials were randomized. The samples were also

independent because the metal rods were placed in separate calorimeters and

jigs. Another assumption was that both the means and the standard deviations of

the populations were not known. In this experiment, the researchers did not know

the true values of these parameters. The final assumption was that both samples

were normally distributed. According to the Central Limit Theory, if the simple

size is 30 or greater the samples are normal. Unfortunately, each sample size


was only 15 trials which meant that the distributions of the samples had to be

checked.

The purpose of conducting the two sample t- test was to compare two

different sample means and check to see whether the null hypothesis was true or

not. The alternate hypothesis was checked against a null hypothesis. In this

scenario, the null hypothesis was that the known and the unknown metal were

the same while the alternate hypothesis was that the metals were different. For

the specific heat experiment, the null hypothesis was that the mean specific heat

for the known metal, S X1 was the same as the mean specific heat for the

unknown metal, S X2. The alternative hypothesis was that the mean specific

heats were different.

Ho: S X1 = S X2

Ha: S X1 ≠ S X2

For the linear thermal expansion experiment, the null hypothesis was that

the mean linear thermal expansion coefficient for the known metal was the same

as the mean linear thermal expansion coefficient for the unknown metal. The

alternative hypothesis was that the mean coefficients were different.

Ho: L X1 = L X2

Ha: L X1 ≠ L X2

Before the t-Test was completed, percent error was calculated for each

trial in order to check the validity of the results. Percent error was calculated

while the experiment was being run in order for the researchers to make sure the

results were consistent.


Table 9. Vanadium Specific Heat Percent Error

Trial Experimental Value

True Value

Percent Error

1 0.514 0.485 6.0362 0.418 0.485 -13.9113 0.589 0.485 21.3444 0.580 0.485 19.5525 0.413 0.485 -14.9086 0.569 0.485 17.3937 0.445 0.485 -8.2318 0.474 0.485 -2.3139 0.448 0.485 -7.689

10 0.374 0.485 -22.79311 0.338 0.485 -30.27312 0.407 0.485 -16.02313 0.810 0.485 67.09614 0.515 0.485 6.28615 0.396 0.485 -18.307

Avg. 0.486 0.485 0.217

Table 9 above shows the percent error data for each trial of the specific

heat experiment for Vanadium. The averages are indicated on the bottom of the

table. The specific heat of Vanadium was used as the true value. The percent

error was then calculated for each trial and shows the percentage of difference

between the experimental and true value. See Appendix E for a sample

calculation. Negative percent error means that the value for specific heat was

lower than the true value. The percent error was constantly being checked during

the experiment to make sure that the results were consistent. Any trials that were

not consistent with the other trials were redone as indicated in the observations

tables. The range of the data was from about 67% to -30%. This large range and


variability indicates a flaw or an error in the experimental design. Using the

absolute values of each trial’s percent error, the average percent error of this

data would have been about 18%. This method was not used because percent

error is actually calculated using the true values. The actual average percent

error was calculated to be 0.217%. Because this value is less than one percent, it

is excellent evidence that the metal is actually Vanadium.

Table 10. Unknown metal Specific Heat Percent Error


True Value

Percent Error

1 0.435 0.485 -10.3972 0.410 0.485 -15.4733 0.398 0.485 -17.9494 0.413 0.485 -14.7755 0.443 0.485 -8.6946 0.372 0.485 -23.2317 0.460 0.485 -5.2218 0.542 0.485 11.8129 0.410 0.485 -15.385

10 0.459 0.485 -5.27111 0.405 0.485 -16.40412 0.397 0.485 -18.11013 0.415 0.485 -14.40114 0.438 0.485 -9.59815 0.458 0.485 -5.563

Avg. 0.430 0.485 -11.244

Table 10 above shows the percent error data for each trial of the specific

heat experiment for the unknown metal. At the bottom of the table, the averages

of the data can be found. The researchers used the specific heat of Vanadium as

the true value while calculating percent error. The percent error was calculated


for each trial. Negative percent error shows that the value for specific heat was

lower than the true value. The range of the data was only from about -23% to

about 12%. This range is significantly smaller than the range of the data for

Vanadium. The average percent error was calculated to be approximately

-11.244%. This value is somewhat far away from the average percent error for

Vanadium, suggesting that the metals are different.

Table 11. Vanadium Linear Thermal Expansion Coefficient Percent Error


True Value

Percent Error

1 5.725 8.4 -31.844%2 6.221 8.4 -25.939%3 5.707 8.4 -32.058%4 4.447 8.4 -47.061%5 4.457 8.4 -46.936%6 5.632 8.4 -32.951%7 4.455 8.4 -46.965%8 5.760 8.4 -31.428%9 5.850 8.4 -30.353%10 5.629 8.4 -32.988%11 5.683 8.4 -32.348%12 5.772 8.4 -31.291%13 6.231 8.4 -25.821%14 6.255 8.4 -25.539%15 6.295 8.4 -25.064%

Avg. 5.608 8.4 -33.239%

Table 11 above shows the percent error data for each trial of the linear

thermal expansion coefficient for Vanadium. The average results are found at the

bottom of the table. The true value is the linear thermal expansion coefficient of

Vanadium. The percent error column shows the percent difference between each

experimental value compared to the true value. All of these values are negative


which means each experimental value was lower than the true value. The range

of the data is from about -46% to about -25%. This small range suggests that

there is small variability in the data. The average percent error was calculated to

be approximately -33.239%. This indicates a flaw in the experimental design. The

percent error should have been close to zero, or very little difference like the

average of the specific heat trials.

Table 12. Unknown Metal Linear Thermal Expansion Coefficient Percent Error


True Value

Percent Error

1 7.795 8.4 -7.1972 7.579 8.4 -9.7703 7.290 8.4 -13.2094 8.406 8.4 0.0735 8.787 8.4 4.6116 8.738 8.4 4.0297 8.577 8.4 2.1068 7.513 8.4 -10.5619 7.528 8.4 -10.38110 8.485 8.4 1.01011 8.370 8.4 -0.35512 8.369 8.4 -0.36913 7.239 8.4 -13.82214 8.238 8.4 -1.93315 8.322 8.4 -0.932

Avg. 8.082 8.4 -3.780

Table 12 above shows the percent error data for each trial of the linear

thermal expansion coefficient for the unknown metals. The averages are shown

at the bottom of the table. The true value is the linear thermal expansion

coefficient of Vanadium. The percent error column shows the percent difference

between each experimental value compared to the true value. The range of the


data is from about -14% to about 4% which suggest small variability ion the data.

The average percent error was calculated to be approximately -3.780%. This

average is conflicting because it is closer to the true value than the Vanadium

used in the experiment. This is more evidence of an experimental design flaw.

The difference between the average coefficients of the two metals is 29.459,

which is a significant amount.

Figure 4.Normal Probability Plot of Vanadium Specific Heat

Figure 4 above is the normal probability plot of the Vanadium specific heat

data. The graph suggests that the data is normally distributed because the data

points are relatively close to the expected z-value line. The first and last data

points stray far from the expected z-value, so they might be considered as

outliers. Most of the data is near or on the line, so they data as a whole can be

confirmed as normally distributed.


Figure 5. Normal Probability Plot of the Unknown Metal Specific Heat

Figure 5 above is the normal probability plot of the unknown metal specific

heat data. The last data point varies far from the expected z-value line, so it may

be considered as an outlier. Overall, the data is fairly close to the expected z-

value which suggests that the data of the unknown metal for specific heat is

normally distributed.

Figure 6. Specific Heat Data Box Plot

Figure 6 above is the box plot of the specific heat data. The overlapping of

the box advocates evidence that the specific heats of the two metals are the

same or very similar. The unknown metal data appears to be precise because it

is contained in such a small area or box. The Vanadium data has high variability

because it occupies a larger area. The drastic differences between the two


boxes, very low and very high variability, suggest that the data may be unreliable.

The outlier of the unknown metal data also suggests the data may be skewed. In

general, the validity of the data is questionable based on high variability and

outliers of the box plot.

As stated earlier, the statistical test used to analyze the data of the

experiment was a two sample t-Test. To determine whether there was a

significant difference between the metals or not, the p-value was calculated. In a

two Sample t-Test, the t-value must be calculated in order to find the p-value.

The t-value was calculated using the formula where this value is equal to the

sample mean of the Vanadium data, x1, minus the sample mean of the unknown

metal data, x2, divided by the square root of the Vanadium sample standard

deviation, s1, squared which is divided by the sample size of the Vanadium data,

n1, and this quotient is added to a second quotient of the unknown metal sample

standard deviation, s2, squared and divided by the unknown metal sample size,

n2.

t=(EQ ¿(x ,ˉ )1−EQ ¿(x ,ˉ )2)

√( s12

n1 )+( s22

n2 )A sample calculation of this test statistic can be found in Appendix E.

Once the t-value is calculated, the p-value is found using either the calculator

software or a statistics table, for this experiment a calculator was used. The p-

value was then compared to the alpha value to determine significance.


Figure 7. Calculator Specific Heat Statistical Test Results

Figure 7 above is the result of the calculator statistical test of the specific

heat data. Each value used in the test statistic has been calculated and defined.

The p-value produced from the data is a value of 0.101697, which is a slightly

large number. A larger number would support the hypothesis that there is no

significant difference between the two metals.

Figure 8. P-Value Plot of Specific Heat Data

Figure 8 above is a p-value plot of the specific heat data gathered in this

experiment. The shaded area of the graph shows the specific heats greater than

the t-value of 1.72897 and less than -1.7289. The negative t-value is shown


because the alternative hypothesis is not equal to. This area accounts for

10.1697% of the bell curve.

With the p-value calculated, the experimenters could review the results of

the statistical test. The results led them to fail to reject the null hypothesis, Ho,

because the p-value of 0.101697 is greater than the alpha level of 0.10. This

means that there is no significant evidence that the specific heat of Vanadium is

different from the specific heat of the unknown metal. There is only a 10.1697%

chance of getting results as extreme as these by chance alone if the null

hypothesis, that the metals had the same average specific heat, were true.

Figure 9. Normal Probability Plot of Vanadium Linear Thermal Expansion

Figure 9 above is the normal probability plot of the Vanadium data for the

linear thermal expansion portion of the experiment. A large number of the data

points vary far from the expected z-value line. This suggests that the data is not

very reliable as it does not seem to be normal. With a small number of outliers,

they could be taken out of the data set and the tests could be run again, but there

are too many here to take out and yield accurately represented data. Overall, the

data cannot be very reliable based on its heavy variability. The results of the


t-Test might not be conclusive due to the fact that these data points are not

normally distributed.

Figure 10. Normal Probability Plot of Unknown Metal Linear Thermal Expansion

Figure 10 above is the normal probability plot of the unknown metal linear

thermal expansion data. For the most part, the data points lie close to the

expected z-value line, which suggest that the data is valid and reliable.

Figure 11. Linear Thermal Expansion Data Box Plot

Figure 11 above shows a box plot of the linear thermal expansion data,

Vanadium is the top box and the unknown metal is the bottom box. The two

boxes do not overlap at any measurement which suggests that the linear thermal

expansion coefficient is different between the two metals. The unknown metal


box is wider which indicates larger variability in the data. A thinner box, such as

the Vanadium box, indicates low variability in the data. There is a slight skew of

the data in the box plot. The Vanadium data box plot is right skewed which

suggests that the sample mean is greater than the median. The unknown metal

data box plot is left skewed which suggests that the sample mean will be less

than the median. Essentially, this graph shows that the data is reliable because

of few outliers and small variability in the data itself.

The same test was used to analyze the data of the linear thermal

expansion portion of this experiment as was the specific heat portion, a two

sample t-Test. All variables in the formula refer to the same values of the data,

just using a different set of data. The formula can be found above Figure 7 and a

sample calculation of the test statistic can be found in Appendix E.

Figure 12. Calculator Linear Thermal Expansion Statistical Test Results

Figure 12 above shows the calculator statistical test results of the linear

thermal expansion data. Each value used to calculate the test statistic, or t-value,

was recorded by the calculator. The p-value is so miniscule that it was recorded


in scientific notation. The p-value of 6.76291E-12 represents a value of

0.00000000000676291. This very small value will provide significance against

the null hypothesis.

Figure 13. P-Value Plot of Linear Thermal Expansion Data

Figure 13 above shows the p-value plot of the test statistic run for the

linear thermal expansion data. The p-value is so small it basically cannot be seen

on the graph. The area that is shaded under this region is 0.000000000676291%

of all the data.

With the p-value calculated, the experimenters could evaluate the results

of the statistical test. The results led them to reject the null hypothesis, Ho,

because the p-value of 6.76291E-12 is less than the alpha level of 0.10. This

means that there is significant evidence that the linear thermal expansion

coefficient of Vanadium is different from the linear thermal expansion coefficient

of the unknown metal. There is only a 6.76291E-12 % chance of getting results

as extreme as these by chance alone if the null hypothesis, that the metals had

the same linear thermal expansion coefficient, were true. This result is conflicting

because the t-Test for specific heat provided evidence that the metals were the

same.


Conclusion

The initial objective of this experiment was to determine if the material

properties of specific heat and linear thermal expansion could be used to

correctly identify an unknown metal as Vanadium. After all of the data collection

and analysis, the researchers were finally able to propose a conclusion. The

hypothesis that, “The experimental data will provide an approximate value of

specific heat and the linear thermal expansion coefficient with which the

experimenters will be able to correctly identify the unknown metal as Vanadium

with one percent error”, was rejected. The data that supports the rejection of the

hypothesis is the data representing percent error. Each of the average percent

errors of the data of the unknown metals were above or below the hypothesized

value of one percent error. The average percent errors of the known metals were

0.217% for the specific heat and -33.239% for linear thermal expansion. The

average percent errors of the unknown metals were -11.244% for specific heat

and -3.780% for the linear thermal expansion.

Even though the hypothesis was rejected, the experimenters were still

able to correctly identify the unknown metal. The researchers observed that the

unknown metal was not Vanadium. The researchers concluded that the metals

were different based on several observations. The p-value for linear thermal

expansion coefficient was extremely small, much less than the alpha value of

0.10. This suggests that the metals were different. The p value for specific heat

was only above the alpha level by 0.001697. This p value is extremely close to

the alpha level but because it is above the alpha level of 0.10, it suggests that the


metals are the same. Although the results were slightly conflicting, the

researchers made an important observation during the experimental procedure.

While placing the unknown metals in the loaf pan on the hot plate to heat up, the

metals were magnetically attracted to the hot plate. This meant that the unknown

metal rods were magnetic. The known metal, Vanadium, is not magnetic. This

means that the unknown metal is either a magnetic element or an alloy with

magnetic properties. Based on all of these observations, the experimenters were

certain that the unknown metal was not Vanadium.

There were some problems that the experimenters encountered during

their research. The experimenters were not familiar with the tools or the

procedures used in the experiment before beginning the trials. Also, the tools

limited the quality of the researcher’s results. The calorimeters and expansion

jigs were built in house and were not exactly laboratory grade. The dial on the

expansion jig was not very accurate and was difficult to get a correct reading.

Many of the values for temperature were not accurate due to the fact that the

procedure was not reproduced exactly the same for each trial. The transfer time

for the metals from the loaf pan to the calorimeter or jig varied greatly each time.

The amount of time the metals spent in the loaf pan was not the same;

sometimes the metals spent almost an extra minute within the pan. The rods

were dropped in and out of the pan and the calorimeters. These chronological

errors were due mostly to human errors. Because these factors changed often,

the data could have been easily skewed. The percent error for the linear thermal

expansion for Vanadium was -33.239%. This value should have been close to


one which shows that there were flaws in the experimental design. To minimize

error, there could have been several improvements to the procedure. The

experiment could be done in an isolated environment such as a temperature

controlled room without doors and windows being opened. This could minimize

confounding variables such as other experiments being conducted and large

changes in ambient room temperature. The researchers would have benefitted

from a more spacious work space as the small table was very cramped with

materials. A larger work space would allow the researchers to be more organized

and not have to sort through materials. The probability of spilling the calorimeters

would also be reduced. Future researchers could run each trial completely

independently. The researchers ran almost all the trials in pairs due to time

constraints. The greatest investment for the experiment would be better

technology. A bomb calorimeter and a steam expansion jig would produce more

accurate results. Several industries would benefit from using these procedures to

identify metals. Companies that use pure elements in their productions would be

able to check to see if their suppliers are selling them what they are paying for.

Random quality control checks could be done to see if the metals are pure

elements and not alloys or elements with similar properties. Businesses such as

construction and plumbing that use metals often could conduct research to find if

there are cheaper options. They could run similar experiments to observe if there

are metals with values of specific heat and linear thermal expansion coefficient

that are alike to the current metals being used. Essentially, this experiment this

could be adapted for many uses.


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Documents

Introduction - Weebly · Web viewVanadium’s elemental symbol is V and its atomic number is 23. Vanadium has an atomic weight of 50.942 amu and a density of 6.1g/cm3, which is semi-dense