Identifying an Unknown Set of Metal Rods as Consisting of Niobium or



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Cieslinski- Maurice

10B Chemistry IDS




Identifying an Unknown Set of Metal Rods as Consisting of Niobium or Not by

Comparing it to a Known Set of Niobium Rods

Raymond Cieslinski and Jeremy Maurice


Macomb Mathematics Science and Technology Center
Chemistry 1 – 10B
Mrs. Hilliard Mr. Supal Mrs. Dewey
May 20, 2014

Table of Contents

Introduction.…………………………………………………………………………...pg. 1

Review of Literature…………………………………………………………………..pg. 3

Problem Statement...……….………………………………………………………… pg. 8

Specific Heat Experimental Design…………………………………………………...pg. 9

Linear Thermal Expansion Experimental Design...………………………………….pg. 11

Data and Observations..……………………………………………………………...pg. 13

Data Analysis and Interpretation………………………………………………….…pg. 21

Conclusion……………………………………………………...……………………pg. 32

Application……………………………………………………………………….…..pg. 36

Acknowledgements…………………………………………………………………. pg. 38

Appendix A………………………………………………………………………..…pg. 39

Appendix B…………………………………………………………………………..pg. 41

Works Cited………………………………………………………………………….pg. 45


Introduction:

Whether it be used as a superconductor or as a material that is used to make a jet engine, niobium has become increasingly important across many industries. When it comes to producing steel, niobium is added because it strengthens the alloy, allowing for a reduced chance of structural failure occurring in a building (Niobium). In the industry of producing electricity, niobium can be used as a superconducting magnet, which can be used to mass produce electricity, which is crucial due to the extensive amount of electricity that is used each year (Niobium). It can even be used to make jewelry, as it has a lustrous appearance, especially when polished.

The purpose of this research was to determine whether or not an unknown sample of metal rods consisted of niobium as the known rods did. Through two experiments, the intensive properties of specific heat and linear thermal expansion were calculated and used to compare the known set of metals to the unknown set, which aided in the decision of whether or not they were of the same element. In the specific heat experiment, the sets of rods were heated on a hot plate for five minutes in boiling water and placed inside of a calorimeter, and over four minutes at a time, the temperature of the water inside of the calorimeter was measured in order to measure the specific heat of each rod. In the linear thermal expansion experiment, the metals were again heated for five minutes in boiling water over a hot plate. When the five minutes had passed, the metals were quickly taken from the water that they were heated in and were quickly placed inside of a linear thermal expansion jig to measure the change in length of the metal as it cooled inside of the jig for five minutes.
Through repetition of the experiments, sufficient data was collected in order to complete a two sample t test that compared the unknown metals to the niobium rods. The purpose of a two sample t test is to compare sample means to determine how likely it is that they came from the same population; therefore, the researchers were able to determine whether or not the unknown metals were niobium by comparing the means of their specific heat values and of their linear thermal expansion coefficients, which would in turn achieve their goal of this research, identifying the sets of metals as being the same or not.

Review of Literature:

The purpose for this research was to determine whether an unknown matched the known metal niobium, using two properties that differ between each element. The two properties used were linear thermal expansion and specific heat because they are both intensive properties, meaning that they are the same, regardless of the sample size.

Linear thermal expansion is an intensive property of an element, meaning that the property remains the same, no matter what the sample size is. It is the measure of the fractional change in size of a material in response to a temperature change. In order to use this property to determine whether two metals were of the same element or not, the coefficient of linear thermal expansion, often referred to as the alpha coefficient, was solved for. This value, usually denoted with the symbol α (alpha), is the ratio of the fractional change in size of a material that occurs when there is a change in temperature and is usually written in terms of the SI unit inverse kelvin (K-1 or 1/K) or in the non SI unit inverse degree Celsius (°C-1 or 1/°C).

In order to determine the coefficient of linear thermal expansion, one can use the linear thermal expansion formula, which relates the change in length, to the change in temperature.



In this equation, represents the change in length, is the initial length of the metal, is the initial temperature of the metal subtracted from the final temperature of the metal, and as mentioned before, α is the coefficient of linear thermal expansion. This formula can be manipulated in order to calculate the alpha value.

In order to obtain the values needed to calculate the alpha value, an experiment was ran which determined the change in length that was associated with a given change in temperature, thus allowing the experimenters to calculate the coefficient of linear thermal expansion. The linear expansion coefficient of niobium is 7.3 x 10-7 K-1, which is relatively low when compared to common elements such as copper, which has a coefficient of expansion of 1.66 x 10-5 K-1, and aluminum, which has a coefficient of expansion of 2.30 x 10-5 K-1. While researching experiments that could be ran to determine the alpha coefficient of the metals, many methods were found. Of all of the methods found, two experiments were found to accurately determine the alpha coefficient.

The first experiment (Measuring the Coefficient of Linear Expansion of Copper, Steel, and Aluminum) involved using an ohmmeter to monitor the change in electrical resistance of a thermistor as the temperature of a metal changed. The initial length of the metal was to be measured, then the metal was placed into a spring-powered dial gauge, which measured the change in length of the material. The metal was to then be heated with steam until the dial gauge was stable, and the change in length, as well as the change in temperature was to be recorded.

Another experiment composed by St. Louis Community College (Coefficient of Thermal Linear Expansion), similar to the first, described measuring the initial length of a metal at room temperature, and placing it inside of an apparatus that would expose it to steam until the dial gauge on the apparatus remained stable, and the change in the dial was recorded as the change in length after the metal had reached one hundred degrees Celsius.

The two methods of measuring linear thermal expansion above provided a strong base to the experimental design that was used to determine the coefficient of linear thermal expansion in many ways, mainly due to practicality of the experiment.

Linear thermal expansion is a very important factor in the industry of concrete manufacturing. This is due to the fact that concrete expands and contracts as the weather changes, and if the expansion of the concrete is not taken into account, the concrete will crack, and the ground that it is placed over will become unstable, causing foundations of buildings to collapse and roads to be unsafe to drive on because of emerging potholes (Thermal Expansion and Contraction). This phenomenon occurs because as the temperature changes, the amount of heat energy exposed to the concrete varies, and as heat energy is added to the concrete in an endothermic process, it expands due to the increased movement in the molecules and contracts when energy is taken from it in an exothermic process, which may crack the cement.

Specific heat is a very unique property, and can be used like a fingerprint to identify substances such as metals when used in an experiment (Heat). This is because it is an intensive property, meaning it is unique to each element. Specific heat is the heat required to raise the temperature of the unit mass of a given substance by one degree Celsius. Specific heat differs between substances due to many factors, one of which being the molecular structure of the substance. Molecular structures that differ may allow more movement within a molecule than others, making them easier to absorb energy. It can be utilized in an experiment that tries to determine an unknown metal (Heat).

Specific heat is important in industry work and can not only be used to determine the identity of an unknown metal, but is also significant in the cooling process. In most light water reactors, water is used as a coolant and a moderator because of its high specific heat of 4.184 J/g°C and abundance (Nave, Carl R). It is also important to know the specific heat of a material because if it is exposed to energy, it is important to know the temperature of the material at any given moment for safety reasons.

When a material is exposed to heat energy, the atoms in it will absorb the energy. The absorbed energy causes the atoms of the material to vibrate, which in turn heats up the material. This change in heat can be observed using a calorimeter to observe the temperature change in the surroundings. A calorimeter is a type of isolated system that can measure the change in temperature of the surroundings. This is based on the kinetic molecular theory, which states that the average kinetic energy of a collection of gas particles depends on the temperature of the gas and nothing else (Heat). It is an intensive property, meaning that the sample size does not matter, which makes it ideal for identifying an unknown material. The units for specific heat are derived from its formula, which says that specific heat of a material, s, multiplied by its mass, m, multiplied by the change in temperature, ∆T, is equal to the specific heat of water, s, multiplied by the mass of the water inside the calorimeter, s, multiplied by the change in temperature, ∆T.



The mass is normally in grams, the change in temperature in either Celsius or Kelvin, and the unit of specific heat is Joules per gram Celsius or Joules per gram Kelvin (J/g°C or J/gK respectively).

While Niobium has a relatively high density of 8.57 g/cm3, compared to water’s density of 1 g/cm3, it has a low specific heat of 0.265 J/g°C when compared to that of water, which is 4.184 J/g°C (Heat Capacity). This means that although Niobium’s atoms are more tightly packed than water’s, it is heated much quicker than water.

Both model experiments have the same basic design—heat water to its boiling point and insert a metal rod into the water and then after waiting for the metal rod to reach thermal equilibrium, and then transferring the rod into a colder water bath, all while recording temperatures—but they have their differences. One experiment goes into detail about calorimeters and tests aluminum, brass, and steel (Experiment VIII), while the other goes into the background of specific heat (Experiment 7). There are a few minor differences, one being the methods of heating used, where one experiment uses a Bunsen burner (Experiment VIII) and the other uses a stove (Experiment 7), but other than that the designs are similar.

In all, the intensive properties of linear thermal expansion and specific heat were chosen among others to run this experiment because they are definite indicators as to whether or not two substances consist of the same element or not, as these properties are unique to each element. They were also picked because they are intensive properties; therefore, the sample size of each substance would not be a factor in running each experiment.

Problem Statement:

To determine and compare the identity of an unknown metal with Niobium using the intensive properties of specific heat and linear thermal expansion.



Hypothesis:

The unknown metal is Niobium if its specific heat and its coefficient of linear thermal expansion are within a five percent error of each respective corresponding value from the known Niobium rod.



Data Measured:

In an experiment to determine the coefficient of linear thermal expansion of the unknown sample, the length of the rod was measured in millimeters, mm, and the temperature was taken in degrees Celsius, °C. The coefficient of linear thermal expansion was measured as the fractional change in length that is associated with the change of one degree Celsius, C-1. In the experiment that determined the specific heat of the unknown sample, and the temperature was quantified in degrees Celsius, the mass was measured in grams, g. The specific heat of the sample was calculated as the heat per gram that is required to increase the temperature of the substance by one degree Celsius, which is in Joules per gram.




Specific Heat Experimental Design:

Materials:


TI-Nspire

(2) Unknown metal rods

(2) Niobium metal rods

Hot plate

Loaf pan

Scale (0.0001g precision)

(2) Calorimeters

Hot pads


Lab Quest

Tongs


Water

Thermometer (0.01°C precision)

Temperature probe (0.01°C precision)

100 mL Graduated Cylinder




Procedure:

1. Randomize the 30 trials using the TI-Nspire randomization function, making sure that there are 15 trials for the unknown metal rod and 15 trials for the niobium rod.


2. Fill the loaf pan three fourths of the way with water.

3. Using the scale, determine and record the mass of the metal rod.

4. Construct the calorimeter. (See appendix A)
5. Measure and record the mass of the metal rod.

6. Fill the calorimeter with 50 mL of water, making sure to leave the metal rod inside.


7. Turn on the hot plate.

8. Place the loaf pan on the hot plate and wait for the water to reach 100°C.

9. When the water is at 100°C, remove the metal rod out from the calorimeter with the tongs and place it in the loaf pan, allowing at most five minutes for it to reach thermal equilibrium with the water.
10. After the five minutes have passed, record the temperature of the water, and assume the temperature of the water is the same as that of the heated metal rod.
11. Set up the Lab Quest and connect the temperature probe.
12. Carefully insert the temperature probe into the calorimeter.

13. Begin collecting the temperature data of the initial temperature of the water in calorimeter for thirty seconds.


14. After thirty seconds have passed, carefully insert the heated metal rod into the calorimeter using the tongs, and close the system so that no heat is released.
15. Allow the temperature of the water to reach equilibrium with the metal rod and record the temperature. Once again assume the final temperature of the water is the same as the final temperature of the metal rod.

16. After the water has reached thermal equilibrium with the metal rod, use the tongs to remove the rod from the calorimeter.

17. Using the data collected, calculate the specific heat of the metal rod.

18. Repeat steps 5-17 for the rest of the trials.


Diagram:

Figure 1. Materials used in the specific heat experiment.

Figure 1 above contains the materials used in the experiment, each individually labeled.

Linear Thermal Expansion Experimental Design

Materials:


TI-Nspire

(2) Unknown metal rods

(2) Niobium metal rods

Hot plate

Loaf pan

Thermometer (0.01°C precision)

Tongs

Linear Thermal Expansion Jig (0.01mm precision)



TESR Caliper 00530085 (0.01mm precision)



Procedure:
1. Randomize the 30 trials using the TI-Nspire randomization function, making sure that there are 15 trials for the unknown metal rod and 15 trials for the niobium rod.
2. Fill the loaf pan three fourths of the way with water.
3. Place the loaf pan with the water onto the hot plate, and turn on the hot plate, using a thermometer to measure the temperature.
4. Using the caliper, measure and record the initial length of the rod in millimeters.
5. Once the water is at 100°C, place the rod into the pan, allowing at most five minutes to allow the metal to reach thermal equilibrium with the water. Assume that the temperature of the metal is the same as the temperature as the water, and record the temperature as the final temperature of the rod.
6. Quickly remove the rod from the pan using the tongs, and insert it into the linear thermal expansion jig. The metal must be placed inside of the jig as quickly as possible because the rod will quickly begin to contract once removed from the water.
7. Once the rod is inside of the jig, quickly mark the initial point that the dial is pointing to with a marker.
8. Once the rod has stopped shrinking, mark the final point that the dial is pointing to, and record the difference between the two points on the dial as the change in length.
9. Use the thermometer to measure the air temperature, assuming that the metal has reached thermal equilibrium with the air, and record it as the initial temperature.
10. Calculate the coefficient of linear thermal expansion using the collected data.
11. Repeat steps 2-10 for the rest of the trials.
Diagram:

Figure 2. Materials used to conduct the linear thermal expansion experiment.


Figure 2 above is a labeled diagram of the materials that were used in the linear thermal expansion experiment.

Data and Observations

Table 1


Data Tables for Niobium Specific Heat Experiment

Trial

Rod

Mass of Metal
(g)

Initial Temp of Metal
(°C)

Final Temp of Metal and Water

(°C)


Mass of Water
(g)

Initial Temp of Water
(°C)

Specific Heat of Metal
(J/g*°C)

1

A

35.7978

100.0

23.8

50

21.3

0.276

2

B

35.6138

98.6

24.2

50

22.0

0.257

3

A

35.8173

99.0

23.6

50

21.3

0.262

4

B

35.6295

97.8

29.1

50

27.0

0.263

5

B

35.6198

98.3

31.0

50

28.8

0.276

6

A

35.7976

97.5

30.9

50

28.8

0.268

7

B

35.6187

98.0

32.1

50

30.1

0.262

8

B

35.6275

98.7

33.8

50

31.7

0.274

9

A

35.7954

97.8

30.3

50

28.3

0.257

10

A

35.7974

98.3

27.9

50

25.7

0.266

11

B

35.6137

98.6

30.2

50

28.0

0.273

12

B

35.6097

97.7

37.5

50

35.5

0.279

13

A

35.8068

97.4

37.4

50

35.6

0.259

14

A

35.8112

97.8

29.1

50

27.0

0.262

15

B

35.6249

98.8

26.8

50

24.4

0.280

Average

35.7054

98.3

29.8

50

27.7

0.268

Table 1 shows the data tables for the known metal niobium, including the mass and both the final and initial temperature for it and water. The calculated specific heat is also included, and it can be seen that the calculated specific heat was fairly consistent ranging from a low of 0.257 J/g*°C to a high of 0.280 J/g*°C. Also, the specific heat included a correction factor that was determined by averaging the difference of the calculated specific heat and the known value of specific heat for niobium.

Table 2

Data Tables for the Unknown Metal Specific Heat Experiment



Trial

Rod

Mass of Metal
(g)

Initial Temp of Metal
(°C)

Final Temp of Metal and Water

(°C)


Mass of Water
(g)

Initial Temp of Water
(°C)

Specific Heat of Metal
(J/g*°C)

1

A

71.0804

97.3

34.1

50

26.2

0.452

2

B

71.1630

97.5

37.4

50

30.3

0.431

3

A

71.0808

98.2

35.2

50

27.9

0.425

4

B

71.1706

97.5

39.7

50

34.6

0.343

5

B

71.1636

97.5

39.1

50

32.9

0.396

6

A

71.0795

95.3

31.8

50

24.0

0.445

7

B

71.1648

97.3

37.1

50

30.2

0.421

8

B

71.1679

97.2

36.6

50

30.1

0.399

9

A

71.0848

98.1

33.7

50

26.2

0.427

10

A

71.0774

97.5

33.4

50

26.6

0.396

11

B

71.1709

97.3

41.4

50

36.1

0.362

12

B

71.1983

97.4

33.7

50

26.1

0.434

13

A

71.0772

98.6

35.7

50

29.0

0.397

14

A

71.0794

97.7

33.1

50

25.3

0.439

15

B

71.1988

96.7

34.2

50

26.5

0.446

Average

71.1305

97.4

35.7

50

28.8

0.414

Table 2 shows the data tables for the unknown metal, including the mass and both the final and initial temperature for it and water. The calculated specific heat is also included for each trial.


Table 3


Observations for Niobium Specific Heat Trials

Trial

Observations

1

Calorimeter A used, good transfer, remained in calorimeter for 5 minutes

2

Calorimeter A used, good transfer, remained in calorimeter for 5 minutes

3

Calorimeter A used, good transfer, remained in calorimeter for 5 minutes

4

Calorimeter A used, consistent specific heat, small percent error, remained in calorimeter for 3 minutes

5

Calorimeter A used, consistent specific heat, remained in calorimeter for 3 minutes

6

Calorimeter B used, good transfer, remained in calorimeter for 3 minutes

7

Calorimeter B used, quickly transferred to calorimeter, remained in calorimeter for 3 minutes

8

Calorimeter B used, good transfer, remained in calorimeter for 3 minutes

9

Calorimeter A used, temps recorded for 4 minutes, extremely fast transfer, remained in calorimeter for 4 minutes

10

Calorimeter A used, fast transfer, remained in calorimeter for 3 minutes

11

Calorimeter A used, fast transfer, remained in calorimeter for 4 minutes

12

Calorimeter B used, fast transfer, remained in calorimeter for 4 minutes

13

Calorimeter B used, fumbled, remained in calorimeter for 4 minutes

14

Calorimeter A used, very quick transfer, remained in calorimeter for 4 minutes

15

Calorimeter A used, great transfer, remained in calorimeter for 4 minutes

Table 3 shows the observations for the specific heat trials performed on the niobium rods. It can be seen that the majority of the trials had fast transfers and remained in the calorimeter for three minutes. This amount was changed during the trials in an effort to improve the accuracy of the results. The calorimeter used was also alternated to remove any bias that could result from one over the other.

Table 4


Observations for the Unknown Metal Specific Heat Trials

Trial

Observations

1

Calorimeter B used, dropped on first attempt, remained in calorimeter for 3 minutes

2

Calorimeter A used, good transfer, remained in calorimeter for 3 minutes

3

Calorimeter A used, great transfer, remained in calorimeter for 3 minutes

4

Calorimeter A used, good transfer, some water splashed, remained in calorimeter for 3 minutes

5

Calorimeter B used, temps recorded for 4 minutes, extremely fast transfer, remained in calorimeter for 3 minutes

6

Calorimeter B used, fumbled, remained in calorimeter for 3 minutes

7

Calorimeter B used, fumbled, remained in calorimeter for 4 minutes

8

Calorimeter A used, fumbled, remained in calorimeter for 4 minutes

9

Calorimeter A used, fast transfer, remained in calorimeter for 4 minutes

10

Calorimeter B used, fumbled on first attempt, remained in calorimeter for 4 minutes

11

Calorimeter B used, good transfer, remained in calorimeter for 4 minutes

12

Calorimeter B used, sloppy transfer, remained in calorimeter for 4 minutes

13

Calorimeter A used, very good transfer, remained in calorimeter for 4 minutes

14

Calorimeter A used, good transfer, remained in calorimeter for 4 minutes

15

Calorimeter B used, slow transfer, remained in calorimeter for 4 minutes

Table 4 shows the observations for the specific heat trials performed on the unknown rods. It can be seen that some trials had a sloppy transfer due to the size of the metal rods. This was fixed by changing the type of tongs that were used, beginning in trial 13, which allowed for much more efficient transfers. The calorimeter used was also alternated to remove any bias that could result from one over the other.

Table 5


Data for the Linear Thermal Expansion Experiment of the Niobium

Trial

Rod

ΔL
(mm)

Initial Length
(mm)

Initial Temp.
(ºC)

Final Temp.
(ºC)

Alpha Coefficient
(°C-1 )

1

A

0.04

129.10

23.9

98.6

4.15E-06

2

B

0.03

128.38

24.8

98.7

3.16E-06

3

A

0.03

129.01

24.2

98.6

3.13E-06

4

B

0.05

128.40

24.1

98.8

5.21E-06

5

A

0.04

129.05

24.1

98.3

4.18E-06

6

A

0.03

129.08

24.0

98.8

3.11E-06

7

A

0.03

129.04

24.0

98.3

3.13E-06

8

A

0.04

129.10

23.3

98.2

4.14E-06

9

B

0.04

128.42

23.9

98.2

4.19E-06

10

A

0.03

129.01

24.6

98.1

3.16E-06

11

A

0.04

129.06

24.0

98.4

4.17E-06

12

B

0.03

128.37

24.1

98.4

3.15E-06

13

A

0.04

129.07

24.2

98.2

6.50E-06

14

B

0.04

128.39

25.0

97.5

6.56E-06

15

A

0.04

129.15

25.0

98.3

8.72E-06

Average

0.04

128.84

24.2

98.4

4.44E-06

Table 5 above contains all of the data collected in order to calculate the coefficient of linear thermal expansion, which included measuring the initial and final temperatures, the initial length, and the change in length of the metal rod. It should be noted that the data remained fairly consistent as the trials were completed.

Table 6


Data for the Linear Thermal Expansion Experiment of the Unknown Rods

Trial

Rod

ΔL
(mm)

Initial Length
(mm)

Initial Temp.
(ºC)

Final Temp.
(ºC)

Alpha Coefficient
(°C-1 )

1

A

0.06

128.75

24.0

97.2

6.37E-06

2

B

0.05

128.90

24.8

96.3

5.43E-06

3

A

0.05

128.77

24.2

97.1

5.33E-06

4

B

0.05

129.00

24.1

97.2

5.30E-06

5

A

0.05

128.70

24.1

97.2

5.31E-06

6

A

0.06

128.74

24.0

97.9

6.31E-06

7

A

0.05

128.70

23.3

97.2

5.26E-06

8

B

0.05

128.94

23.9

98.2

5.22E-06

9

A

0.05

128.68

24.6

97.5

5.33E-06

10

B

0.05

129.09

24.0

97.7

5.26E-06

11

A

0.05

128.80

24.1

95.5

5.44E-06

12

B

0.06

128.87

26.8

98.4

6.50E-06

13

A

0.06

128.8

26.6

97.6

6.56E-06

14

B

0.08

129.06

27.0

98.1

8.72E-06

15

A

0.05

128.76

26.3

98.3

5.39E-06

Average

0.05

128.84

24.8

97.4

5.85E-06

Table 6 above contains all data that was collected during the linear thermal expansion trials of the unknown rods, including the change in length, initial length, and the initial and final temperatures of the metal rods. It should be noted that the data recorded was fairly consistent as the trials were completed, resulting in consistent coefficients of linear thermal expansion.
Table 7

Observations for Niobium Linear Thermal Expansion Trials



Trial

Observation

1

jig 1a used, metal in jig quickly

2

jig 1a used, shrunk very little

3

jig 1a used, smaller percent error than before

4

jig 1a used shrunk more than previous trials

5

jig 1a used, shrunk more than previously

6

jig 1a used, shrunk as much as previous trials

7

jig 6b used, in jig quickly, change in length consistent

8

jig 6b used, in jig quickly, jig bumped

9

jig 6b used, in jig quickly

10

jig 1a used, in jig quickly

11

jig 1a used, in jig quickly

12

jig 6b used, rod in jig was slightly off center

13

Jig 12 used, change in length measured in inches, quick transfer

14

Jig 12 used, change in length measured in inches, shrunk at normal rate

15

Jig 12 used, change in length in inches, quick transfer

Table 7 above is of the observations recorded during the linear thermal expansion experiment for the niobium rods. It should be noted that the same two jigs were used to collect data, except for the last three trials, where a different jig was used because the other two were not available. It should also be noted that though jig twelve measured the change in length in inches, data was converted to millimeters before being put inside of the data table for use.

Table 8


Observations for Unknown Rods Linear Thermal Expansion Trials

Trial

Observation

1

jig 6b used, metal dropped before inside jig, metal still hot after 6 min

2

jig 6b used, metal in jig quickly

3

jig 6b used, consistent change in length

4

jig 6b used, consistent change in length

5

jig 6b used, shrunk consistent with other trials

6

jig 1a used, changed slightly more than previously

7

jig 1a used, fumbled into jig

8

jig 1a used, fumbled into jig

9

jig 6b used, slightly fumbled into jig

10

jig 6b used, dropped on first attempt, slight fumble on second attempt

11

jig 1a used, temp in hot plate lower than previously, fumbled into jig

12

Jig 12 used, change in length measured in inches, quick

13

Jig 4 used, change in length measured in mm, quick

14

Jig 12 used, change in length measured in inches, normal

15

Jig 4 used, change in length measured in mm, slow

Table 8 above contains the observations that were recorded for while running the linear thermal expansion trials for the unknown rods. It should be taken note of that the same two jigs were used to carry out the experiment, with the exception of the last four trials. This is due to the lack of availability of the preferred jigs. Since jig twelve measured the change in length in inches, data was converted to millimeters before being entered into the data table for use, as the linear thermal expansion equation used required lengths to be in millimeters.


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