Paper ID #12001
A Simple Hands-On Experiment for First Year Undergraduates that Con-nects the Electrical and Thermal Properties of Metals
Dr. Kathleen Meehan, University of GlasgowProf. Robert H Hadfield, University of Glasgow, UK
Robert Hadfield is Professor of Photonics and Head of the Division of Electronic and Nanoscale Engi-neering at the University of Glasgow, United Kingdom.
Andrew Phillips
c©American Society for Engineering Education, 2015
Page 26.109.1
A Simple Hands-On Experiment for First Year Undergraduates
that Connects the Electrical and Thermal Properties of Metals
Abstract
The undergraduate engineering programmes at the University of Glasgow were recently revised
to include a common core of classes in Year 1 and Year 2. Materials I, an introductory materials
science course, is now taken by all Year 1 engineering students. The lectures in the course were
modified to include topics that are of interest to electronic and electrical engineering students,
electrical and optical properties of materials. A hands-on laboratory experience has been developed
to support student learning on electrical resistivity and thermal conductivity. The hands-on
experiment about optical reflectivity will be added to the laboratory in the near future. This paper
describes the laboratory exercise – the intended learning outcomes, the laboratory procedure, an
evaluation of the student performance, and a discussion on improvements that will be made to
increase student understanding of the topics and ancillary subjects.
I. Background on Hands-On Learning in Materials Science
Many institutions of higher learning have adopted a common set of engineering and science
courses into their engineering degree programmes, where an introductory materials science course
is often one of the core courses. Recognizing the universality of certain experiences (snapping a
metal paperclip as a result of cold working, for example), routine choices that involve material
selection (purchase of a bicycle is driven by cost. weight, and material composition), and the fun
that student can have making and destroying objects while learning concepts from materials
science, measuring material properties, and designing structures that rely on the proper selection
of materials, educators have designed hands-on laboratory exercises that allow students to explore
the properties of materials and how their knowledge of these properties can guide the selection of
materials for specific applications1
23
–4
5.
However, an issue that arises when reviewing the lab exercises is that the concepts that are
demonstrated during these labs tend to emphasize the mechanical and thermal properties of
materials. While these concepts are useful for all engineering students to understand, few of the
experiments explore and emphasize the concepts about and the relationships between the electrical,
optical, and magnetic properties of materials67. These concepts have more immediate relevant to
students in electronic, electrical, and computer engineering and are increasingly important to
students in all fields as microcontrollers and sensors are pervasive elements in almost all
engineering designs. Hence, there is a need to design hands-on activities in these materials science
courses that expose students to the non-mechanical properties of materials.
II. Course Redesign at the University of Glasgow
The inclusion of materials science into the core engineering courses taken by undergraduate
students in Electronic and Electrical Engineering (EEE) at the University of Glasgow occurred
during the restructuring of all of the engineering programmes in 2012. This prompted a review of
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the instructional materials by the staff to ensure that topics relevant to the discipline-specific
courses taken later in the EEE students’ academic careers were introduced to students during this
Year 1 one-semester course without significantly decreasing the instruction on topics that are
needed by students in other engineering programmes. As a result of the review, the course was
revised and additional lectures on the electrical, optical, and magnetic properties of materials along
with discussions about the requirements for the materials used in electronics such as solar cells,
high speed transistors, and magnetic storage were inserted into the course.
The first cohort of Year 1 students took the revised course in Fall 2013. While the students in
general gave the course high marks in the end-of-semester course evaluation, a number noted that
one aspect of the course did not contain any material related to EEE – the labs still were traditional
experiments on the strength of materials. This was not an oversight by the staff involved in the
course revision; the time required to revise the lectures precluded the development of a new
experiment on the electrical, optical, and magnetic properties of materials.
After the course was taught for the first time, attention was shifted to the development of a lab
exercise in which students would apply some of the concepts on the electrical and optical
properties of metals presented in lectures. Since the electrical, optical, and thermal properties of
metals are related to the concentration of electrons in the ‘sea of electrons’ and the electron-
electron and electron-lattice interactions, it was decided to design a lab that allowed students to
measure these properties and determine experimentally the relationships between the properties.
III. Experimental Apparatus
Constraints on the development of the lab were the usual ones – space, cost, time, and safety. The
electronics lab classrooms were the only rooms available to host the new materials lab. Since one
of the measurements was the electrical resistance of lengths of wire, the digital multimeters that
were located at each laboratory station could be used. However, the experimental apparatus
required for the thermal and optical characterization of metal samples did not exist. Thus,
additional lab equipment had to be purchased or developed. It was decided that the electronic
laboratory staff would design the apparatus such that it met the following general constraints. The
apparatus had to fit on the lab benches and be portable so that it could be removed when the rooms
would be used for electronics labs. Thus, the apparatus had to have a small footprint and,
preferably, would require only the measurement equipment already at the benches. To limit the
cost of running the new lab, the apparatus and the consumables were designed to last for multiple
years. Lastly, the apparatus had to be available in time for the scheduled lab sessions. After
reviewing the schedule for the design and testing of initial prototypes and a build cycle for the 40
sets of apparatus needed to supply each lab session, it was agreed to concentrate efforts on the
design of the apparatus required for the experimental determination of the thermal properties of
metals. The design of the apparatus for the reflectivity measurements would be delayed and the
experimental determination of the optical properties of metals would be added to the laboratory
procedure in 2015.
To determine the thermal conductivity, the apparatus required had to heat metal samples while
students made measurements of the sample’s temperature. Thus, the design requirements for this
specific piece of equipment were as follows. There had to be a hot surface of relatively uniform
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temperature upon which a block of metal would sit. The hot surface had to be held at a fixed known
temperature during the experiment. Thus, a provision for a measurement of the heat sink
temperature should be incorporated into the design. The opposite surface of the metal block to the
one on the heat sink had to be accessible for temperature measurements.
A 100 Watt power resistor with integrated heat sink (Arcol HS100 Series, 15Ω ± 5 %) was used
as the source of thermal power. The maximum temperature that the surface of the heat sink could
reach was 100 oC when the power resistor dissipates 100 W when the integrated heat sink is
secured to a secondary heat sink. It was decided that the safety precautions, which would be needed
to prevent accidental burns, were too onerous at this temperature. Thus, it was decided that thermal
control would be design to limit the temperature of the heat sink to nominally 50 oC. Students
would be provided tweezers to move the metal blocks between a thermally isolated storage bin
and the hot surface of the heat sink to further limit the potential for accidental burns. As a safety
measure, a thermal switch was added to the design to insure that power to the resistor would be
disconnected should the temperature of the heat sink exceed 70 oC.
The thermostat that was designed to regulate the temperature of the power resistor’s heat sink was
a bang-bang controller; the layout of the printed circuit board (PCB) for the thermostat is shown
in Figure 1. Feedback to the thermostat circuit was provided by a resistance measurement a
thermistor (RS 10 kΩ NTC, type E95) mounted to the top surface of the heat sink near the location
where the metal blocks would be placed. It was experimentally determined that the controller could
regulate the temperature of the heat sink of the power resistor to within +/- 1 oC once steady state
operation was reached. However, there was a lengthy warm-up time as the drive current to the
power resistor was restricted to a maximum of 0.8 A, the maximum current that the 12V AC-to-
DC adaptor used as the power supply for the apparatus could drive through the 15 power resistor.
The circuit had to be turned on for approximately 20 minutes before the apparatus was ready for
use by the students. As students would perform the measurements needed to calculate electrical
resistance prior to the measurements needed for the calculations of thermal conductivity and
specific heat capacity, the warm-up time was acceptable as long as the apparatus was turned on at
the beginning of the lab session.
A power switch was integrated into the circuit along with two LED indicators, a yellow LED to
show that power was supplied to the power resistor and a green LED to show that the temperature
of the heat sink was within the desired temperature range. There was overshoot in temperature of
~ 0.5 oC before a steady-state temperature of nominally 50 oC was maintained. Given the minimal
temperature overshoot, the thermal control provided by the bang-bang controller was sufficient to
provide a well-regulated heated stage for the experiment.
Measurements were made of the temperature uniformity across the surface of the heat sink. The
results were used to select the width of the metal blocks that would be in contact with the heat sink
on its narrower dimension. The maximum width of the metal blocks such that there was a 1 oC
change in the temperature of the surface of the heat sink was 5/8”, which was sufficiently large to
allow easy handling of the blocks with the tweezers. The depth of the blocks was chosen to be the
same dimension. The length of the blocks was determined after an analysis of the transient
response of various metals when heated under these conditions. To insure that students placed the
metal blocks on the center of the heat sink, a square hole in the thermostat circuit PCB was aligned
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over the heat sink of the power resistor. The square hole can be seen in the lower left corner of the
PCB in Figure 1. Mechanical stand-offs were used to prevent contact between the PCB and the
heat sink.
In addition to the thermistor mounted to the power resistor heat sink, three thermistors were wired
to banana jacks on the PCB, which are located on the right side in Figure 1. Each thermistor was
epoxied to the top surface of one of the metal blocks used in the section of the experiment on the
thermal properties of metals. The banana jacks allowed students to easily switch between
thermistors when measuring the resistance of the heat sink and of the metal block under test.
A total of 40 printed circuit boards were constructed at a cost of £55.78 per printed circuit board.
The cost included the components. The assembly and testing of the PCBs was done in-house. The
40 spools of Al, Cu, and Fe wire were ordered from Crazy Wire and Wire.co.uk at a total cost of
£142.90. The bar stock of Al and Cu used to fabricate the metal blocks for the thermal conductivity
and heat capacity measurements were ordered from John Hood (£28). The bar stock were
machined into 5/8”x 5/8” x 3/4" blocks in-house. All costs provided do not include the value-added
tax (VAT). The reliability of the apparatus was good. Only one repair during the semester was
required on a board, found during the second laboratory session. We speculate that the board was
Figure 1: Printed circuit board (6” x 6”) for a temperature-controlled heated stage with a ¾” x ¾” mask for samples (yellow square on lower left), plug for ac-to-dc adapter on upper left, and banana jack plugs for thermistors to monitor temperature of the heat sink and metal blocks.
Page 26.109.5
accidentally not tested after assembly. There were no other failures of the PCBs during the seven
laboratory sessions.
IV. Intended Learning Outcomes
The purpose of the laboratory was to provide students with practical experience on the
measurements and calculations used to determine the electrical and thermal properties of metals.
From this and other intended learning outcomes of the experiment, students should be able to:
Calculate the diameter of a metal using the measurement of electrical resistance when given
the length of the metal sample.
Determine the electrical resistivity of an unknown metal from the relationship between
measured electrical resistance of a metal sample of known length and calculated diameter.
Use the measured temperatures of a metal sample and its dimensions to determine the
power per area transmitted from a heated surface to the metal.
Determine the thermal conductivity of an unknown metal from the relationship between
the calculated power per area delivered to one surface of metal, the maximum temperature
of the opposite surface of the metal, and the dimensions of the sample.
Use look-up tables, which are either provided or must be found by the student, to determine
wire gauge, electrical resistivity, thermal conductivity, and temperature.
Fit a set of data to an exponential function using the built-in macro in Microsoft Excel.
Calculate the specific heat capacity of aluminum (Al), copper (Cu), and an unknown metal
using thermal conductivities, the lengths of the samples, and the exponential exponent
obtained from Excel.
Identify the unknown metal by comparing the calculated electrical resistivity, thermal
conductivity, and specific heat capacity from a subset of metals, provided to the students.
Use the relationship between the ‘sea of electrons’ and the electrical and thermal properties
of metals, which is described in the Wiedemann-Franz law, to calculate the Lorenz number.
Explain the accuracy of the identification of the unknown metal through an evaluation of
uncertainties calculated for the electrical resistivity and thermal conductivity of the metal,
the calculated values for specific heat capacities and the Lorenz numbers for Al and Cu.
Identify potential sources of errors in their experimental measurements.
V. Scaffold of the Experimental Procedure
The lab procedure was written to be a stand-alone document. This was, in part, necessary because
the course textbook, Materials Science and Engineering: An Introduction by Callister and
Rethwisch, is recommended rather than required. In addition, the laboratory sessions were
scheduled to be held throughout the semester because of the number of laboratory sessions that
were required for the 275 students in the course coupled with the availability of the laboratory
classroom and instructors. Thus, some of the students performed the lab before the material
introduced in the course lectures; although most of the students performed the lab after the lectures
were completed.
The document was written in four sections. A general description of the structure of each section
is provided here. First, general background on the origins of the ‘sea of electrons’ is given followed
by a brief mention of orbital hybridization. Two metals, Al and Cu, are used as examples. The
Page 26.109.6
experimental procedure is then divided into three sections: electrical properties of metals, thermal
properties of metals, and the relationship between the electrical and thermal properties. The
experimental procedure will be expanded to include the theory on the optical properties of metal
with emphasis on reflectivity in the near future and the last section will be revised to include the
relationship between electrical and optical properties in the future. Within each of the sections on
electrical and thermal properties of metals, the theoretical concepts that relate the material from
the general background to the specific material property are presented. As the measurements that
the students will perform are influenced by the physical geometry of the samples, the equations
that connect the measured quantities of electrical resistance, temperature, and time with the
fundamental material properties of electrical resistance, thermal conductivity, and molar heat
capacity are given. Then, the steps that the students must perform to make the measurements on
two known and one unknown metal samples and the calculations using the measured quantities
were provided. The specific steps carried by students in each of the last three sections of the
experimental procedure are described more completely below. At appropriate points after certain
calculations, students are asked to identify the metal of the unknown sample by comparing the
calculated electrical and thermal resistivities and specific heat capacity of the unknown metal with
the accepted values of each of these material properties for the metals and other materials that are
provided in tables in the procedure. Students must also determine the uncertainties associated with
each of the calculated material properties. In the final section of the laboratory procedure, the
connection between the electrical and thermal properties, as given by the Wiedemann-Franz Law,
is described. The students are asked to calculate L, the Lorenz number, using the experimental
values for resistivity and thermal conductivity. As a final step, students are asked to comment on
the accuracy of the calculated values of resistivity, thermal conductivity, and specific heat capacity
and how this may have affected the identification of the unknown metal.
Additional material provided in the laboratory procedure were a periodic table to support the
discussion in the second on general background, a table of electrical resistivities and a table of
thermal conductivities and specific heat capacities for a selection of metals and other materials,
Table I and II, respectively. Lastly, a lookup table of thermistor resistances and temperature was
also provided. A worksheet was also devised and distributed to students at the beginning of the
laboratory session for data entry, the results of their calculations, and comments.
a. Experiment Procedure: Resistivity and Resistance
In this section, the relationship between the concentration of electrons in the ‘sea of electrons’, the
mobility of the electronics, and the electrical resistivity of the metal is presented. As the
measurable quantity is electrical resistance, the relationship between electrical resistivity and the
physical geometry of the metal is described.
Students are given three lengths of wire. The metal used to fabricate two of the wire samples are
known – a 60 m length of aluminum wire coated with green enamel and a 90 m length of copper
wire coated with blue enamel. They are also given a 20 m length of iron wire coated with orange
enamel. The students are told the composition of the Al and Cu wires and the relationship between
the average of the diameters of the Al and Cu wires and that of the unknown wire, which was 1.6
times larger. The difference in diameter between the known wires and the unknown wire was due
to the availability of the materials; however, the diameter of each of the wires is not given. The Page 26.109.7
lengths of each of the wires are also provided to the students as measurement of these lengths of
wire would have been too difficult.
The required measurement is simply the electrical resistance of each length of wire. Students are
then asked to calculate the diameters of the Al and Cu wires, given their electrical resistivities
(Table I). They, then, determine the gauge of each wire using tables for American Wire Gauge
(AWG) and Standard Wire Gauge (SWG), which they are expected to find on the internet. The
next calculation is the average of the two wire diameters with the uncertainty associated with this
average. Using the average diameter of the Al and Cu wire, they calculate the diameter of the
unknown wire with its uncertainty as well as its gage. The last calculations are this section is the
electrical resistivity of the unknown and the associated uncertainty using the calculated diameter
with its uncertainty, known length, and measured resistance of the unknown wire. The students
then must make an educated guess to identify the metal by comparing the calculated resistivity
with the accepted resistivities of several metals provided in a table inserted in this section of the
experimental procedure (see Table I).
Table I: Resistivity of Selected Materials at 20 oC8
Modified from http://hyperphysics.phy-astr.gsu.edu/hbase/tables/rstiv.html
Material
Resistivity ρ
(-m) Material
Resistivity ρ
(-m)
Silver 1.59 x10-8 Mercury 98 x10-8
Copper 1.68 x10-8 Nichrome
100 x10-8 Copper, annealed 1.72 x10-8 (Ni,Fe,Cr alloy)
Aluminum 2.65 x10-8 Constantan 49 x10-8
Tungsten 5.6 x10-8 Carbon*
3-60 x10-5 Iron 9.71 x10-8 (graphite)
Platinum 10.6 x10-8 Germanium* 1-500 x10-3
Manganin 48.2 x10-8 Silicon* 0.1-60 ...
Lead 22 x10-8 Glass 1-10000 x109
Hard rubber 1-100 x1013 Quartz
7.5 x1017 (fused)
Stainless Steel 5 X10-5
b. Experiment Procedure: Thermal Conductivity and Specific Heat Capacity
In the next section, the concepts that relate heat, the material properties of thermal conductivity
and molar heat capacity, and the ‘sea of electrons’. The equations that relate the power transmitted
through the surface of a sample, the temperature of the surfaces of a sample that has infinite area
but finite length, and thermal conductivity. In addition, the relationship between thermal
conductivity and specific heat capacity is given along with the equations that relate the rate of rise
in temperature to the specific heat capacity of a material.
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Students first measure the dimensions of the samples – two known blocks of metal, one composed
of Al and the other of Cu, and a third block of metal. Again, the composition of the third block is
not disclosed; students must identify the metal after determining its thermal conductivity and heat
capacity. The unknown metal is the same metal as the unknown metal that the students identified
in the previous section, which is necessary if the students are to calculate the Lorenz number for
the unknown metal.
The students then measure the rate at which blocks of Cu, Al, and the unknown metal reached a
steady-state temperature after being placed on the heated stage. After recording the resistance of a
thermistor epoxied to the surface of the power resistor’s heat sink, the students place one of the
metal blocks on the center of the heat sink. Working in pairs, students record the resistance of a
thermistor, which has been epoxied to the top surface of each metal block, every 30 seconds until
the top surface of the block has reached a steady state temperature. Once one measurement is
completed, the students remove the metal block from the heat sink and repeat the process with the
next block until measurements have been made on all three blocks of metal. The students are
provided with a lookup table to relate the thermistor’s resistance to temperature.
Table II: Thermal Conductivities and Specific Heat Capacities of Selected Materials9,10
From Callister & Rethwisch, Materials Science and Engineering: An Introduction Wiley 9th
Edition, Appendix B and www.engineeringtoolbox.com
Material Thermal Conductivity
(W/m-K)
Specific Heat
(J/kg-K)
Density
(g/cm3)
Silver 428 235 10.5
Copper 338 385 8.79
Cooper, annealed
Aluminum 6061 180 896 2.7
Tungsten 155 138 19.2
Iron 36 544 7.87
Platinum 71 132 21.5
Manganin 22 406 8.4
Hard rubber 0.14 2010 1.2
Mercury 8.69 140 13.6
Nichrome (Ni, Fe, Cr, alloy) 11.3 450 8.4
Constantan 19.5 390 8.89
Carbon (graphite) 130 830 2.09-2.23
Germanium 5.32
Silicon 141 740 2.33
Glass 1.4 840 2.2-5.9
Quartz (fused) 1.4 740 2.65
Stainless Steel 304 16.2 500 7.75-8.05
Using the maximum and minimum temperatures of the block of metal and the thermal
conductivities of Al and Cu (Table II), the calculated power per area transferred to the metal blocks
Page 26.109.9
can be calculated. Students average of the power per area and determine the uncertainty associated
with this value. Students then calculate the thermal conductivity of the unknown metal and the
uncertainty using the maximum and minimum temperatures that were measured as the unknown
metal was on the heat sink. Students compare the calculated thermal conductivity of the unknown
metal with the thermal conductivities for the metals listed in the second table (see Table II) to
identify the composition of the unknown block.
The students are then asked to fit the temperature vs. time data to an exponential expression using
Excel for each of the blocks of metal. They calculate the specific heat capacities from the
exponents for Al, Cu, and the metal that was identified from the previous calculations of thermal
conductivity. The students are asked to compare the calculated specific heat capacities with the
accepted specific heat capacities of Al, Cu, and the metal listed in Table II. They are also asked to
compare the specific heat capacity of the unknown metal to the list to determine if there is another
material listed in the table (Table II).
c. Experimental Procedure: Wiedemann-Franz Law
In the final section of the laboratory procedure, a brief explanation of the Wiedemann-Franz Law
is given along with the equation to calculate the Lorenz number from the electrical resistivity and
thermal conductivity. Students calculate the Lorenz number using the accepted material properties
for Al and Cu. The students are told at this point that the wire and block are composed of the same
metal. They then calculate the Lorenz number and the associated uncertainty for the unknown
metal. Lastly, students explain whether they think that their identification of the unknown metal is
accurate and reasons why the identification may be incorrect.
VI. Results
a. Student Preparation
During a conversation with the course instructor for Electronic Engineering 1X, a course taught to
Year 1 students in the same semester as Materials I, we learned that students were no longer
engaged in hands-on laboratories, but were running simulations using PSpice instead. Thus, a set
of instructions on how to make resistance measurements was written shortly before the first
laboratory session.
The laboratory procedure was not available to the students in the first laboratory session until they
arrived in the lab classroom. It was posted on the course Moodle site earlier that day. Nonetheless,
most students in that lab session as well as the subsequent lab sessions completed the experiment
within two hours, the amount of time time-tabled for this experiment. All of the students were able
to make the measurements described in the experimental procedure with minimal guidance from
the laboratory demonstrators (2 to 3 graduate students per lab session). Although no data was
collected to support the following opinion, it was felt that the length of the write-up (14 pages in
total, not including the worksheet or the instructions on the measurement of electrical resistance)
discouraged students from reading the laboratory procedure prior to their lab class. As it is unlikely
that the course textbook will be required in future semesters, the volume of background material
for this laboratory experiment will continue to be needed. It is possible that some of the material
will be incorporated into the course lecture notes, which would mean that the laboratory procedure
could be condensed.
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b. Grading
As is general practice in all of the engineering laboratories, each student was required to bring an
experimental laboratory notebook to this laboratory class to log data and to write observations.
Given the number of students in the course (275), a method to reduce the amount of time to grade
the student work was needed that also eliminated the constraint of collecting and returning student
laboratory notebooks in time for the second Materials I experiment on the mechanical properties
of metals. Rather that grading each lab notebook or requiring that each student write a lab report,
each student was expected to submit a worksheet for this experiment, even though they worked in
pairs when collecting the experimental data. The worksheet was designed with specific locations
for students to enter data, the results of their calculations, the educated guess of the unknown metal,
and their comments about the accuracy of the identification of the metal and the causes of the
uncertainty associated with several calculations, written in MS Word. This eliminated the need to
search through the students’ lab notebooks or through lab reports to locate the work upon which
they would be graded.
After grading the worksheets submitted by the students in the first laboratory session, it was found
that there were large variations in measurements, errors in calculations, wrong numbers found
from lookup tables, and incorrect identification of the unknown metal. All of which contributed to
make grading very difficult, even with worksheet. An Excel spreadsheet was created to reduce the
time required to grade each worksheet. Twenty four measurements were entered from the student
worksheet – resistances of the three samples of wire, the minimum and maximum resistance of the
thermistors attached to each metal block, the exponent from the exponential fit of data in Excel,
and the dimensions of the blocks of metals. (Note that each block was nominally the same
dimension as the other two so these numbers were not changed unless there was a measurement
error by the student. The results of the calculations were displayed so that the grader could verify
that the student calculations were correct. Using the results that the students should have
calculated, the identity of the metal was found using a lookup table embedded in the Excel
spreadsheet. While still time-consuming, this did simplify grading as the propagation of errors
from an initially incorrect measurement leading to the wrong identification of metals was tracked
automatically.
We are considering incorporating the worksheet as a quiz in Moodle, a virtual learning
environment11, and to have the calculated results and identification of metals graded automatically
without any assistance of a grader. As there are computers at each lab station, students would be
able to electronically enter the measurements. We have to determine if each student will have to
electronically enter the data or if there is a way to share the entered data on Moodle between the
pairs of students. Furthermore, it is not clear if there is an easy way to incorporate a lookup table
into the quiz format that will allow automatic grading of the identification of the unknown metal.
Nevertheless, we expect to be able to use quizzes in Moodle to reduce, if not entirely eliminate,
the need for graders to review the student work.
c. Analysis of Student Work
i. Electrical Resistivity
Out of 275 students enrolled on the course, 265 completed the experiment and submitted
worksheets. When comparing the accuracy of the student calculations on all sections of the
experiment, the calculations performed to find the diameters of the Al and Cu wires and the
Page 26.109.11
electrical resistivity of the unknown metal wire, were the most accurate. The results of our
evaluation of student performance in this section of the experiment are shown in Figure 2. A
description is provided below along with comments on student errors and a systematic error in
measurement.
A common error in the calculation of the diameters of the Al and Cu wires appears to have been
the use of an incorrect equation for area of a circle [ 𝜋𝑟2 = 𝜋𝑑2/2 instead of 𝜋(𝑑 2⁄ )2], which led
to an incorrect calculation diameters, resistivity of the unknown metal, and finally to an incorrect
identification of the metal. However, an exact determination of the reasons for all of the errors in
the calculation of the electrical resistivity of the unknown metal wire using their measurements of
resistance could not be deduced as students were not required to show their calculations on the
worksheet. There were four instances (1.5 %) where students identified stainless steel, which
appears to the result of incorrect reading of the range on the digital multimeters.
While only 58 students (21.9 %) correctly identified the unknown metal as iron, there was a
systematic error in the measurement of resistance that caused 158 students (57.5 %) to identify the
metal as platinum and 2 students (0.7%) who identified the metal as silver instead. The error was
likely caused by the difficulty in making good contact between the metal wires with the probes of
the multimeter as the wire gauge for the Al and Cu wires was 24 (AWG)/25 (SWG) and the fact
that the bare ends of the Al wires oxidized rapidly. Thus, the resistance of the Al wire in particular
was larger than it theoretically should have been, which caused the calculated resistivity of the
unknown block to be smaller than it was in actuality. Soldered connectors to the ends of the metal
wires will be added before the next offering of the laboratory to eliminate both of these sources of
error.
Figure 2: Assessment of student work for the calculation of resistivity of the unknown metal,
identification of the unknown metal from its electrical resistivity (), calculation of thermal
conductivity (), and calculations of the specific heat capacity (Cp) of the three metal blocks.
Page 26.109.12
While these results indicate that there was a high level of success on this section of the experiment,
there was some evidence that some students either misread the information on Table I or concluded
that their calculations were incorrect and selected either iron or platinum, likely after hearing that
other students had identified one of the two materials for the unknown metal. When taking this
into account, 167 students (60.7 %) calculated the resistivity of the unknown material correctly
using their experimental data and the electrical resistivities of Al and Cu and 159 of the 167
students (95.2 % or 57.8 % overall) used their calculated results to identify the appropriate metal.
Lastly, a total of 6 students (2.2 %) did not perform the required calculations, although they had
written resistance measurements on the worksheet and 7 students (2.5 %) did not attempt to
identify the metal.
We note that, in the assessment of student work, credit was given to students who calculated the
electrical resistivity of the unknown metal correct using their resistance measurements and
additional credit was given if the students then selected the most appropriate metal from the list in
Table I, even if the metal selected was not iron. Credit was not given to those students who
identified the metal as iron, but whose calculations of resistivity did not support that conclusion.
ii. Thermal Conductivity and Heat Capacity
We knew prior to running the experiment that there would be considerable errors in the
measurements. First, the blocks were of finite cross-sectional area. Secondly, there were
convective losses. Furthermore, there was a gradient in temperature across the heat sink and, thus,
the power transferred to the block was dependent on the exact placement of the block on the heat
sink. We had attempted to minimize gradient in temperature by masking of all but the center region
of the heat sink so that each block was placed in the same location on the heat sink (see square
opening in lower left in Figure 1). In the future, the blocks will be placed in an insulating sleeve
to prevent heat loss from the sides of the blocks. Cooling of the power resistor heat sink when the
metal blocks were placed on its surface was a concern, but was determined to be a small effect
experimentally. No noticeable change in the heat sink temperature was observed when each of the
metal blocks was placed on its surface.
Unfortunately, it became clear that there was a significant flaw with the design of this portion of
the experiment, which we had not recognized when characterizing the experimental apparatus used
in this section of the experiment. After analyzing the data collected by the students, it appears that
the measurement of thermal conductivity and heat capacity were dominated by the temperature
rise of the thermistor epoxied to the metal blocks rather than by the metal blocks themselves. The
epoxy chosen for the experiment should have been an adhesive with a high thermally conductivity
instead of a general-use epoxy. Moreover, the shape of the thermistor was not optimal and one
with a flat bottom surface and small volume would have help limit the amount of epoxy used to
fix the thermistor in place.
Given these issues, the emphasis in assessing student work was placed on the correctness of the
temperature as determined by the resistances of the thermistors, the calculation of the power per
area transferred to the Al and Cu blocks, and the thermal conductivity of the unknown metal block
using the flawed measurements of thermistor resistances. Of the 271 responses recorded, 142
students (52.4 %) correctly calculated the thermal conductivity of the unknown metal using the
thermistor resistance data. The thermal conductivity determined by 125 students (46.1 %) was
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calculated incorrectly from the data collected and no calculations were performed by 4 students
(1.5 %), as shown in Figure 2.
No effort was made to determine if the students obtained the correct exponential fit of their data.
The worksheets were then graded on the correctness of the calculated specific heats for each of the
metals using the student-reported exponents. It was clear that the calculation of specific heat was
the greatest cause of confusion amongst the students. Only 23 students (8.4 %) calculated a correct
value for the specific heat of two or all of the metals using the exponents obtained from Excel. 198
students (72.3 %) made errors in the calculation of two or all three of the values for specific heat
capacity. A significant number of students (53 or 19.3 %) failed to enter values for the exponent
and, thus, did not perform the calculations. We speculate that there are three reasons for the
demonstrated results (or lack thereof). First, the students may not have understood the directions
provided in the procedure on how to use the fitting routine in Excel. A separate write-up that
includes screenshots collected while performing a similar calculation will be available when the
experiment is next assigned. Secondly, the time required to complete the relatively complex
calculations was greater than the amount of time that the students were willing to put into a
calculation when the total contribution of the grade on the worksheet to the final course grade is
5%. Lastly, the students may have suspected that the calculations would result in bogus answers,
after their calculated thermal conductivity of the unknown metal was an order of magnitude or
more from the thermal conductivity of the metal that they had identified using their values for
electrical resistivity.
There were three common errors made by students when calculating the thermal conductivity of
the unknown metal block and the specific heat capacity of each of the three metals. The first error
was the incorrect interpolation using the table of temperatures and thermistor resistances. The
lookup table listed the thermistor temperature at increments of 1 oC. As the maximum temperature
of the block was limited to 50 oC (or about 33 oC above room temperature) to minimize the
possibility of a burn should a student touch the heat sink or a hot metal block, an error of 1 oC
either the maximum or minimum temperature of the block produces significant error in the
calculated thermal conductivity. The second error was a mistake in the measurement of the
dimensions of the block. The blocks were 5/8”x5/8” in cross-section and 3/4” in length. The ruler
provided to the students was marked using the metric system. Again, a mistake in the measurement
of any of the dimensions of a block translated to an incorrect value for the thermal conductivity.
Note that an error in the measurement of the dimensions did not affect the credit received for the
student work. Lastly, there were a number of students who appeared to have made one or more
errors in converting units of length between mm, cm, and m and units of mass between g and kg.
Since we accepted the student-reported exponents without investigating their correctness, we do
not have data on how accurately the fits were performed. We are currently evaluating how best to
determine if the students have performed the exponential fit properly from their data sets of
temperature and time without increasing the time and effort required to grade the work
significantly.
iii. Uncertainty
A surprise when grading the worksheets was the discovery that students could not calculate the
uncertainty associated with the values for electrical resistivity and thermal conductivity. 94
students (34.2 %) calculated the uncertainty associated with the thermal conductivity of the
Page 26.109.14
unknown metal block correctly. Another 198 students (57.8 %) calculated the uncertainty
incorrectly and a further 22 students (8.0 %) made no calculation as shown in Fig. 2. This has been
an area in which supplemental learning materials will be developed so that students can learn how
to perform these calculations.
Students were asked to comment on their results, the uncertainties associated with their
calculations, and to speculate on the causes of errors. 126 students (45.8 %) of the students
provided an acceptable answer. A number of these students wrote several paragraphs, even using
space on the back of the worksheet, to explain their ideas on the reasons why the metal was not
the same in each of the three times that they were required to identify the composition of the
unknown metal. Of the remaining students, only 67 (24.4 %) wrote an answer, though most were
one sentence in length and, in general, stated that the results of the calculations were inaccurate or
identification of the unknown metal was wrong. The remaining 82 students (29.8%) did not
provide any response to the question. It is likely that the reasons why students did not calculate the
specific heat capacity could be applied here. It is also possible that the Year 1 students have little
experience evaluating the accuracy of their results and to speculate on possible causes. We will
revisit this in the future, after we have revised the experiment to improve the quality of the data
used to calculate the thermal conductivity and specific heat capacities.
VII. Conclusions
A hands-on experiment on the electrical and thermal properties of metals was developed for an
introductory materials science course at the University of Glasgow. The laboratory procedure was
designed to guide the students to meet the intended learning objectives. The instrumentation used
in the experiment included digital multimeters, which are commonly available in most electronics
laboratory classrooms and an inexpensive temperature-controlled heater stage (the heat sink of a
power resistor), which was designed in-house that allowed students to monitor the temperature of
metal blocks as well as the temperature of the heat sink. Using a combination of experimental data
collected during the laboratory session and the accepted values of resistivity and thermal
conductivity for aluminum and copper, students were able to calculate the electrical resistivity and
thermal conductivity of an unknown metal. Students were asked identify the unknown metal by
comparing these calculated values with accepted values for selection of metals. Due to known
experimental errors in the electrical resistance measurements, most students selected platinum
rather than iron. Other errors included incorrect calculation of the diameter of a wire and
misreading of the multimeter display. A flaw in method used to attach a thermistor to the metal
blocks led to inaccurate predictions of the thermal conductivity of the unknown block. Students
had significant difficulties with the calculations of the specific heat capacity and the uncertainty
of each of the calculated answers. Supplemental learning material on the use of the fitting routine
in Excel and an explanation on how to calculate uncertainty when adding, multiplying, and
dividing numbers will be provided to the next cohort of students to participate in the laboratory
experience.
Acknowledgements: The authors wish to acknowledge the financial support from the School of
Engineering at the University of Glasgow The authors acknowledge the dedication and assistance
Page 26.109.15
of laboratory demonstrators: Mr. R.A. Kirkwood, Mr. K. Erotokriutou, Mr. G. Orchin, Mr. S.
Tabor, and Mr. P. Ohiero.
References
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Annual Conference, Session 1664. 2 D. Roylance, Innovations in Teaching Mechanics of Materials in Materials Science and Engineering Departments,
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