Inter American University of Puerto Rico
Bayamon Campus
Mechanical Engineering Department
Mechanical Measurement and Instrumentation
MECN 4600
Semester and Year:
Jan-May 2013
Name of Team Leader:
Name of Lab Instructor:
Omar E. Meza Castillo
Lab Section and Meeting Time:
Experiment Number:
Tuesday-Thursday 10:30-12:50 pm
1
Title of Experiment:
Regression Analysis
Date of Experiment Performed:
Instructor Comments:
01/31/2013
Date of Report Submitted:
2/7/2013
Names of Group Members:
Grade:
Table of Contents
Abstract .............................................................................................................................. 3
Objectives and Introduction ........................................................................................... 4
Equipment Description and Specification .................................................................... 5
Results and discussion .................................................................................................... 11
Conclusions ...................................................................................................................... 13
References ....................................................................................................................... 14
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Abstract
Since we have only these fixed temperatures to use as a reference, we must use
instruments to interpolate between them. But accurately interpolating between
these temperatures can require some fairly exotic transducers, many of which
are too complicated or expensive to use in a practical situation. We shall limit
our discussion to themost common temperature transducers: thermistor. In this
laboratory these procedures will come to practice with a thermistor to check
the accuracy of the results comparing them with a lead resistance. In this
laboratory 10 V were carried to a Wheatstone bridge and the Eout was read.
The thermistor along with the Wheatstone bridge was found to be very accurate
in the experiment. Tabulated tables explaining the values of the data are
included in the conclusion explain the accuracy of the thermistor. The value of β
obtained was 4138 K.
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Objectives

To familiarize the student with measurement of temperature using a
thermistor.

To mount the setup of the laboratory using a Voltage divider circuit.
Introduction
A thermistor is a type of resistor whose resistance varies significantly with
temperature, more so than in standard resistors. The word is a portmanteau of
thermal and resistor. Thermistors are widely used as inrush current limiters,
temperature sensors, self-resetting overcurrent protectors, and self-regulating
heating elements.2 in other words athermistor is a resistor, or type of sensor used
to regulate and measure temperature, such as heat and cold. A thermistor is
made up of ceramic with a high precision at a specific temperature level. The
thermistor
contains
electrical
networks,
circuits
and
wires.
The
main
characteristics of a thermistor are: power, noise, tolerance, temperature and
resistance. You can use a thermistor for many different things such as Meter
Compensation, Inrush-Current Device, Automotive Applications, Differential
Thermometers and Master-Slave Control as well as others. For this lab report
we’re going to be using the thermistor for the measurement of temperature with
the relation of resistance.
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Theory
The idea of a thermistor, or thermally sensitive resistor, has been around for over
150 years. Although one of his lesser-known discoveries, the first documented
use of an NTC, (Negative Temperature Coefficient, something to be returned to
in the theoretical basis section), thermistor came from Michael Faraday in 1833.
After the initial discovery, it was quickly realized that thermistors could be
separated entirely into two different categories: NTC and PTC thermistors.
Interestingly, the classification didn’t solely depend on metallurgical properties
due to the fact that at certain temperatures some types can actually switch
categories. Silicon is one such example that exhibits NTC properties until 250K,
where a positive temperature coefficient sets in. All thermistors are made using
semi-conducting metallic compound oxides such as manganese, copper,
cobalt, and nickel, as well as single-crystal semiconductors silicon and
germanium [1].
Many different types of thermistors exist for different uses. The coated lens type is
one example. While Faraday was first to discover the thermistor properties of
semiconductors, Samuel Ruben was quickest to perfect it and seal it under a
U.S. patent. Almost a century after Faraday’s breakthrough, Ruben released his
“Electrical Pyrometer Resistance” findings in which housed a special technique
to “cook” a copper base in an oxidizing atmosphere to create a cuprous oxide.
After being cleansed in hydrochloric and nitric acid, a thin film of this oxide
remained that gave his thermistor a negative temperature coefficient without
the drawbacks of standard semiconducting materials. He explains in his patent
that as he experimented with adding heat to the device, its resistance dropped
noticeably and reproducibly.
As a final notable mention, Rueben explains similar phenomena occurred when
mixing the cuprous oxide with cuprous sulphide, or melting antimony sulphide
with cuprous sulphide. The practicality of this intricate thermistor was
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widespread, as it drove applications in voltage protection, temperature control,
and calorimetric to name a few. The notion of resistance increasing with
temperature in regular conducting materials, however, is not a new one by any
means. A. E. Kennelly and Reginald A. Fessenden write in 1893 in the Physical
Review about the linear relationship between increased temperature and
resistance in a sample of copper. In their testing between the ranges of -69⁰C
and123⁰C, the same range we have worked in, they explain how copper’s
temperature coefficient is a positive 4.18% per degree Celsius.
It was only a few decades’ later whenphysicists made perhaps the most
astonishing discovery relating to electricalconductivity. On April 8, 1911,
Kamerlingh Onnes and his cohorts experimented with vapor pressures of liquid
helium to drop the temperatureof mercury to a level where resistance
“practically”
disappeared.
Today,
we
denote
this
phenomenon
as
superconductivity and it involves similarquantum effects explored in the theory
section of this report on thermistors. Historical experimenting has proven to us
that the relationshipbetween resistance and temperature can take wildly
different
turns
given
thecircumstances
and
materials
used.
Some Formulas Used For the experiment:

The calibration equation for an Thermistor is given by an expression of the
following form:
R
 exp 
R0
1 1 
  
 T T0  …………………….. (1)
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
Setting the experiment:
Figure 1: Thermocuple Setting
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Experimental Methods
We began this experiment by acquiring ice and mixing it with tap water. The
instruments
necessary
for
the
procedures
were
conveniently
laid
out
beforehand, and thus we were able to begin immediately. Before connecting
the canister to the wall outlet, we brought the metal inside down to roughly 0⁰C
by flushing it with ice-cold water from the large beaker. Another pre-experiment
task was to determine the lead resistance on the wires we had for use. This was
determined by inserting them into the multi-meter, ensuring the multi-meter was
on and reading resistance on a Ω scale, and rubbing the leads together to
remove a bit of corrosion.
Once satisfied, we left the water inside the canister, plugged in the resistance
heater, and opted to begin with the copper coil apparatus. We placed it snugly
onto the canister, inserted the thermometer and observed the multi-meter to
ensure a proper connection had been made. The temperature was brought up
to 10⁰Cfor the first data point, and the data collection was underway. Thus, we
were able to observe the linear relationship between Resistance and
Temperature on the fly during the copper experiment to ensure all equipment
and procedures were optimal. We attempted, and mostly succeeded, in taking
data points for every 10⁰C increase in temperature. Therefore, a total of nine
data points were taken ending with a 90⁰C data point. Once this portion of the
lab had concluded, we removed all the components, turned off/unplugged
electronics, and cleaned beakers in order to prepare for the next usage [2].
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Equipment description & Specification
Figure 2: Thermistor
Thermistor is athermally sensitive resistor hence the name (Figure 2). Thermistor is
a solid semiconducting material. Unlike metals, thermistors respond inversely to
temperature. i.e., their resistance decreases as the temperature increases. The
thermistors are usually composed of oxides of manganese, nickel, cobalt,
copper and several other nonmetals.
Figure 3: hot beaker and water.
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• Hot plates (Figure 3) are laboratory tools used to uniformly heat samples. Hot
plates provide less heat, but do so without the danger associated with the open
flame and higher temperatures of a Bunsen burner. Hot plates are available with
a number of different heating top styles. The most common types include those
constructed from aluminum, ceramic materials or enamel. Aluminum topped
hot plates provide a rapid heating surface, which retains and distributes heat
very well.
Figure 4: Mercury Thermometer
• A mercury-in-glass thermometer, also known as a mercury thermometer, was
invented by German physicist Daniel Gabriel Fahrenheit in 1714 and is a
thermometer consisting of mercury in a glass tube. Calibrated marks on the tube
allow the temperature to be read by the length of the mercury within the tube,
which varies (nearly linearly) according to the temperature of the mercury. To
increase the sensitivity, there is usually a bulb of mercury at the end of the
thermometer which contains most of the mercury; expansion and contraction of
this volume of mercury is then amplified in the much narrower bore of the tube.
The space above the mercury may be filled with nitrogen or it may be less than
atmospheric pressure, which is normally known as a vacuum.
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Figure 5: Multi-Meter
• HP-Digital Multi-Meter (HP-DMM)
Digital multi-meters or multi-meter, (Figure 5) are instruments that are used to
measure electrical quantities such as voltage, current, resistance, frequency,
temperature, capacitance, and time period measurements. Basic functionality
includes measurement of potential in volts, resistance in ohms, and current in
amps. Multi-meters are used to find electronic and electrical problems.
Advanced units come with more features such as capacitor, diode and IC
testing modes.4
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Figure 6: Voltage Divider Circuit
• Voltage Divider
In electronics, a voltage divider also known as a potential divider (Figure 6) is a
linear circuit that produces an output voltage (Vout) that is a fraction of its input
voltage (Vin). Voltage division refers to the partitioning of a voltage among the
components of the divider.
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Results and Discussion
Data was taking using different temperatures. The data was analyzed and
applying the formula given in class the following results were obtained
Table 1: Data Of the thermistor
T (˚C)
V (V)
RTH
(kΩ)
RTH / R0
23
-2.062
6.4419
1
26
-1.78
5.6430
0.876
T0 (˚C)
23
28
30
32
34
36
38
40
42
44
46
-1.4
-1.26
-1.04
-0.838
-0.587
-0.423
-0.219
-0.0235
0.133
0.369
4.7644
4.4858
4.0877
3.7592
3.3930
3.1754
2.9255
2.7053
2.5411
2.3116
0.7396
0.6963
0.6345
0.5836
0.5267
0.4929
0.4541
0.42
0.3945
0.3588
Ein (V)
10
Ein (V)
10
Rw (kΩ)
2.68
R (kΩ)
3.25
Rw (kΩ)
2.68
R0 (kΩ) 6.4419
Eout (V) R (kΩ)
-0.496
3.27
Table 2: Data Analyzed
T (˚C)
23
26
28
30
32
34
36
38
40
42
44
46
T(K)
296.15
299.15
301.15
303.15
305.15
307.15
309.15
311.15
313.15
315.15
317.15
319.15
(1/T-1/To)
0
-3.4E-05
-5.6E-05
-7.8E-05
-1E-04
-0.00012
-0.00014
-0.00016
-0.00018
-0.0002
-0.00022
-0.00024
RTH / R0
1
0.875987
0.739608
0.696349
0.63455
0.583561
0.526707
0.492927
0.454143
0.419959
0.39447
0.358844
ln()
0
-0.1324
-0.3016
-0.3619
-0.4548
-0.5386
-0.6411
-0.7074
-0.7893
-0.8676
-0.9302
-1.0249
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The graph of the data analyzed is presented:
Thermistor Analysis
-0.0003
-0.00025
-0.0002
-0.00015
-0.0001
y = 4138.4x - 0.029
R² = 0.9951
0
-0.00005
0
-0.2
Rth/Ro
-0.4
-0.6
-0.8
-1
Rth/R0
-1.2
Graph 7: Rth/Ro results
It represents the slope of the data taken by the thermistor. The results came
quite correct due to the precision of the procedures used. Each data points
represent a linearity equation of a 0.0029 slope representation. The value of β
obtained was 4138 K, this value is close to the manufacturer value.
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Conclusion
After finishing the experiment, we understood the relationship of Resistance and
temperature of athermistor. After performing the experiment all the objective
were successfully accomplished. A least square analysis was performed of the
obtain data to establish a linear equation that will describe the behavior of the
thermocouple. The established equations were compared to those calculated
by Excel and were close enough. A least square with a 0.989 and a linearity error
of 0.02% suggest that the thermistoris very accurate compared with the
resistances. The value of β obtained was 4138 K, this value is close to the
manufacturer value.
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References
[1]
O. Meza “Lecture08: Measurement of Temperature – Thermistor”
http://facultad.bayamon.inter.edu/omeza/
[2]
Stig
Ekelof
“Wheatstone
bridge”
http://en.wikipedia.org/wiki/Wheatstone_bridge”
[3]
McGee, Thomas
(1988). "Chapter 9". Principles and Methods of
Temperature Measurement.John Wiley & Sons.p. 203.
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