Experiment No. 1:
Temperature is probably the most important and most measured property in science and
engineering. Many different temperature measuring devices have been devised and are in
common use today. Each device has its own strengths and weaknesses, and is generally
designed for a fairly specific application. As engineers, it is important for you to select
the best possible instrument for the job.
In this experiment, we will examine four types of thermometers: a liquid in glass
thermometer (LIGT), a pyrometer, two thermocouples, and a platinum resistance
thermometer (PRT). You should walk away with not only an appreciation for the wide
range of temperature measuring instruments available, but also a sense of the limitations
of each. Furthermore, you should become aware of the statistical nature of measurement
and the myriad variables that can affect accuracy and precision.
Liquid in Glass Thermometers. Everyone is familiar with liquid in glass thermometers
(LIGTs). In fact, the first known thermometers were of the LIGT type. Although they
are decidedly “low tech” devices, LIGTs of extremely high accuracy and precision can be
constructed today. The concept behind LIGTs is very straightforward: a liquid in a
narrow sealed glass tube expands and contracts with temperature, and temperature is read
by a scale alongside the tube. For a number of important reasons, the liquid is typically
mercury, although alcohol and other organic liquids can also be used. Several criteria for
the liquid must be met to make a good thermometer:
Liquid must remain a liquid over a wide temperature range
Liquid should have a low vapor pressure
Liquid should have a linear expansion vs. temperature response
Liquid should not wet the glass
Liquid should have a large expansion coefficient for sensitivity
Mercury is superior to organic liquids in all the above criteria except the last.
However, mercury freezes at -38.9°C; to measure temperatures below this, organic
liquids must be used.
Although they are seemingly simple devices, many subtle details must be
incorporated into the design of LIGTs to insure accuracy, fast response, sensitivity, and
durability. For example, uniformity of the bore diameter is critical for accuracy. Of
course, as temperature increases, the glass expands, and the bore size slightly increases.
This effect must be taken into account in high accuracy thermometers.
The thermometer we will be using in this experiment has been calibrated against a
standard at the National Institute of Standards and Technology (NIST). A calibration
certificate was shipped with the thermometer. This certificated certifies the
thermometer’s accuracy as ±0.04°C within the temperature range of 0 to 100°C.
Please Note: This thermometer is an extremely accurate instrument and it is very
expensive (over $400!). In addition to the cost factor, there is also a safety concern about
mercury exposure if the thermometer breaks. Due to both the safety and cost concerns,
please exercise great care when handling the thermometer. Return it to its protective
case when it is not in use. Remember this is a thermometer, not a stir rod!!
Resistance Thermometers. Most metals exhibit an increase in their electrical resistance
as their temperature is increased. Although a variety metals can be used, platinum has
become the metal of choice for precision resistance thermometers. It offers a large
measuring range, is very stable, and can be made very pure. Platinum resistance
thermometers (PRTs) are typically made of a thin coiled platinum wire placed in a
protective sealed metal or glass sheath. The sheath serves to guard the element against
contamination, oxidation, and mechanical strain.
Our PRT is based on the ITS-90 standard, which states the thermometer should be
useful in the range of 13.8K to 962°C. In addition, the thermometer’s resistance has been
made so that it is 100 at 0°C.
One source of inaccuracy in PRTs is the lead wire resistance. The lead wires will
have a small amount of resistance, which also changes with temperature. Some PRTs are
specially designed so that the lead wire resistance can be measured and factored out of
the resistance measurement. Our PRT has no such capability.
Thermocouples. In 1821, Thomas Seebeck discovered that when two different metals
are joined at two different junctions, an electrical current will flow if the temperatures of
the two junctions are different (Fig. 1). Using this principle, if the temperature of one
junction is held constant and the circuit is broken at the other junction, a temperature
measuring element is created. By measuring the so called “Seebeck Voltage” across the
open circuit, the temperature can be determined by the equation:
VAB = AB ∙ T (Eq. 1)
where AB is the Seebeck coefficient for metals A and B (V/°C), and T is the absolute
T1 I T2
If the two leads of the thermocouple are attached directly to a voltmeter (Fig. 2a), the
wire connections to the instrument will create additional thermocouples at room
temperature and the voltage readings will be meaningless (Fig. 2b).
Metal A Metal A
V I Tmeas Vmeas = V1 + V2 V1
+ - V2 +
Metal B Metal A Metal B
Fig. 2a Fig. 2b
To avoid this problem, a reference point junction called an “ice point” is used (Fig. 3).
By cooling the unwanted junctions to 0°C in an ice-water bath, a fixed voltage difference
between the unknown temperature and the 0°C junction is created which allows the
unknown temperature to be measured accurately. With this setup, V2 is set to 0, so Eq. 1
can be used to measure temperature:
Vmeas = V1 + V2 = AB(Tmeas - 0) = AB Tmeas
Metal A Metal A
Tmeas Vmeas = V1 + V2 V1
+ - V2 + - V2 +
Metal A Metal B
Metal A Metal B
Thermocouples are designated by letter to indicate the types of metals used in them.
In this experiment, we will be using J, K, and T type thermocouples. Each type has a
standard connector color. Table 1 lists the composition of each thermocouple and their
connector colors. The three thermocouples generate approximately 42-55V/°C in the
temperature range being used in our experiment. Typically, thermocouple charts of
voltage vs. temperature can be found in the CRC handbook of Physics and Chemistry.
Type + wire - wire Connector
J Iron Constantan Black
K Chromel Alumel Yellow
T Copper Constantan Blue
Table 1. Thermocouple materials
Constantan, Alumel, and Chromel are trade names for specific alloys:
Constantan: 55% Cu, 45% Ni (all percentages are by weight)
Alumel: 95% Ni, 2% Mn, 2% Al, 1% Si
Chromel: 84.5% Ni, 14.2% Cr, 1.4% Si
These alloys and metals have been chosen because they have large Seebeck coefficients.
The larger the Seebeck coefficient, the more sensitive the thermometer is.
Pyrometers. Pyrometers read temperatures by measuring the intensity of infrared
radiation emitted from an object. Because they provide a non-contact method of
measurement, they can be used to measure extremely high temperatures. In addition,
because they do not need to equilibrate to the temperature they are measuring, they can
have very rapid response times. Pyrometers are useful in situations where actually
contacting the object to be measured is impractical or impossible.
The theory behind pyrometers is based on Planck’s law for a blackbody radiator. A
blackbody radiator is an object which absorbs all incident radiation and emits radiation in
a spectral distribution that depends on its temperature. All objects above 0°K emit some
amount of thermal radiation. The radiation is not emitted at a single wavelength, but over
a range of wavelengths that can be described by Planck’s famous equation:
W ( , T ) (Eq. 2)
5 (e hc / kT 1)
where: W = radiant power intensity over a hemisphere (energy/volume)
h = Planck’s constant = 6.626×10-34 J∙s
c = speed of light in a vacuum = 2.998×108 m/s
= wavelength of radiation emitted
k = Boltzmann’s constant = 1.38×10-23 J/K
T = absolute temperature of radiator
Figure 2 shows a plot of the output of several blackbody radiators at different
Fig 2: Planck's Law for a Blackbody Radiator
Radiant Intensity (W/cm 2 m)
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5
Wavelength ( m )
Planck’s law is only valid for blackbody radiators, which do not exist in nature (all
objects will reflect or transmit a certain amount of incident radiation). To correct for this,
a material property called emissivity is used. Emissivity is defined as:
=1–r–t (Eq. 3)
where r and t are reflectance and transmittance. Thus, for a blackbody, will be 1; all
other objects will have an emissivity < 1. If an opaque object is being measured, then t
can be neglected. Multiplying Planck’s Law by emissivity of a non-blackbody radiator
will approximate the output of the object.
Integrating Planck’s Law over the entire spectrum gives the Stefan-Boltzmann Law:
W = ∙T4 (Eq. 4)
where is the Stefan-Boltzmann constant, 5.6687×10-8 J/K4∙m2∙s. This law gives the
power output of the radiator across the whole spectrum. Multiplying the right hand side
of Eq. 4 by emissivity will give the total power output for a non-blackbody radiator.
Our pyrometer works basically by measuring the spectral emission of an object
between 8 and 14m and comparing it to the Stefan-Boltzmann and Planck laws. The
emissivity of the object being measured must be known and entered into the pyrometer.
Thus, the accuracy of the temperature measurement is highly dependent on how well you
know the emissivity. Oxidation, dirt, and other surface deposits will all affect the
emissivity of an object. In addition, emissivity will change with viewing angle,
wavelength, and temperature.
Time Constant. If a measuring element is subjected to a step change in temperature
from its surroundings, the response of the element is not instantaneous. If this
temperature change is not too large, it reacts as a first order system, according to
Newton’s law of cooling:
(T (t ) T f )
where T is the temperature of the element (function of time) and Tf is temperature of the
cooling bath (a constant).
The above relation can be made into an equation by using a proportionality constant:
dT 1 (Eq. 5)
(T (t ) T f )
where is the time constant.
This equation is a first order linear ODE, which has the initial condition of:
Tt=0 = Ti
The solution to the differential equation is:
T(t) = Tf + (Ti – Tf)∙exp(-t/) (Eq. 6)
The physical meaning of this solution is that when one time constant has passed, the
change in the temperature from the initial temperature is (1 – 1/e) times the total change
that will occur. The time constant represents a measure of the response time of an
instrument to a sudden (step) change in the temperature of its surroundings.
Please bring a 3.5” floppy disk or a Zip disk to store data on.
1) The precision of two thermocouples will be investigated. You will be measuring
the temperature of Hotplate 2 via the surface mount thermocouples. First, flip the
toggle switch to Hotplate 2. Now, double-click on the “Hotplate” icon on the
Windows desktop. This Labview program allows you to control and monitor the
hotplate’s temperature. Set the hotplate’s temperature to 80°C and turn it on.
When it has stabilized, record temperatures from the K-type and T-type
thermocouples at least 30 times at regular intervals. Labview will store the
results in an Excel file for you to copy from.
2) Calibrate the platinum resistance thermometer (PRT) and the K and T-type
thermocouples with the NIST standard thermometer. Prepare four baths at 0, 20,
40, and 75°C. The 0°C bath can be made by filling a Dewar flash with crushed
ice and distilled water. Make the 20°C bath by letting DI water equilibrate at
room temperature (it is understood that the temperature will not be exactly 20°C).
The 40°C and 75°C baths are available in the laboratory and are electronically
heated by thermostatic control.
Measure the resistance of the PRT via the multimeter at each of the four
temperatures to calibrate it. At the same time, measure the temperature using the
NIST thermometer. Measure the temperature at least 4 times for each bath.
Do the same to calibrate the K and T-type thermocouples. Use the “Hotplate”
program again to record the temperatures.
3) The time constant will be measured for the T-type probe thermocouple. Double-
click the “Time Constant” icon on the Windows desktop. This program provides
a real-time chart output of the thermocouple temperature. Heat the probe in an
85°C water bath. Once the temperature of the thermocouple has stabilized at
85°C, hit the “Record” button, and then quickly transfer it to the 40°C bath. Do
not end the run until steady state is reached. Perform this measurement at least
4) Use the pyrometer to measure the emissivity of three unknown samples. You will
be using Hotplate 1 to conduct the measurements. Flip the toggle switch to
Hotplate 1, then double-click the “Pyrometer” icon on the Windows desktop.
This program controls and monitors the hotplate’s temperature via the surface
mount T-type thermocouple. Set the hotplate to 80°C. Place each sample
material near the center of the hotplate and measure its temperature with the
pyrometer. Be sure the object fills the circle in viewfinder of the pyrometer, and
measure directly above it. Adjust the emissivity value until the temperature reads
the same as that on the computer screen. Record the emissivity, the hotplate
temperature as read by the computer, and the temperature as read by the
pyrometer. Repeat this measurement at least 4 times.
Results and Analysis Sections:
JMP or other statistics software may be used for the analyses.
1) Generate histograms of the data taken from the two thermocouples in Part 1 of the
experiment. Calculate the mean, standard deviation, and variance. Report the
95% confidence limits.
2) Report the calibrations along with 95% confidence limits for the two
thermocouples and the resistance thermometer. Display the confidence intervals
on the graph. Report an equation in the form of y = mx + b, where x is the
temperature of the standard, y is the temperature of the instrument being
calibrated, m is the calibration slope, and b is the calibration intercept.
Remember, T must be expressed in absolute units (K). Present all of your
calibrations graphically in the Results section. Note: The output from the PRT
must be converted from ohms to °C—see the ITS-90 standard PRT conversion
table attached to this handout.
3) From the calibration data, generate a plot of (Texpt – TNIST) v. TNIST for each
thermocouple and for the PRT. (Plot all three on one graph. This lets you
compare overall accuracy visually.)
4) Report the mean time constant and its 95% confidence limits obtained for the T-
type thermocouple. Use two methods to solve for the time constant. Method A:
To find the time constant, plot a graph of ln(T-Tf) vs. t for all runs. Show the
graph for one run in the Results section of your report. Method B: algebraically
solve for the time constant in Eq. 6 of this handout. (Readjust your time values so
that time=0 when temperature change begins to take place.) Using this new
equation, plot a graph of time constant vs. time. For the interval of time where
temperature change is taking place you should see a horizontal line in your graph
(demonstrating that the time constant is independent of time). Use the equation of
the mean of this line to report the mean time constant and its 95% confidence
limits. Show the graph for one run in the Results section of your report.
Important: You will need to use your calibration equation for the thermocouple to
adjust the temperatures to their correct values.
5) Calculate and report the mean emissivity values for each sample along with the
standard deviation, variance, and 95% confidence limits (assuming the data has a
normal distribution). You will be given one or more mystery samples. Use the
emissivity value you attain along with the table of emissivity values to identify
the mystery material(s).
1) Discuss the relative precision of the K and T-type thermocouples based on the
measurements taken in Part 1 of the experiment. Discuss what you know about
2) For calibration portion of the experiment (Part 2), comment on the relative
precision and accuracy of the PRT and the K and T-type thermocouples. Discuss
qualitatively and quantitatively how you arrived at your conclusions. Does the
most accurate device change at different temperature intervals? (Hint: look at the
difference plot generated from analysis #2.)
3) Can you use the calibration data from the probe type thermocouples to calibrate
the surface mount thermocouples? Why or why not? State any assumptions that
4) How would the time constant change if your initial bath temperature was 100ºC?
If you had started recording data after the thermocouple was placed in the ice
bath, how would that affect your results?
5) Did different methods for solving the time constant produce different results?
Discuss how different mathematical techniques can sometimes produce different
results even when the original data has not changed. Which method of the two did
6) Discuss the accuracy and precision of the pyrometer. Discuss how the accuracy
of the emissivity measurements can be improved.
7) Using the experimentally determined emissivities and 95% confidence limits,
deduce the identity of the unknown materials using the emissivity chart provided
by your teaching assistant.
8) Report any other observations regarding the relative (or absolute) performance of
the instruments. What factors besides precision and accuracy are important in
choosing a temperature measuring device for a particular application? Give
specific examples of where each device might best be used.
9) Address the errors (both known and unknown) associated with all the
experiments. This question should be answered very thoroughly. Are there
systematic errors in the experiments? How could the accuracy of the experiments
1) Show the calculations used for the linear regression analysis and confidence limits
(for both m and b) for any one calibration curve.
2) Show how you calculated the time constants, their average, and their confidence
Resistance vs. Temperature values for an
ITS-90 standard platinum resistance thermometer (SPRT)
263 to 282K
Temp (K) Ohms Temp (K) Ohms Temp (K) Ohms Temp (K) Ohms
263 96.03 293 107.74 323 119.34 353 130.84
264 96.42 294 108.12 324 119.72 354 131.22
265 96.81 295 108.51 325 120.11 355 131.60
266 97.20 296 108.90 326 120.49 356 131.98
267 97.59 297 109.29 327 120.88 357 132.37
268 97.99 298 109.68 328 121.26 358 132.75
269 98.38 299 110.06 329 121.65 359 133.13
270 98.77 300 110.45 330 122.03 360 133.51
271 99.16 301 110.84 331 122.42 361 133.89
272 99.55 302 111.23 332 122.80 362 134.27
273 99.94 303 111.61 333 123.18 363 134.65
274 100.33 304 112.00 334 123.57 364 135.03
275 100.72 305 112.39 335 123.95 365 135.41
276 101.11 306 112.78 336 124.34 366 135.79
277 101.50 307 113.16 337 124.72 367 136.17
278 101.89 308 113.55 338 125.10 368 136.55
279 102.28 309 113.94 339 125.49 369 136.93
280 102.67 310 114.32 340 125.87 370 137.31
281 103.06 311 114.71 341 126.25 371 137.69
282 103.45 312 115.10 342 126.63 372 138.07
283 103.84 313 115.48 343 127.02 373 138.45
284 104.23 314 115.87 344 127.40 374 138.83
285 104.62 315 116.26 345 127.78 375 139.21
286 105.01 316 116.64 346 128.17 376 139.59
287 105.40 317 117.03 347 128.55 377 139.96
288 105.79 318 117.41 348 128.93 378 140.34
289 106.18 319 117.80 349 129.31 379 140.72
290 106.57 320 118.18 350 129.69 380 141.10
291 106.96 321 118.57 351 130.08 381 141.48
292 107.35 322 118.95 352 130.46 382 141.86
Table of Emissivity Values
Aluminum (oxidized) 0.11 Gold 0.02
Brass 0.04 Nickel 0.05
Graphite 0.76 Steel 0.07
Glass 0.92 Silver 0.01
Chromium 0.08 Shale 0.69
Copper (unoxidized) 0.03 Lampblack 0.95
Mercury 0.10 Ceramic (white) 0.90
Inconel 0.28 Platinum 0.05
Iron (oxidized) 0.74 Marble (white) 0.92
Iron (unoxidized) 0.21 Silicon 0.65
Lead (oxidized) 0.28 Iridium 0.45