9-22-2022 Pyrometry Report Chris Mack
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Experiment 2
Pyrometry Analytics
Christopher Mack
Robbie Nollet & Youfu (Edward) Qian
MSE 307 Section AB2
Due Date: 09/22/2022
Date Received: __________________________
Abstract
Pyrometry is the ability to measure the temperature of a substance without direct contact, such as a thermometer. Understanding how pyrometry works is crucial to understanding how one measures the
temperature of such substances. By using a concept know as a black body, one can accurately depict the amount of energy being released by a material using its emissivity. Black bodies, emitted energy, and emissivity constants are all explained by Stefan-Boltzmann’s laws and theorems, which are explored in this report. After data has been collected and analyzed, the emissivity values of stainless steel 321 and graphite have been determined to be close to the accepted values. This inspection has been completed using Stefan-Boltzmann’s equations and statements about black bodies and energy emission. Objectives & Procedure
1
Pyrometry is the methodology of measuring the temperature of a substance when using a standard thermometer is not permitted. Studying and conducting experiments on pyrometry will help understand emissivity and what is known as a “black body.” A black body is a material/surface that absorbs all incoming energy (in the form of radiation) yet releases all its excess energy. Emissivity is defined as the “effectiveness in emitting energy as thermal radiation” [1], where its value is from 0 to 1. The black body is going to modeled by a graphite well sample, which has a theoretical emissivity of 1. The purpose of this lab is to test the emissivity of real-world materials, such as stainless-steel.
The setup of this lab has three main devices: the furnace, chopper, and pyroelectric detector (PD). The furnace is used to heat up to the sample at a specified temperature. The chopper is a device that cuts the EM waves from the furnace before reaching the PD. This is set up because the pyroelectric detector is quite sensitive and will detect light coming in from other outside sources. By chopping the energy emitted, the minute amount of energy that is emitted can be detected accurately. See Pictures 1a & 1b
for more detail:
Pictures 1a & 1b: Picture 1a
shows the alignment of the furnace, chopper, and PD. Picture 1b
shows heat resistant gloves, metal tray and tongs
for removing hot samples from the furnace
Once the furnace, chopper, and PD are lined up in order, the calibration can begin. This uses the graphite well sample (the “black body”) to determine the optimal frequency to set the chopper for the 2
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other trials. Heat the furnace to 250 degrees C and place the graphite sample inside. Once it has been heated for a few minutes, sweep the frequency values from 10
110 hertz in intervals of 10 hertz, recording the voltage reading each time. Repeat this for 300, 350, 400, & 450 degrees, and on the flat side of the graphite sample. Once the optimal frequency has been found (by plotting previous data), the actual experiment can be done. The same procedure as before is performed again, but this time the frequency is constant, and the sample is a stainless-steel 321 rod of specified composition. Place the sample inside the furnace and read the voltages at each temperature. Flip the sample so both shiny and dull sides are recorded. Results and Discussion
To dissect the data gathered, the calibration records must be analyzed first. Calibration must be done to find the optimal frequency for our device. The chopper cuts the energy source from the sample,
and ensuring the optimal frequency is necessary for accurate and reliable data. Without this step, the results will be heavily skewed. The PD uses Signal Recovery (software) to read the voltage that is produced by the sample. Figure 1
shows the relationship between temperature, frequency, and voltage output. 3
Figure 1:
Shows the relationship between temperature, frequency, and voltage output (voltage & frequency are in log format). The legend on
the right is in degrees Celsius
Looking at this graph, it can be said that some of the temperatures do not have as much data as others. This is because the PD does not read values that are above 1.2 volts. If a value is to breach above
1.2 volts, the detector does not output any value - it is not graphed. The 450 degree C data is the scarcest; this makes sense because the furnace is inputting as much energy into the sample as possible, causing the PD to overload often. Since the graphite well is the black body, the frequency value will be set at a value that allows all temperatures of the black body to be detected by the PD. The graph shows that there is an inverse relationship between frequency and voltage: as frequency increases, the voltage
decreases. This makes sense, as the PD measures voltage by detecting changes in the atomic structure of a material that leads to a change in polarization [3]. By increasing the frequency, the material has less time to deform back into its original orientation, thus increasing the polarization readings by the PD. For our data, we chose 90 hertz since the PD detected all data at this frequency.
For the purposes of this lab, the voltage read by the PD is analogous (and in this case, equal) to the radiation energy. This is useful for Equation 1.1
[1], as this explains the main breakdown of this analysis:
E
r
=
ϵk T
N
(1.1)
In this equation, E
r
is the radiation energy (or voltage), ϵ
is the emissivity of the material, k is a constant, T is temperature, and N is also a constant that must be solved. This equation was developed by Stefan-Boltzmann; he found that, in a perfect experiment, that N should be equal to 4. The accuracy of the data collected will be tested to see how closely it follows this equation and, most specifically, test the value of N and ϵ
.
4
To do so, log manipulations must be performed to Equation 1.1
. N will be much clearer to see once these manipulations have been performed. The following equation is derived by taking Equation 1.1
and taking the 10-base log of both sides and using power-log rules to rearrange the terms in
y
=
m
(
x
)
+
b
format:
log
(
V
)
=
Nlog
(
T
)
+
log
(
kϵ
)
(
1.2
)
In this case, when the data is graphed, log(T) is analogous to the independent variable x, N is the slope m, and log
(
kϵ
)
is b, or the y-intercept. The data is then plotted and analyzed for the N values – all this entails is inputting a line of best fit and looking at the slope m. Below is Table 1
, which shows all the log graphs and N values of each sample. The N values have been rounded to the closest integer for simplification purposes.
Table 1
: N values for specified samples
Sample
Graph
N Value
5
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Graphite Well
2.1132
2
Graphite Flat
2.144
2
Stainless Steel Shiny
1.7423
2
Stainless Steel Dull
2.0125
2
As one can see, the values of N for all four samples are approximately 2. This is quite far off from the accepted value of 4; a possible reason for this error could be that the PD is accepting other light sources 6
into the data, or perhaps the sample wasn’t heated up fully to the proper temperature (this second reason is unlikely, since the samples are metals and transfer heat exceptionally well). Furthermore, the emissivity constants of each material need to be determined. There are two methods that can be used to determine this: the first methodology is using Equation 1.2
and the y intercept to approximate ϵ
and k, and the second is to use a ratio of sample and blackbody voltages to solve for emissivity. Unfortunately, running the numbers through the first method provides results that are futile. The emissivity values of several of the above samples are above 1, which obviously is impossible and doesn’t align with the black body concept. So, the ratio method is used to approximate the emissivity constants. This is a small derivation of the equation [3]:
V
d
,sample
V
d
,well
=
ϵ
sample
k T
N
ϵ
well
kT
N
=
ϵ
sample
ϵ
well
=
ϵ
sample
(
2.0
)
In this equation, the voltage of the specific sample is divided by the voltage of the well at a specified temperature. This allows Stefan-Boltzmann’s equation to be substituted in for the voltages and
many terms will cancel out; this equation assumes that the N values for the sample and black body are equal, as well as the emissivity of the graphite well is 1. The first assumption is correct since all the calculated N values have an approximate value of 2. Below is Table 2
, which presents the emissivity constants of each sample at each temperature, along with the averages:
Table 2:
Emissivity constants for each sample at each temperature
Temperature (Celsius)
Flat Graphite
Shiny Steel
Dull Steel
7
250
0.905
0.416
0.470
300
0.940
0.376
0.470
350
0.919
0.371
0.465
400
0.948
0.338
0.449
450
.924
0.335
0.446
Average
0.927
0.367
0.460
While these values may seem promising, proven literature declares otherwise. Figure 2 [4] shows the accepted values of stainless steel 321 that is polished and unpolished:
Figure 2:
Shows the different emissivity values for stainless steel 321. The middle column is applied temperatures in Fahrenheit (Celsius in
parenthesis) and the range of emissivity constants to the right
The collected data states that the shiny (polished) steel has an emissivity of 0.367 and the unpolished has a value of 0.460. For the polished steel, the emissivity does fall inside of the accepted range. Alas, the emissivity of the unpolished steel falls significantly outside the proven range. The reason
why the polished steel has a lower emissivity value compared to the unpolished steel is because if a material is a good absorber, it is a good emitter (of energy). Polished steel is quite shiny (bad absorber), so that means it is a bad emitter. As for the carbon flat side, ThermoWorks provides an emissivity of 0.98 [5], which is close to the value from the experiment. The reason why the well and flat sides of the carbon have different 8
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emissivity values is due to the geometry of the two. The well side has a concavity that reveals more surface area of the sample, whereas the flat side has much less surface area. Surface area plays a large role in the emission of energy; more area provides more opportunity for energy to be released in that portion of the sample, due to the volume to surface area ratio. This difference in surface area explains why the two will have different values, as well as why the dull side of the stainless steel will have a higher emissivity, too.
Each of these values obtained through the lab have proven to be relatively similar to the accepted values but did not exactly line up exactly. A possible source of error could be the furnace; as seen in Picture 2
, the furnace has two openings that lead to energy being emitted out of both ends. The PD only detects the radiation emitted through one of the sides, so some of the energy could have possibly leaked out of the opposite end of the furnace. The difference in polish-ness could a potential source of error, too. Producing materials with exact polishes is extremely difficult and the variety of dullness could be a factor that would affect the emissivity of each sample. Not to mention that each sample could vary in exact composition, which, again, would affect the energy emissions.
Picture 2
: Shows the furnace and its opposite opening. The graphite sample is inside, hence why the furnace cannot be looked all the
way through
Conclusion
9
This experiment has shown how emissivity works and how it is calculated for different materials.
By using Stefan-Boltzmann’s law along with several mathematical manipulations, the emissivity constants of different materials (graphite, stainless-steel 321) have been calculated as well as the N values. This can be used to further develop understanding of how pyrometry works; using emissivity constants, the temperature of certain materials can be measured accurately without conventional contact thermometers. Not only that, but the knowledge of black bodies and how they function have also been expanded upon and how they can be used in the real world. As for the data collected, some of
the emissivity values are not as close the expected values. This could be due to a variety of different circumstances – more data is required for further analysis. References
10
[1] “Emissivity,” Wikipedia
, 15-Sep-2022. [Online]. Available: https://en.wikipedia.org/wiki/Emissivity. [Accessed: 19-Sep-2022]. [2] “Pyrometer,” Wikipedia
, 03-May-2022. [Online]. Available: https://en.wikipedia.org/wiki/Pyrometer. [Accessed: 19-Sep-2022]. [3] J. TerBush, “Pyrometry lecture Fall 2022.” University of Illinois Urbana-Champaign, Urbana-
Champaign, 2022. [4] “Emissivity chart non-metal and metal materials non-metal ... - klein tools,” Klein Tools
, 2022. [Online]. Available: https://www.kleintools.com/sites/kleintools/files/instructions/Emissivity-Chart-
139697ART.pdf. [Accessed: 20-Sep-2022]. [5] “Infared Emissivity Table,” ThermoWorks
. [Online]. Available: https://www.thermoworks.com/emissivity-table/. [Accessed: 20-Sep-2022]. 11
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