University of Florida
Department of Mechanical and Aerospace Engineering
Title of Experiment
EML 4147C – Thermal/HeatDesign and Lab
Prepared by: Nicholas Stiesi
Date: 4/08/08
ABSTRACT
The purpose of this experiment was to characterize the performance of a Moll's Thermopile.
Most importantly, the question to be answered is if the thermopile intercepts all incident radiation, or if
it effectively ignores radiation from the surroundings and reads only radiation incident from a direct
target. To test this, a rig was set up consisting of the thermopile and an oven, which were pointed
directly at each other with a known distance in between. Readings from the thermopile were taken and
compared to theoretical calculations. These calculations predicted amounts of radiation incident from
the oven as well as the surroundings. After this analysis, it was found the the thermopile is, in fact,
directional. The experimental data for incoming radiation matched the calculated values of incident
radiation from the oven alone. In fact, when the surroundings were taken into account in the theoretical
calculation, the results were counterintuitive. The thermopile, being heated by the oven, actually
resided at a higher temperature than the surroundings, and would in theory be radiating energy to the
surroundings, rather than accepting radiation from the environment.
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OBJECTIVE
The purpose of this experiment was to predict the behavior of an unknown Moll's thermopile.
The unit was obtained with limited documentation as to performance. Therefore, it was of interest to
know if the unit intercepts radiation from all directions, or if it absorbs in a directional manner. It was
also of interest to know the approximate accuracy of the unit compared to theoretical estimations.
APPARATUS/PROCEDURE
The rig used to carry out this experiment consisted of the Moll's Thermopile, and a 200 Watt
oven. The oven body was shielded by a water cooled radiation shield with a 2cm aperture through
which radiation is to escape. The thermopile consisted of a metal housing that contained 16
thermocouples which output voltage to a data acquisition system. The thermopile housing featured a
2.5cm aperture through which radiation was to be absorbed. The unit was attached to an adjustable
mount which slid along a track which was graduated in units of centimeters. This allowed for knowing
the exact distance between the thermopile and the oven.
W
2 cm
2.5 cm
Blackbody
Aperture
Receptor
Aperture
Figure 1: Geographic arrangement of the test rig
The procedure for the experiment consisted simply of warming the oven to approximately
900°F. Once the oven temperature stabilized, the thermopile was moved to a linear distance of 10cm
from the oven. The voltage reading from the thermopile was taken, and the distance was increased by
5cm. This process was repeated for distances up to 50cm.
TECHNICAL APPROACH
Experimentally, the technical approach to this experiment consisted of calculating thermopile
power and temperature values from output voltage and the unit's appropriate calibration figures. First,
from the output voltage, the intercepted power can be found by:
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P  Voltage *
1mW
0.075mV
The thermopile temperature can be calculated by:
Tthermopile 
Voltage
16 * 0.04mV / C
Much more rigorous calculations are necessary to calculate the predicted radiant power intercepted by
the thermopile. Starting with the thermopile’s intercepted radiation based on the oven only, one would
first need to find the view factor for the pair. This dimensionless number can be thought of as the
fraction of radiation leaving the oven that is actually intercepted by the thermopile. The oven and
thermopile apertures can be thought of as coaxial parallel disks, meaning their view factor is well
defined, and given by:
roven
L
rthermopile
Rthermopile 
L
2
1 Rj
S  1
Ri2
Roven 
Foven  thermopile 

1
S  S 2  4(r j / ri ) 2
2

From here, one could now calculate qoven->thermopile, or the net rate at which the thermopile intercepts
radiation that is emitted by the oven:
4
4
qoventhermopile  Aoven Foventhermopile (Toven
 Tthermopile
)
The next exercise would be to calculate the amount of radiation intercepted by the thermopile that
originated from the surroundings. To do this, it is best to think of the entire rig as an enclosure. Said
enclosure would look like conic solid; a cylinder with different diameters at either end. In this case, the
circular surfaces would be the thermopile and oven apertures, and the remaining surface of the solid
would be the area of the surroundings. Also, the surroundings could also be approximated as a black
body, since the material of the surroundings is air, and should reflect only negligible amounts of
incident radiation. That being said, there is no well defined method of finding the view factor of a
conic solid surface with respect to the perpendicular disk. However, the summation rule of view
factors states that in an enclosure, the sum of all view factors with respect to a given surface are equal
to 1. So, in the assumed enclosure that is the experimental rig, there are only 3 surfaces: oven,
thermopile, and surroundings. Since the view factor of the oven with respect to the thermopile is
already known, it follows that:
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Fsurroundings  thermopile  1  Foven  thermopile
(note that since the thermopile aperture is a plane surface, it does not “see” itself, so
Fthermopile->thermopile is equal to zero).
With the view factor known, the area of the surroundings is a simple geometric exercise. This allows
for the calculation of the net radiation gained by the thermopile due to the surroundings:
4
4
qsurroundingsthermopile  Asurroundings Fsurroundingsthermopile (Tsurroundin
gs  Tthermopile)
RESULTS
Below are some tabulated results for this experiment. (a full spreadsheet of results can be found
in the appendix).
Length (m)
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
Intercepted
Energy (mW)
72.40
34.67
20.40
13.07
8.93
6.40
4.80
3.73
2.80
ΔIntercepted
Energy (mW)
0.067
0.067
0.067
0.067
0.067
0.067
0.067
0.067
0.067
Thermopile
Temperature (°C)
29.59
25.17
23.50
22.64
22.16
21.86
21.67
21.55
21.44
Table 1: Experimental results
The above table shows the data for both intercepted radiation and temperature for the thermopile based
on the output voltage readings. As expected, the amount of radiation intercepted by, as well as the
temperature of the thermopile decrease as the distance from the oven increases.
Length
(m)
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
qsurroundings->thermopile
(mW)
-100.67
-71.30
-55.63
-44.41
-36.37
-30.37
-26.01
-22.75
-18.95
Δqsurroundings->thermopile
(mW)
9.10E-003
1.32E-003
3.41E-004
1.19E-004
5.13E-005
2.54E-005
1.40E-005
8.35E-006
5.22E-006
qoven->thermopile
(mW)
84.98
38.36
21.69
13.92
9.68
7.12
5.45
4.31
3.49
Δqoven->thermopile
(mW)
4.69E-001
9.16E-002
2.87E-002
1.17E-002
5.59E-003
3.00E-003
1.76E-003
1.09E-003
7.15E-004
%Error
14.8
9.6
6.0
6.1
7.7
10.1
12.0
13.4
19.8
Table 2: Predicted and theoretical results
This table shows the theoretical values of net radiation to the thermopile due to the individual
contributions of the oven and the surroundings. Also shown is the percent error between the
experimental data and the theoretically calculated radiation flux due to the oven alone. These errors are
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a measure of the unit’s accuracy, as well as it’s resistance to the effects of the surroundings. Also,
notice the sign on the values of the surroundings contributions to net radiation. The negative numbers
indicate that the thermopile would actually be radiating TO the surroundings, not the inverse. This
result makes sense because the driving potential for radiation exchange between black bodies is
temperature differential. Since the oven is effectively heating the thermopile to temperature higher
than ambient, the thermopile would then radiate to the surroundings. However, for the purpose of this
experiment, these values are more than likely inflated. They were calculated using the absolute room
temperature, and do not take into account the temperature gradients that exist in the air around the test
rig.
Now, if the contributions of the surroundings were to be taken into account, the % error as
shown above would be inflated by orders of magnitude, and the radiation curve for the thermopile
would not even show itself on the graph below. This would be due to the net radiation gained by the
thermopile being negative, which is due to the fact that the radiation loss to the surroundings is actually
greater in magnitude than the gain from the oven. However, experimental data dictates that this isn’t
the case, and the thermopile is actually quite ignorant of ambient conditions.
Incident Radiation vs. Distance
Emitted Power (mW)
100
qoven->thermopile (mW)
Intercepted Energy (mW)
10
1
1
10
100
Distance (m)
Figure 2: Incident radiation to the thermopile vs. distance for both experimental and theoretical data.
CONCLUSION
In conclusion, the thermopile in question is a solid unit, but should not be used in situations
where tight constrictions are made on accuracy. The unit proved to be accurate to about 11% on
average, but also exhibited deviations from the theoretical calculations as high as 20%. However, other
factors could have influenced those errors besides unit accuracy (including the effects of the
surroundings), so further and perhaps more controlled accuracy testing is recommended. For the
question of surrounding radiation, though, this unit proved to be very efficient in blocking out the
effects of the surroundings. Theoretically, this unit should have been losing radiation to the ambient
faster than it could gain from the oven, but experimental data proved that this is not the case.
Therefore, the conclusion can be drawn that the thermopile effectively does not “see” the surrounds,
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and this unit could be confidently pointed at a dime-sized target in order to read the emitted radiation
from the target only.