THERMAL.1
THERMAL RADIATION
The electromagnetic radiation emitted by a hot tungsten filament will be studied.
Theory:
The Stefan-Boltzmann Law relates the rate at which an object radiates thermal energy to T, the
absolute temperature of the object (in Kelvin). The radiant energy, Q, emitted in a time t is:
Q = eT 4At
The rate of radiant energy emission, the radiant energy emitted per unit time (the radiated power,
P) is given by
P = Q/t = eT 4A
(1)
where  = 5.67  10–3 W/m2K4
e = emissivity of the object (1 for a black body)
A = surface area of object
The power radiated per unit surface area (the intensity, I), is given by
I = P/A = eT 4
(2)
When the temperature of a black body increases, the peak of the radiation curve (intensity as a
function of wavelength) moves to shorter wavelengths. This is known as Wien’s displacement
law. The product of the peak wavelength and the absolute temperature is found to be a constant:
peakT = 2.898  10–3 mK
Apparatus:
Figure 1. Equipment Setup
(3)
THERMAL.2
In this experiment, the thermal radiation emitted by a lamp filament will be studied. The
temperature, T, of the lamp filament is related to its resistance, R. The temperature can be
determined by measuring the filament resistance as the temperature of the lamp filament rises
above room temperature, and interpolating a conversion table.
The voltage signal, Vdet, produced by the Radiation Sensor used to detect the thermal radiation is
proportional to the intensity of the thermal radiation striking the detector (Iabsorbed) minus the
intensity of the thermal radiation emitted by it.
i.e.
Vdet  Inet = Iabsorbed – Iemitted
Since the lamp filament temperature will be much higher than the temperature of the detector
(which is essentially at room temperature), this equation may be simplified to
Vdet  Iabsorbed
That is, the Radiation Sensor voltage signal will be assumed to be directly proportional to the
intensity of the thermal radiation emitted by the lamp filament.
In addition to the equipment shown in Figure 1, an Ocean Optics Red Tide USB650
spectrometer will be used to measure the radiation emitted in the 350 to 1000 nm range of
wavelengths. Data from the USB650 will be collected by an Xplorer GLX and then transferred
to a PC.
Figure 2. Light pipe, Red Tide Spectrometer, Xplorer GLX
THERMAL.3
Figure 3. Complete Equipment Setup
Procedure and Experiment:
This experiment must be done with the room lights turned OFF.
1. Set up the equipment as shown in Figures 1 and 3. The voltmeter should be connected
directly to the terminals of the Stefan-Boltzmann Lamp. The ammeter must be used in the
10 A DC mode, as filament currents will range from about 1 A to 3 A. The Radiation Sensor
should be at the same height as the filament, with the front face of the Sensor approximately
6 cm away from the filament. The entrance angle of the sensor should include no close
objects other than the lamp. The end of the optical fibre that directs light to the Red Tide
spectrometer should also be at the same height as the filament.
2. Place the reflecting shield between the lamp and the radiation sensor. To prevent heating the
radiation sensor, THIS SHIELD MUST BE LEFT IN PLACE AT ALL TIMES EXCEPT FOR THE FEW
SECONDS NEEDED TO READ THE MILLIVOLTMETER.
3. Record the value of Rroom, the resistance of the filament at room temperature, which is
printed on the lamp base.
4. The proper location for the end of the optical fibre that directs light to the Red Tide
spectrometer is determined as follows:

Turn on the power supply. Set the voltage control to minimum and the current control
to maximum. THE VOLTAGE ACROSS THE LAMP MUST NEVER EXCEED 13 V as
higher voltages will burn out the filament.

Turn on all the multimeters. Slowly increase the power supply voltage until the
voltmeter on the power supply reads approximately 12 V.
THERMAL.4

Turn on the Xplorer GLX and wait for initialisation of the Red Tide spectrometer to
complete. Accept the defaults for the Data Acquisition parameters by pressing F4
(Close).

Press the large arrow button to acquire data. If the light from the filament is too
intense, the spectrum displayed on the Xplorer GLX will ‘flat-top’. If this happens,
move the end of the optical fibre further from the filament. Press the large arrow
button twice to save the spectrum to the GLX’s memory. (The GLX screen will
refresh, which indicates that the data was saved.)

Press the large arrow button again to acquire a new set of data. The proper location of
the end of the optical fibre is such that the spectrum is as high as possible without
overloading the spectrometer (‘flat-topping’).
5. Set the power supply voltage to about 1 Volt. Record the exact filament voltage, V, filament
current, I, and Radiation Sensor reading (in mV). Also acquire and save the spectrum using
the GLX. Be sure to record the GLX Run # corresponding to the acquired spectrum.
6. Repeat step 5. for power supply voltages from 1 to 12 V in 1 V increments.
7. After all the data have been collected, connect the GLX to a USB port of the PC by using the
black USB cable. DataStudio should automatically open and prompt for the transfer of data
from the GLX RAM to the PC. See the pages at the end of this manual for instructions on
manually opening the GLX File Manager and transferring files.
8. The file that you transferred will have a .GLX extension. In DataStudio, click File | Open
Activity… and select your .GLX file. The data in the file can now be displayed as a graph in
DataStudio. To export the data so that it can be opened and manipulated in Excel, click File |
Export Data…
Analysis:
1. Calculate R, the resistance of the filament at each of the applied voltages (R = V/I).
2. Calculate
R
Rroom
.
3. Use the provided Tungsten Temperature and Resistance data to determine the temperature of
the filament corresponding to each of your runs. Hint: The data in Table 2 can be fitted to a
second-order polynomial with a high degree of accuracy.
4. From the GLX data, determine the peak wavelength for each of your runs.
5. Do your data support the Stefan-Boltzmann Law? i.e. Is Vdet  T 4?
6. Do your data support Wien’s Displacement Law? i.e. Is peak  1/T?
7. In your report, be sure to discuss any approximations, assumptions, and/or simplifications
that were made.
Thermal Radiation System
012-04695D
Table 2 Temperature and Resistivity for Tungsten
R/R 300K
1.0
1.43
1.87
2.34
2.85
3.36
3.88
4.41
4.95
Temp Resistivity
°K
µΩ cm
300
400
500
600
700
800
900
1000
1100
5.65
8.06
10.56
13.23
16.09
19.00
21.94
24.93
27.94
R/R 300K
5.48
6.03
6.58
7.14
7.71
8.28
8.86
9.44
10.03
Temp Resistivity
°K
µΩ cm
1200
1300
1400
1500
1600
1700
1800
1900
2000
R/R 300K
30.98
34.08
37.19
40.36
43.55
46.78
50.05
53.35
56.67
10.63
11.24
11.84
12.46
13.08
13.72
14.34
14.99
15.63
Temp Resistivity
°K
µΩ cm
R/R 300K
Temp Resistivity
°K
µΩ cm
2100
2200
2300
2400
2500
2600
2700
2800
2900
16.29
16.95
17.62
18.28
18.97
19.66
26.35
3000
3100
3200
3300
3400
3500
3600
60.06
63.48
66.91
70.39
73.91
77.49
81.04
84.70
88.33
Temperature versus Resistivity for Tungsten
20
19
18
17
16
15
14
13
Relative
Resistivity
RT
R 300K
12
11
10
9
8
7
6
5
4
3
2
1
0
0
500
1000
1500
2000
Temperature (Kelvin)
4
2500
3000
3500
92.04
95.76
99.54
103.3
107.2
111.1
115.0