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 4 At 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 4 A (1) where = 5.67 10 3 W/m 2 K 4 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: peak T = 2.898 10 3 m K (3) Apparatus: Figure 1. Equipment Setup
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, V det, produced by the Radiation Sensor used to detect the thermal radiation is proportional to the intensity of the thermal radiation striking the detector (I absorbed ) minus the intensity of the thermal radiation emitted by it. i.e. V det I net = I absorbed I emitted 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 V det I absorbed 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 R room, 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. R room 3. Use the provided Tungsten erature 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 V det 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 erature and for Tungsten 1.0 1.43 1.87 2.34 2.85 3.36 3.88 4.41 4.95 300 400 500 600 700 800 900 1000 1100 5.65 8.06 10.56 13.23 16.09 19.00 21.94 24.93 27.94 5.48 6.03 6.58 7.14 7.71 8.28 8.86 9.44 10.03 1200 1300 1400 1500 1600 1700 1800 1900 2000 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 2100 2200 2300 2400 2500 2600 2700 2800 2900 60.06 63.48 66.91 70.39 73.91 77.49 81.04 84.70 88.33 16.29 16.95 17.62 18.28 18.97 19.66 26.35 3000 3100 3200 3300 3400 3500 3600 92.04 95.76 99.54 103.3 107.2 111.1 115.0 20 erature versus for Tungsten 19 18 17 16 15 14 13 Relative R T R 300K 12 11 10 9 8 7 6 5 4 3 2 1 0 0 500 1000 1500 2000 2500 3000 3500 erature (Kelvin) 4