P112L07_Lab_Manual_v20230201

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University of Illinois, Chicago *

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Dec 6, 2023

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UIC Physics Department Physics 112 Laboratory Manual Introduction to Thermal Radiation. The Inverse Square Law Page 1 of 5 Introduction to Thermal Radiation. The Inverse Square Law Experiment objectives: Make measurements testing the Stefan-Boltzmann law in high-temperature range and inverse square law. Background In the previous lab, you studied the thermal radiation by using Leslie’s Cube and made measurements testing the Stefan-Boltzmann law in low-temperature range ሺbelow 100 – 120  Cሻ which, as you may well know by now, states that the amount of radiation emitted by a black body per unit area is directly proportional to the fourth power of the temperature. This law is perfectly true only for ideal black body, and object that absorbs all the radiation that strikes it. In this lab, first you will experimentally test the Stefan-Boltzmann law in high-temperature range using Stefan-Boltzmann Lamp ሺ~ 1500 – 2000 Kሻ and then you will test one of the very important relations in physics, namely the inverse square law. It can be found in different branches of physics such as the theory of gravitation, electromagnetic theory, and radiation. You will experimentally test that the intensity of the radiation, ࠵? ሺor net power absorbed by detector per its active area, in W/m 2 ሻ, is proportional to the inverse square of the distance, ࠵?, from that source, i.e. ࠵? ൌ ௉ ஺ ∝ ଵ ௗ మ ሺ1ሻ Figure 1 illustrates how the energy per unit area changes according to Eq. ሺ1ሻ. As you can see, the illuminated area increases by the factor of 4, 9, 16 etc. when the distance between the source of radiation and area increases by factor of 2, 3, 4 and so one. Equipment  Optics bench ሺPasco, OS-8508ሻ,  Stefan-Boltzmann lamp ሺPasco, TD-8555ሻ equipped with light protective shield,  Radiation Sensor ሺPasco, TD- 8553ሻ,  Millivoltmeter ሺDigital Multimeter CEN-TECH P35017ሻ,  DC Power supply,  Analog DC voltmeter ሺ0 – 10 Vሻ,  Analog DC ammeter ሺ0 – 5 Aሻ,  Two foam sheets fastened to each other with an air gap between the sheets and with one of its surfaces covered with aluminum heat reflecting tape,  Transparent right-angle triangle. Figure 1. The inverse-square law in action. Figure 2. Experimental setup.

UIC Physics Department Physics 112 Laboratory Manual Introduction to Thermal Radiation. The Inverse Square Law Page 2 of 5 Introduction to Thermal Radiation. The Inverse Square Law ሺExperimental Procedure and Data Analysisሻ Lab Section ሺDay & Timeሻ: ________________________________ Name: ________________________________________________________________________ Station#: ____________ Partner: ______________________________________________________________________ Initial Setup  Make sure that the Power Supply is turned OFF, its left switch is set to “0 – 16 V” voltage range and its right switch is set to “Normal” mode, and the output voltage control knob should be turned all the way counterclockwise and set to position “A”.  Check the following connections:  Power Supply’s black plug and Voltmeter’s black plug must be connected to each other by 12” black jumper cable,  Power Supply’s black plug must also be connected to Stefan-Boltzmann lamp’s black plug using 24” black cable,  Power Supply’s red plug and Voltmeter’s red plug must be connected by 12” red jumper cable,  Power Supply’s red plug must also be connected to Ammeter’s red plug by 24” red cable,  Stefan-Boltzmann lamp’s red plug and Ammeter’s black plug must be connected by 24” brown cable,  P35017 multimeter must be connected to the thermal radiation sensor as shown in Figure 1. Warning: Do not touch the bulb with your fingers! If you touch the bulb with your fingers, the salts and oils from your skin will damage the bulb and cause the heat to concentrate. This can significantly reduce the life of the bulb or even worse cause it to shatter.  Place the sensor a few centimeters from the left corner of the protective light shield and cover the front face of the sensor with double foam sheet. In the first part, you will determine the temperature dependence of the power emitted from a heated tungsten filament of the Stefan-Boltzmann lamp and compare with that predicted from the Stefan- Boltzmann law. The lamp will be at a relatively high temperature ሺ~1000 Kሻ so the ambient temperature can be ignored, and the calculation of the filament temperature is quite straightforward. The resistance of the filament of the Stefan-Boltzmann lamp at ࠵? ௥௘௙ ൌ 22  C or 295 K ሺ1K ൌ 1  C ൅ 273.15ሻ, ࠵? ௥௘௙ , is: ࠵? ௥௘௙ ൌ 0.27  at ࠵? ௥௘௙ ൌ 295 K  Measure and record the slit position ሺthe position of the filamentሻ. ࠵? ଴ ൌ _____________ ሺcmሻ Important note: The slit position should not be changed during experiment. Wednesday 8 : 00 AM Brick Minh Ngegen 10 Rose 100

UIC Physics Department Physics 112 Laboratory Manual Introduction to Thermal Radiation. The Inverse Square Law Page 3 of 5 Experimental Procedure and Data Analysis 1. Place the front face of the sensor approximately 5 cm away from the filament ሺi.e. 5 cm from ࠵? ଴ positionሻ. Note: This is where the gray bases of the sensor and lamp touch each other. In other words, you should simply slide the sensor until it touches the base of the lamp. Important Note: Make each Sensor reading quickly. Between readings, slide the sensor 10-15 cm away from the lamp and place both sheets of insulating foam between the lamp and the sensor, with the silvered surface facing the lamp, so that the temperature of the sensor stays relatively constant. 2. Set the P35017 multimeter to read the voltage drop across thermopile ሺ rangeሻ. 3. Turn on the power supply and at each voltage setting listed in Table 1, record ࠵? ሺammeter readingሻ and ࠵? ௦ ሺthe potential drop across the thermopile due to the thermal radiation from the lampሻ. Warning: The voltage into the lamp should NEVER exceed 10 V. Higher voltages may permanently damage the lab equipment. ࠵? V ࠵? A R  ࠵?/࠵? ௥௘௙ ࠵? ௦ K ࠵? ௦ ସ K ࠵? ௦ mV 1 2 3 4 5 6 7 8 9 10 4. Calculate the resistance of the filament, ࠵? ൌ ࠵?/࠵?, at each of the voltage settings, then divide ࠵? by ࠵? ௥௘௙ to obtain the relative resistance, ࠵?/࠵? ௥௘௙ , and record your results in Table 1. You will be provided with a laminated sheet containing a table called “Temperature and Resistivity for Tungsten” allowing you to convert the relative resistance, ࠵?/࠵? ௥௘௙ , to the filament temperature, ࠵? ௦ , in Kelvin. 5. Convert the ࠵?/࠵? ௥௘௙ to the temperature, ࠵?, of the lamp filament at each voltage setting, then calculate ࠵? ௦ ସ for each value of ࠵? and record the results in Table 1. 6. Plot the ࠵? ௦ vs ࠵? ௦ ସ , then add a linear trendline to your data points, and record the fitting parameters ሺincluding its unitsሻ and the coefficient of determination ሺR 2 ሻ below. Slope ൌ ________________ ሺunitsሻ Intercept ൌ __________________ ሺunitsሻ R 2 ൌ __________ Table 1. Experimental results ሺStefan-Boltzmann Lawሻ 0.80 1.25 4.63 1060 1.26 x 10" 0.3 1. 10 1.82 6.73 1430 4. 18 x 101 1.5 1.30 2.31 8.55 1730 8.96x101 3.8 1.60 2.50 9.26 1888 1.25 x 1013 7.0 1.88 2-78 10.29 2030 1.50 x 1013 11.2 2.00 3.08 11. Il 2190 2.30 x 1013 15.2 2.20 3.18 11.78 2295 2.77 x 1013 2 0.5 2.35 3.40 12.61 2430 3.49 x 10" 26.2 2.50 3.60 13.33 2558 4.23 x 10" 32.3 2.70 3. 70 13.72 2600 4.57x 1813 38.5 1.Ox 10 4 3.ox10" K 0.9899

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UIC Physics Department Physics 112 Laboratory Manual Introduction to Thermal Radiation. The Inverse Square Law Page 4 of 5 Snap a picture of the ࠵? ௦ vs ࠵? ௦ ସ graph (including trendline) and add it in the space provided to the right. 7. Is your graph a straight line? Do your experimental results support the Stefan-Boltzmann Law? Briefly discuss any deviations that exist. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ In this part of the lab, you will experimentally verify that the radiation intensity is inversely proportional to the square of the distance from the source of radiation. Before running measurements, make sure that the voltage is set to 10 V and the front face of the sensor is approximately 10-15 cm away from the filament and its front covered with the double foam sheetሻ Remove the foam sheet and measure the ࠵? ௦ ሺthe potential drop across the thermopile due to the thermal radiation from the lampሻ at different distances between the slit and the front of the sensor, ࠵?, listed in Table 2, and record the ࠵? ௦ values in Table 2. Hint: Use the transparent right-angle triangle to measure accurately position, ࠵?, of the front of the sensor, then calculate the ࠵? ሺ࠵? ൌ |࠵? െ ࠵? ଴ |, where ࠵? ଴ is the slit positionሻ. 8. Calculate 1/࠵? ଶ and record your results in Table 2. 9. Plot the ࠵? ௦ vs 1/࠵? ଶ . According to the Stefan-Boltzmann Law, the data should fall along a straight line. 10. Add a linear trendline to your data points and record the fitting parameters ሺincluding its unitsሻ and the coefficient of determination ሺR 2 ሻ below. Slope ൌ ________________ ሺunitsሻ Intercept ൌ __________________ ሺunitsሻ R 2 ൌ __________ ࠵? cm 1/࠵? ଶ cm 2 ࠵? ௦ mV 5 8 11 14 17 20 23 26 29 32 Table 2. Experimental results ሺInverse Square Lawሻ My graph is really close to a straight line => My results support the Stefan - Boltmann Law the errors or deviations could be due to the timing of recording the current of the filament. 0.040000 37.5 0.015625 19.8 0.008264 11.5 0.0 05102 7.7 0.003468 5.3 6.002588 3.6 0.00 1890 2.5 8.001479 1.9 0.00 1189 1.5 0.000977 1.2 10499 Yim" 0.0016 " 6.9813

UIC Physics Department Physics 112 Laboratory Manual Introduction to Thermal Radiation. The Inverse Square Law Page 5 of 5 Snap a picture of the ࠵? ௦ vs 1/࠵? ଶ graph (including trendline) and add it in the space provided to the right. 11. The inverse square law states that the radiant energy per unit area emitted by a point source of radiation decreases as the square of the distance from the source to the point of detection. Does your data support this assertion? ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ 12. Is the Stefan-Boltzmann Lamp truly a point source of radiation? If not, how might this affect your results? Do you see such an effect in the data you have taken? _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ 13. What sources of thermal radiation, other than the lamp filament, might have influenced your measurements? What effect would you expect these sources to have on your results? _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ 14. Is the filament of the Stefan-Boltzmann lamp a true black body? _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ Yes, it does support this assertion. Yes. Our bodies are also sources of thermal radiation. However, the lamp was blocked by a metal sheet, so it should not affect the result No

P112L07_Lab_Manual_v20230201

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