# THERMAL RADIATION (THERM)

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1 UNIVERSITY OF SURREY DEPARTMENT OF PHYSICS Level 2 Classical Laboratory Experiment THERMAL RADIATION (THERM) Objectives In this experiment you will explore the basic characteristics of thermal radiation, particularly emission, reflection and transmission. You will test the inverse square law of thermal radiation. Additionally, you will verify the Stefan-Boltzmann law for a black body at high and low temperatures. Background: Thermal energy is transferred from one place to another by three processes: convection, conduction or radiation. In convection, matter moves away from a region and carries heat with it. A common example is the heating (or cooling) of an object by the movement of surrounding air. In conduction, the atoms or molecules making up a substance interact in order to transport hear. An example is the vibration of atoms in a crystal lattice transporting heat along a metal rod. (Heat conduction is studied in another second year laboratory experiment.) In this exercise, you will be focussing on the third of these mechanisms, thermal radiation in the form of electromagnetic waves. Thermal radiation of objects near room temperature (and also near the temperature of the human body) is mainly in the infrared region of the electromagnetic spectrum. At higher temperatures - about 600 or 700 C - radiation will start to be in the visible region. Thus, an object glows red or orange at such temperatures. At even higher temperatures, emission of light will be throughout the visible region and the object might be described as white hot. The wavelength of radiation at which the power is a maximum, λ, varies as the reciprocal of absolute temperature, T. Wien s law states that λ = b/t where b is a constant equal to mm.k. The amount of thermal radiation given off by an object obviously varies with its temperature. In 1879 Josef Stefan found an empirical relationship between the absolute temperature of an object, T, and the thermal power (P) per unit area (A) radiated by an object, denoted by R: 1 of 10

2 R = P/A = eσt 4 where e is called the emissivity, and the constant of proportionality, σ, is equal to x 10-8 Wm -2 K -4. Emissivities vary between 0 and 1. Ludwig Boltzmann derived this equation theoretically in the 1880s, and so it is now referred to as the Stefan-Boltzmann law. An ideal black body perfectly absorbs all radiation that strikes it and is also a perfect emitter and has e = 1. When radiation falls on an object, a portion of the radiation is reflected and the remainder is absorbed. Dark objects absorb more radiation than light objects and so usually have higher emissivities. Lighter objects are better reflectors. Just as the Stefan-Boltzmann law describes how radiation emission varies with temperature, the radiation absorbed, Rabs, can be described by: Rabs = P/A = aσt 4, where a is the coefficient of absorption and, like the emissivity, varies between 0 and 1. When a hot object is in surroundings at a lower temperature, it emits more radiation than it absorbs. When the object is in thermal equilibrium with its surroundings, then the rate of emission and absorption of radiation must be the same, and so e = a. The net power per unit area radiated by an object at a temperature T in a room at a temperature To is then R = eσ(t 4 - To 4 ). You will attempt to verify the Stefan-Boltzmann law in the laboratory. At very high temperatures, the amount of radiation absorbed is negligible compared to that emitted, and so it can be neglected. Overview of the Experiments: Over the two weeks of this experiment, you will perform a series of four experiments to study: Thermal Emission, Reflection and Transmission Stefan-Boltzman Law at Low Temperatures Inverse Square Law Stefan-Boltzman Law at High Temperatures and to do this you have the following equipment: a radiation cube (known as a Leslie s cube) a lamp with a tungsten filament a radiation sensor. The cube is simply an aluminium box containing a 100 W light bulb. The temperature of the four vertical faces of the cube can be varied up to a maximum of about 150 C by varying the power to the light bulb. A thermistor ( measuring temperature-dependent resistance) allows the 2 of 10

3 determination of the cube temperature. Each face of the cube has a different treatment: black paint, white paint, smooth polish, and rough texture. Using the lamp, you can generate temperatures of up to 3000 C in the filament by varying the current. The electrical resistance of the filament varies with temperature, which enables its temperature to be tracked as the current is changed. The radiation sensor contains a miniature thermopile, constructed from thermocouples, that produces a voltage proportional to the incoming radiation intensity in its region of sensitivity, namely the infrared region from about 0.5 to 40 µm in wavelength. Week 1 Thermal Emission and Transmission First, you will study how different surfaces compare in terms of the amount of radiation they emit when they are at the same temperature. Then, you will observe how different materials transmit thermal radiation, and finally you will measure quantitatively how the radiated power varies with temperature. These measurements will all use the Leslie s Cube apparatus. 1.1 Emission and transmission for different surfaces: 1. You need to connect the two digital multimeters (DMMs) to the two devices used for these experiments, namely: to the Radiation Cube (to read the resistance of its thermistor) to the radiation sensor (to read its output voltage) 2. Measure the resistance in ohms of the thermistor in the cube. This will be your reference measurement at room temperature. 3. As soon as possible, after you have measured its resistance, switch on the power to the Leslie cube, to get it heating up to the required temperature. You need it to equilibrate at a setting of about 5, to get good results. You can gain time in the heating by initially setting the power to high, for a few minutes. (The panel of the Leslie s cube is shown below:) 4. While the cube is heating, set up the sensor so that you will be ready to make the measurements described in item (7) below. Also, work out how to compute the temperature of the cube from the measured resistance of the thermistor as discussed in (6) below. 5. Allow the cube to reach thermal equilibrium at a setting of about 5. 3 of 10

4 6. Values of resistance from the temperature sensor (thermistor) in the cube correspond to the temperature values shown in the table on the side of the cube. These values have been put into a spreadsheet that is available for download at called leslies-cube.xls, and this includes code for linear interpolation between the data points. (Alternatively, typing cd drhosea heateng at the C:\ prompt will run a program on the PC near the experiment that also does a linear interpolation, or you can write your own code to do the interpolation). 6. Measure the resistance of the thermistor in the equilibrated cube, so that you can calculate its temperature. 7. Use the sensor to measure the radiation from one of the vertical faces of the cube. To ensure that the sensor is held at a fixed distance from the cube surface for each measurement, place the sensor so that the posts on its end are in contact with the surface. For the measurement, press to open the cover on the sensor, note the reading on the DMM, and release to close the cover again. This procedure prevents the sensor itself from being heated up. The reading will be measured in mv. 8. Repeat for each surface, recording the sensor reading in mv, the thermistor resistance, and the corresponding temperature of the cube. 9. Turn the power setting on the cube to HIGH and wait for the cube to reach equilibrium. 10. Measure the four faces of the cube again to measure the radiation emitted from each surface, at the higher temperature. Analysis: construct a table showing how emissivity varies with temperature and with the type of cube surface. Normalise your relative measurements of the emissivity to a value of unity for the black surface (as your closest approximation to an ideal blackbody) in order to be able to quote absolute values and compare with published data. Do all surfaces at a given temperature emit the same amount of radiation? Explain your findings. 1.2 Transmission: 1. With the cube is at its highest temperature, as at the end of the previous measurements, place the sensor (on its stand, with its shield covering it) at a distance of about 4 cm from the black surface. 2. Open the shield and quickly record the sensor reading, and then close the shield. 3. Next place a sheet of glass between the sensor and the cube. 4. Quickly open the shield, take a reading, and close the shield again. 5. Repeat with the glass removed, to ensure reproducibility with no absorber. 6. Repeat this procedure with a piece of paper and with the black cloth and the space blanket material provided. Analysis: how does the transmission of radiation through glass, paper and cloth etc. compare? From your findings, explain how a greenhouse functions. 4 of 10

5 Question: calculate how much net energy a person will radiate in a room at 20 C. Note that skin temperature is usually about 33 C, and assume that the surface area of the person is 1.4 square metres. Discuss your findings. 1.3 Stefan-Boltzmann Law at Low Temperatures: 1. Maintain the setup from the end of the previous measurement, i.e. with the cube is at its highest temperature and the sensor (on its stand, with its shield covering it) at a distance of about 4 cm from the black surface. 2. Make a sensor reading to record the radiation level, then close the shield. Also, measure the resistance of the thermistor, to give the temperature of the cube. 3. You should aim to make as many additional measurements as you can, going down in temperature in steps of about 15 C, without disturbing the setup of the sensor relative to the cube. You can use your earlier measured temperature, for a cube power setting of 5, to get an idea of what adjustment to make to the cube power between measurements. 4. At each temperature, check that the cube s temperature has stabilised sufficiently to make the measurement, by monitoring the thermistor resistance. Take the readings of the sensor output and the thermistor resistance at the same, as closely as possible. 5. During your measurements, take the opportunity to use your measured resistance of the thermistor at room temperature to deduce the value of the room temperature according to the thermistor (needed in the analysis). Analysis: you will need to take into account the fact that the radiation sensor is itself radiating thermal energy (according to the Stefan-Boltzmann law). The voltage reading of the radiation sensor is proportional to the amount of radiation striking it minus the radiation being emitted. Mathematically, we can write that the radiation sensor voltage, V, will vary as: V ~ σ(t 4 - T det 4 ) where T is the absolute temperature of the radiation source and T det is the temperature of the detector (room temperature). You have thermistor measurements to give you each of these temperatures. Plot V against (T 4 - T det 4) and comment on how your data compare to the expected straight line. What is the y-intercept? Interpret your results in terms of the Stefan- Boltzmann law. 5 of 10

6 Week 2 Thermal Emission and Reflection/Absorption You will mainly use the lamp and the radiation sensor for these measurements, but you need the Leslie s Cube at room temperature for the first set of measurements. The lamp is used as a high temperature thermal point source. You will measure the fall-off of radiation flux with distance, and the variation with temperature of the amount of power radiated in a higher temperature regime than could be accessed with the Leslie s cube. For the measurements to examine the Stefan-Boltzmann Law, you will need to know the resistance of the lamp filament at room temperature very accurately, and that will be the first measurement (before the lamp heats up). 2.1 Experiment to examine the Inverse Square Law The inverse square law states that the radiation flux from a point source varies as one over the square of the distance from the source. You will measure the thermal radiation at various distances from the lamp to test this law. 1. With a sensitive DMM and banana plugs, measure the resistance of the lamp filament at ROOM TEMPERATURE. Accuracy is important. Read the resistance to as many digits as possible. Also find out and note the measured room temperature. 2. Connect the lamp to the power supply, but keep it switched OFF. 3. Connect a DMM to the thermopile radiation sensor. 4. Tape a metre rule to the bench top, such that the lamp is at one end of the metre stick with the centre of its filament is exactly over the zero-point of the rule. 5. Attach the sensor to the stand and adjust its height so that it is exactly the same height as the lamp s filament. 6. Align the axes of the lamp and the sensor with that of the metre rule. 7. With the lamp OFF, record the ambient radiation level in the room at four or five distances along the meter stick. Determine the average value. 8. Turn on the power supply to the lamp, and set the voltage to about 10 V. 9. If the sensor heats up, the readings would be affected. Therefore shield the sensor between readings with the reflective heat shield. 10. Record the radiation sensor readings at distances between 2.5 cm and 80 cm from the lamp. Recommended distances are: from 2.5 cm to 5.0 cm in steps of 0.5 cm; then in steps of 1 cm up to 10 cm; then 20 cm to 80 cm in steps of 20 cm. (This gives 15 data points; discuss why the spread of values is reasonable for the particular measurement being made). 11. Keep the lamp on, and the sensor set up for the following experiments. Analysis: subtract the ambient radiation level from your readings of the lamp s radiation. Plot the radiation level (in mv) against the inverse square of the distance between the sensor and the lamp filament. Do your data fall on a straight line? For a power law y x α as exemplified here by the inverse square law, a plot on a log-log graph is useful, since y = c x α means that ln y = α (ln x) + c (where c = ln c) 6 of 10

7 and the result is a straight line with a slope equal to α (in this case, 2). Comment on your results. What are sources of error in your experiment? Is the lamp a good approximation to a point source? How could you improve your measurements or your analysis? 2.2 Reflection of thermal radiation This should be a quick few measurements that you can make between the Inverse Square experiment and the final part, where you will measure the Stefan-Boltzmann variation of power with temperature, at high temperatures. You will collect results for reflection (i.e. a measure of absorption) that you can compare with the Week 1 results for emission from the Leslie cube surfaces. 1. Keep the experimental setup from the previous experiment to examine the Inverse Square law (but there is no further need for the metre rule). 2. You will use the lamp to direct thermal radiation at the surfaces of the Leslie s cube, and the sensor to record the reflected radiation. The cube does not need to be connected to the power because you will leave it unpowered, at room temperature. Take the sensor on its stand and point it at about a 45 angle to the polished surface of the cube. The distance from the sensor to the cube should be less than about 10 cm. The shield on the sensor should be covering the sensor. 3. The lamp should still be set at about 10 V from the previous experiment now, increase the voltage to about 11.5 volts. DO NOT EXCEED 12 V. 4. Position the lamp filament at a 45 degree angle to the cube surface, so as to allow radiation from the lamp to be reflected to the sensor. 5. Wait for the temperature of the filament to stabilise so that you can compare the measurements you will make with different surfaces. 6. When the temperature of the lamp Remove the shield from the sensor and quickly record the sensor reading. 7. Repeat this experiment under identical conditions for the three other surfaces of the cube, and finally repeat the polished surface to check for consistency. Keep the lamp powered on for the next experiment. Analysis: construct a table showing how reflectivity varies with the type of cube surface. Normalise your relative measurements of the reflectivity to a value of unity for the polished surface (as your closest approximation to an ideal reflector) in order to be able to quote absolute values and compare with your data for emissivity. Explain how and why emissivity and reflectivity are related. 2.3 Stefan-Boltzman Law at High Temperatures You will measure the thermal radiation from the lamp at varying high temperatures to examine the Stefan-Boltzmann law. In order to determine the temperature of the lamp, you will measure the electrical resistance of its filament. As its temperature increases, so does its resistance. You require just the lamp and the sensor and the two DMMs for this measurement. 7 of 10

8 1. Make a note of the measurement of the resistance of the lamp filament at ROOM TEMPERATURE that you made at the beginning of Keep the lamp set up and powered to about 11.5 V as in the previous experiment. 3. The thermopile radiation sensor should already be connected to its DMM and mounted on its stand. Position its end to a distance of 6 cm from the lamp filament. 4. Check that the height of the sensor is at the same level as the filament. 5. Make your first measurement: record the radiation flux at this temperature of the filament. Try to make the measurement quickly (open the shutter for a short time) so as not to heat up the sensor. 6. Measure the resistance of the lamp filament at the present temperature by using the DMM to measure voltageand also noting down the current from the power supply. You can convert the deduced resistance to a measurement of the filament temperature using your room temperature measurement and the data for tungsten included in Annex I. Details are given below. You can also use the measured current and resistance (or voltage) to calculate the power input into the lamp. 7. You should record the radiation flux for a range of temperature values of the filament, coming down from the maximum at which you began. Choose temperature values according to the time available and knowing that you plan to verify the Stefan-Boltzmann equation. At each temperature, record the values of the radiation flux, the filament resistance and the current from the power supply while the temperature is sufficiently steady at a constant value during the measurements. 8. It is by comparing the results from different temperatures that you can verify the Stefan-Boltzmann equation, so it is important to measure for several temperatures. Temperature of the filament: The thermistor calibration data in Annex I use the ratio of the resistance at temperature T to the resistance at 300K, in order to deduce the value of T. You have a reference measurement at room temperature, but you need to convert it to a reference measurement at 300K in order to use the thermistor data accurately. By linear interpolation using the data in Annex I, you can deduce the ratio between the room temperature resistance and the resistance at 300K, and compute the latter quantity (equivalent to a correction of up to a few percent). The tabulated values in Annex I have been put into a spreadsheet called tungsten-resistivity.xls and downloadable from The spreadsheet includes some code for calculating this correction to your measured room temperature resistance. With your computed 300K resistance, you are then ready to calculate temperature by using the resistance R(T) measured at temperature T, expressed as the ratio R(T)/R(300K). The instructions for using either a fit to the data, or a quadratic interpolation procedure, to convert any measured ratio of resistance into temperature are given in the spreadsheet, or you can calculate the interpolations without the spreadsheet. 8 of 10

9 Analysis: 1. Prepare a log-log plot of radiation (measured in mv) against absolute temperature (K). (See discussion of log-log plots under 2.1). Perform a linear regression analysis on your data to determine the power of the dependence. 2. Does radiation vary with the fourth power of temperature? Does the dependence hold better at higher or lower temperatures? What are the main sources of error?is it valid to ignore the background at these higher temperatures (compared to experiment 1.3)? The glass in the lamp absorbs some infrared radiation. Do you think this has a significant effect? 3. Is the lamp filament a black body? 4. Use the Stefan-Boltzmann law to calculate the power of thermal radiation per unit area, R, in W/m 2 produced by the lamp filament at a few different temperatures. (You will need to estimate a value for the emissivity.) How does this value compare to the energy input into the lamp (equal to IV) divided by the surface area of the filament? (You will need to estimate the surface area of the filament.) Comment on the values obtained. This script is an update of the experiment developed by J.L. Keddie and is adapted from the script by MS and JLK dated 22 October W.N. Catford, September (end) 9 of 10

10 These data are also available electronically in the file tungsten-resistivity.xls at 10 of 10

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