## PHYSICS 320 LABORATORY  Blackbody Radiation

Object

• To investigate the properties of blackbody radiation.

Apparatus

IR-12K infrared emitter with reflector and thermocouple, regulated DC power supply, radiometer, Boston Electronics IR563 cavity blackbody source, and Oriel MIR8025 FTIR spectrometer with computer.

Theory

At the turn of the 20th century, two relationships were known to govern the temperature dependence of blackbody radiation: the Stefan-Boltzmann law for the integrated intensity and Wien's displacement law for the peak wavelength.  Stefan discovered that the power (P) or rate at which an object radiates its energy is proportional to its temperature (T) raised to the fourth power: P = s AeT4, where P is in MKS units joules/second (watts), s is a constant equal to 5.6696x10-8 W/m2× K4, A is the surface area of the object in square meters, e is the emissivity constant, and T is the temperature measured in Kelvin. The emissivity, which can vary between zero and one depending on the properties of the object, is a measure of how "good" a radiator an object is.  The ideal radiator, e = 1, is also an ideal absorber. Such an object is referred to as a "black body". In contrast, an emissivity of zero would correspond to an object which neither absorbs nor radiates energy.  Wien demonstrated a reciprocal relationship between the peak wavelength and temperature: lmaxT = 2.898x10-3 m× K.  Planck found that both of these results could be explained by the Planck radiation law (eq. 3.23 in the text), whose derivation relied on the quantization of energy.  We will explore these relationships in this lab.

The electrical energy delivered to the infrared emitter is predominately radiated as electromagnetic energy by the filament.  By comparing the measured radiation from the emitter and temperature of the filament, the performance of the filament as a blackbody and its compliance with these laws can be tested.

### I. Stefan-Boltzmann Law

Procedure

1.  Before you begin your experiment with the infrared emitter, you should turn on the IR563 blackbody source and set the temperature to 500 C.  This source takes over half an hour to warm up to this temperature, so you need to get it started first.  The IR563 is located in the semiconductor spectroscopy lab (B049).  To set the temperature, use the up/down arrow keys to select the setpoint, use the right arrow key to edit the temperature, and use the up/down arrow keys to obtain the desired temperature.  Use the left arrow key to enter this temperature and return to the main menu.

2.  Now go to the optics lab (B018) to conduct the Stefan-Boltzmann experiment.  Measure the diameter of the aluminum IR-12K reflector and then place the infrared emitter directly in front of and close to (less than 1 cm away from) the radiometer aperture.  The reflector should be facing and aligned with the radiometer aperture. Connect the power supply to the terminals of the emitter.  Before turning on the supply, turn the current knobs completely clockwise and the the voltage knobs completely counter-clockwise.  This puts the supply in voltage limited mode.

3.  Turn on the power supply, thermocouple, and radiometer.  Darken the room and make sure no radiating objects are in the field of the radiometer.  Do this by setting the radiometer on the 1 W/m2 range.  With the shutter closed, adjust the Zero.  Open the shutter and note the reading.  If it is over 0.2W/m2, find the source of radiation and remove it.  Now adjust the Zero, with the shutter open.

4.  Adjust the voltage to read 1.5V.  Note:  Do not let the voltage across the filament exceed the emitter's maximum ratings.  For the IR-12K, do not go over 6.5V!

5.  Wait for the thermocouple to reach a nearly constant temperature.  Then record the voltage, temperature, and open the shutter to read the radiometer signal.  Note: when you change scales on the radiometer, you may need to re-zero the instrument.  Adjust the radiometer scale as needed and always re-zero when changing scales (you should zero with the shutter closed on the higher scales).

6.  Increase the voltage 0.5V and repeat step #5.  Continue recording the temperature and radiometer measurements every 0.5V up to 6V.

Analysis and Questions

If we assume that the reflector collects and collimates all of the radiation from the IR-12K emitter, then the intensity of the reflected light will be equal to the power emitted divided by the area of the reflector.  As describe in the theory above, the power emitted is given by P = s AeT4, where A is the area of the emitter (3.5mm x 3.5mm).  Hence, the measured intensity should be given by I = s AemittereT4 /Areflector.  Plot the log of the measured intensity I as a function of log(T).  Is this relationship linear over the entire range of measurements?  If not, discuss reasons for non-linear behavior.  What is the slope and y-intercept of the plot?  What should each be if the filament is an ideal blackbody (e =1)?  Compute the percent error for each.

We will use the Fourier Transform Infrared (FTIR) spectrometer in the Semiconductor Spectroscopy Lab to observe how the blackbody spectrum changes with temperature. Please CLICK HERE for an introduction to FTIR spectroscopy.  The radiation from the IR563 cavity blackbody source is reflected off of a gold mirror and directed into the FTIR spectrometer.  For this experiment, it is critical to realize that the sensitivity of the HgCdZnTe detector mounted on the spectrometer is highly wavelength dependent, so we will need to correct for this detector bias in our analysis.  In addition, the HgCdZnTe is only sensitive to radiation with wavelengths between ~2 and 6 micrometers (2000 – 6000 nm) so if the blackbody spectrum extends beyond this range, it will be severely suppressed or unobservable in this measurement.

Procedure

1. If you set the IR563 to 500 C at the beginning of lab, it should now be stable at this temperature.  Confirm that this is the case by noting the blackbody temperature on the controller.

2. Start by opening the FTIR software that controls the FTIR spectrometer (you should see an FTIR link on the desktop).  If the software fails to open and freezes, restart the FTIR spectrometer (toggle the FTIR power switch, which has a circle and vertical line on it), then restart the FTIR software.  If the computer is unresponsive, you will need to restart the computer.  Be patient, and repeat if necessary - eventually you will get it working!   When the software is open and running, select continuous to begin acquiring spectra. The top panel shows the signal as a function of mirror position (this representation is called an interferogram) and the bottom panel shows the Fourier transform of this signal, which is the spectrum of the incident light (shown in units of cm-1).  If the interferogram is not centered at zero, you need center it.  Click single to acquire a single spectrum, then click stop.  Right-click on the FTS_AX container window and click the Enable ZPD Adjust box.  Click OK and then click single on the main window a couple of times to obtain a new spectrum.  The interferogram should now be centered.  If it is not, repeat the centering procedure until it is!

3. Record the cavity temperature.  Set the coadd # to 100 and select coadd to average 100 measurements. When data acquisition is complete, the coadd # will turn red. Push the lower SPV (spectral viewer) button to open a new window where you can edit the x-axis. Select um (micrometers) and set the lower and upper limits of the x-axis to 1 and 7 micrometers (the approximate range of the detector). This operation will show the spectrum of the radiation as a function of wavelength in micrometers. Finally, push the Save Data button to save the spectrum. Give the file a txt extension so that it will be recognized as a data file by Origin. A single data file can be read into Origin using the Import ASCII function, and multiple spectra can be opened simultaneously using the Import Multiple ASCII function.

4. Set the temperature on the IR563 to 600 C and wait for the cavity to reach this temperature (this will take about 15 minutes).  Repeat Step #3 at this temperature and in 100 degree increments up to 900 C.  Note: each temperature change will take about 15 minutes, so you should work on your analysis of Part I between measurements.

6. When you are finished acquiring spectra, turn the IR563 off, exit the FTIR software, and shutdown the computer.

Analysis and Questions

As noted in the introduction to Part II, we need to correct our measured spectra for the detector bias.  Here's how we'll do that:  We start by assuming that the 800 C spectrum produced by the blackbody source is a perfect blackbody spectrum.  In general, this kind of assumption can be dangerous, but the IR563 is designed to serve as a blackbody reference source, meaning it should closely mimic an ideal blackbody emitter.  With this assumption, we can generate a transfer function that corrects our intensity measurement at each wavelength.  The transfer function is the ratio of the true intensity and the measured intensity at each wavelength.  Hence, when a measured spectrum is multiplied by the transfer function, the true spectrum is obtained.

2.   Now create new worksheets for each of the other temperatures, insert the data, and add three columns.  In each worksheet, copy the transfer function from part #1 into the first additional column and multiply your measured spectrum by the transfer function in the second column.  This column is your corrected spectrum.  In the third new column, calculate the theoretical spectrum for the given temperature.  For each temperature, plot the corrected and theoretical spectra together and compare them.

3.  Now plot all of your corrected experimental spectra on a single graph in Origin to see how the spectrum changes with temperature (label each spectrum with the temperature).  Do your spectra have the expected temperature dependence?  Explain.

### III. Wien's Displacement Law

1.  Use the Screen Reader (cross-hairs) tool to measure the peak wavelength of your corrected spectra at each temperature.

2.  Plot the peak wavelength against the reciprocal of the temperature and compare your slope with the Wien's Law prediction (compute the percent error).  Now use Wien's Law to calculate the expected peak position at each temperature and add these results to your plot.  How do your measurements compare with Wien's prediction?

FOR FURTHER THOUGHT

The Stefan-Boltzmann, Wien Displacement, and Planck radiation laws are exactly applicable for perfect blackbodies.  Do your results indicate that the emitters you have studied behave as ideal blackbodies?  Discuss how the instrumentation limits your ability to test some of the blackbody radiation laws.