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Blackbody Radiation
Experiment |
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The first crisis in classical physics was
the ultraviolet divergence of the Blackbody Spectrum. A sequence of well-accepted
assumptions and straightforward manipulations led to a preposterous result: warm objects
radiate an infinite amount of ultraviolet energy. |
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Max Planck put forth, as an ad hoc hypothesis, that the radiated energy was quantized, and
he showed that this gave the correct radiation spectrum. As Einstein, Bohr, and others
subsequently demonstrated, this computational device had important physical reality and
could explain several other mysteries that classical physics could not.The
Stefan-Boltzmann law is a corollary of the Planck distribution with many important
applications. In this lab, you will verify the Stefan-Boltzmann law using nothing more
than a light bulb and two multimeters. |
 (This
picture is on p. 66 of Rohlf.) |
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Pre-Lab questions |
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- What voltage does a light bulb operate at, here in these United States? What current
does a 25W light bulb draw? What is the filament temperature at that power?
We usually write the equation for resistivity and resistance as
Now, we could use this: we can measure the length of the filament (you'll need this
value anyway; use the broken bulb in the lab) and we can estimate its area using the SEM
micrograph below. Unfortunately, the uncertainty will be catastrophically high.
Anyway, there's a better method: measure the resistance at room temperature!
We know the resistivity at room temperature (You will need a table of resistivity
vs. temperature for tungsten); the geometrical factor is constant and we can solve for it:
Thus the equation we really want is
- Suppose the resistance of the bulb is 45 ohms at room temperature. You can find the
resistivity at any other temperature, given the voltage and current. What is the
resistivity at room temperature (0 V and 0 mA)? What is the resistivity at 25V and 90 mA?
- Use the resistivity at 25V and 90 mA to find the temperature of the filament at that
current.
- Briefly outline the procedure you will follow, including the ranges and variables you
will record.
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 Rohlf, Modern Physics, p.70 |
It would be nice if we could verify the Planck
distribution directly. It is possible, but not easy: even verifying the Wien law (for the
peak wavelength) can be problematic. These questions are simply to point out why we do not
measure the Planck distribution directly.
- What bandwidth must you scan to determine the shape of the spectrum over the range 300
– 4000 K? (The graphs at the right give the blackbody distribution for three
different temperatures). What range must you scan to identify the peaks? Comment.
- A good visible spectrometer, for instance the H2D2 monochromator, will scan from 200 to
800 nm. What temperatures do we need to examine to get interesting results? Comment.
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Procedure notes |
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The blackbody that you will use is the tungsten filament
of a normal unfrosted 25W aquarium light bulb. The procedure is simply to measure the
current as you vary the voltage across the light bulb. With this data alone, you can find
the power radiated by the filament and its temperature. Before you start, while the
filament is still at room temperature, remember to measure the resistance across the
filament. You will also need the length of the filament. We have a broken light bulb that
your TA can get out for you. Needless to say, it should be handled very carefully. We also
have an optical pyrometer – which exploits the same phenomenon you are studying to
determine the temperature visually – that you may play with.
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Points to consider during your analysis |
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The data collection for this lab is
straightforward, but the analysis should be in-depth, and will require a lot of effort.
Does the filament behave as a blackbody? How can we model any departures from the ideal?
What approximations did you make? (Any time you make an approximation, you should give an
estimate or limit of how it affects your result). |
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| You will need to find a table of properties for
tungsten. The table in the CRC will be enough to complete the pre-lab but is not suitable
for your analysis. The Engineering library has books entirely devote to tungsten or to
light bulbs; find one of them. You will need to know the geometry and size of the
filament. The filament is in fact an incredibly fine, regular spiral. (One of the
interesting things about this lab is its interplay with engineering. How do they make such
an incredibly fine, regular spiral? What is the actual material of the filament? Why?). An
SEM micrograph of our actual filament, courtesy of Dr. DeLouzanne’s lab, appears at
the right. The reference line is 100 microns long. (We have a full size version of the image, useful for your analysis).
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References |
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 | Preston, D.W. and Dietz, E.R., Art of Experimental Physics (Wiley 1991), p 152.
Advanced for this class but often contains useful information. |
| Brehm, J.J. and W.J. Mullin. Introduction to the Structure of Matter (Wiley
1989). |
| Dryzek, J. and K. Ruebenbauer. Am. J. Phys. 60 (1992), p. 251. |
| Kittel, J. C. and H. Kroemer. Thermal Physics 2nd Edition (Freeman 1980). |
| Pippard, A. B. elements of Classical Thermodynamics (Cambridge U. Press, 1957). |
| Reif, F. Fundamentals of Statistical and Thermal Physics (McGraw-Hill 1965). |
| Zemansky, M. W. Heat and Thermodynamics, 4th Edition. (McGraw-Hill 1957). |
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