Notes2C - Blackbody Radiation Theory I. History of...

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Unformatted text preview: Blackbody Radiation Theory I. History of Blackbody Radiation A. What is a blackbody? A blackbody is an object that absorbs all radiation that is incident upon it. When radiation falls upon an object, some of the radiation may be absorbed, reflected, or transmitted. Most objects that appear black are poor reflectors of optical radiation but they are not blackbodies since they still reflect some radiation. A good approximation of a blackbody is a cavity. In the cube below, the radiation entering the cavity is continually reflected around the cavity. Thus, the cavity acts like a minnow trap. It is easy for the light to enter but not exit. This is why a cavity always looks black at room temperature regardless of the color of the inside of the cavity. Front View Side View of Cavity B. Emission Spectra When a body is at thermal equilibrium, it must re-emit all the radiation that it absorbs. Blackbodies are interesting because the color of their emission depends only on their temperature and not upon their shape or composition. Thus, their emission spectrum can be used as a pyrometer (temperature gauge). The processing of steel became of great importance during the industrial revolution of the late 1800's. Thus, blackbody pyrometers were extremely useful tools for determining the temperature of steel ovens and other processing equipment. Although light bulb filaments and many other regular objects are not true black bodies, their temperature can be approximated from their emission spectra by assuming that the object is a blackbody. Thus, blacksmith's used the color of the heated steel to determine the processing of steel when making buggy springs, horse shoes etc. C. Experimental Emission Spectra We can see from the graph that the maximum emission frequency shifts to higher frequency as the temperature is raised . We can also see that the total energy emitted (area under curve) increases at increasing temperature . D. Stephan-Boltzman Equation The power density emitted by a blackbody is proportional to the 4th power of its temperature. 4 T A P = 2 8 K/m W 10 x 5.670 - = E. Wien's Displacement Law Blackbody Emission Frequency Energy Densi Higher T The peak of the blackbody emission spectra is inversely proportional to the temperature. T 2.898 K mm max = F. Ultra-violet Catastrophe The theory of blackbody radiation would appear to be a straight forward application of classical electromagnitism and classical physics. Although classical physics produced a workable theory at low frequency (long wavelengths), it failed at high frequencies (short wavelengths). Since the theory predicted an infinite amount of energy radiated at short wavelengths, it was called the "ultra-violet catastrophe." II. Density of States For An E&M Wave In A Blackbody Radiator Since the emission spectrum of a blackbody radiator is independent of the shape of the blackbody, we are free to choose the simplest shape possible in deriving the density of state function. Thus, we choose a cube with sides of length L....
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Notes2C - Blackbody Radiation Theory I. History of...

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