answers-04-21-2011

answers-04-21-2011 - Answers to Physics 176 One-Minute...

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Unformatted text preview: Answers to Physics 176 One-Minute Questionnaires April 4 through April 21, 2011 How is that we can begin looking for energy spectra inside a black box (quite literally) and then apply that to energy emissions of objects like stars, plants, etc which aren’t enclosed in a box? Or, put another way, why is the Planck spectrum applicable to many examples of radiation not inside the conditions by which it was derived? The answer is given briefly (and somewhat incompletely) on pages 302-303 of Schroeder, which I did not have time to mention in the last lecture. It was Kirchhoff (the same Kirchhoff of the Kirchhoff laws you learned about in your intro physics course regarding laws for electrical circuits) in 1859 who argued that a black (i.e., perfectly absorbing) surface in equilibrium with a photon gas (say the wall lining a box containing the gas) must radiate away exactly as much radiation per second and per unit area, with the same Planck spectrum, as the wall receives in order for the wall and gas to be in equilibrium. But the radiation of light from the wall does not depend on the presence of the photon gas itself and so one concludes that the surface of an opaque object that is in equilibrium with temperature T must itself produce (radiate away) light that is consistent with being in equilibrium, i.e. light that satisfies the Planck spectrum and Stefan’s law of radiation, Eq. (7.98) on page 303 of Schroeder. The argument depends on the existence of solid filters of different kinds that can pass light only over a small range of frequencies or that only let linearly or circularly polarized light through. Such filters are readily constructed for light in the visual range, but only exist in principle for all bands of wavelengths. Refinements of Kirchhoff’s argument also leads to the conclusion that an equilibrium photon gas must be homogeneous (have the same energy density U/V everywhere in space), isotropic (photons move in all possible directions with equal likelihood) and unpolarized. For example, if the light in an equilibrium photon gas were partially polarized, you could place a linear polarizing filter in the gas, which would not affect thermal equilibrium (if the filter has the same temperature as the gas) but would cause a temperature difference to arise by letting some light through and blocking other light, contrary to the assumption that the gas is in equilibrium and so that the temperature is everywhere the same. The Wikipedia article “Kirchhoff’s law of thermal radiation” gives more information, and the book by F. Reif on the 176 reserve in the library has 1 a particularly clear (although detailed) discussion of the Kirchhoff radiation law....
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answers-04-21-2011 - Answers to Physics 176 One-Minute...

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