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Assuming that the spectrum of blackbody radiation is given by Planck's law (2.1), prove the following. (a) Show that the total energy density of blackbody at temperature T is given by U=aB T^4 where aB=(8 πκB^4)/(c^3 h^3) ∫0^∞ (x^3 d x)/(e^x-1) (Note: this integral can be evaluated exactly and can be shown to be equal to .π^4 / 15 .) (b) Show that the total energy radiated in unit time from unit area on the surface of a blackbody is given by σT^4, where σ=(c aB)/(4) (c) Show that the frequency v
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