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∞ ∞ ∞ IT 2V • Energy density per interval U = ω f (ω ,T )dk x dk ydkz Mω 8π 3 ∫∫∫ h , − ∞− ∞− ∞ n ∞ u (ω ) = hω f (ω ,e T )D(ω) 2V 2 o = ω f (ω ,T )4 πk dk 3 h t 3 ∫ h hω C 1 l 8π 0 = a Planck’s law π 2 c 3 ⎛ ⎞ ∞ 2 g hω m 2V ω ω n exp⎜ r ⎟ −1 ⎛ ⎞ ⎛ ⎞ a e⎜ k T ⎟ = 3 hω f (ω ,T )4 π ⎜ ⎟ d ⎜ ⎟ ⎝ B ⎠ 8π ∫ ⎝ c ⎠ ⎝ c ⎠ G h n 0 • Intensity:/T energyio flux per unit ∞ 2 © r s U ω t lsolida angler = hω f (ω , T ) 2 3 dω V ∫ c h o e 0 π g v i S 3 ∞ r dAnp cu(ω) ω 1 y t o I ()ω = = h = ωf (ω , T )D(ω)d ω p c 3 2 ∫ h o e C 4π 4π c ⎛ hω ⎞ 0 ir exp⎜ ⎟ −1 C y ⎜ k T ⎟ ∞ D g ⎝ B ⎠ 7 7 er = ∫ u ()ω d9ω 9 Solid Angle Per unit wavelength interval 0 9 9 En . . l dA I(ω)d ω 4π c 1 2 2 a dΩ = p I ()λ = = h r ic R2 d λ λ5 ⎛ 2π c ⎞ D(ω)-densityo of statestr per exp⎜ h ⎟ −1 unit volumeF per cunit whole space ⎜ k Tλ ⎟ e ⎝ B ⎠ angular frequencyEl interval 4π Planck’s law –WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT Thermal Radiaton: Planck’s Law IT
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2.997 Direct Solar/Thermal to Electrical Energy Conversion Technologies Fall 2009
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