12_-_Radiative_Transfer

12_-_Radiative_Transfer - 12 – Radiative Transfer 2 The...

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Unformatted text preview: 12 – Radiative Transfer 2 The Plan • Review how the heat gets out of the Sun in our toy model • Beer’s Law • One level higher sophistication • More dimensions, a whole new can of worms 3 One-Dimensional Radiative Transfer T+ ∆ T T A ∆ L τ = ∆ L / n σ = 1 This condition puts the lower box with the upper one. ( ) ( ) 4 4 3 3 3 Q is the net upward heat flux Expand the first term to 4 4 (1) Δ is the distance for 1 Δ (2) Combining 1 and 2 1 4 Q A T T T Q A T T dT Q A T l dl l l dT Q A T dl σ σ σ κ ρ σ κ ρ Δ Δ = + Δ- Δ = Δ Δ = Δ = Δ = 4 Luminosity 3 2 3 4 2 3 4 3 1 4 1 L R 1 L R dT Q A T dl T T R GM T KR GM M KR R R G L M K σ κ ρ σ κ ρ μ μ σ κ σ μ κ Δ = ≈ = ≈ ≈ κ = 0.39 cm 2 /g 5 I I-dI Opacity & Beer’s Law 1 or ln( / ) or = mean free path 1 when 1 then = o lx o o dI n dx dx I I I lx I I e l n l I lx I e σ ρ κ σ ρ κ-- = -- = - = = = This assumes that the material (n σ or ρκ ) is cold and therefore doesn’t emit. ) is cold and therefore doesn’t emit....
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This note was uploaded on 04/05/2009 for the course ASTRO 3332 taught by Professor Houck,j during the Spring '09 term at Cornell.

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12_-_Radiative_Transfer - 12 – Radiative Transfer 2 The...

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