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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 κρ σ κρ 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 κρ σ κρ μ μ σ κ σ μ κ Δ = = κ = 0.39 cm 2 /g

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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 ρκ σ ρκ - - = - - = - = = = This assumes that the material (n σ or ρκ ) is cold and therefore doesn’t emit. That is a bad assumption inside a Star! It’s fine for light going through a block of glass.
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