# lec21 - Lecture 21 Energy Generation in Stars Purdue...

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Unformatted text preview: Lecture 21 Energy Generation in Stars Purdue University, Astronomy 364 1 Lecture 21 Convective Transport Lecture 21 Purdue University, Astronomy 364 2 P b b P b +dP b b +d b P P+dP +d r r+dr A blob stays in hydrostatic equilibrium with the surrounding as it rises up, P b = P , P b + dP b = P + dP Convection occurs, when b +d b < +d or d b <d , if b = The blob expands adiabatically, PV γ ∝ P ρ γ = const Ideal Gas Lecture 21 Purdue University, Astronomy 364 3 The condition for convection requires ρ γ P dP dr dr = d ρ b ≤ d ρ = d ρ dr dr ⇒ 1 γ P dP dr ≤ 1 ρ d ρ dr ln ρ b = 1 γ ln P b + const ⇒ d ρ b ρ b = 1 γ dP b P b ∴ d ρ b = ρ b γ dP b P b = ρ γ dP P = ρ γ P dP dr dr For ideal gas, P = ρ μ m p kT ⇒ dP dr = ρ k μ m p dT dr + kT μ m p d ρ dr = P T dT dr + P ρ d ρ dr Eq. of Convective Transport Lecture 21 Purdue University, Astronomy 364 4 1 ρ d ρ dr = 1 P dP dr − 1 T dT dr ⇒ 1 γ P dP dr ≤ 1 P dP dr − 1 T dT dr ∴ dT dr ≤ 1 − 1 γ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ T P dP dr Convective instability: Maximum achievable temperature gradient: dT dr = 1 − 1 γ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ T ( r ) P ( r ) dP dr Radiative and Convective Zones Lecture 21 Purdue University, Astronomy 364 5 Equation of Energy Generation...
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lec21 - Lecture 21 Energy Generation in Stars Purdue...

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