14-Stellar Interiors - Physics

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$1 Ch. 22 â Reflection and Refraction of Light 22.1 The ... - Physics$

EQUATION OF STATE FOR PERFECT GAS WITH ABUNDANCES X, Y, ZIf µ ≡ m m Hwhere:then P g= ρkTµm Hm = µm H=P g= nkT = ρkTmwhere m =∑mass of sample# free particles = mass densityparticle number density =i∑im in iin i∑∑im in in i=∑zn z∑iweight of atom A zm H( )n z ( 1+ η z )A z = atomic weight of element of atomic number zη z = # of electrons contributed per atom of element z (1+ η is # of electrons plus the nucleus).So,1µm H=∑z∑zn z ( 1+ η z )n zA zm HLet the fractional mass density of element z be X z= n z A z m Hρ,=∑zn z ( 1+ η z )ρ1µm H=∑zX zρA zm Hρ( 1+ η z )or 1 µ =X∑zzA z( 1+ η z )8
Let X = mass fraction of HY = mass fraction of HeZ = mass fraction of everything else combined = 1 - X - YVALUES OF X z ( 1+ η z )= 1 A zµTYPE OF GAS H He “Heavies”FULLYX 1+ 1 Y 1+ 2IONIZED= 2X= 3Y 4 Z A z2( )1NEUTRAL X ( 1+ 0)= X1FULLYIONIZED(electrons only)( )1X 1= X( )4Y ( 1+ 0)= Y 4 4Y ( 2)= Y 4 2roughly( )( )A z= Z 2Z 1+ 0A z(>> 1) ≈ 0 usually( )A z= Z 2Z A z2µ FIG=µ NG=µ e FIG− E=12X + 3 Y + 1 Z = 46X + Y + 24 212 ≤ µ FIG ≤ 21 ⎛X + 1 Y unless H is all H 2 → 11X + 1 Y = 2 ⎞X + 1 Y4 ⎝⎜2 4 2 ⎠⎟1X + 1 2 Y + 1 2Z=1− X −Y=2X + 1 1 ≤ µ FIG ≤ 2Where we have used the fact that X +Y + Z =1 to simplify.So, P FIG=NGFIG−EρkTµ FIGNGFIG−Em HEquation of State (Ideal Gas Law)Here, all the compositional effects are included in oneparameter - µ. This will be our Equation of State for mostof the models we will be considering.9
Page 1: Our goal is to derive models of the
Page 4 and 5: GAS PRESSURE - Ideal Gas LawFor a m
Page 6: RELATIVISATIC DEGENERACYP = 8π3h 3
Page 11: Equation of Hydrostatic Equilibrium

14-Stellar Interiors - Physics

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