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Homework 4 Solutions

It can be defined by the distribution function fe

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Unformatted text preview: temperature, Tc, assuming an ideal, fully ionized gas with X = 0.00, Y = 0.36, Z = 0.64 (Note: this is different than the atmosphere!). Is this sufficient for proton fusion? ρ0 = (3/4π) x (2x1030 kg)/(7x108 m)3 = 1392 kg/m3 (just above water) Pc = 0.119 x 6.67x10 ­11 m3/kg ­s2 x (2x1030 kg)2/(7x108 m)4 = 1.3x1014 N/m2 = 1.3x109 bar For an ionized gas, 1/µ = 2X + 0.75Y + <1+Z/A>Z = 2(0) + 0.75(0.36) + 0.5(0.64) = 0.59 P= ρkT P µmH ⇒T = µmH ρk = (1.3x1014 N/m2 x 1.67x10 ­27 kg)/(0.59 x 1392 kg/m3 x 1.38x10 ­23 J/K) = 2x107 K Definitely hot enough for fusion! (3) Degenerate Matter [40 pt] Degenerate matter is defined as fermionic matter that has filled all of its available quantum states. Electron ­degenerate gas characterizes the interiors of the lowest mass stars, brown dwarfs, planets and white dwarfs. It can be defined by the distribution function: f(E) = constant for E ≤ εF = 0 for E > εF where εF is the Fermi energy (a) [10 pts] Show that, in the case of a nonrelativistic electron gas, the momentum volume element can be written in terms of energy: d3 p =...
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