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Unformatted text preview: Answers Theoretical Problem No. 3 Why are stars so large? 1) A first, classic estimate of the temperature at the center of the stars . 1a We equate the initial kinetic energy of the two protons to the electric potential energy at the distance of closest approach: c rms p d q v m 2 2 4 ) 2 1 ( 2 ; and since 2 2 1 2 3 rms p c v m T k , we obtain 9 2 10 5 . 5 12 k d q T c c K 1.5 2) Finding that the previous temperature estimate is wrong. 2a Since we have that 2 r M G r P r r , making the assumptions given above, we obtain that: R M G P c c . Now, the pressure of an ideal gas is p c c c m T k P 2 , where k is Boltzmanns constant, c T is the central temperature of the star, and p m is the proton mass. The factor of 2 in the previous equation appears because we have two particles (one proton and one electron) per proton mass and that both contribute equally to the pressure. Equating the two previous equations, we finally obtain that: pressure....
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