[題目] Statistical Mechanics

看板Physics作者teddy0819 (在一步就是天堂地獄)時間13年前 (2013/02/10 22:27)推噓5(5推 0噓 12→)

留言17則, 5人參與討論串1/1

[領域] Statistical Mechanics (題目相關領域) [來源] 教授突發奇想 (課本習題、考古題、參考書...) [題目] A solution of DNA molecules at fixed temperature, T, and unknown molecular weight is placed in a planar centrifuge. The centrifuge rotates at a fixed angular frequency ω. Because of the rotation of the centrifuge, the DNA density, ρ(r) in the centrifuge is a function of distance r from the rotation axis. A) Find the molecular weight defined as μ = NA m (m is the mass per molecule and NA is Avogadro’s number) as a function of {T, ω , r1, r2, ρ( r1 ), ρ( r2 )}, where ρ( r1 ), ρ( r2 ) are the DNA density at two points, r1 and r2. B) What assumptions/ approximations did you make on this ensemble of DNA molecules? Hint: Each DNA molecule will rotate at the same angular frequency ω. Assume the DNA molecules follow a classical MB distribution. [瓶頸] (寫寫自己的想法，方便大家為你解答) 題目其實只是想要考假設DNA follow Boltzman distribution. 在離心機中兩點密度的差異是怎麼跟分子量, 角速度有關我的問題是在老師的解答中他只有計算因離心加速度造成的位能 F=-m*r*w^2/2 (向心力?!) U=Integrate[F*dr,{r,r1,r2}]=-m(r2^2-r1^2)*w^2/2 然後利用兩點的位能差異帶入 Exp[-U/kT] 想法一: 可是我一開始覺得在這兩點的能量應該是位能加上動能可是這樣總能量就變成 0 了想法二: 如果我們把離心機想像成太空中的太空站利用旋轉離心力假想成重力那麼裡面的人真的可以分辨出重力和離心力的差異嗎? 地球上旋轉太空站中離心機重力離心加速度造成離心力地板的正向力太空站的正向力 / DNA分子彼此推力 -GMm/r1-(-GMm/r2) -m(r2^2-r1^2)*w^2/2 -m(r2^2-r1^2)*w^2/2 麻煩大家幫我想一下或者有沒有強者出來解釋離心機根本沒辦法測分子量... -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 98.242.70.169

→

caseypie

02/10 23:13, , 1^F

02/10 23:13, 1^F

→

teddy0819

02/11 00:54, , 2^F

02/11 00:54, 2^F

→

teddy0819

02/11 00:57, , 3^F

02/11 00:57, 3^F