理想气体
Download
1 / 10

理想气体 压强公式 的量纲分析 - PowerPoint PPT Presentation

  • 167 Views
  • Uploaded on

理想气体 压强公式 的量纲分析. 设气体的压强为 p ， 分子数密度为 n ； 分子的质量为 m ， 平均速率为 v ， 由于气体压强是一种动力学效应，所以 p 应与 n 、 m 、 v 有关，. 它们之间的关系可以表示为 p  n  m  v  式中的  、  、  均为待定常数。. dim n = L -3 ( 曾用[ n ] 表示 dim n )， dim m = M， dim v = LT -1 ， dim p = (dim F )/L 2 = L -1 MT -2.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' 理想气体 压强公式 的量纲分析' - libba


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
理想气体压强公式的量纲分析

P n m v p n m v
设气体的压强为 p，分子数密度为n；分子的质量为m，平均速率为v，由于气体压强是一种动力学效应，所以p应与 n、m、v有关，

P n m v
它们之间的关系可以表示为p  nmv式中的、、均为待定常数。

Dim n l 3 n dim n dim m m dim v lt 1 dim p dim f l 2 l 1 mt 2
dimn = L-3(曾用[n]表示dimn)，dimm = M，dimv = LT-1，dimp = (dimF)/L2 = L-1MT-2.

Dim p dim n m v dim n dim m dim v l 3 m lt 1 l 3 m t
dimp = dim(nmv) =(dimn)(dimm)(dimv) = (L-3)M(LT-1) = L -3MT-.

1 2 1 3 1 p nmv 2
 = 1， = 2， = (1+)/3 = 1.故由量纲分析得： p  nmv2.

Dim n l 3 dim m m dim v lt 1 dim p dim f l 2 l 1 mt 2
[另一解法] dimn = L-3，dimm = M，dimv = LT-1， dimp = (dimF)/L2 = L-1MT-2

Dim p l 1 mt 2 l 2 3 mt 2 l 3 m l 2 t 2 dim n dim m dim v 2 dim nmv 2 p nmv 2
dimp = L-1MT-2= L2-3MT-2 = (L-3)(M)(L2T-2) =(dimn)(dimm)[dim(v2)] = dim(nmv2).故由量纲分析得：p  nmv2.

A p a nmv 2 a 8
设A为一无量纲量，则有压强公式：p = Anmv2.可以证明在此压强公式中的A = /8.

经验表明：由量纲分析所得结果中的无量纲量A的数量级往往为1.

ad