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理想气体 压强公式 的量纲分析

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.

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理想气体 压强公式 的量纲分析

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  1. 理想气体压强公式的量纲分析

  2. 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，

  3. 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。

  4. dimn = L-3(曾用[n]表示dimn)，dimm = M，dimv = LT-1，dimp = (dimF)/L2 = L-1MT-2.

  5. dimp = dim(nmv) =(dimn)(dimm)(dimv) = (L-3)M(LT-1) = L -3MT-.

  6.  = 1， = 2， = (1+)/3 = 1.故由量纲分析得： p  nmv2.

  7. [另一解法] dimn = L-3，dimm = M，dimv = LT-1， dimp = (dimF)/L2 = L-1MT-2

  8. 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.

  9. 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.

  10. 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.

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