气体动理论

<span class="equation-text" contenteditable="false" data-index="0" data-equation="N_A=6.022\times10^{23}mol^{-1}"><span></span><span></span></span>

R=8.31J<span class="equation-text" contenteditable="false" data-index="0" data-equation="\cdot"><span></span><span></span></span><span class="equation-text" contenteditable="false" data-index="1" data-equation="mol^-1"><span></span><span></span></span><span class="equation-text" contenteditable="false" data-index="2" data-equation="\cdot"><span></span><span></span></span><span class="equation-text" contenteditable="false" data-index="3" data-equation="K^{-1}"><span></span><span></span></span>

pV=<span class="equation-text" contenteditable="false" data-index="0" data-equation="\nu"><span></span><span></span></span><span class="equation-text" contenteditable="false" data-index="1" data-equation="RT "><span></span><span></span></span><br><span class="equation-text" contenteditable="false" data-index="2" data-equation="\nu=\frac{m}{M}"><span></span><span></span></span>

<font style="font-size: inherit;" color="#000000">p=n</font><font style="font-size: inherit;" color="#000000">kT</font><span style="font-size: inherit;"><font color="#000000"> </font>(n:分子数密度）</span><br>pV=<span class="equation-text" data-index="0" data-equation="\frac{N}{N_A}RT" contenteditable="false"><span></span><span></span></span><br><span class="equation-text" data-index="1" data-equation="k=\frac{R}{N_A}" contenteditable="false"><span></span><span></span></span><br>

<span class="equation-text" contenteditable="false" data-index="0" data-equation="\bar{v_x}=\bar{v_y}=\bar{v_z}=0"><span></span><span></span></span>

<span class="equation-text" contenteditable="false" data-index="0" data-equation="\bar{{v_x}^2}=\bar{{v_y}^2}=\bar{{v_z}^2}={1 \over 3}\bar{v^2}"><span></span><span></span></span>

压强&nbsp;<span class="equation-text" contenteditable="false" data-index="0" data-equation="p={1\over 3}nm_0\bar{v^2}"><span></span><span></span></span>=<span class="equation-text" contenteditable="false" data-index="1" data-equation="{2 \over 3}n({1 \over 2}m_0\bar{v^2})={2 \over 3}n\bar{\epsilon_k}"><span></span><span></span></span>

分子平均平动动能&nbsp;&nbsp;<span class="equation-text" data-index="0" data-equation="\bar{\epsilon_k}=" contenteditable="false"><span></span><span></span></span><span class="equation-text" data-index="1" data-equation="{1 \over 2}m_0\bar{v^2}" contenteditable="false"><span></span><span></span></span>

温度公式&nbsp;<span class="equation-text" contenteditable="false" data-index="0" data-equation="\bar{\epsilon_k}="><span></span><span></span></span><span class="equation-text" contenteditable="false" data-index="1" data-equation="{1 \over 2}m_0\bar{v^2}={2 \over 3}kT"><span></span><span></span></span>

气体分子的方均根速率&nbsp; &nbsp;<span class="equation-text" contenteditable="false" data-index="0" data-equation="\sqrt{\bar{v^2}}=\sqrt{3kT \over m_0}=\sqrt{3RT \over M}"><span></span><span></span></span>

<span class="equation-text" contenteditable="false" data-index="0" data-equation="{1\over2}m_0\bar{{v_x}^2}={1\over2}m_0\bar{{v_y}^2}={1\over2}m_0\bar{{v_z}^2}={1 \over 2}kT"><span></span><span></span></span>

理想气体每个分子的平均能量&nbsp; &nbsp;<span class="equation-text" contenteditable="false" data-index="0" data-equation="\bar{\epsilon_k}={i \over 2}kT"><span></span><span></span></span>&nbsp; &nbsp;(i=t+r+2s)

单原子分子 i=3<br>双原子分子 i=5<br>多原子分子 i=6

1mol理想气体的内能&nbsp;&nbsp;<span class="equation-text" contenteditable="false" data-index="0" data-equation="E_m=N_A{i \over 2}kT={i \over 2}RT"><span></span><span></span></span>

<span class="equation-text" contenteditable="false" data-index="0" data-equation="\nu mol"><span></span><span></span></span>理想气体的内能&nbsp; E=<span class="equation-text" contenteditable="false" data-index="1" data-equation="\nu{i \over 2}RT"><span></span><span></span></span>

速率分布函数&nbsp; f(v)=<span class="equation-text" contenteditable="false" data-index="0" data-equation="{dN \over Ndv}"><span></span><span></span></span>&nbsp;<br>物理意义&nbsp; 速率在v~v+dv的单位速率区间的分子数占分子总数的百分比<br>f(v)dv代表处在v~v+dv内分子数占总分子数的百分比

最概然速率&nbsp;<span class="equation-text" contenteditable="false" data-index="0" data-equation="v_p=\sqrt{2RT \over M}"><span></span><span></span></span>

实验测定&nbsp;<span class="equation-text" contenteditable="false" data-index="0" data-equation="v={\omega D^2 \over 2L}"><span></span><span></span></span>

<span class="equation-text" contenteditable="false" data-index="0" data-equation="\bar{\lambda}={1 \over \sqrt{2}\pi d^2n}"><span></span><span></span></span><span class="equation-text" contenteditable="false" data-index="1" data-equation="={kT \over \sqrt{2}\pi d^2p}"><span></span><span></span></span>