Help:Equations/Kinetic Theory of Gases: Molecular Speeds

<math>PV=nRT=\tfrac{\text{1}}
{\text{3}}Nm\text{(}u^{\text{2}}\text
{)}_{\text{ave}}</math>

<math>\text{3}RT=\frac{Nm}{n}
\text{(}u^{\text{2}}\text{)}_{\text
{ave}}</math>

<math>M=\frac{Nm}{n}</math>

<math>\begin{align}
  & \text{                 
                      3}RT=M(u^
{\text{2}})_{\text{ave}} \\ 
 & \text{or                       
            }(u^{\text{2}})_
{\text{ave}}=\frac{\text{3}RT}{M}
 \\ 
 & \text{so that                 
              }u_{rms}=\sqrt{\text
{(}u^{\text{2}}\text{)}_{\text{ave}}}
=\sqrt{\frac{\text{3}RT}{M}} \\ 
\end{align}</math>