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# Help:Equations/Kinetic Theory of Gases: Molecular Speeds

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Equation Wiki Code Other Info
$PV=nRT=\tfrac{\text{1}}{\text{3}}Nm\text{(}u^{\text{2}}\text{)}_{\text{ave}}$
$PV=nRT=\tfrac{\text{1}} {\text{3}}Nm\text{(}u^{\text{2}}\text {)}_{\text{ave}}$
$\text{3}RT=\frac{Nm}{n}\text{(}u^{\text{2}}\text{)}_{\text{ave}}$
$\text{3}RT=\frac{Nm}{n} \text{(}u^{\text{2}}\text{)}_{\text {ave}}$
$M=\frac{Nm}{n}$
$M=\frac{Nm}{n}$
\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}
\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}