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# The average speed of molecules in an ideal gas is$$\overline{v} = \frac{4}{\sqrt{\pi}} \left (\frac{M}{2RT} \right)^{\frac{3}{2}} \int_0^\infty v^3 e^{\frac{-Mv^2}{(2RT)}}\ dv$$where $M$ is the molecular weight of the gas, $R$ is the gas constant, $T$ is the gas temperature, and $v$ is the molecular speed. Show that$$\overline{v} = \sqrt{\frac{8RT}{\pi M}}$$

## $\sqrt{\frac{8 R T}{\pi M}}$

#### Topics

Integration Techniques

### Discussion

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

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### Video Transcript

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WZ

#### Topics

Integration Techniques

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

Lectures

Join Bootcamp