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The average velocity of gas molecules is...

The average velocity of gas molecules is `400 m s^(-1)`. Calculate their `rms` velocity at the same temperature.

Text Solution

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`"Average speed, "u_(av)=sqrt((8RT)/(piM))`
`"Root mean square speed, "u_("r.m.s")=sqrt((3R)/(M))`
`therefore" "(u_("r.m.s"))/(u_("av"))=sqrt((3RT)/(M))//sqrt((8RT)/(piM))`
`sqrt((3pi)/(8))=sqrt((3xx3.143)/(8))=1.085`
`therefore" "u_("r.m.s")=1.085xxu_("av")`
`=1.085xx400=4.34ms^(-1)`.
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