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At what temperature, will the rms veloci...

At what temperature, will the rms velocity of a gas at `50^(@)C` be doubled ?

A

626K

B

1019K

C

`200^(@)C`

D

`1019^(@)C`

Text Solution

Verified by Experts

The correct Answer is:
D
`u_("r.m.s.") = sqrt((3RT)/( M)) :. u_("r.m.s.") prop sqrt( T )`
For `u_("r.m.s.") ` to be doubled, temperature must be raised by 4 times.
`T = ( 50 + 273 ) K = 323 K`
`:. 4T = 4 xx 323 K = 1292K`
`= ( 1292 - 273) C = 1019^(@)C`
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