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The r.m.s. velocity of molecules of a ga...

The r.m.s. velocity of molecules of a gas of density 4kg `//m^(3)` and pressure `1.2 xx 10^(5) N//m^(2)` is

A

900 `m//s`

B

`120 m//s`

C

`600 m//s`

D

`300m//s`

Text Solution

Verified by Experts

The correct Answer is:
D
r.m.s. velocity `= sqrt(( 3RT)/( M ))`
Density , `d = ( P M)/( RT)`
`:. ( RT)/( M ) = ( P )/( d)`
`:.` r.m.s. velocity ` = sqrt(( 3P )/( d)) = sqrt(( 3 xx 1.2 xx 10^(5) Nm^(-2))/( 4kg m^(-3)))`
`= sqrt(( 3 xx 1.2 xx 10^(5) kg ms^(-2) m^(-2))/( 4 kg m^(-3)))`
`= 300 ms^(-1)`
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