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The molecules of a given mass of a gas h...

The molecules of a given mass of a gas have rms velocity of `200 m//s at 27^(@)C and 1.0 xx 10^(5) N//m_(2)` pressure. When the temperature and pressure of the gas are respectively `127^(@)C and 0.05 xx 10^(5) Nm^(-2)`, the rms velocity of its molecules in `ms^(-1)` is

A

`(100sqrt(2))/(3)`

B

`(100)/(3)`

C

`100sqrt(2)`

D

`(400)/(sqrt(3))`

Text Solution

Verified by Experts

The correct Answer is:
D
As, `v_(rms)=sqrt((3k_(B)T)/(m))`
`therefore (v_(27))/(v_(127))=sqrt((27+273)/(127+273))=sqrt((300)/(400))=sqrt(3)/(2)`
or `v_(127)=(2)/(sqrt(3))xxv_(27)=(2)/(sqrt(3))xx200ms^(-1)=(400)/(sqrt(3))ms^(-1)`
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