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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^-1` at `27^@C` and `1.0 times 10^5 N.m^-2` pressure. When the temperature and pressure of the gas are respectively. `127^@C` and `0.05 times 10^5 N.m^-2` the rms velocity of its molecules in `m.s^-1` is

A

`400/sqrt3`

B

`(100sqrt2)/3`

C

`100/3`

D

`100sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
A
rms speed of gas molecules `c prop sqrt T`
`thereforec_1/c_2=sqrt(T_1/T_2)=sqrt((27+273)/(127+273))=sqrt(300/400)=sqrt3/2`
or,`2/sqrt3c_1=2/sqrt3times200=400/sqrt3 m//s`
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