The absolute temperature of a gas is increased to 3 times. What will be the increase in root mean square velocity of the gas molecule.

Explanation

rms velocity in terma of Boltzman constant (K)
`c=sqrt((3Kt)/m)`
At temperature `T_1,c=sqrt((3kT_1)/m)`
Now, `T_2=3 T_1`
`thereforec_2=sqrt((3kT_2)/m)=sqrt((3ktimes3T_1)/m)=sqrt3.sqrt(3kT_1)/m`
or,`c_2=sqrt3c`
If the temperature of the gas increases 3 times, then the root mean square velocity of the gas particles increases by a factor of `sqrt3`.