The molecules of a given mass of a gas have root mean square speeds of `100 ms^(-1) "at " 27^(@)C` and 1.00 atmospheric pressure. What will be the root mean square speeds of the molecules of the gas at `127^(@)C` and 2.0 atmospheric pressure?

Explanation

We know that for a given mass of a gas
`V_("rms")=sqrt((3RT)/(M))`
Where R is gas constant
T is temperature in kelvin
M is molar mass of the gas.
`" Clearly "" "V_("rms") propsqrt(T)`
AS R,M are constants,
`(V_("rms"))_(1)/(V_("rms"))_(2)=sqrt((T_(1))/(T_(2)))`
`"Given"" "(V_("rms"))_(1) =100m//s`
`T_(1) =27^(@)C =27 +273 =300K`
`T_(2) =127^(@)C =127 +273 =400 K`
`:.` From Eq (i)
`(100)/((V_("rms"))_(2)) = sqrt((300)/(400)) =sqrt(3)/(2)`
`rArr " "(V_("rms"))_(2) =(2xx100)/(sqrt(3))= (200)/(sqrt(3)) m//s`