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

Given, At `27^(@)C,` root meann square speed
`v_(rms)=100ms^(-1)`
`(v_(rms_(1)))=sqrt((3p_(1))/(d_(1)))=sqrt((3p_(1)V_(1))/(M))`
According to ideal gas equation
`(p_(1)V_(1))/(T_(1))=(p_(2)V_(2))/(T_(2))` `Rightarrow" " (V_(1))/(V_(2))=(p_(2)T_(1))/(p_(1)T_(2))=(2xx300)/(400)=(3)/(2)`