Prove that `c_(rms)=sqrt((2E)/(M))` [E=total kinetic energy of the molecules of 1 mol of a gas, M=molar mass of the gas, `c_(rms)=`root mean square velocity of gas molecule].

Explanation

We know, `c_(rms)=sqrt((3RT)/(M)) or, c_(rms)=sqrt((2)/(M)xx(3)/(2)RT)` the totla kinetic energy of the molecules of 1 mol gas,
`E=(3)/(2)RT" "therefore c_(rms)=sqrt((2E)/(M))` (Proved).