Calculate the kinetic energy per molecule and also rms velocity of a gas at `127^@C` .
Given `k_B = 1.38 xx10^(-23) J "molecule"^(-1) K^(-1) ` and mass per molecule of the gas `=6.4xx10^(-27)` kg .

Explanation

Here, T = 127 + 23 = 400 K,
`m =6.4 xx10^(-27) kg`
(i) Kinetic energy per molecule
`=1/2mv_(rms)^2=3/2k_BT`
`=3/2xx1.38xx10^(-23) xx400`
`=8.28xx10^(-21)J`
(ii) Now `1/2mv_(rms)^2=8.28xx10^(-21) J`
`:.v_(rms)=sqrt(2xx8.28xx10^(-21))/m`
`=sqrt((2xx8.28xx10^(-21))/(6.4xx10^(-27)))`
`=1.608xx10^3 ms^(-1)`