Question

Question #1dbe9

Answer 1

Both of them are different things.

The average kinetic energy is simply the mean kinetic energy a molecule possesses.
From equipartition theorem, this is given to be,

`E = (fk_BT)/2`

Where `f` is number of degrees of freedom of the molecule, `k_B` is the Boltzmann constant, and `T` is the absolute temperature.

On the other hand, if out of a total `N` molecules in a system, `n_1` Molecules have a velocity `v_1`, `n_2` molecules have a velocity `v_2` and so on, then the mean velocity or average velocity is defined to be,

`v_(mean) = (n_1v_1 + n_2v_2 + ....)/(n_1 + n_2 + ....)`

`implies v_(mean) = (sum n_iv_i)/N`

Where, `N = sum n_i` is the total number of molecules in the system.