Question #1dbe9

Jun 6, 2017

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,

$E = \frac{f {k}_{B} T}{2}$

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,

${v}_{m e a n} = \frac{{n}_{1} {v}_{1} + {n}_{2} {v}_{2} + \ldots .}{{n}_{1} + {n}_{2} + \ldots .}$

$\implies {v}_{m e a n} = \frac{\sum {n}_{i} {v}_{i}}{N}$

Where, $N = \sum {n}_{i}$ is the total number of molecules in the system.