Question #ae66c

Jun 2, 2017

Yes. They do change.

Explanation:

The energy of an ideal gas molecule can be given according to the equipartition theorem as derived from statistical thermodynamics.

It states that the energy is equally divided among all the degrees of freedom with each of them having an energy $\frac{1}{2} k T$ where $k$ is the Boltzmann constant and $T$ the absolute temperature.

Thus, for a gas molecule with $f$ degrees of freedom, the mean energy is,

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

Now, $E = \frac{m {v}^{2}}{2}$
This gives, $\frac{m {v}^{2}}{2} = \frac{f k T}{2}$
$\implies {v}_{r m s} = {\left(\frac{f k T}{m}\right)}^{\frac{1}{2}}$

Thus rms velocity is dependent on the number of degrees of freedom.