Question #ae66c

1 Answer
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 1/2kT12kT where kk is the Boltzmann constant and TT the absolute temperature.

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

E = (fkT)/2E=fkT2

Now, E = (mv^2)/2E=mv22
This gives, (mv^2)/2 = (fkT)/2mv22=fkT2
implies v_(rms) = ((fkT)/m)^(1/2)vrms=(fkTm)12

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