Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

We know that

$$n(E) ~=~ \frac {2 \pi (N/V)}{(\pi k_B T)^{3/2}} E^{1/2} e^{-E/(k_B T)} dE,$$

where $V$ is total volume.

If then, how do we derive total energy per unit volume from this equation?

share|cite|improve this question

Integrate n(E)*E over all possible energies and divide the result by the total volume, this gives the average energy per unit volume.


share|cite|improve this answer

You should first wonder what is the total energy per unit volume. Your formula gives n(E): the density of particles whose energy is between E and E+dE. There is n(E)*V such particles, each one carris the energy E. Their combined energy is thus: n(E)*V*E. Integrate over E to get the total energy of your system. At last divide by V to get the average energy by unit volume.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.