The internal energy is the canonical mean of the energy:
(1)
Holding the external mechanical parameters fixed, so that the spectrum and degeneracies do not change when differentiating with respect to , gives
(2)
Comparison yields
(3)
An explicitly temperature-dependent effective Hamiltonian would require care: differentiating its partition sum would also differentiate the assigned energy levels. The stated result uses the fixed physical spectrum of the canonical system.

Ancestors (14)

  1. C9
  2. Section C
  3. Paper 2
  4. 2021
  5. Past exam of the physics B course of the University of Cambridge
  6. Physics B course of the University of Cambridge
  7. Physics course of the year 2 of the natural sciences course of the University of Cambridge
  8. Year 2 of the natural sciences course of the University of Cambridge
  9. Year of the natural sciences course of the University of Cambridge
  10. Natural sciences course of the University of Cambridge
  11. Course of the University of Cambridge
  12. University of Cambridge
  13. List of universities
  14. Home

View article source

Discussion (0)

New discussion

There are no discussions about this article yet.

Articles by others on the same topic (0)

There are currently no matching articles.
See all articles in the same topic Create my own version