1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Does the N! Gibbs factor SAVE or DESTROY extensivity?

  1. Jan 11, 2012 #1
    So we all know the argument that shows that a factor [itex]\frac{1}{N!}[/itex] makes entropy extensive: it makes the entropy the same for system A and system B where system A is a box of indistinguishable/indistinguished particles and where B is system A is split into two isolated parts.

    But regard this slight variation, where system A is the same as above, and where system B is again a splitting of system A, but now we let the two parts interchange energy: i.e. instead of isolated, the two parts are simply closed (= interchanging energy but not particles).

    Wouldn't we expect the relation [itex]\Omega(E) = \int \mathrm d E_A \Omega_A(E_A) \Omega_B(E-E_A)[/itex] to hold for the latter A and B (a form of extensivity)? However, this formula is only true if we do not include the Gibbs factor!
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted