1. Not finding help here? Sign up for a free 30min 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!

Statistical mechanics/Thermodynamics two spin-1/2 subsystem

  1. Sep 30, 2013 #1
    1. The problem statement, all variables and given/known data
    Consider two spin-1/2 subsystems with identical magnetic moments (μ) in equal fields (B). The first subsystem has a total of NA spins with initially "a" having magnetic moments pointing against the field and (NA - a) pointing along the field, so that its initial energy is UiA = μB(a - (NA - a) = μB(2a - NA). The second subsystem has a total of NB spins with "b" having moments initially pointing against the field so that its initial energy is UiB = μB(2b - NB). Now suppose that the two subsystems are brought together so that they can exchange energy. Assume that B = constant and a, b, NA, NB >> 1. Show that in equilibrium, a0/NA = b0/NB, and this implies that the two subsystems will have the same "magnetization," i.e. total magnetic moment/spin.


    2. Relevant equations
    I'm not really sure what equations are useful in this case because I'm having trouble understanding what I need to be doing. I think I need to use multiplicity so
    Ω(N,n) = N!/(n!(N-n)!)


    3. The attempt at a solution
    I think that I have to first figure out the most probable macrostate because that is where the systems would be in equilibrium(?). So do I go along the lines of solving Ω(NA, a) and Ω(NB, b)? I don't even know if that makes sense or what a0 and b0 represent in this question.
     
  2. jcsd
  3. Oct 1, 2013 #2

    DrClaude

    User Avatar

    Staff: Mentor

    You're going in the right direction. Have you seen entropy yet? If so, can you express the conditions for equilibrium in terms of S and U?

    My guess is that a0 and b0 are the number of spins pointing against the field at equilibrium.
     
  4. Oct 1, 2013 #3

    BruceW

    User Avatar
    Homework Helper

    exactly. But also, don't forget to constrain the total energy! And yeah, as DrClaude says, the a0 and b0 seem to simply be a and b once equilibrium is achieved.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted