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 physics

  1. Feb 23, 2006 #1
    Hi.

    I'm having trouble with this statistical physics thing again. I am given this exercise:

    Problem 9 – A spin model

    In a solid at temperature T the atoms have spin 1 so that the m quantum number takes on the values m = 0, ±1. Due to an interaction with the electrostatic field in the crystal, the states with m = ±1 have an energy which is higher by ε than the state with m = 0.

    1. Find the average energy E(T) of the nuclei and the associated heat capacity [tex]C_V(T)[/tex]. Sketch both functions.

    I'm really confused about some basic things here. The Boltzmann distribution states that:

    [tex]p_r = \frac1{Z}\exp{(-E_r/kT)}.[/tex]​

    This is the probability that the system will be in a particular state r with energy [tex]E_r[/tex], right? I don't know the number of states of the system or their energies - I know only the individual energies of the atoms.

    I have nevertheless tried to determine the mean energy as a function of the temperature in various ways and I always end up with a function that approaches some constant value asymptotically at large temperatures. This would correspond to the heat capacity approaching zero as T tends to infinity (the heat capacity, [tex]C_V(T)[/tex], being the derivative of E(T)), which I don't think makes sense. I don't know if I'm making myself clear...

    Any help would be appreciated.
     
  2. jcsd
  3. Feb 23, 2006 #2

    Physics Monkey

    User Avatar
    Science Advisor
    Homework Helper

    Hi broegger,

    In your case the spins don't interact with each other, so the energy states of the whole system can be labeled by the individual spin states. Because the spins are independent, the whole partition function factors into a piece for each spin, and it's just a few lines to obtain the full partition function. Also, the energy should approach an asymptotic value in the limit of high temperature. This becomes obvious when you think about the fact that the energy of the system is bounded from above.

    hope this helps.
     
  4. Feb 24, 2006 #3
    Yea, thanks. So if there is N atoms we would have [tex]Z_{tot} = Z^N[/tex]?

    I think what was confusing me was the fact that I used to think of the heat capacity intuitively as "the amount of energy needed to raise the temperature by 1 degree", and so, the heat capacity approaching 0 seems to imply that you could raise the temperature indefinitely without supplying any energy. What does in fact happen if you keep supplying heat even though the system can't absorb any - there seems to be many possibilities?

    Thanks for helping out.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Statistical physics
  1. Statistical Physics? (Replies: 2)

  2. Statistical physics (Replies: 1)

  3. Statistical physics (Replies: 8)

  4. Statistical Physics (Replies: 0)

  5. Statistical Physics (Replies: 0)

Loading...