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!

Chemical potential different for different systems?

  1. May 12, 2007 #1
    1. The problem statement, all variables and given/known data
    For a given phenomena of macroscopic particles.

    If we model it using the canonical ensemble then we get a certain chemical potential u.

    But if we model it using the Grand Canonical system, we get a varying chemcial potential that depends on the average number of particles in the system.

    So two different chemical potentials for the two systems. But in the thermodynamic limit of n-> infinity, both u equals each other.

    That sounds right dosen't it?
     
  2. jcsd
  3. May 13, 2007 #2

    cepheid

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Yeah, you're basically right.

    In any of the systems in the canonical ensemble, the chemical potential is given by

    [tex] \mu(T,V,N) [/tex]

    whereas in any of the systems in the grandcanonical ensemble, it's given by

    [tex] \mu(T,V,\langle N \rangle) [/tex]

    Now, in the "thermodynamic limit" as you have called it, the number of particles in any of the grandcanonical systems is *MUCH* more likely to be equal to [itex] \langle N \rangle [/itex] than to any other number. So it's equivalent to having a closed system with a fixed number of particles [itex] \langle N \rangle [/itex].

    If I have an open system and I want it to be equivalent to a closed system with a particular number of particles [itex] N_0 [/tex], I'd have to somehow pick or set the value of [itex] \mu [/tex] such that [itex] \langle N \rangle = N_0 [/itex] for that system.
     
    Last edited: May 13, 2007
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Chemical potential different for different systems?
  1. Potential Difference (Replies: 2)

Loading...