Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The second law

  1. Apr 7, 2005 #1
    Hi all,

    Can the second law of Thermodynamics be proven? (I mean, starting with the definition S=kln(Ohmega).)

    If not.. is it just an empiric fact?
     
  2. jcsd
  3. Apr 7, 2005 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Yes,the second law of thermodynamics can be proved via statistical methods for both reversible & irreversible processes...

    Daniel.
     
  4. Apr 7, 2005 #3
    S=kln(Omega) is an empirical fact. But the 2nd law, both clausiius and Kelvins laws taken together, is just a statment that no engine can be 100% efficient.. its pretty easy to proove this: by a compostie system with a carnot and kelvin violator (i think)??
     
  5. Apr 7, 2005 #4

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Nope.In the axiomatical approach to equilibrium SM,Boltzmann's formula

    [tex] S\left(E,V,N)=k\ln \Omega^{*}_{E,\Delta E} (E,V,N) [/tex]

    is just a result,a theorem if u prefer.

    Nothing is "empirical" in SM...

    Daniel.
     
  6. Apr 7, 2005 #5
    its a postulate - its consistent with what happens in nature. its not proovable is it?
     
  7. Apr 7, 2005 #6

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Experiments can confirm/infirm what a postulate afirms...But that doesn't make the postulate (in this case,the theorem) "empirical",by any means...

    Daniel.
     
  8. Apr 7, 2005 #7

    ZapperZ

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor

    You might want to read this:

    http://arxiv.org/abs/cond-mat/0208291

    Zz.
     
  9. Apr 7, 2005 #8
    First of all thanks to everyone.

    dextercioby- you say Boltzmann's formula is a result. What is then the def. of entropy?

    ZapperZ- Thanks, I'll go over it tommorow.
    If it's not in ZapperZ's link, what is the proof then of the second law?
    I asked my Prof. if it could be proved, and he told me it was an empirical fact. It seemed odd so I asked here. Seing he says it's empirical, I have little faith he's gonna prove it. And I have no intention to go through my first class of SM without knowing the proof...
     
  10. Apr 7, 2005 #9

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    For a classical statistical equilibrium ensemble,the statistical entropy is defined as - Boltzmann's constant multiplied with the average* of the logarithm of the density probability.

    Daniel.

    -------------------------------------------
    * average on the ensemble

    [tex] S_{stat}=:-k\langle \ln\rho \rangle_{\rho} [/tex]
     
  11. Apr 7, 2005 #10
    Palindrom,

    The empirical fact on which SM is based is that the energy (or at least part of the energy) contained in a system is the kinetic energy of random motion. From that point on, SM is just math, and therefore provable.
     
  12. Apr 7, 2005 #11

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    SM is a theory.It's in the realm of theoretical physics.It has an axiomatic structure,just like QM,SR,GR,CM,...

    As in any of the afore mentioned theories,math is extremey important,but physics is there,too...

    Daniel.
     
  13. Apr 8, 2005 #12
    OK now it's getting interesting.
    Do you have a recomendation for a good and high leveled book in SM?
    I like to see the math in the physics btw, as well as the physics in the math.
    So how about that book?
    Thanks everyone!
     
  14. Apr 8, 2005 #13

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    3 volumes of Landau & Lifschitz's series are on SM...5,9 & 10.

    For nonequilibrium SM,i'd vote for Balescu's "Equilibrium & nonequilibrium statistical mechanics".

    Daniel.
     
  15. Apr 8, 2005 #14
    Thanks a lot!
    I'll go find them tommorow.

    Do you know F. Reif's "Fundamentals of Statistical and Thermal Physics"?
    How is it?
     
  16. Apr 8, 2005 #15

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    It's too easy.Meaning it's an introductory/undergraduate course,just like any of the 5 vols which compile the Berkley series.

    Also F.Schwabl has a modern (new) text on SM.And Greiner has a very good calculatory book...

    Daniel.
     
  17. Apr 8, 2005 #16
    Ok, so you've given me a few of books. Which one do you think I should start with?
    I'd like to be able to go through it during this semester, and study from it. I don't really have time for more than 1 book...

    Sorry for the multiple questions.
     
  18. Apr 8, 2005 #17

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Greiner is a good intro book.It has many applications...W.Greiner:"Thermodynamics and statistical mechanics",Springer Verlag.Any edition (i think there are only 2,but i'm not too sure).It's one of the books in the "Greiner series".

    Daniel.
     
  19. Apr 8, 2005 #18
    Thanks a lot!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: The second law
  1. Second Law (Replies: 9)

Loading...