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!

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
    2016 Award

    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...