1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: The entropy when T=>0

  1. Jun 7, 2007 #1
    1. The problem statement, all variables and given/known data

    hi, I have this problem that sounds easy (at least I hope so) the question is prove that the entropy goes to zero as the temperature goes to zero

    2. Relevant equations

    segma= -(omega+meo*average{N} -U}/kT

    segma=the entropy
    omega=grand canonical ensemble partition function
    meo=the chemical potential
    U=the internal energy
    k=boltzman constant
    T=the temperature

    3. The attempt at a solution

    I usually use this information (segma=>0 when T=>0) to answer other problems, but here I have to prove it. I thought of taking the limit of segma forT=>0, and change the variabels on the RHS as a function of T, then solve it, but it didn't work:frown:, I have 3 more days before I hand it over, and I'm revising for another exam :cry:. if any one can give me a hint or know a web site can help (I allready search), please do and I'll be thankfull.
  2. jcsd
  3. Jun 8, 2007 #2


    User Avatar
    Science Advisor
    Gold Member

    This might be helpful:

    Another suggestion:
    Last edited by a moderator: Apr 22, 2017
  4. Jun 8, 2007 #3
    thanks for trying to help chronos, but those doesn't involve the grand canonical ensemble partition function, although I still believe that taking the limit of the entropy at T=>0 will solve it,I think it's just math works, where I have to change:

    averageN= {V/lamda^3) EXP(meo/kT)

    omega= -kT {V/lamda^3} EXP(meo/kT)

    but I couldn't have the answer????
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook