# The entropy when T=>0

1. Jun 7, 2007

### angel 42

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, I have 3 more days before I hand it over, and I'm revising for another exam . 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. Jun 8, 2007

3. Jun 8, 2007

### angel 42

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????