# The entropy when T=>0

## Homework Statement

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

## Homework 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

## 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.

Chronos
Gold Member
www.physics.unc.edu/classes/fall2006/phys100-001/HawChengLecture.pdf[/URL]

Another suggestion:
[url]http://arxiv.org/pdf/physics/0609047[/url]

Last edited by a moderator:
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????