Realisability of the third law?

[pivoxa15]

My lecture notes had S=A{3nR[ln(T)]/2+nR[ln(V)]}. A arbitary, is the entropy equation for a monotomic ideal gas.

The third law demands S->0 as T->0. But as T->0 in the above equation, S -> -infinity assuming V fixed.

What is wrong?

Or is it the case that S-> -infinity is equivalent to minimum entropy?

V can be made arbitarily small but non zero so when T=0, the entropy must be smaller than any S when T is non zero. This can only happen if S-> -infinity as if it's a finite number than V can always be made smaller so that there exists a V and T such that S is smaller than S when zero T.

 

[pivoxa15]

I just realized that S can be combined to get S=AnR[ln(T^(3/2)V)] with A an arbitary constant than do S=BnR[ln(T^(3/2)V+1)] with B to scale S in order to account for the addition of 1 in the logarithm. So T=0 => S=0 and so the third law is satisfied. Is this accurate?