Re: [Phys-l] third law of thermo

[John Denker <jsd@av8n.com>]

On 02/17/2010 08:22 AM, Carl Mungan wrote:
> I recognize that there are many different views on the 3rd law. 
> Specifically S does not always go to zero as T->0. However, I thought 
> one could safely say it approaches a constant (often called the 
> residual entropy) with zero slope, ie dS/dT->0 as T->0 (technically 
> it's a partial derivative with N,V,B,etc held constant). Apparently I 
> must be wrong about that however. Consider an ideal fermi gas. It has 
> C linearly proportional to T at low T. Then dS/dT=C/T=nonzero 
> constant as T->0.
>
> Do others agree with my analysis or am I missing some key idea?

I agree.  The analysis is completely logical.  Also, here's
some experimental evidence;  see figure 6.5 in:
  http://www.pit.physik.uni-tuebingen.de/PIT-II/teaching/ExPhys-IVb_(2)SS_03/ExP-IVb-ch6.pdf


On the other hand, I don't expect mere logic and evidence
to persuade those who believe in the third law as an
article of faith.  There are those who would argue, based
on "the" third law, that at sufficiently low temperature,
"everything" will become an insulator, a ferromagnet, or
a superconductor ... i.e. some sort of ordering transition,
whereby the electron entropy goes to zero one way or another.  
Who knows, it might even be true.  Or it might not.  It's
certainly not true for the spin entropy in a spin glass.

Some parts of "ideal" Fermi gas story may end up being a 
cat-and-mouse game:  I can always imagine a more ideal i.e.
more-dilute less-interacting system, and the other guy can 
always imagine a lower temperature......

===========

I can't get too excited about it.  My attitude has always
been, "even if the third law were true, why should I care?"

I care about the absolute entropy;  I just don't care whether
it "always" goes to zero or not.

My policy is to just forget I ever heard of the third law.

Not only is zero entropy at T=0 not the universal behavior,
trying to create a zero-entropy system is hard work. I
reckon I could do it, to a good approximation, using
liquid helium ... but I cannot think of even one other
system where the entropy actually goes to zero.