Re: [Phys-l] Gibbs paradox (redux)

[chuck britton <cvbritton@mac.com>]

Interesting - so we would expect macroscopic cooling to accompany 
this increase in entropy of mixing??

	(an adiabatic unmagnetization of sorts??) ;-)

ah, but you say that the T doesn't differ from the 'unlabeled' case.

I'm confused as when an increase of the Entropy of Mixing does or 
doesn't lead to a change in T.

.
At 12:26 PM -0700 6/23/11, John Denker wrote:
> One way to think about the real physics is to consider a gas of
> particles that have a nonzero nuclear spin, such as 3He.  At
> ordinary (not too cold) temperatures, the nuclear spin has no
> effect on the equation of motion, i.e. on the particle/particle
> scattering events.  The spin is just a label.  Let's put up-labeled
> particles on one side and down-labeled particles on the other
> side and pull out the partition.  Mixing occurs.  In terms of
> macroscopic pressure and temperature and heat capacity this
> scenario is not appreciably different from the corresponding
> unlabeled scenario ... but the entropy is different!  There is
> entropy of mixing of the labeled particles.  For some purposes
> you may not care, but you will for sure care if you ever try to
> separate them.  You will have to expend energy on the order of
> T dS to unmix them.