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

[John Denker <jsd@av8n.com>]

On 06/23/2011 12:43 PM, chuck britton wrote:
> 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.

Good question.

Here's how to think about it:  For the gas of distinguishable
(labeled) particles, when we pull out the partition,
the gas from the right compartment undergoes free expansion to
the left, and vice versa.

Free expansion of an ideal gas does not result in cooling ...
so mixing under these conditions will not result in cooling.

  By way of contrast, if you had some wonderful semi-permeable
  pistons so that you could let each sample of gas expand
  while doing work against the pistons, then the gases would
  cool while mixing.

OK?