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

[Carl Mungan <mungan@usna.edu>]

> The explanation is too long and detailed for email.  I wrote it up
> at
>  http://www.av8n.com/physics/thermo/z-particles.html#sec-z-ideal-gas
> wherein the bottom line is
>  http://www.av8n.com/physics/thermo/z-particles.html#eq-s/v-snow

Wow, that's great! Did you just add this stuff, or has it been in there a while? Each term I re-read this thermo document of yours, you've added more goodies to it.

Anyways, back to that equation, specifically say your (25.21):

S = 1.5Nk + Nkln(V/u) where u is the cube of the thermal de Broglie wavelength.

Suppose we have a glass of milk (or snow). Now insert a partition dividing that glass into 2 equal portions. Each of the new portions has entropy:

S_new = 1.5(N/2)k + (N/2)kln(V/2u).

So the change in entropy of all the milk is 2S_new - S = -Nkln2.

By dividing the glass of milk into 2 equal portions, I seem to have decreased the entropy of the system. This seems like a strange result: where is corresponding gain of entropy in the surroundings to ensure the 2nd law is not violated?