[Phys-l] Gibbs paradox (redux)

[Carl Mungan <mungan@usna.edu>]

A few months ago I highlighted a paper by Swendsen in AJP about 
entropy: April 2011 p. 342.

Swendsen argues that for an ideal gas of DISTINGUISHABLE particles, 
the entropy is extensive but that the formula for the multiplicity 
has to be modified. Recall that I summarized his proposed 
modification here:
http://usna.edu/Users/physics/mungan/Scholarship/DistinguishableEntropy.pdf

Now there is another AJP article by Versteegh that takes a different 
viewpoint: July 2011 p. 741.

Versteegh argues that for such a gas, the traditional formula for 
multiplicity should NOT be modified (ie. there is no factor of N! 
since the particles are distinguishable) and thus that the entropy is 
NOT extensive. This leads him in turn to claim that the thermodynamic 
formula for entropy (dS = dQ/T) is NOT equal to the stat. mech. 
formula (S = k ln W).

Wow, I must say I find this situation confusing and I'd again invite 
discussion. Obviously Swendsen and Versteegh can't both be right. In 
fact, both might be wrong. In particular, I'm bothered by the fact 
that Versteegh nowhere discusses the fact that dQ has to be for an 
equivalent reversible process if the actual process is irreversible.

Another helpful recent reference on the topic of mixing of gases is:

A. Ben-Naim, "Entropy: Order or Information," J. Chem. Educ. 88:594 
(July 2011).
--
Carl E Mungan, Assoc Prof of Physics  410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363
mailto:mungan@usna.edu     http://usna.edu/Users/physics/mungan/