Re: [Phys-L] thermodynamics of open systems

[John Denker <jsd@av8n.com>]

On 07/17/2012 04:24 PM, Bob Sciamanda wrote:
> IMHO the point of Carl's paper was that associating dS with only Q/T
> does not account for the additional change in S that can result from
> an increment in mole number.

A) If you define "dQ" to be an abusive shorthand for T dS, then
 the problem does not arise.  Obviously dS = "dQ" / T.  Period.

B) Here's the other possible way of defining "dQ" operationally:
 Very commonly, people measure the change in energy dE under 
 this-or-that conditions and call it "heat" and denote it "dQ".
 IMHO it would be better to call it dE, since that is what was 
 measured, and since dE exists whereas dQ does not.  In this 
 case dS = dE/T under some conditions and not others.  The 
 relevant conditions can be figured out from the equation
           dE = TdS - PdV + μdN
 which is tantamount to equation [1] in Carl's paper
    http://usna.edu/Users/physics/mungan/Scholarship/OpenSystems.pdf
 assuming there are no other relevant variables.

 Specifically:  Obviously dE/T = dS if and only if PdV = μdN.

 In introductory presentations, it is common to assume PdV = μdN = 0,
 which is sufficient but not necessary for making dE/T = dS.

========

This does not seem complicated or tricky to me ... but perhaps there
is some subtle issue that I have overlooked.  If so, please let me
know.

I emphasize that it costs nothing to write dS = dE/T subject to
appropriate conditions, avoiding dQ, and thereby avoiding crimes
against the laws of mathematics.