Re: [Phys-l] Reversible versus quasi-static processes (was Re: PV question)

[John Denker <jsd@av8n.com>]

On 01/24/2010 02:19 PM, John Mallinckrodt wrote:
> Okay, this seems to be a valid point.  You do hear people describe a  
> slow leak as a quasi-static process. 

OK.

> On the other hand, you also  
> hear people offer the opinion that, in a quasi-static process, "the  
> system" remains at or near thermodynamic equilibrium.  

I would say the quasistatic system is everywhere 
_locally_ at or near thermodynamic equilibrium.

This is consistent with the example of Joule-Thomson 
expansion through a porous plug, which is quasistatic
yet highly irreversible ... so no "other hand" is 
required.

> Clearly, if  
> "the system" consists of all gas on either side of the porous plug,  
> then "the system" is nowhere near thermodynamic equilibrium.  Maybe  
> we need to alter the definition to allow systems that are in  
> piecewise thermodynamic equilibrium?  Not completely sure how you'd  
> do that.

People do that all the time.  You cannot even begin
to discuss a Carnot heat engine without doing that.

Globally, the heat engine is very far from equilibrium,
since the upper and lower heat reservoirs are at very
different temperatures.

However, the engine is contrived so that at the places
where "interesting" heat transfers are taking place,
the system is _locally_ near thermal equilibrium.

> So I wonder if anything important would be lost if we refined these  
> ideas to say that the gases on either side of the porous plug undergo  
> quasi-static processes, but that the gas as a whole doesn't.

That is the standard way of analyzing the J-T expansion
example.  Works for me.
 
> I do recognize that this raises an important question about "where"  
> the dissipation is taking place and I'm not particularly comfortable  
> saying that it happens in or "near" the porous plug.  

The standard analysis says it happens _in_ the porous
plug ... more specifically in the gas inside the porous 
plug.

If it makes you feel better, replace the porous plug
with a long bamboo-like structure, with many compartments
separated by transverse membranes, each membrane having
a pinhole.  The gas in compartment N+1 is at all times
very nearly in mechanical and thermodynamical equilibrium
with the gas in compartment N.  In the large-N limit you
get the familiar Joule-Thomson result.  

Each membrane is so thin that nothing happens "in" the
membrane.  But clearly 100% of the dissipation occurs
somewhere within the bamboo-like structure.

AFAIK this line of reasoning goes back to Joule and/or 
Thomson.

Real-world _mufflers_ use a somewhat similar structure,
for a distantly-related purpose.