Re: [Phys-l] PV question

[John Mallinckrodt <ajm@csupomona.edu>]

A process is reversible if it does not increase the entropy of the  
universe.  That's relatively easy in the case of a rigorously  
thermally-insulated system, you just have to work slowly  
(technically, infinitely slowly.)

For a process that involves thermal energy transfer, you have to work  
slowly *and* insure that the system is always in direct thermal  
contact with a large (technically, infinite) reservoir that is, at  
each step of the process, only infinitesimally different from the  
system temperature.

In the case of an isothermal process, you only need one reservoir.   
For a nonisothermal process involving thermal energy transfer (e.g.,  
an isobaric or isochoric process), you will need a large number  
(technically, an infinite number) of reservoirs at different  
temperatures.

Obviously, given the above, real processes are unavoidably  
irreversible to some extent, but any process during which the system  
is never allowed to deviate substantially from a thermal equilibrium  
state (including ideal gas processes drawn as paths on a PV diagram)  
can, in principle, be performed in a manner that is arbitrarily close  
to reversible.

John Mallinckrodt
Cal Poly Pomona

On Jan 22, 2010, at 5:04 PM, Philip Keller wrote:

> I've been following this thread and now recently find an issue of  
> vocabulary that I want to ask about:  I thought that isobaric and  
> isochoric changes were NOT considered "reversible", whether done  
> fast or slow.  I think we need another word for what they are,  
> perhaps "undoable but not time-reversible".  I thought that  
> "reversible" meant more than that you can return your cylinder to  
> its previous state but that the interaction between the system and  
> its environment could be time-reversed without breaking the second  
> law.  If isochoric or isobaric changes were reversible in that  
> sense then there would be nothing special about the Carnot cycle.   
> Do I have this wrong?  And as long as I am asking questions, say  
> you have a gas in a cylinder.  Is any process reversible other than  
> isothermal and adiabatic expansion/compression?
> ________________________________________
> From: phys-l-bounces@carnot.physics.buffalo.edu [phys-l- 
> bounces@carnot.physics.buffalo.edu] On Behalf Of John Mallinckrodt  
> [ajm@csupomona.edu]
> Sent: Friday, January 22, 2010 6:56 PM
> To: Forum for Physics Educators
> Subject: Re: [Phys-l] PV question
>
> Biran Whatcott wrote:
>
> > If one specifies a straight line on such a PV graph, then the curve
> > describing the pressure volume and temperature change during its
> > compression  will necessarily cut some isotherm (actually many of
> > them)
> > TWICE.
>
> Not so.  Not in the case of an isobaric or isochoric process or, for
> that matter, many other processes.  Consider, for instance, any
> process for which P(V) = P_o + C (V - V_o) with C a positive
> constant.  In fact, depending on starting and ending volumes, many
> processes with negative C also satisfy the requirement.  All of these
> processes can be carried out reversibly.
>
> > The implication (for me) is that this straight line is not a
> > description
> > of a reversible adiabatic. process.
>
> That's *certainly* true, but you don't need to and, in fact, can't
> deduce that result from any of the foregoing observations.  A
> reversible adiabatic process is described by a curved line on a PV
> graph, period.
>
> John Mallinckrodt
> Cal Poly Pomona
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