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Re: [Phys-l] PV question

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-] On Behalf Of John Mallinckrodt []
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

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
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
Forum for Physics Educators
Forum for Physics Educators