Re: Quasistatic conditions (was: Re: Relativity question)

[pvalev <pvalev@BAS.BG>]

--- David Bowman <dbowman@TIGER.GEORGETOWNCOLLEGE.EDU> wrote:

> Regarding Pentcho's question:
>
> > --- David Bowman <dbowman@TIGER.GEORGETOWNCOLLEGE.EDU> wrote:
> > > Recall that both joules and bits
> > > measure *extensive* quantities and temperature is an *intensive*
> > > quantity that can be expressed as a partial deriviative of
> > > extensive internal energy w.r.t. extensive entropy (under
quasistatic
> > > conditions where no macrowork is done during the variation).
> >
> > Weren't quasistatic conditions ones in which maximum work is
> > extracted from the system?
>
> No.  Quasistatic conditions are those that perturb an equilibrated
> system during a process so slowly and gently that the system
> effectively doesn't significantly fall out of equilibrium during the
> change.  At each moment during a quasistatic process the system can
> be considered as being in equilibrium (or at worst maybe a
metastable
> state that acts like equilibrium).  The quasistatic limit is the
> limit whereby a process-caused change occurs much more slowly than
> the characteristic equilibration time for the system.  Whether or
not
> work is done during such a process is irrelevant to the definition
of
> being quasistatic.

This definition implicitly involves a serious problem. It can
be traced back to Carnot and his formulation of a necessary and
sufficient condition for maximum efficiency of the heat engine:
BODIES OF DIFFERENT TEMPERATURE SHOULD NOT COME INTO DIRECT
THERMAL CONTACT. The modern understanding of "quasistatic", or
at least one of the understandings, is in accordance with
Carnot condition. The standard example is a very slow isothermal
ideal gas expansion - maximum work is extracted from the
system, the system is in equilibrium all along and THE
TEMPERATURE OF SYSTEM AND SURROUNDINGS IS THE SAME.
     Now the problem. The fact that a system is in equilibrium
all along does not guarantee that the change it undergoes is
quasistatic in the above sense. We can imagine a system
thermally isolated from HOTTER surroundings but still a thin
wire connects them so that the temperature of the system
increases very slowly. The system is in equilibrium (passes
through a succession of equilibrium states) but....what
type of process is this????
    It is extremely important for us to answer this question.
Classically, the entropy is defined through dS=dQrev/T, but the
subscript "rev" may mean, according to textbooks, two things.
Either the system just passes through a succession of
equilibrium states, or the system passes through a succession
of equilibrium states but, in addition, exchanges heat with
the surroundings ONLY WHEN SYSTEM AND SURROUNDINGS ARE OF THE
SAME TEMPERATURE.
     Most textbook authors adopt the former definition of "rev"
although they would never discuss the thin-wire example. When
a system receives
heat from hotter surroundings, these authors just apply
dS=dQ/T although some might argue that dQ is not dQrev and,
therefore, since dS is equal to dQrev, it cannot simultaneously
be equal to dQ.
     Of course, nobody argues - those who disagree just write
separate textbooks where "rev" is in accordance with Carnot
condition - heat exchange between system and surroundings can
only be "rev" if system and surroundings are of the same
temperature. These textbooks are inconsistent however - sooner
or later they come to the example where the entropy change of
two heat-exchanging gas systems - hotter and colder - must be
calculated and the definition of "rev" fails. But the authors
don't care.
     I dont know what else I could say.

Pentcho