The principle of excess absurdity (was: Quasistatic conditions

[pvalev <pvalev@BAS.BG>]

--- "Carl E. Mungan" <mungan@USNA.EDU> wrote:

> Pentcho wrote:
>
> >      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.
>
> Interesting question.
>
> But have you considered the possibility that there is a temperature
> gradient along the wire so that each "mesoscopic portion" (in the
> sense discussed by David) of the materials involved are in contact
> with adjacent mesoscopic portions at only very slightly higher or
> lower temperatures? Isn't this implied in the fact that the wire is
> "thin"? Carl

No my only purpose was to guarantee that the heat exchange is very
slow, the system passes through a succession of equilibrium states
and T in dQ/T is defined. However the crucial question remained
unresolved: Is this dQ/T worthy of the sign "dS", provided the heat
exchange occurs between hotter surroundings and a colder system?
Textbooks deal with such thermodynamic questions by applying what
might be called the principle of excess absurdity. There is absurdity
in any discipline but, when its amount is "normal", on noticing it,
students may become more active and try to resolve it, together with
the teacher. When its amount is excessive however, the critical
abilities of both teachers and students are paralysed and learning by
rote remains the only option.
     Consider, for example, the following text on p.127 in the most
famous physical chemistry textbook (P. Atkins, Physical Chemistry,
Oxford University Press, 5th ed.):

"We shall set the temperature of the surroundings equal to that of
the system.... so that they are in thermal equilibrium and the
transfer of heat is reversible."

The conclusion a student can draw is: "The temperatures being equal
is a condition for the heat transfer to be reversible; if they are
not equal, the transfer is NOT reversible." On the next page (128)
the student reads:

" dS = dq_rev / T
...............
That is, the entropy change of a system when it changes between two
specified states can be determined by finding the heat necessary to
take it along a REVERSIBLE path between the same two states."

Everything seems clear. When a system receives heat from another
system at the SAME temperature, dq can aquire the subscript "rev" and

dS = dq /T = dq_rev / T

When the heat donor is at a higher temperature, dq cannot acquire the
subscript "rev" and accordingly dS cannot be equal to dq / T.
     The excess absurdity comes a few pages further - on p. 133.
Under the heading "Spontaneous couling" it is claimed that, as two
systems at different temperatures exchange heat, the entropy change
of either of them is dq / T. The blatant contradiction acts in a
paradoxical way - instead of criticism, religious awe fills the
reader.

Pentcho