Dear At,
>Will something (Gibbs or you) have to give in, or will
>some new understanding emerge?
Gibbs have to give in? Never! I would give my selfresponsibility to
someone. I would never blame someone else for my incapability to
understand his ideas. So have I to give in? The matter is too important
and the result would be immergence.
So before I feel free enough to follow your path, I need to collect my
baggage of some questions, which tell me, that they have a point, and of
which I don't know, whether they are right or wrong or both.
>What remains of Gibb's expression?
>/_\F < 0
>which can be taken as the definition of a spontaneous process.
>
>But, Winfried, note what you did -- you wanted the following to be:
>/_\F > 0.
You have cited, what I want in the beginning of your answer:
>>My guiding idea about the digestive phase of learning is, that the
>>task of this phase is to increase the systems F: /_\F(SY) > 0
While I fully agree that necessarily /_\F < 0 for a spontanous
process, I was thinking about it in a way, that
/_\F = /_\F(SY) + /_\F(SU) < 0 in such a way, that /_\F(SY) > 0. There
is no logical contradiction, as long as /_\F(SU) << 0 ("<<" meaning
"sufficiently smaller than").
>You want
>/_\F > 0
>because you need free energy, but Gibbs says that for all spontaneous
>processes, even the Ostwald digestion process,
>/_\F < 0.
>The two expressions are contradictory to each other. In other words,
>the proposed model of the Digestor seems to be useless for your needs.
>It cannot both raise and lower its free energy FOR THE SAME PROCESS
>of some Ostwald digestion. You have arrived at the point of a logical
>contradiction.
I could express my guiding idea, without the contradiction in words as
follows:
While the crystal has less free energy than the sum of the free energy of
the grains with the same mass as the crystal, its free energy is surely
increased compared to the free energy of the one grain out of which it
grew.
This is in words nothing else that in the formula above:
/_\F(SY) = F(final state) - F(initial state) = F(crystal) - F(initial
grain) > 0
means that F of the grown crystal is increased compared to F of the
initial grain. Still the total F decreased, because :
/_\F(UN) = F(grown crystal) - F(all grains, which became the crystal)
< 0. This is what Gibbs and the Ostwald digestor require in order to
be spontanous crystal growth out of the precipitate. No, Gibbs has not
to give in.
To put it together in one yes/no-question:
Do you agree that F(crystal) - F(only the initial grain) > 0 ?
If yes, I have not to give in either, and there is no contradiction.
If no... hm, I just cannot imagine.
>We cannot sell the cake and eat it. In the SPONTANEOUS process
>along
>the PATH of Ostwald digestion the free energy F has to DECREASE, i.e.
>/_\F<0. The free energy of the result, namely larger crystals
>(increased m) because of more perfections (increased M), cannot be
>applied to REPEAT THE SAME PATH again spontaneously. The free
>energy for that path has become so low that it cannot decrease even
>further as before. We have reached the limit (essensiality spareness)
>for that path.
Of course. There is no spontanous way back to the many grains, the
precipitate. External work W has to apply: Erosion due to the hammering of
water and wind for example, both in neverending movement due to the work,
that a constant stream of sunlight makes available, some of which has been
captured on the course of millions of years in the reservoirs of fossile
fuel.
At, I forgot to thank you for your reply and I know, there are more, and
more important, points in it. But before I can start to work on them, I
need your confirmation of my one question. I cannot go on before, because
otherwise someone would have given in and I hope for something new to
emerge. It woun't be Gibbs, so you or I or both of us.
Liebe Gruesse,
Winfried
--"Winfried Dressler" <winfried.dressler@voith.de>
Learning-org -- Hosted by Rick Karash <rkarash@karash.com> Public Dialog on Learning Organizations -- <http://www.learning-org.com>