Dear Organlearners,
Greetings to all of you.
Yesterday I was at a large factory producing many kinds of plastic pipes.
My order was a miserable spot against the large orders which they get from
firms. Yet the lady (one out of six) in the sales office was very friendly
with me. It took het fifteen minutes to fill in four different forms on
the computer. I could see that she was frustrated despite her
friendliness.
So I asked her why she had to fill in four different forms. She replied
that management decided to have certain information on all sales.
Meanwhile, as a result of previous decisions, the three other forms had to
go to production, warehouse/security and accounts, each with its own
peculiarities. I was astounded. Does their management not know anything
about a relational database, that she could fill in one form and that they
could duplicate particular sections of it for particular applications? She
grimaced and said that a few months ago they were simply told that they
had to use the new computer system.
It was late in the afternoon just before closing and I was the only
customer. I asked her what usually happens during the day. She said to me
that early in morning everything goes fine; then as the customers increase
their office comes closer to chaos; finally in the late afternoon it
becomes somewhat normal again. I could clearly imagine in my mind the
energy-entropy dynamics involving: 4.forms + 5.sellers + nr.customers +
nr.items + ... => ...@#$%&*.
While driving back to my home, I thought this dynamics over once
again for any chemical reaction. The general symbolic expression
for any chemical reaction is:
aA + bB + cC + ... => dD + eE + fF + ...
Here the small letters a, b, c, ..., d, e, f, ... symbolise numbers. The
capital letters A, B, C, ..., D, E, F, ... symbolise compounds. Those
on the left side (A, B, C, ...) are called the reagents because they are
consumed by the reaction. Those on the right side (D, E, F, ...) are
called products because they are produced by the reaction. The
aA + bB ... means that a number "a" of compound "A" needs a number
"b" of compound "B" ... to react. This will produce a number "d" of
compound "D" as well as a number "e" of compound "E" ..., symbolised
by dD + eE + ...
Each of the compounds has its own total energy, entropy and free energy.
Each of the compounds have its own number of them available.
Consider compound A. This number of units of compound A need not be the
same as the number "a" of the compound participating in the reaction. When
we multiply the number of units of compound A available with the total
energy of compound "A", then do the same to B, C and the other reagents
and finally add them all together, we will get the "total energy of the
system". We will symbolise this as E(sy) where E="total energy" and
(sy)="of system". We will do the same to get the entropy S(sy) and "free
energy" F(sy) of the system.
As the first number "a" of the total number of A disappear together with
the first number "b" of the total number of B and the other reagents, the
total energy E(sy) of the system will change by an amount /_\E(sy). As the
second number "a" of the remaining total number of A disappear together
with the second number "b" of the total remaining number of B and the
other reagents, the total energy E(sy) of the system will change by
another of the same amount /_\E(sy). This means that as the reaction
proceeds forward, the total energy E(sy) of the system will change in a
linear manner.
I have prepared a rather complex set of graphs to show how it happens. The
uniform change in /_\E(sy) is depicted by the second graph from the
bottom.
[Host's Note: To see At's graph, point your browser to
http://www.learning-org.com/graphics/LO26947.gif
In this msg, the characters /_\ are the Greek letter delta which is the
mathematical symbol for "change in ..." ..Rick]
On the horizontal axis I have indicated how the reaction proceeds. In the
beginning (to the left) 100% of A, 100% of B, 100% of C, ... are
available. Then step by step less of them remain as they proceed through
80%, 60%, ... to the right of the graph.
I have also depicted on the graph how the entropy S(sy) of the system
changes by /_\S(sy). I should have given only one graph because the system
has only one for /_\S(sy). But I have taken the liberty to show two such
graphs for /_\S(sy). The third one from the bottom is for an anabolic
reaction while the second one from the top is for a catabolic reaction.
Please note that each of them are straight lines as is the case for
/_\E(sy). The anabolic means that at least one of the products (D, E, F,
...) has a far greater entropy than any of the reagents (A, B, C, ...).
That is why the graph runs in an upward direction. However, the catabolic
means that one of the reagents have an entropy far greater than any of the
products. That is why the graph runs in a downward direction.
So what has become of LEP (Law of Entropy Production) which says that the
entropy has to increase. It seems as if the catabolic reaction defies LEP.
No, what we have done with the entropy S(sy) of the system, is merely to
find the sum of all the entropies of all its constituents. We have NOT
ALSO added the production of entropy during the reaction because of such a
reaction. Sometimes the reaction will liberate heat (exothermic) and
sometimes it will take up heat (endothermic) as part of its entropy
production. Sometimes the reaction will change from a homogenous mixture
(eg solution) to different phases (solid and liquid) and sometimes the
opposite will happen. All these happenings result from the entropy
production.
Should we take them also into consideration in our calculation, we will
now find the entropy S(un) of the universe (system plus surroundings which
do change). This entropy S(un) of the universe will change with /_\S(un)
as a result of the reaction. See the top graph. The gradual change in
/_\S(un) is not linear as in the case of /_\S(sy) for the system alone! At
first it increases rapidly, but then the increase slows down until it
reaches the maximum value at some 70% conversion of the eaction. The
remaining 30% of the reagents will not react anymore. The system has
reached its equilibrium state.
Obviously, we have indicated only those changes to the universe UN as a
result of this specific chemical reaction. A zillion of other things also
happens in the universe. We have not taken them into consideration. But
all those becomings which are chemical reactions, will behave the same as
our general example. Perhaps other kinds of becomings may also do so,
perhaps not.
When we look at the bottom graph for the change of the free energy F(sy)
OF THE SYSTEM, it looks very much like an inversion of the top graph for
the change of the entropy S(un) OF THE UNIVERSE. Whereas /_\S(un) will
have reached its maximum value at 70% conversion, the /_\F(sy) will have
reached its minimum value at the same point of conversion. That point at
which the reacion stops although complete conversion had not been
obtained, is called the equilibrium point.
I hope it becomes clear to you fellow learners that the equilibrium state
can be reached from both sides: either 100% reagents and 0% products, or
0% reagents and 100% products! This gives many students the idea that a
chemical reaction is reversible. It is not. When on the left side of the
equilibrium point, the reaction will proceed irreversibly to the right so
as to reach the equilibrium point. When on the right side of the
equilibrium point, the reaction will proceed irreversibly to the left so
as to reach the equilibrium point. In neither cases will it ever overshoot
the equilibrium point.
In a chemical clock reaction the equilibrium point is not rigid, but
shifts harmonically through a region, say 50% to 80%. As the clock runs
down, the region becomes smaller until it stops in a rigid point. In this
case people theorising about complexity speaks of the "region with the
fixed point" as a "strange attractor".
Now let us go back to the factory where I have been yesterday.
Remember how I have depicted it:
4.forms + 5.sellers + nr.customers + nr.items + ... => ...@#$%&*.
I could clearly picture in my mind how during each day, these unfortunate
people in the sales office were subjected to a catabolic reaction (four
different less complex forms to complete rather than one more complex
formfeeding a data base). Since catabolic reactions are usually exothermic
(liberating heat) I could clearly picture in my mind how the heat between
these people and their customers would built up during the day. Round
about two clock the system will have been driven to its limits. To
counteract this depletion of their "free energy", they then do nothing,
just waiting for the odd customer like me to show up. Meanwhile they eat,
drink coffee and do all sort of things to at least regain their physical
free energy. All the signs are there in the waste paper baskets and ash
trays.
I asked the lady what does management say when they go in the idling mode.
She said to me that management is threatening them that two of them will
have to go since they have made such a huge investment in the new computer
system. I then asked her whether the remaining three will cope with the
sales office. She said to me: "No, but neither does management care." I
said aloud "I wish I had a big box of chocolates to offer to all you
willing and friendly people." They smiled. But as I walked out, I said to
myself "Another factory is going to hit the dust because it is burning out
its heart."
With care and best wishes
--At de Lange <amdelange@gold.up.ac.za> Snailmail: A M de Lange Gold Fields Computer Centre Faculty of Science - University of Pretoria Pretoria 0001 - Rep of South Africa
Learning-org -- Hosted by Rick Karash <Richard@Karash.com> Public Dialog on Learning Organizations -- <http://www.learning-org.com>
"Learning-org" and the format of our message identifiers (LO1234, etc.) are trademarks of Richard Karash.
