Entropy LO22406 -was: Free energy and work

AM de Lange (amdelange@gold.up.ac.za)
Wed, 4 Aug 1999 11:36:26 +0200

Replying to LO22387 --

Dear Organlearners,

Stan Schellenburg <stanschellenburg@hotmail.com> writes:

>Thank you for clarifying the relationship between free energy and
>work for me. I notice that even my question embodied a false

Greetings Stan,

Its a pleasure.

I did not notice the false assumption! I would like you to point it out
and explain to me.

The relationship between free energy F and work W has far
reaching consequences. All our tools depend on it. Life also
depend on it as I will show in my contribution "Effficiency and

But we must never fix our attention on only one relationship. This
also applies to the relationship between free energy F and work
W. We must shift our focus from relationship to relationship
wherever the web of wholeness takes us. The relationship
between free energy F and entropy S is just as important. This
is exactly what you have been doing:

>Now I have been thinking about entropy, specifically the equation
>that describes entropy as a function of the energy needed to
>maintain the present organization of a system and absolute
>temperature: S=(E-F)/T.

E is specifically the TOTAL energy within the system. It is also
called the INTERNAL energy E of the system.

It is NOT the total energy E which is needed to maintain the
present organisation of the system. Maintaining the present
organisation is the function of the entropy S of the system. That
is why the entropy S can be used to measure (express) a
system's PRESENT organisation.

In terms of energy it means that only part of the total energy E
is locked up in the present organisation of the system. The rest
of the total energy E is nothing else than the free energy F. This
is why F gets the "free" in its name -- it is energy free from the
organisational constraint. In other words, (E-F) is that part of the
total energy E locked up in the present organisation of the
system. That is why (E-F) is in some way related to the entropy
S. It was the genius of Gibbs to realise that the relationship is
S = (E-F)/T
where T is the absolute temperature.

The absolute means that we should begin with the temperature
scale at its lowest possible value. The celcius centigrade scale
begins at zero degrees. It is the freezing point of water and
definitely not the lowest temperature possible. Thus the celcius
scale give a relative temperature. The lowest temperature possible
begins at -(minus) 273 degrees celcius. This is where the zero of
any absolute temperature scale has to begin.

Maxwell with his Molecular Kinetic Theory gave us the insight that
the absolute temperature T is proportional to the AVERAGE kinetic
energy and thus the AVERAGE velocity squared of every molecule.
The more the diversity in velocity, the higher the average velocity
an thus the higher the absolute temperature T.

>What happens when temperature increases in a system?
>Intuitively, I would think E-F automatically would increase, i.e.,
>that more energy would be required to maintain the present
>organization and F would be absorbed -- decrease -- into E-F.
>If T goes up with no change in E-F, then, is there automatically
>an immergence? But if T goes up and E-F doesn't change, S
>decreases. How can that happen, that is, how can entropy
>decrease? Does entropy of the system decrease while still
>entropy of the surrounding universe increase?

Wow, what a bunch of questions? The clue in answering them
is to answer them emergently, i.e, one by one, each time
comparing the answer to a new question to the answers of the
previous questions for consistency and coherency.

Your intuition is correct. When T increase, the "diversity of motion"
(which we call traditionally "chaos") increases. If S measures the
organisation of the system and if we consider "chaos" as part of
a system's organisational makeup just as "order" (diversity of
structure), then S has to increase. Thus (E-F) also have to increase.

The danger is to assume that S increases linearly with T. I can
quote many formulas from text books on physical chemistry which
will illustrate that the increase is non-linear. In simple systems the
increase is logarithmitically. An even greater danger is to assume
that both E and F change in the same manner as S with T so that
(E-F) will change in the same manner as S. Actually, E and F can
change in many ways different to each other and S while the
difference (E/T)-(S/T) changes in the same manner as S as is

The greatest danger is to assume (which most students do,
ignoring their intuition) that (E-S) is constant when T changes.
In this case S will decrease as T increases. This is the second
possibility which you have offered. What you have done, is to
compare your first possibility [(E-S) changes with T] with the
second possibility [(E-S) is constant with T]. The different
consequences of these two possibilities acted as an entropic
force which shocked your mind into an emergence (or close to it).
Suddenly you began to wonder -- HOW does entropy get
changed (decreased as you asked, or increased for the same
matter). If I may say so, you have now entered the Prigoginian
state of mind with this HOW ( Please note that you are not
schocked any more by the fact THAT the entropy gets changed.
This is a considerable advancement in itself!)

Entropy gets changed (decreased, but also increased) in two
fundamentally different ways. The one way is by PORTATION
and the other way is by PRODUCTION. The portation can be
an export so that the system's entropy decrease or it can be
an import so that the system's entropy increase. It is not the
entropy which is portated, but some of the system's total
energy E. We must never think fragmentedly of the energy E
as merely having quantity/content, but always think of it as
something which which also has form/quality which is
expressed by S. It means that we have to think of energy as
something which has organisation. In other words, by changing
(importing or exporting) some of the system's total energy E,
the entropy S of the system also gets changed (respectively
increased or decreased).

This PORTATION of some of the total energy E (content) and
thus its associated entropy happens REVERSIBLY. The
"reversible" means that what has been imported, can equally well
be exported and vice versa. The entropy of the universe remains
constant for this reversible portation. In other words, what the
system gains/loses in total energy E and associated entropy
S, the environment (surrounding systems) respectively
loses/gains in equal values.

But is its completely different with the second way in which
entropy S can change, namely PRODUCTION. The entropy
production happens IRREVERSIBLY. The "irreversible" means
that what has been done cannot be undone. The entropy of the
universe increases for this irreversible production. The production
is always a gain in entropy, either in the system, or in the
surroundings or even in both. Whereas the portation concerns
the shipping of some total energy E between the system and
its surroundings, the production concerns the using of free
energy F in some system! Please note (the sign == means
portation == change in total_energy /_\E
production == change in free_energy /_\F

Obviously, the initial production of entropy can be further
subjected to subsequent portations of entropy.

I know it is very tricky to understand this difference between
reversible portation of entropy and irreversible production of
entropy. Many scientists work through Prigogine's publications,
see him making the distinction
dS = dS(rev) +dS(irr)
but fail completely to understand it so that entropy production
remains a mystery for them. Please take care here.

So far my discussion seems to concern only physical systems.
But I have carefully expressed it in such a manner that it also
applies to spiritual systems. The previous paragraph has a very
important bearing to one of the main differences between the LO
(Learning Organisation) and KM (Knowledge Mangement). In
KM (first and second generation) the focus is on the portation
of knowledge which happens reversibly. This is typical
of traditional education.

But in a LO, for me, the focus has to be on the production
of knowledge which happens irreversibly. This is typical of
competency based education and personal mastery. KM is
concerned with a reversible shipping of some spiritual total
energy E and its associated entropy S (the organisation of E).
But in a LO we are concerned with more than that. We are
also concerned with utilising the spiritual free energy F.

Maybe it is a little bit more clear why free energy F is needed
to produce entropy and why entropy has to be produced to
change organisation. Since the entropy S measures the
PRESENT organisation of the system so that part of its
total energy E is locked up to maintain the PRESENT
organisation of the system, we have to use that part of the
total energy E NOT locked up, namely the free energy F, to
produce additional entropy. We have to PRODUCE additional
entropy so that we can change the present oganisation into
some FUTURE organisation. Whether the future organisation
is constrcutive or destructive in terms of the present
organisation, depends entirely upon us and how we employ
the seven essentialities.

>With an emmergence, does S go up?

Yes. But when S goes up, think of it as some tiny part of it
which is going up so that the whole S also goes up. It may
easily happen that when this tiny part goes up, some other
bigger part goes down as a result of portation. Thus S will
actually go down, the tiny up-going shielded by the bigger
export shipping. I can give you thousands of examples in
chemical reactions. This shielding effect is always a source
of confusion for the majority of students.

>Proportionally, can you give me an idea of what S is for a
>person versus for, say, a cat or a car? I'm wondering what
>some actual S numbers are for things.

Stan, I like your intuition, wanting to compare the entropy of
things/entities with each other. I will try to answer you some
distance along the way. But first I have to make two warnings.

Warning (1). It is better to focus on the CHANGES in entropy
S, free energy F and total energy E than on the ABSOLUTE
values. The reason is practical. When we want to focus on the
absolute values, we need all the information on evolution since
the beginning of time at the Big Bang. For example, atoms of
different elements have different total entropy (values at specified
conditions) because they have evolved differently. Check any
list of standard thermodynamical properties of the elements
to see how much they differ.

Warning (2) When we compare the absolute entropy (at say
standard conditions for temperature and pressure) of SINGULAR
entities, the fact that we compare one entity with one entity is
not enough. We must also make sure that their masses are the
same since mass, a "condensed" form of energy, is always
organised (it has a chemical composition). Thus it is foolish to
compare the entropy of a baby to the entropy of an adult.
Obviously the baby will have less entropy because it has less
mass and thus less of each chemical compound needed to make
up a living body.

To calculate the entropy of a human body is a far more complex
than to calculate the national budget of the USA. Give me a team
and I will do it. But on my own I have too little time and
data. Yet, I will make some calculations to give you an indication
of order rather than exact magnitude. Let us compare a car with a
certain mass with an animal of the same mass. A small car and a
cow, or a truck and an elephant will do. I do not know of a car
with the mass equal to that of a human body, say 100kg.

I assume that the mass of the car, like the mass of the cow, is
1000 kg. I assume that the car is constructed typically from iron,
aluminium, glass, plastic and rubber. Varying the ratios of the
iron, aluminium, glass, plastic and rubber will change the outcome.
In the case of the cow I have to consider the ratio of water, protein,
fat and bone. My rough calculations (taking more than an hour,
because I had to search for data) is the following:
(1000 kg each)
S(iron) = 0.4 MJ/K
S(car) = 0.8 MJ/K
S(water) = 3.8 MJ/K
S(cow) = 4.6 MJ/K
The MJ/K means "megajoule per kelvin".

For comparison I have also included the entropy of pure iron
and the entropy of pure water. I have not taken into account
any level of organisation higher than the molecular one of
chemistry. In other words, I have not taken into account how
the macroscopical morphology (internal organs) of the cow
add to the final entropy. But I suspect these macroscopical
organisations of the cow and the car to increase the final
values by less than 5%.

How do you like it? Should entropy be merely a measure
of chaos as the traditionalists insist, then cars are quite
ordered entities while cows are much more chaotic.

When comparing the entropy of an adult human and a cat, we
have to take a cat with sufficient mass like a lioness. I
will calculate only the physical contribution to the entropy.
It is impossible for me to include the spiritual contributions. My
calculations indicate:
(100 kg each):
S(tree) = 0.42 MJ/L
S(cactus) = 0.40 MJ/K
S(lioness) = 0.45 MJ/K
S(human) = 0.47 MJ/K

The slight difference is mainly to the bone structure (scelet)
which is slightly more massive in the case of the lioness than
the huamn. I have also included the entropy of a two kinds of
plants (a young pine tree and barrel cactus) for comparison.
The cactus, although evolutionary much younger than the pine
tree, has less entropy than the tree because of a higher water
and lower cellulose content. Please remember that the above
is based on only approximate calculations. So do not make
far reaching conclusions on these approximate values.

May I remind you of the difference between the genetical make
up of a human and a chimpanzee. It is a little more than 1%.
However, for that mere 1% difference in the genes, the culture
of humans differ vastly from the behaviour of chimpanzees.
The closer two entities become in quantities, it is not the
difference in those quantities which count, but the difference
in their emergent qualities.

>Thank you,

Thank you Stan for asking such difficult questions. It is
trying to answer them which makes life so interesting.
If my explanations sometimes come wierd through,
please remember that English is not my mother tongue.

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

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