Dear Organlearners,
Stan Schellenburg <stanschellenburg@hotmail.com> writes:
>At,
>
>If /_\F < W, (Free energy is less than Work), how does work
>happen? I keep stumbling over this.
Greetings Stan,
It is good that you have asked. It gives me the opportunity to tell that
at least 50% of students in chemistry also struggle with this problem. I
myself as a student more than thirty years ago also had a problem with it.
In other words, if you or anyone else find it puzzling, you are not the
exception, but rather the rule.
To understand the relationship
/_\F < W
one must think like an accountant of a monetary system. First think of
money flowing OVER THE BORDERS of the system. Any money which goes out of
the monetary system is given a negative sign (debit) while any money which
comes in is given a positive sign (credit). Then think of money moving
around inside the system. When the money in any account in the system
decreases, it is again given a negative sign, but when it increases, it is
given a positive sign.
Now swop the "monetary" in "monetary system" with "energy" to give
"energy system".
Work is a form of energy. Work has two important properties
among many others:
(1) it always flows over the border of the system
(2) it flows orderly and leads to a constructive outcome.
Now for the signs. When the system perform works on its surroundings, the
sign is negative because energy leaves the system. But when the
surroundings perform work on the system, the sign is positive because
energy enters the system.
Free energy is also a form of energy. It is the most general name
we can give to all forms of energy since it consists of one or more
forms of potential energy. Every system has a total amount of
energy, called the total energy and symbolised by E. Some of this
total energy E is needed to maintain the present organisation
(chaos and order) of the system. All the rest of the total energy E
is called the free energy F. The free energy F is the energy which
the system has to change its own organisation or that of any other
system in its surroundings. In other words, free energy F has three
important properties among many others:
(1) its availbility depends on how much of the total energy E is
locked up in the present organisation of the system
(2) it is a "being" property of the system and not a "becoming"
associated with the borders
(3) it is available for any system to change its future organisation
by conversion into chaos (usually heat) or order (usually work).
Now for the signs. When the system's free energy F increases, the change
/_\ of the free energy F, namely /_\F is given a positive sign. But when
the system's free energy F decreases, the change in free energy /_\F is
given a negative sign.
Let us now play with W and /_\F and see how they are related in terms of
their signs!
Assume that the system uses some of its free energy F to do
some work on the surroundings. Assume the free energy F had
an initial value
F(begin) = 120J
(The J refers to the unit of energy, namely the "joule"). Because
the system has used some of this free energy by converting it
into work, its final value must be lower, say
F(end) = 100J
Thus the change in free energy /_\F is given by
/_\F = F(end) - F(begin)
= 100J - 120J
= -20J
The negative sign tells us that it has been decreasing.
Since the free energy converted into work is performed on the
surroundings, works flow out of the system. Thus the sign of
W must be negative. Consider two possible values for W, one
on each side of the -20J for /_\F, namely -30J and -10J.
Is the value W = -30J possible according to /_\F < W?
Remember that the sign < means "is smaller than". Well,
let us substitute the values for /_\F and W and observe the
outcome:
/_\F < W
become
-20J < -30J
Note that positive 20J is indeed smaller than positive 30J
because +30J lies further to the positive side than +20J.
Now, negative 20J is not smaller than negative 30J since
-30J lies further to the negative side than -20J. In other words
the claim
-20J < -30J
for
/_\F < W
is false.
Never think only in terms of numbers for a formula. Always think
in terms of concepts. In other words, give a meaning to
-20J < -30J
for
/_\F < W
It means that the system cannot deliver (negative sign) more work
(30J) than the amount of free energy (20J) which becomes
converted (negative sign) into work. Why not? Because then the
Law of Energy Conservation would become invalid since 10J (the
difference between -20J and -30J) would have been created. In
other words, the MAXIMUM amount of work which the system
can deliver when the free energy decreases with an amount
/_\F = - 20J
is
W = -20J
Let us consider the other case for
W = -10J
We now have for
/_\F < W
the values
-20J < -10J
The claim is indeed true. The system can deliver less work
than the amount of free energy converted. So what happens
to the rest of the free energy since accordding to LEC we
cannot create, nor destroy energy? Well, the other 10J of
free energy has become converted into thermal energy of
which some may escape the system as heat.
Up to now we have considered the case of a system which
delivers work. What about the opposite case, namely, that
the (some system in the) surrounding performs work on the
system so that the system's free energy increases, say with
/_\F = +20J
Again consider two cases for W, namely +10J and +30J.
First consider
W = +10J
for
/_\F = +20J
Thus the claim
+20J < +10J
for
/_\F < W
is false.
What does it mean in words? To raise the system's free energy
with +20J, the minimum amount of work needed is +20J. The value
+10J is less than this minimum amount of work. Should the
system's fre energy F increase with +20J when only +10J of work
is added to it, then 10J of energy has been created. LEC forbids
this.
Now secondly consider
W = +30J
for
/_\F = +20J
Thus the claim
+20J < +30J
for
/_\F < W
is true.
What does it mean in words? To raise the system's free energy
with +20J, the minimum amount of work needed is +20J. But
now 10J of work more than 20J has been pused into the system,
i.e 30J work in total. So what has become of that extra 10J? It
has been converted from work into anything else, usually heat,
but definitely not work. It cannot disappear because then energy
world have been destroyed which LEC forbids.
Here is some practical examples for the two valid cases of
/_\F < W, namely
-20J < -10J
and
+20J < +30J
For
-20J < -10J
think of a battery which looses -20J of its free energy to turn
a motor. The bearings of the motor is partly locked up so that
only -10J of work appears. The other -10J of free energy appears
as heat in the bearings and windings of the motor.
For
+20J < +30J
think of a flat battery which has to be charged by +20J in its free
energy, using 30J of energy from a generator. The battery may
be partially short circuited by some lead sulphate precipitate
touching its plates. The extra 10J of work is used up to heat
this internal resistance caused by the lead sulphate. After the
charging, the battery becomes flat again by current flowing
through this internal short circuit.
Stan, I hope that that the order relationship
/_\F < W
has now become more clear to you. If anything is still murky,
please ask. Students sometimes keep on asking even after
understanding how it works. When I ask them why they ask
me again and again, some tell me that although the it seems
to work, they do not trust it. For them I say "Hurray, now
you begin to think like a scientist". A few others tell me that
/_\F < W
seems to be more complex than
/_\F = W
They want to make sure that they do not get lost in this
complexity. For them I say "Hurray, now you begin to think
like a modern scientist".
It is very, very important that you feel at ease with this
relationship. There are some incredibly important insights
to be gained from it. In fact, the past few days I have been
preparing (a very long contribution) with the topic head
"Efficiency and Emergence". In this contribution this order
relationship plays a central role. So before I submit that
contribution, try to get at ease with the order relation. It
will definitely pay dividends.
I once gave a short summary on this list of the "ethics of
work" which one may create from the order relation
/_\F < W
I still feel the gooseflesh on me form when I think that this
order relation is the stepping stone to a scientific ethics
of work. Perhaps I should one day go into detail in this
ethics again.
Please remember, numbers with signs are not really confusing.
What is confusing to a rock? Numbers are like rocks. What
makes numbers confusing is when we neglect or fail to
conceptualise the meaning of these signed numbers. The more
we string concepts to these signed numbers so that the
MORE COMPLEX our conceptualisation becomes, the LESS
our CONFUSION (COMPLICATION) becomes.
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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