(Fundas Master Vidyadhar Tilak has clarified my
physics concepts which has helped this article)
Entropy is introduced
as a variable in Thermodynamics. Then its nature is declared by a value-loaded
term ‘Disorder’. Then Second Law of thermodynamic is paraphrased as “Even when
you manage to decrease entropy in your enclosure under consideration (enclosure
is unnecessarily called ‘system’) it is only at the ‘cost’ of increasing
entropy in the universe.” There is further news that Entropy involves
Randomness. If Randomness is going to increase, human grip on causality will be
loosened, one thinks. Pessimist philosophers rejoice the scientific news as a
proof for their position. Engineers impressionistically remember that after
drawing Pressure-Volume diagram there was a custom of also drawing a
Temperature-Entropy diagram and if you follow the custom your Thermodynamics
Papers are cleared and then you can permanently pass out from the little
embarrassment that you have not understood it. You have never bothered to ask
as to what are dimensions of Entropy in terms of length, mass and time. Entropy
is not perceptible as temperature, pressure, volume etc are. There is no
Entropy Meter instrument in our labs. It remains something far from ‘clear’ and
much less ‘intuitive’.
In all walks of
life everyone accepts that
(Available form of)
Energy expended = (Application form of) Energy reaped + Losses.
This applies to
materials too. You know that area of cloth gone in your garment is less than
area of the cloth that you purchased, without maligning the bona fides of the
tailor, because it is technically inevitable. Of course we know that energy and
matter are (even if inter-convertible) never generated and never destroyed,
they are conserved. All equations are based on this axiom.
Then what we mean
by losses? It is none other than conversion into a form that we don’t
value. When a sculpture is carved, the chips can be used as rubble for filling
up say plinth. Value of chips is much lower than the value of the sculpture.
But value of the Rock which was converted into Sculpture + Rubble was much less
valuable than even rubble. So economically there is outright gain. No one ever
despairs the fact that whole of the rock could not be converted into sculpture.
Rubble is a loss as compared to sculpture. It is not wastage. Had sculpture
been broken while finishing it, such event would count as wastage. Chipping out
material is an integral part of carving, as constructive as retaining the
material which constitutes the sculpture.
Suppose if I tell
you, “The pigment that you put in water for coloring the water, gets dispersed
into water. As it disperses it loses its coloring power which it would have
had if it were not dispersed.” How
can I prove (or refute) my statement? Because we simply can not have it
concentrated and disperse it too! We can not know its coloring power had it not
been dispersed. But wait! We can color different volumes of water up to exactly
same shade and see how much pigment it takes and see if the relation is linear
or otherwise. Before going into Entropy with full throttle, let me simply
mention that it has a lot to do with dispersal.
‘Losses’ is very
important variable not for physical but for economic
considerations. Get maximum output in minimum input, is one of the dictums of
engineering. Always remember that ‘input’ and ‘output’ are anthropocentric
terms depending upon, what you are ready to forgo(cost) for what you want to
get(price). In nature, without any cost-sensitive animal, there is neither any
input nor any output. Cheetahs are cost sensitive. They mutely calculate how
much to tire for a game and how much energy they would get by eating the game and
probability of success in the game. Although Thermodynamics is more notorious
for its losses, no process is loss-free.
To see the
relation between losses and re-distribution, let us conduct a simple
experiment.
There are devices
called capacitors. It is two conducting plates divided by an insulating layer.
If we push in electrons on one side it attracts holes (positive charge) on
other. So it can store static electricity. As it goes on storing charge it
develops an opposing voltage (electrons will try to repel each other, won’t
they?). If you try to push beyond its capacity it explodes. Q = CV charge is
capacitance into voltage built up.
Suppose we have
one charged capacitor and one uncharged capacitor. We connect them together in
parallel.
First let us find
out energy available
The energy stored in
the charged capacitor is ½(capacitance)(voltage2) = ½CV2.
Now instead of using conservation of energy let us use conservation of charge because electrons can not escape out.
The initial voltage = charge/capacitance, V = Q/C.
charge conserved = Q
capacitance doubled = 2C
voltage =
charge/capacitance = Q/2C = ½V
The stored energy ½(capacitance)(voltage2) =
½(2C) (½V)2 = ¼ CV2.
Now the question is where the half of energy is gone?
Answer is that we assumed no resistance in the circuit. This is never the case.
When charge is transferred there is bound to be a flow of current (decreasing
as equilibrium is reached) energy I2R is consumed in transfer.
This is an extreme example but makes clear as to what are
the losses involved in re-distribution.
The main point is that any re-distribution of energy does
consume some energy even in electrical form which is the most efficient form.
Heat is the worst form of energy and we will soon see why it is so.
Temperature is much analogous to ‘head’ in Hydraulics,
‘voltage’ in electricity, ‘force’ in mechanical systems at a gross level.
Similarly, friction in mechanical processes is analogous to resistance in
electrical circuit. Let us repeat the experiment above in conduction of heat.
There are two identical cubes, made of very good heat conducting materials,
insulated from the surroundings. One is initially heated up to 800C.
Another is heated up to 400C and are joined fast with full surface
pressing on each other. After letting some time while away, would we expect
them to settle at 600C? We would certainly not and rightly so as per
observation as well as contemplation, for we have just seen that there is loss
in re-distribution. Don’t jump to conclusion that Entropy can be simply
countenanced as ‘resistance in heat transfer’. This is because entropy does cause losses but
all losses are not caused by it. Also its dimensions would have been same as
that of ‘energy’. M (L/T)2 because losses are in terms of energy,
this however is not correct. It is a pure number like radians.
Now let us observe the curious thing that we call
temperature and what it means at macro level and at micro level. In case of
Thermodynamics the terms macro and micro have a particular meaning. Any thing
or enclosure under consideration (unnecessarily called system which contributes
to the enigma.) is at some temperature. One cube was at 800C another
at 400C. There was certainly a potential difference and heat does
move from higher to lower, but there was one more difference hidden in the
thermodynamic entity
Temperature represents potential energy at
macro (solid piece/enclosure) level but what constitutes Temperature at micro
(molecules) level, is Kinetic energy viz. vibrations or collisions of
molecules
In case of capacitors in first example it was not an issue
at all as to whether the charge and voltage were equally distributed within a single
capacitor or not.
The macro entity (i.e. enclosure) contains
in its turn, the holders and carriers of heat within itself and the energy in
the enclosure is not equally distributed amongst the holder/carriers viz.
molecules. It
is precisely this difference that makes Thermodynamics less intelligible than
other branches of physics (save nuclear physics).
How can we agree that molecules are vibrating or colliding with
different amplitudes and velocities? Let us take example of evaporation of
water at temperature much less than its boiling point. If all molecules of
water at say 300 C were vibrating with equal kinetic energies
corresponding to the level of 300 C, no molecule could have escaped
the liquid state and merrily entered gaseous state.
So there has to be a
huge variation in the kinetic energies of the molecules. There is a further bad
news that these energy levels are discrete rather than continuous. There is
still worse news that distribution of number of molecules amongst the energy
levels available at given macro temperatures is probabilistic. Which molecule
will happen to be at a particular energy-level at a given point in time is not
knowable. However, pattern and total energy (thank God) are knowable. All these
breaking news were given by Boltzman who went on calculating Entropy at micro
level.
But we are not going to get disheartened. Analogy is far
better than mathematics when it comes to intelligibility and if possible
perceptibility. Let us go for an altogether different ‘input’ and ‘output’.
Suppose we are in a material packaging business. Batches of small uniform items
are to be sent in containers requiring minimum volume. Customer is very kind to
us in allowing whatever way the items are stacked. Had items been spheres they
would have spontaneously conglomerated in minimal volume by sufficient
percussions given to the containers. But unfortunately the items are cubes! If
we stack very meticulously we can form big cubes of stack from small cubes,
thus requiring lowest volume. Labor cost is too high to do this and customer’s
workers are ready to pick up cubes from any configuration in which they come.
So we can pour cubes in containers and let them form a heap wherein they are
randomly oriented. Each container must carry fixed weight of cubes without any
condition of array. We are least bothered about which corner of which cube will
be touching (prick into) which surface of which cube! (They are tough.) So the
volume required by each of our batch will be different. We will chose worst
possible dis-array of maximum volume for designing our containers. Therefore
almost all of our containers will be underutilized. However container cost is
too low than the labor cost involved in meticulous array. Volume was our input and
number of cubes delivered was our output. We are making losses in the input but
still doing good business.
As we accepted dilution of our cubes similarly a Thermodynamic
enclosure has to accept dilution of energy because of differential internal
distribution. If more volume is allowed to the nasty molecules they have
more opportunity for more differential internal distribution. Now we have an explanation (and a scientific
one) for the results of the Joined Conductors. When they were allowed to
redistribute their internal energies, displayed lesser gross temperature than
one would expect under the condition of conservation of energy.
By dilution of energy, the energy per se
is not depleting but perhaps (as we shall see soon) its convertibility to
mechanical work may reduce. It does reduce drastically which is one of the reasons why
thermodynamic engines are in-efficient.
Before going into Entropy which is more differential
internal distribution we must take into account another independent &
important cause of the under-efficiency of thermodynamic engines.
If we take a thermodynamic enclosure for giving heat and
taking out work (essence of the concept ‘engine’) we face a problem which
we never face in case of electric motor or mechanical converter, say gear box.
When we supply electricity to an electric motor no mass is put in or thrown
out. No copper, no iron, no insulator, goes in or comes out of the motor. But
the gross occupier of Thermodynamic enclosure which is called the working substance,
has to be replaced en-mass in each cycle. For example the weakened steam
that is thrown out of a steam engine contains lot of heat which is an outright
loss. But this loss is very simple to understand than the dreaded Entropy.
Now we will consider what Boltzman did. Suppose there is a
pair of dice, six surfaces marked by 1 to 6 dots. Drawing a 2 is only one
possibility {1,1}. Drawing a 12 is also only one possibility {6,6}. But drawing
a 7 can happen in six ways {1,6}, {2,5}, {3,4}, {4.3},{5.2},{6,1}. So there is
a pattern of distribution derivable from number of dice and number of sides
they have.
Like our heap of cubes the underutilization can be
theoretically calculated by number of energy-levels available and number of
molecules available. Boltzman derived a
dimensionless number (like radians in case of angle which is length upon length)
and a Boltzman-Constant which made it into temperature. Co-efficient of
differential internal distribution is Entropy and multiplied by temperature
(varying instant to instant so calculus is involved) gives dimension of energy.
We will skip the derivation for it will only further discourage us.
Let us assume that Boltzman was right mathematically. But
Boltzman made a huge terminological goof by calling it co-efficient of Disorder(!)
instead of Co-efficient of differential internal distribution. Suppose N
molecules are colliding in volume V at temperature T. Then somehow we manage to
double the volume. By using Boltzman equation we predict a temperature
significantly less than T/2 and empirically verify it then where is the
disorder? Why it is the case that at initial volume the molecules were behaving
more orderly and in double volume they have qualitatively changed into more
nasty molecules? The double volume could have been the initial volume. Accepted
that work-extractability of a gas goes down more rapidly than linear proportion
with volume. There are non-linearities in many functions in physics. If our
macro-level calculations are coming right why we should be uneasy simply
because a derivation did involve probability calculations?
Dis-order is a misnomer. Philosophers and ideologues are
lurking around to latch on misnomers. In natural languages, disorder is read in
context of health/wellbeing etc. Boltzman was after all a scientist. What the
hell good philosophers were doing while Entropy ballooned scandalously?
Randomness is not always a liability. It has been the
greatest asset in evolution. Had there been no random mutations in the genes where
is the question as to, which will be eliminated and which will be retained
(don’t call it Selected). Many possibilities are produced by Randomness. Some
are good, some are bad and many are redundant. Is it not good to have some good
possibilities than having no possibilities at all? Creativity in humans is
possible due to possibilities in making new combinations. Constructive labor
creates Order, out of what would look like disorder, after the product is made.
If figurative use is allowed, (most of it is already figurative) evolution and
human progress are Negentropic processes taking place in the same universe!
In physicists’ own derivation they call the hot conductor
as system (enclosure) and its cooler partner as ‘environment’! Furthermore
everything except what you take into consideration is pitched against it as
Universe! How you are going to calculate the entropy of the Universe? Are you
not overstepping the limited scope of science by bringing in the infinite? They
also envisage a heat death of the universe when all temperatures will become
equal. All stars including our Sun will be extinguished. Who knows the process by which stars might be
getting generated. Whatever that existed before big bang must be infinitely negentropic!
Let us not indulge in speculative metaphysics any further.
Concentration of internal thermal energy
is better than its dilution for its work-extractability is all that Entropy
means. Is this
always disadvantageous to humans?
Let us take Light as an example. Laser-Rays are made
parallel and synchronized. This not only increases their burning power but also
renders very precise and accurate human control over them. We know how easier and
safe eye-operations are made possible owing to the advent of Laser technique. On
the other end there lies diffused Light. What a huge and probabilistic
calculation would be required to measure diffused-ness of light! Does that make
diffused light useless? The reality is completely opposite. It is the diffused
light that enables us to view in areas where direct and hot sunlight is not
available. In fact what we generally mean by light is diffused light. Otherwise
their would have been dazzling objects such that we would require sunglasses to
look at them on the one hand and light up our torches in the darkest shadow.
Indirect lighting is more comforting while designing interiors of houses. Output
in case of light is not ‘work-done’ but soothing visibility. Output increases
with ‘entropy’ of light!
Drip irrigation and spray irrigation is highly productive
than flow irrigation in agriculture. Water is a scarce resource and plants are
in fact harmed if subjected to too much irrigation. Even land gets saline due
to over-irrigation. Probability of locating molecules correctly is high in case
of flow irrigation than spray irrigation. ‘Entropy’ of water is more in spray
than in flow. Water productivity increases with water ‘Entropy.’ People enjoying themselves in a garden or in a
funfair are highly ‘Entropic’ than soldiers in a Parade.
When the unscientific concept of ‘Entropy as a bane’
ballooned, academicians started seeing Entropy everywhere. There came a thing
called information entropy. They calculated probability of how many times an
alphabet occurs in English. They defined the reciprocals of such alphabet
probability as ‘information-content’! Why? Because a lesser likely news is more
of a news! If lesser likely alphabet goes uncorrupted through your noisy
channel you decreased the Entropy of information. I have never come across more
of a misuse of the category ‘Form-Content’ than this.
As dE = dU + dW that is energy is equal to internal energy
plus work done, they found an analogy in economics, Income = Expenditure +
Savings and went on calculating economic Entropy.
The paradox viz. Temperature is potential energy at
enclosure-level and Kinetic Energy at molecular level is particular to Heat.
Unless you find such paradox you can not go on applying Entropy
indiscriminately everywhere.
The Moral of the story is, “With dilution of insight ‘Entropy
in usage of terms’ certainly increases.”
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