Date: Mon May 30 1994 19:33:10
From: Ken Stuckas
Subj: Entropy...last word
Aha! I knew that presumptious message title would catch someone!
I have become increasingly annoyed at suggestions here
and elsewhere that Evolution violates the second law of
thermodynamics. So, I hereby offer this monograph on the
subject of the second law and entropy. And I then offer a
challenge to anyone who is willing to use the substance of
this piece to demonstrate how Evolution could possibly
violate the second law.
My qualifications? I have a degree in aeronautical and
astronautical engineering and am a registered professional
The Second Law of Thermodynamics and Entropy
by Ken Stuckas
There are several ways to express the second law of thermodynamics:
Kelvin-Planck: No _cyclic process_ is possible whose result
is the flow of heat from a single heat
reservoir and the performance of an equivalent
amount of work on a work reservoir.
Energy interchanges can take place in any direction
between any pair of work reservoirs, but energy
exchange between a work reservoir and a single heat
reservoir, _with no outstanding changes in other
systems_, can proceed in one direction only -- that
in which the work reservoir does work and the heat
reservoir absorbs heat.
Clausius: No _cyclic process_ is possible whose result
is the flow of heat from a heat reservoir at
one temperature and the flow of an equal
quantity of heat into a second reservoir at a
It is, however, possible to carry out a _non-cyclic_
process in which there is a flow of heat out of a heat
reservoir at a lower temperature and a flow of an equal
quantity of heat into a reservoir at a higher temperature.
- - -
Temperature is a measure of heat added or rejected for any substance
undergoing a process at constant pressure or constant volume as long
as the values of the factors of proportionality for the substance are
known. These values are called the "specific heat at constant pressure"
and the "specific heat at constant volume."
It would be convenient to have a factor of proportionality with which
temperature could be used to measure the heated added or rejected for
_any_ process, not just processes at constant pressure and volume.
As luck would have it, such a property exists. It is called _entropy_.
Mathematically, T ds = dq, where T is the temperature of a substance,
ds, is the incremental change in entropy and, dq, is the incremental
corresponding incremental change in heat.
- - -
_Back To The Second Law_
Besides the Kelvin-Planck and Clausius statements, the second law may
also be expressed in terms of entropy.
Entropy: In a real _closed_ system, total entropy
can never decrease.
It is important to note the restriction that the system must be
closed -- that is, neither energy nor mass may cross the boundaries
of the system. In other words, all elements initially in the system
must be present and accounted for in the final reckoning.
The entropy in parts of a closed system may decrease, but that
decrease will be more than offset by an increase in other parts
of the closed system.
Let's look at a couple of semi-real examples. (Truly isolated
systems do not exist.)
I have a swimming pool divided into two halves by a thin dividing
wall. Into one half I pour ink and into the other I pour water.
I remove the divider and wait. The ink gradually mixes with the
water (ignoring natural convection) and eventually I have a fairly
uniform mixture. The entropy of the pool contents has spontaneously
increased through the process of molecular motion. I can reverse
the process only by introducing into it Ken's magical ink-water
separater. Using energy I have brought into the formerly closed
system, I put the dividing wall back into place and grab all the
ink molecules and put them in one side while at the same time
moving all the water molecules to the other side. This could take
a while... 8*)
I have restored the swimming pool to its original condition, but
only by breaking into the closed system using energy I took from
another closed system (one which I constructed around the pool
before my original experiment began). Ken's magical ink-water
separater runs off batteries which are now depleted so the
entropy of the second closed system has increased as well.
I could recharge the batteries, but I would have to go outside
the second closed system and get an extension cord -- well, you
get the idea.
Here's a different example:
I have a closed system, a box of air through which neither energy
nor mass may be transfered. In the center of the box I have one
ice cube. The air is at 70 F and the ice cube is at 20 F. I return
to the box some time later and notice a puddle of water where the
ice cube used to be. The ice cube has spontaneously gone from a
state of lower energy to a state of higher energy while the entropy
of the ice cube itself has increased (water molecules move about
at random, but are prevented from migrating in their solid
state). The entropy of the surrounding air which has decreased in
temperature has decreased (the pressure in the box has decreased
due to decreased molecular motion of the air). The entropy of the
entire contents of the box has remained unchanged.
Now that we have a better, non-ICR, understanding of what entropy
is all about we can talk further about the misuse of the concept
in areas other than thermodynamics.
The concept of entropy, that is, the concept that things spontaneously
move toward randomness and disorder has been captured and used as a
metaphor in areas other than thermodynamics. These metaphorical
applications of entropy are useful up to a point. They have been
applied to social dynamics and information theory, but herein lies the
rub. Metaphor has it's limitations. We learn about new things through
metaphor. But unthinking extrapolation of a metaphor often fails.
If I ask you what a UFO looks like, having never seen one myself, you
might say, "It's just like an upside-down dinner plate that zooms
through the air -- sort of a "flying saucer." You have just used
metaphor to explain to me something to me that I have no acquaintance
with. So far, so good. Carrying the metaphor too far, I imagine in
my mind that a UFO is also made of plastic and has little daisies
around the edges just like the dinner plates I have at home.
See the problem? Metaphor has its limits. The generalization that
"everything tends toward disorder" when carried away from the subject
of thermodynamics can easily lead to false impressions and error.
Notice that in the Kelvin-Planck and Clausius expressions of the
second law, I used some terms that have very specific meanings
which may be easily misunderstood by those not familiar
with the esoteric language of thermodynamics.
One must have a thorough understanding of the definitions of heat
reservoir and work reservoir. As in mathematics, precision of
definition is demanded to avoid obfuscation.
I hereby challenge anyone to use the strict definitions of the second
law of thermodynamics to demonstrate that the fact of evolution in any
way violates the second law. This is called science.
Put up or shut up.