|
ENTROPY
FOREVER Alvin Lowi, Jr. P.E. Entropy is a word of
questionable etymology. It entered the vocabulary via the obscure science of
thermodynamics back in 1860. While the word has precise meaning in this field
of science, its popular usage is largely jargon. Wikipedia gives the
derivation of the word from the Greek as follows: Entropy: εν or en = inside + τρέπω or
trepo = to chase or escape From its etymology, entropy means “to chase your tail.” That result,
intellectually speaking, has been prevalent among philosophers. Even to a
student of classical thermodynamics, the meaning of the word is not obvious.
Even less obvious is its connection to the popular notion of inevitable
disorder or chaos. Rudolph Clausius discovered and defined entropy as
a consequence of codifying the Second Law of Thermodynamics back in 1862 when
it was known as Sadi Carnot's principle. Clausius denoted the ratio of an
infinitesimal quantity of heat flow to the temperature prevailing at the
interface across which the heat flows as a infinitesimal quantity of
“entropy” having the dimensions of specific heat or heat capacity. Clausius’ definition of entropy cannot even be
properly written without resort to differential calculus, expressed in the
equation where ds
denotes an infinitesimal change in entropy, dq denotes an infinitesimal amount of heat energy and T is the absolute temperature at the
point of heat flow. To denote the magnitude of entropy, one must first
define a thermodynamic cycle and the processes involved, then solve the
equation from integral calculus as follows: Where S
is the magnitude of entropy change for the cycle denoted by the symbol for
cyclic integration or summation over the cycle step-by-step,
process-by-process. Clausius found entropy plays an utterly unique role in
thermodynamic reasoning but he would be surprised to see the word bandied
about in the common language as it now is. "Entropy" is a mysterious notion even in
physics where it was conceived and labeled. It is at least one of the several
thermodynamic properties of matter that physicists use to define the
equilibrium state of a thermodynamic system, such as a heat engine. It is
indispensable to engineers designing and applying steam engines, air
compressors and such. While most of the thermodynamic properties are real
to the human sensory organs, the notion of an equilibrium state is only an
abstraction. Equilibrium is an analytical tool of classical thermodynamics,
like a snapshot to an anthropologist. The analyst wishes the world would hold
still while he gets a grip on the situation. But time waits for no one. Since
classical thermodynamics is valid only for systems in equilibrium, it has
been suggested that the study should be called
"thermostatics." Entropy happens to be one of the so-called
independent variables among which are pressure, temperature, mass and volume.
But unlike those measurable properties, entropy is a pure abstraction. It is
not directly measurable. There is no such thing as an entropy meter. In addition to the independent variables, there are
four other thermodynamic properties known as dependent variables or
potentials. These are internal energy, enthalpy, Gibbs free energy and
availability. The latter two are defined in terms of entropy. Any three of
these variables can define the state of a thermodynamic system. This means
some of the properties are redundant in any given situation. Entropy has no meaningful absolute value. It is
defined only for change. Thanks to Clausius and others that followed, we now
know that an increase in the ratio defining entropy indicates a reduction in
the potential of a system to convert heat energy to work where “work” is that
particular form of energy that is equivalent to the lifting of a weight
against gravity. The lifting of a weight against gravity is the burden of
humanity. Thus, work is the prize offered to humanity by thermodynamics. The First Law of Thermodynamics is also known as
the law of conservation according to which the total amount of energy in an
isolated system is always the same. Applied to an isolated system it means
that energy-in equals energy-out. Nothing is created or destroyed and
whatever is accumulated is eventually expelled. However, the form of energy
leaving the system may be altered from what entered depending on what the
system is doing and how. If the universe was a closed system, thermodynamics
would consider its total energy content to be fixed and unchanging. According to the Second Law of Thermodynamics, the
ability of the system to convert a given amount of the energy entering to an
amount of useful work output depends on its relationship to the environment
in which it exists and from whence the energy came and went. If the
environment provides a high temperature source of heat from which the system
can draw, and a low temperature sink to which the system can deliver the heat
it must reject as a consequence, the system can be shown to have a high
potential for doing useful work with the quantity of heat available. It turns
out in all real situations that this work production is likely to increase
the entropy of the system. Such an entropy increase signals that the system
is losing some of its capacity for doing further useful work with the passage
of time. This observation gives rise to the notion of wear and tear. If the
universe was a closed system, thermodynamics would consider its total entropy
to be ever increasing without bound. Does this mean the world is a machine
that is wearing itself out? The relationship between an increase in entropy and
a decrease in the work potential is called "availability." The
Second Law dictates that the total change in the entropy of a system in
process of doing work must sum to zero or more. To expect a reduction in
entropy would imply perpetual motion, which is impossible for a heat engine
according to the principles of thermodynamics. This is the significance of
the famous "Inequality of Clausius," a corollary of the Second Law
of Thermodynamics that states that the change in the entropy of a system in
isolation is equal to or greater than zero. Entropy is not a form of energy. It is not
equivalent to energy in any form. Although it goes on forever, it is not
conserved in thermodynamic processes. To the contrary, according to the
principles of thermodynamics, the entropy of systems in isolation (except for
heat transfer) must remain the same or increase. Never decrease. To decrease
the entropy of a system, a system must receive work from the
environment. This is the reverse of the classical notion of a heat engine as
a machine that receives heat from the environment and does work. An event that requires work is an event that
requires know-how. Know-how is not a thermodynamic phenomenon. Know-how does
not exist in the physical environment like heat. It is the product of human
creativity, which is expressed only in a social environment. Know-how is not
a thermodynamic processes. It is a scarce human resource that is external to
thermodynamic systems. Heat engines are thermodynamic machines that
convert heat derived from various energy sources into “useful” work. Reverse
heat engines use work to convert heat from a lower to a higher level of
availability. Such conversion is sometimes called heat-pumping, otherwise
known as refrigeration. In the normal heat engine, heat is transferred from
one part of the system (the engine) to another, always from a higher
temperature region to a lower one. Reverse heat engines apply work to “lift”
heat from a lower to a higher temperature level. But for the lifting process, heat transfer requires
a temperature gradient. Likewise, temperature gradients evidence heat flow,
which, like mechanical friction, produces random molecular motions. Random
molecular motions once produced never revert to their original order,
whatever it was. Such changes are said to be irreversible, and an increase in
the entropy of the system measures the degree of the irreversibility.
Irreversibility in thermodynamics is like the fate of that famous egg Humpty
Dumpty: Humpty Dumpty sat on a
wall. Humpty Dumpty had a
great fall. All the king's horses
and all the king's men Couldn't put Humpty
together again. The history was irreversible even if ordered
otherwise by edict of the king. But by the well placed application of work, a
new form of order arises amid the mounting chaos. The direction of heat flow
can be reversed. The result of the disorganizing phenomenon in
thermodynamics was referred to as "molecular chaos" by James Clerk
Maxwell. He then proceeded to invent a statistical means of coping with it
mathematically. Maxwell developed a calculus that relied on the existence of
this chaos but his result was anything but chaotic. Thanks to Maxwell,
molecular disorder does not prevent us from determining the thermodynamic
properties of macroscopic systems including their entropy. To the contrary,
it unites Boyle's and Charles' Laws of gases into Maxwell's Universal Gas
Law, one of the paramount achievements of physics in the describing the
behavior of large aggregates of gaseous molecules. But what of a rarefied
atmosphere? That is another matter. Maxwell knew years before Planck and
Heisenberg that the temperature of a single molecule cannot be distinguished
from its velocity. From this simple check on hubris developed the general
recognition of limits to determinacy. Physicist Erwin Schrödinger considered such a
conclusion as Russell's to be an unwarranted reductionism. In his inquiry
into the meaning of human life, he found a vital counterweight to the
inorganic degradation visualized by Russell, namely biological reproduction,
human creativity and innovation. Although Schrodinger could not see how
entropy could be "dumped" or even dissipated on a global basis, he
found instead that it is counteracted by life processes and creative human
endeavor resulting in new organizations of natural resources co-existing with
the degradation of the old. He recognized that heat engines do not do
creative work but that living organisms do. Human beings do even more so, but
they must enjoy a social environment in which to function in that creative
manner. He further observed that the social environment is something other
than the physical environment. It was Schrodinger's conclusion that given a
social environment, man can harness the physical environment indefinitely. It
is know-how (technology), ingenuity, enterprise and the capital to apply them
that enables man not only to sustain himself and his kind but also to
progress to higher levels of viability. Schrodinger thus defined
progress. Unlike entropy, heat can be dumped. Indeed, for a
heat engine to continue doing work while receiving heat from an environmental
source, heat must be dumped to an environmental sink. The Second Law of
Thermodynamics ordains this discipline. Otherwise, heat engines would be
perpetual motion machines, which are said to be "impossible." That
no such machines have ever been demonstrated is a testimonial to the truth of
the Second Law. A perpetual motion machine of the second kind is a
heat engine that receives heat from a source and does work without any
further ado. The Second Law of Thermodynamics is the law of nature that says
for work to continue, some of the heat received must be returned to the
environment in "good" form. To take heat from nature to do work
incurs a debt that must be paid with interest. However, thermodynamics is
moot on the human subject of profit and loss. It offers no insight on what
becomes of the work and how it can become regenerated by the investment of
intellectual capital. It is tempting to follow the lead of mathematician
Russell and extrapolate the simple laws of thermodynamics to the universe as
a whole including humans. However, the physicist Schrodinger sets a better
example. He avoided the temptation to reduce social studies to thermodynamic
abstractions, realizing that the human domain of phenomena involves matters
other than mere physical ones from which the laws of thermodynamics were
derived and for which and only which the laws of thermodynamics apply.
Sentient and conscious human beings are more than a mechanical assembly of
assorted molecules. We all know this from our own experience. Biological life
introduces spontaneous organization (replication and reproduction) from
something more than ordinary physical phenomena. Then from some special but
unknown place within the biological domain comes the human kind that brings
volitional social order as well as biological and physical order to the
universe by synthesis. Thermodynamics has its place but it takes more than
knowledge of a dumb machine to account for the effects of human action in
nature. In the vernacular, the First Law says you can't get
something for nothing. The Second Law says you can't even do that well. What
is left unsaid in this quaint interpretation of the laws of thermodynamics is
the color of human value judgments, like "well" and
"good." No mere molecules can account for such preferences. What is
said loud and clear is that there is a price for everything and whatever the
price, it must and will be paid for services rendered. But clearly, society is something other than a heat
engine subject merely to the laws of thermodynamics. The physical world is
deterministic. Left alone by itself there is nothing new under the Sun. Enter
the volitional world and find new and unique surprises every moment. |
