WHAT IS ENTROPY?
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An additional concept
of heat arises out of a basic theme of the Newtonian universe: the
idea that the world is like a machine whose parts never wear out,
and which never runs down. This idea inspired the search for conservation
laws applying to matter and motion. We can measure "matter" by mass,
and "motion" by momentum or by kinetic energy. By 1850, the law of
conservation of mass had been firmly established in chemistry, and
the laws of conservation of momentum and of energy had been firmly
accepted in physics. Yet these successful conservation laws could
not banish the suspicion that somehow the world was running down,
and the parts of the machine were wearing out.
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Energy may be conserved
in burning fuel, but it loses its usefulness as the heat diffuses
into the atmosphere. Mass may be conserved in scrambling an egg, but
its organized structure is lost. In these transformations, something
is conserved, but also something is lost. Some
processes are irreversible -they will not run backwards. There
is no way to command a scrambled egg to reorganize into the original,
although such a change would not violate mass conservation. There
is no way to instigate a sudden cooling of the air that then converges
on a blackened wood stick and pulls converging smoke back into a match.
There is an arrow of time that points in one direction.
WHAT IS ENTROPY?
AN IMPORTANT IDEA--THE HEAT ENGINE!
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Carnot's analysis of steam
engines shows that there is an unavoidable waste of mechanical energy,
even under ideal circumstances. The total amount of energy that was
in the high- temperature steam, is conserved as it passes through
the engine; part of it is transformed into useful mechanical energy
and the rest is discharged in the exhaust and joins the relatively
low temperature pool of the surrounding world. Carnot's reasoning
led to the conclusion that there always must be some such "rejection"
of heat from any kind of engine. It is this rejected heat that dissipates
into the surroundings and becomes unavailable for useful work.
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These conclusions
about heat engines were incorporated into thermodynamics and became
the basis for formulating the Second Law. This law has been
stated in various ways, all of which are roughly equivalent; it expresses
the idea that it is impossible to convert a given amount of heat fully
into work. The first attempts to formulate quantitative laws for irreversible
processes in physics were stimulated by the development of steam engines.
During the eighteenth and nineteenth centuries, the efficiency of
steam engines - the amount of mechanical work that could be obtained
from a given amount of fuel energy-was steadily increased.
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In 1824 a young French
engineer, Sadi Carnot, published a short book entitled Reflections
on the Motive Power of Fire. Camot raised the question: "Is
there a maximum possible efficiency of an engine?" Conservation
of energy, of course, requires a limit of 100%- the energy output
can never be greater than the energy input. But, by considering the
flow of heat in the engine, Camot proved that there is a maximum efficiency
that is always less than 100%- that is, the useful energy output can
never be even as much as the input energy. There is a fixed upper
limit on the amount of mechanical energy that can be obtained from
a given amount of heat by using an engine, and this limit can never
be exceeded regardless of what substance -steam, air, or anything
else-is used in the engine. (In addition to the existence of this
limit on efficiency even for ideal engines, real engines operate at
still lower efficiency in practice.) For example, heat usually leaks
from the hot parts of the engine to the cooler parts without passing
through the part of the engine where this natural flow can be put
to use to generate mechanical energy.
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THE SECOND
LAW OF THERMODYNAMICS...
A SUMMARY!
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In 1852, Lord Kelvin
generalized the Second Law of Thermodynamics by asserting that there
is a universal tendency in nature toward the "degradation" or "dissipation"
of energy. Another way of stating this principle was suggested by
Rudolf Clausius in 1865. Clausius introduced a new concept, entropy
(from the Greek word for transformation). In thermodynamics, entropy
is defined in terms of temperature and heat transfer, but it will
be more useful to us to associate entropy with disorder. Increases
in entropy can be identified with increasing disorder of motion in
the parts of the system. For example, think of a falling ball. If
its temperature is very low, the random motion of its parts is very
low and the motion of all particles during the falling is mainly downward
(and hence "ordered"). But after several bounces, during which the
mechanical energy of the ball decreases and the ball warms up, the
random thermal motion of the parts of the heated ball is far more
vigorous. Finally, the ball as a whole lies still (no "ordered" motion),
and the disordered motion of its molecules (and of the molecules of
the floor when it bounced) is all the motion left. Saying that bouncing
balls - and all motion of all whole bodies - will run down and come
to rest is therefore saying that the motions tend from ordered to
disordered. In fact, entropy can be defined mathematically as a measure
of the disorder of a system.
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The
general version of the Second Law of Thermodynamics, as stated by
Clausius, is therefore simply that the entropy of an isolated system
will always tends to increase or at best remain constant.
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