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[Ulalhematics in
porpelual motion
It really does keep going,
and going, and going . . .
by Anatoly Savin
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HE WORDS "PERPETUAL
motion" (p erp etuum mobile in
Latin) are usually associated
with a machine like the one
you see in figure 1. According to the
inventor's conception, this wheel
with several balls rolling inside
must not only rotate for an infinitely
long time, it can also set in motion
other machines-looms, lathes, and
so on. By the time we graduate from
high school we all know that such a
machine can't work, because it
would contradict the law of conservation
of energy. Yet year afteryear
academies of sciences the world
over receive hundreds of new (and
not new) designs for such machines.
Physicists call them "perpetual engines
of the first sort." So-are there
"perpetual engines of the second
sort"? Yes, there are. And that's
what I'm going to discuss here.
Here's an idea for such an engine.
Suppose we have two equallyheated
bodies. As it works, the engine
transfers some heat from one body
to the other without expenditure of
energy/ and then obtains kinetic
energy by means of a heat engine
that uses the temperature difference
thus created. The work of the heat
engine leads to a leveling of the temperatures
of the two bodies, so the
entire process can be started again:
heat is transferred from one body to
the other, work is extracted ftom the
temperature drop-and so on to infinity,
A perpetual engine of the second
sort doesn't contradict the law of
conservation of energy. In this case,
energy neither appears nor disappears-it
merely passes from one
body to the other and then is spent
in the heat engine to perform some
work. In so doing, the temperature
of both bodies becomes lower than
it was initially, but this loss can be
compensated by the heat of the surroundings.
However, there is another law
that prevents the construction of a
perpetual engine of the second sort.
The idea of this law first appeared in
works by the prominent French
physicist and engineer Sadi Carnot,
a son of the outstanding figure in
the French Revolution and weliknown
mathemati cian Lazare C ar -
not. Later it was developed by the
English scientist William Thomson
and the German physicist Rudolph
Clausius. This law is called the second
law of thermodynamics and
reads as follows: It is impossible to
transfu heat from one body to another
without expenditure of energy
if the temperature of the first body
is no higher than that of the second.
This prohibition doesn't look all
that convincing. Does it always
work? The great English physicist
|ames Clerk Maxwell conceived of a
device, called Maxwell's demon, intended
to refute this law. Imagine a
box divided in half with a partition
that has a small hole in it and a " demon"
sitting near the hole. FiIl the
box with any gas and ask the demon
to let only fast molecules from the
left half of the box into the right half
and leave allslow molecules in the
left half. Since the temperature of a
gas is characterized by the average
Figure 1
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