What a pleasure it is to be young, and hopeful, and
unsophisticated. All things are possible and we are ready,
in our heart of hearts, to believe that a fairy godmother
might just come and wave her wand and turn our rags
into a lavish costume and our hovel into a mansion. Why
shouldn’t an enchanted ring exist somewhere which will,
at a rub, load our pockets with gold and jewels?
If this has not happened, we might wistfully imagine, it
is because we just haven’t been lucky enough to find the
fairy godmother, or the enchanted ring, or the jinn. All
we need is that incredible stroke of luck and we will have
something for nothing.
But never mind fairies, rings, and jinn; in the real World
it is energy that is the prime mover of all.
We can define energy as anything that makes it possible to do work; anything capable of bringing about movement against resistance.
In that case, we see at once that
there must be various forms of energy.
Heat will make a thread of mercury rise against the
pull of gravity; light will turn the vanes of a radiometer
against the slowing effect of friction; electricity will turn a
motor; magnetism raise a pin; a moving bat hurl a baseball over the fence; exploding dynamite lift a boulder; a
hydrogen bomb in action heave a mountain.
Heat, light, electricity, magnetism, motion, sound,
chemical bonds, nuclear forces—all represent forms of
energy, and all are different forms of essentially the same
thing, for one form can be freely turned into another.
Electricity moving through a wire can produce light,
and a paddle rotating rapidly in water can produce heat.
Magnetism can be turned into electricity; chemical explosions into motion; nuclear reactions into sound; and so on.
We have now sharpened the problem of getting something for nothing, and can consider it realistically. Whatever we want costs us energy, for it is only energy (by
definition) that will allow work to be done. To be sure,
we may need other things as well, for to build a palace
we need not only the energy to lift materials but also a
certain architectural knowledge—but we need energy at
Without energy, all the architectural knowledge in
the world won’t budge one grain of sand.
To get something for nothing, then, is just another way
of saying that we want to create energy.
But alas, this apparently can't be done. In the 1840s,
as a result of careful experimentation and measuring,
several physicists came more or less simultaneously to the
conclusion that energy cannot be created
(see the earlier
). One form of energy can be converted into
another, or transported from one place to another, but
that is as far as it can go. But wait, that isn’t all. If energy cannot be created,
neither can it be destroyed. When energy is used, it doesn’t
disappear; it merely goes elsewhere or is changed into
The light that streams out of a candle does
not vanish; it heats up the air and surroundings about
itself. The hot water in a kettle may cool down but the
heat does not disappear; it is transferred to the outside
To express all this, we can say: “Energy can be transferred from one place to another, or transformed from
one form to another, but it can neither be created nor
destroyed.” Or we can put it another way: “The total quantity of
energy in the Universe is constant.”
When the total quantity of something does not change,
we say that it is conserved. The two statements given
above, then, are two ways of expressing “the law of
conservation of energy.” This law is sometimes considered
the most powerful and the most fundamental generalization about the Universe that scientists have ever been
able to make.
No one knows why
energy is conserved and no one can
be completely sure it is truly conserved everywhere in the
Universe and under all conditions. All that anyone can
say is that in over a century and a quarter of careful
measurement, scientists have never been able to point to a
definite violation of energy conservation either in the
familiar everyday surroundings about us, or in the heavens
above, or in the atoms within.
The study of changes of energy from one form to
another, or the transport of energy from one place to
another, is called “thermodynamics” (from Greek words
meaning “heat-motion”) because the earliest studies of
the sort were made on the manner in which heat flowed
from one part of a system to another. For that reason the law of conservation of energy is
sometimes called the “First Law of Thermodynamics.”
is first because it is the starting point for all else in the
study. Before you can come to any useful conclusions in
thermodynamics you must accept the fact that energy can
neither be created nor destroyed.
Once that is accepted, we might decide that even so we
have not entirely lost. In the great game of the Universe,
maybe we can still win. If we can’t get something for
nothing, maybe the First Law will allow us to get something for almost nothing. For instance, heat is a form of energy and we can
make it do work. Suppose we take a quantity of heat and
change it into work. In doing so, we haven’t destroyed
the heat, we have only transferred it to another place or
perhaps changed it into another energy form. Why can’t
we then simply gather it up wherever it is and in whatever
form, and use it again, and then again, and then still
If that is so, then even if we can’t create energy out of
nothing, we can at least start with just a little energy and
make it do any amount of work. By using the energy of
a burning candle over and over we could move the world;
and it would be a greedy man indeed who wouldn’t be
satisfied with that or who would complain he wasn’t really
getting something for nothing.
Alas, it sounds good, but it can’t be done. The trouble
is that once energy is used, it still exists, yes, but it is
spread out thinner. The heat of the burning candle spreads
out into the air all about and into all the things the
warmed air comes into contact with. To put that heat back to work again, it has to be collected from the surroundings and concentrated again so
that the candle flame is re-created. Heat can be concentrated, energy can be collected—but it takes energy to do
so, invariably more energy than the energy you are concentrating and collecting. What is the sense in using fresh energy to collect dissipated old energy, and using more to get less? You might
as well use the fresh to begin with. It would be more
economical. In short, in your attempt to use the same old energy
over and over again, you would be using up more energy
than if you made up your mind to use each bit of energy
just once. You can’t get round it. What the First Law of Thermodynamics really means is that in the great game of the
Universe, you can't win! You can’t get something for
nothing, or even for nearly nothing.
This is a hard thing to accept and the indomitable
human spirit is bound to fall back to the next line of
defense. If it is true that you can’t win, then perhaps you
can at least break even. In other words, given a certain
supply of energy, perhaps you can at least turn it all into
This problem came up when the steam engine was first
developed in the eighteenth century. To begin with, the
early engines were extremely inefficient. Great quantities
of fuel were burned but most of the energy was wasted
in heating up the world generally; very little ended in such
useful work as pumping water.
Naturally, one assumes that if one could only cut down
on friction, prevent the flow of heat in unwanted directions, make the general design more efficient, one could
eventually build a machine that would turn all the energy
The first person to point out that this was not so, that
even a perfect
steam engine could not turn all energy into
work, was a French physicist named Nicolas Léonard Sadi
. He demonstrated, in 1824, that the steam engine did
work because part of its system was quite hot (the part
that consisted of steam) and part was quite cold (the part
that consisted of the cold water that condensed the
steam). The heat energy present was, in other words, in
greater-than-average concentration in one place and in
less-than-average concentration in another. We can quite
easily measure the heat-concentration, which we usually
call “temperature.” The fraction of the energy that can be
turned into work by a steam engine depends, then, upon
the difference in temperature between the hot part of the
system and the cold part. The greater the difference in temperature between two
parts of the same system, the greater the fraction of the
heat energy we can tum into work. This difference in
temperature becomes a maximum when all the heat in the
system is concentrated in one part and none is concentrated in another. The trouble is that physicists have shown it is impossible
to concentrate all the heat in a system in one particular
part of it. Even to approach total concentration takes an
If a steam engine uses ordinary steam for its hot part
and ice water for its cold, the difference in heat concentration or temperature is such that only 27 per cent of
the total heat energy can be converted into work, even if
the steam engine were perfect in every other respect: if it
lost no heat to the outside world, if there were no friction, and so on.
This is true for any system which uses energy of any
kind. To make any system useful, to allow it to turn
energy into work, there must always be a difference in
energy concentration in different parts of the system.
There must be a high energy concentration here and a
low energy concentration there, and the work to be gotten
out of the system depends not on the total energy, but
on the difference in energy concentration within the system.
We can say: “No device can deliver work unless there
is a difference in energy concentration within the system,
no matter how much total energy is used.” That is one way of stating what is called the Second
Law of Thermodynamics.
Since there is never any way of reaching an ultimate
difference in energy concentration, never any way of putting all the energy into one part of the system, and none
into another, we can never turn every bit of the energy of
a system into work. Some of the energy always manages
to get away from us without being turned into work. What the Second Law tells us, then, is that in the great
game of the Universe, we not only cannot win, we cannot
even break even!
Given energy at two different levels of concentration,
we will note as part of the common experience of mankind that there is always a spontaneous transfer of energy
from the place of higher concentration to the place of
lower concentration; and never vice versa.
For instance, heat will flow, of itself, from a hot body
into a cold body, but not vice versa. Water will spontaneously flow from hilltop to hill bottom, but not vice
We can say: “Energy will always flow spontaneously
from a point of high concentration to one of low concentration.”
Physicists can show that it is because this statement is
true that devices will convert energy into work when
there is a difference in energy concentration within the
system. It is the spontaneous energy flow from high to low
that produces the work. The statement about spontaneous energy-flow is therefore another way of expressing the Second Law.
But work is never done instantaneously. It invariably
occupies time. What happens during that time?
Suppose we consider a steam engine with a portion of
itself that is at high heat-concentration and another portion that is at low heat-concentration. By the Second Law,
the heat flows from high to low and that heat flow is
turned into work. If the heat flow happened all at once
and was converted into work in zero time, then we would
at least get all the work out of the energy flow that we
But it takes time, and as time passes, some of the heat
in the high-concentration portion is pouring out into other
parts of the Universe. Meanwhile heat from other parts of
the Universe is pouring into the low-concentration portion. In other words, the hot part of the steam engine is
cooling faster than you would expect just from its transfer
of heat to the cold portion. The cold portion, on the
other hand, is warming faster than you would think just
from its receipt of heat from the hot portion.
The difference in temperature is dropping faster than
you would expect from the work done.
Since the amount of work you can get out of any
device depends upon the difference in temperature, it
would seem that the quantity of energy capable of conversion into work decreases with time. The quantity of
energy not capable of conversion into work increases
with time. A German physicist, Rudolf Clausius, pointed this out
in 1865. He invented a quantity consisting of the change
in heat with time, divided by temperature, and called it
“entropy.” He showed that entropy was a measure of the
quantity of energy not capable of conversion into work.
In any physical change that takes place by itself the
entropy always increases.
In the case of the steam engine this comes about
because there is heat flow to and from the Universe. If a
boulder rolls down the mountainside there is increase of
entropy because of friction and air resistance. An electric
current flowing from one pole of a battery to another
encounters resistance from whatever it passes through
and hence experiences increase in entropy.
To be sure, we can imagine ideal cases. A hot and cold
area might be perfectly insulated so that heat flows only
from one to the other; a rock may fall through a perfect
vacuum; an electric current may flow through a perfect
conductor. In all cases. there is no entropy increase.
Approximations to such ideals (a planet moving through
outer space; an electric current moving through a superconducting metal) are highly special. If we consider the
ordinary systems we work with, we can say: “In any
energy transfer, there is an increase in entropy.” This, too, is a way of expressing the Second Law. In fact, a good brief way of stating the First and Second Laws of Thermodynamics is: “The total energy content of the Universe is constant and the total entropy is
continually increasing.” This means that although the Universe never loses any
energy, less and less of that energy can be converted into
work as time goes on.
The Second Law can be interpreted in terms of atomic
theory, and the Scottish mathematician and physicist,
James Clerk Maxwell did so in the 1860s.
Heat can be viewed, for instance, as being represented
by the random movements of the separate particles (either
atoms or molecules) making up some body of matter. The
greater the average
velocity of particle motion, the higher
When two particles collide, they bounce apart and
some momentum (mass multiplied by velocity) is transferred from one to the other. The transfer can take place
in any fashion, but the most likely result is that the particle with more momentum will lose, and the particle with
less momentum will gain. If all the particles are the same
size, we can say that the faster particle will slow down
after collision, the slower particle speed up. It is possible,
of course, that the fast particle may just happen to bounce
off faster, and the slow one slower, but it is unlikely.
(If a rich man and a poor man put all their money in
a single pile and each grabbed what he could, the chances
are the rich man would end up with less money than he
started and the poor man with more.)
Where more and more particles are involved, it
becomes less and less likely that a large proportion of the
fast particles will all bounce off slow particles and end by
moving still faster.
Let us suppose there is a one-in-ten chance that a fast
particle will bounce off a slow particle and become faster
in the process. The chance of six fast particles all
bouncing off faster from six slow particles will be one in ten
times ten times ten times ten times ten times ten, or one
in a million. The chance of ninety-six fast particles all
bouncing off faster at the same time from ninety-six slow
particles would be only one in a trillion-trillion-trillion-trillion-trillion-trillion-trillion-trillion.
Suppose you took a kettle of water containing
uncounted trillions of particles and put it over a fire. It
might be that more than half the hot, very fast-moving
particles in the hot gases of the fire might strike the kettle
and bounce off still faster-moving. In that case, the water
in the kettle would get cooler while the fire would get
hotter. This is possible, but the chance of its happening is
so small that there is no way of writing it in ordinary
figures. If you tried to write: one chance in such-and-such a number, the surface of the earth wouldn’t be large
enough to hold all the zeros you would have to write
down for “such-and-such a number.”
That is why the entropy of the Universe constantly
increases—because the collisions of atoms and molecules
tend always to chop off energy extremes. Wherever energy
is more concentrated than usual, that concentration drops;
where it is less concentrated than usual, that concentration rises.
It is also possible to think of entropy in terms of
“order” and “disorder.” Something is orderly when its
individual parts are arranged according to some simple
rule we can quickly grasp. We can then predict from each
part something about the next part. The simpler the rule,
the easier the prediction, and the greater the order.
Consider a deck of cards. You might have it arranged
as follows: ace of spades, two of spades, three of spades,
and so on, followed by hearts, clubs, and diamonds, each
suit arranged from ace to king. That is very orderly, for
if you show me any card (the seven of clubs, for
instance), I will instantly tell you the next card (the eight
Or you might arrange the suits in another order; or
each suit might run from king down to ace; or you might
have the four aces in a certain order of suits, then the
four twos, then the four threes, and so on. These all represent order.
We might also arrange the cards so that they are alternately red and black without any consideration for numbers or suits. We can then still make some prediction. If
I am shown the seven of clubs, I know the next card
must be a red one. That is some information, but not
much, so that the red and black in alternation still represents some order, but not much.
It should be obvious, though, that if you consider all
the possible arrangements of the cards in a deck, the
number of arrangements that allow you to make predictions about each card from the one before is a very small,
small, portion of the whole.
Suppose you shuffle a deck in such a way that it can
take on any
arrangement. The chances that the arrangement will be one of the few that will allow even a small
amount of prediction and will therefore have at least a
small amount of order is not great. There are so many
utterly disorderly arrangements possible that one of those
is just about sure to be obtained.
That is why, when you shuffle cards thoroughly, you
would be most astonished to find, when you were through,
that the cards have ended up arranged ace of spades,
two of spades, three of spades, and so on—or even red-black-red-black-red-black and so on.
Let us take another example from the world of life.
When a platoon of soldiers marches by four abreast and
in perfect step, that represents a high degree of order.
When we see one group of four soldiers move by, we can
predict exactly when the next group will pass by, how
many will be in the group, whether they will be moving
their right foot or left at the moment of passing, and so
Other examples of order would have soldiers moving
two abreast; or in single file; or one row marching and
the next skipping, in alternation; and so on.
But suppose you considered all the different possible
ways in which the individual soldiers of a platoon could
pass by if each consulted his own tastes only and paid
no attention to the others. Some might be strolling, some
walking, some running, some hopping perhaps, some in
this direction, some in that. The number of ways of passing without
any perceptible order is much, much higher
than the number of ways with
Consequently, if you told the soldiers of a platoon to
move from one point to another at will, you would be
utterly surprised if, when each did exactly as he pleased,
they just all happened to move four abreast and in step.
In fact, if they were already moving four abreast and in
step and were suddenly told to do as they pleased, you
would expect the entire platoon to break formation and
In short, in every possible situation you can think of,
the number of ways of being disorderly is much, much,
much, much greater than the number of ways of being
This is exactly comparable to the fact that the number
of ways in which extremes get chopped off in the random
collisions of particles is much, much, much, much greater
than the number of ways in which extremes get more
Another way of stating Second Law, then, is: “The Universe is constantly getting more disorderly.”
Viewed that way, we can see Second Law all about us.
We have to work hard to straighten a room, but left to
itself, it becomes a mess again very quickly and very
easily. Even if we never enter it, it becomes dusty and
musty. How difficult to maintain houses, and machinery,
and our own bodies in perfect working order; how easy
to let them deteriorate.
In fact, all we have to do is nothing, and everything
deteriorates, collapses, breaks down, wears out, all by
itself—and that is What Second Law is all about.
You can argue, of course, that the phenomenon of life
may be an exception. Life on earth has steadily grown
more complex, more versatile, more elaborate, mom
orderly, over the billions of years of the planet’s existence.
From no life at all, living molecules were developed, then
living cells, then living conglomerates of cells, then worms,
vertebrates, mammals, finally man. And in man is a
three-pound brain which, as far as We know, is the most
complex and orderly arrangement of matter in the Universe. How could the human brain develop out of the
primeval slime? How could that vast increase in order
(and therefore that vast decrease in entropy) have taken
The answer is it could not
have taken place without a
tremendous source of energy constantly bathing the
Earth, for it is on that energy that life subsists. Remove
the Sun and the human brain would not have developed
—or the primeval slime, either. And in the billions of
years that it took for the human brain to develop, the
increase in entropy that took place in the Sun was far
greater—than the decrease represented
by the evolution of the brain.
But where did it all start? If the Universe is running
down into utter disorder, what made it orderly to begin
with? Where did the order come from that it is steadily
losing? What set up the extremes that are steadily being
Scientists are still arguing the point. Some think the
Universe originally had its matter and energy all smashed
together into one huge “cosmic egg”—a situation something like a tremendous deck of cards all arranged in
order. The cosmic egg exploded and ever since, for billions of years, the Universe has been running down; the
deck of cards is being shuffled and shuffled and shuffled.
Others think that there are some processes in the Universe that spontaneously decrease entropy; some natural
process which unshuffles and re-orders the cards. We don’t
know what it can be, perhaps because it takes place under
conditions we cannot observe and cannot duplicate in the
laboratory—say, in the center of exploding galaxies. Perhaps, in that case, as some parts of the Universe run
down, others build up.
Then again, it may be that once the Universe runs
down, the random collisions of particles may—after
umpty-ump years—just happen to bring about an at least
partial unshuffling. After all, if you shuffle cards and shuffle cards and shuffle cards ceaselessly for a trillion years,
you may end up with an arrangement possessing at least
order, just by the laws of chance.
Once that happens, the Universe begins to run down
again at once. Perhaps, then, we live in a Universe that
was partially unshuffles after a quadrillion years of having been run-down. We are now running down again and
after the Universe is all run-down, another quadrillion
years or another quadrillion quadrillion years may see a
section of it unshuffled once more.
Stars and galaxies will then re-form, and life may be
established here and there, and finally some science writer
will sit down and begin to wonder again where it all
came from and where it will all end.