Chemist, professor, writer—Dr. Asimov kindly helps you understand the second law of thermodynamics

By *Isaac Asimov

In the game of energy  and thermodynamics you 

can’t even break even

Two great laws describe flow and change  of the universal prime mover; it  is never created and never disappears.

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 may just come and wave her want, and turn our rags into a lavish costume and our hovel into a mansion.  Why shouldn’t an enchanted ring exist somewhere that will, at a rub, load our pockets with gold and jewels?  Or why should not a jinn, slave to our commands, build a castle for us in the twinkling of an eye and fill it with dancing girls?

     If this has not happened, we might wistfully imagine that it is only 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 jinns; 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.  

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*Chemist, professor, writer—Dr. Asimov kindly helps you understand the second law of thermodynamics

Smithsonian, v. 1, no. 5, (August, 1970), p. 4-11.

     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 huge 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 paddly 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.  To build a palace we need not only the energy to lift materials but also a certain architectural knowledge—but we need energy at the very least.  Without energy, all the architectural knowledge in the world wouldn’t budge one grain of sand.

     To get something for nothing, then, is just another way of saying this: We want to create some energy that did not exist before. 

     But, alas, this apparently can’t be done.  In the 1840s, as a result of careful experimentation and measurement, several physicists came more or less simultaneously to the conclusion that energy cannot be created.  One form of energy can be converted into another, or transported from one place to another, but that is as far as we 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 another form.  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 world.

     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 be neither 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 considered the most powerful and 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.      

 

Conservation is the starting point

The study of changes of energy from one form to another and 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 sometime called the First Law of Thermodynamics.  It 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 be neither created nor destroyed. 

     Once that is accepted, we might decide that even so we have not entirely lost.  In the 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.  Moreover it is all around us—in the earth under our feet, in the air, in lakes and oceans and winter snows. 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 again and again?

     If we can do 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, or who would 

Smithsonian, v. 1, no. 5, (August, 1970), p. 4-11.

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, 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 warm air comes into contact with. 

     For that heat 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. 

     (Think of your air conditioner.  It collects heat from a cool room and discharges it, at higher temperature, into the outside air.  Why not use just such a heat pump to concentrate heat where we want it?  Then we could let the heat flow once again from a hot place to a cold place, making it turn motors, lift weights and generate electric currents as it went.  We’ve found a jinn after all!  But there is a joker in the deck that overrides the jinn.  More energy is needed to run the air conditioner than we can get back by letting the heat run back from hot to cold.)

     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 is 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 around it.  What the laws of thermodynamics really say 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.

     (Through the centuries inventors have been trying to beat this game and invent perpetual-motion machines.  With rolling balls and swinging weights and spinning wheels they have tried repeatedly to make a machine that would run on, once strated, getting just a little energy from gravity or some other source to overcome the little bit of friction in its bearings.  Such a machine, if you could make it, would be a perpetual-motion machine of the kind that would violate the laws of thermodynamics.  Nobody has succeeded; nobody ever will; very few, if any, are still trying.)

All work and no waste are impossible

This impossibility 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 work.

Smithsonian, v. 1, no. 5, (August, 1970), p. 4-11.

     This problem came up when the steam engine was first developed in the 18th 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 into work. 

     The first person to point out that this was not so, that even a perfect steam engine could not turn all energy to work, was a French physicist, Sadi Carnot.

     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 less-than-average concentration in another.  The engine worked by taking some heat from the hot part, transforming some of it into work, and dumping some of the heat into the cold part.  Unfortunaetely you always had to dump some heat into the cold part; you couldn’t transform all the heat you extracted into useful work.  The fraction of energy that could be turned into work by a steam engine depended upon the difference in heat concentration (that is, “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 turn 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 enormous effort.

     If a steam engine uses ordinary steam for its hot part and ice water for its cold, the difference in temperature is such that only 27 percent of the total heat energy could be converted into work, even if the steam engine were perfect in every other respect, if it lost no heat to the outside, if there were no friction, and so on.

Like water, energy flows downhill

This is true of any system that 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 got out of the system depends not on the toatl 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.  It is one of many ways; all of them are equivalent although some very sophisticated mathematics and physics is involved in showing the equivalence.

     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

Smithsonian, v. 1, no. 5, (August, 1970), p. 4-11.

body into a cold body, but not vice versa.  Water will flow sponatneously downhill, but not vice versa.      Physicists can show that this principle explains why devices will convert energy into work when there is a difference in energy concentration within the system.  Spontaneous energy flow from high to low produces the work.

     The statement about spontaneous energy flow is therefore another way of expressing the Second Law.  It is equivalent to our earlier expression (the impossibility of converting all of any amount of energy into work) in the following sense: The energy that cannot be converted must be dumped into a cold place, and hence we have a flow of this energy from hot to cold.

     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 in the process some of the heat 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 could.  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.

     A German physicist, Rudolf Clausius, pointed out this fact in 1865.  He invented a quantity consisting of the change in heat divided by the temperature, and called it “entropy.”  He showed that entropy was a measure of the quantity of energy not capable of conversion into work.

Energy available is always getting less     

In any physical change that takes place by itself the entropy always increases.  In the case of the steam engine it is 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 rock might fall through a perfect vacuum; an electric current might flow through a perfect conductor.  In these cases, there is no entropy increase.

     But 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 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 the temperature.

     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 greater momentum will lose some, and the particle with less momentum will gain.  In short, if all the particles are the same size, the faster particle will slow down after collision and the slower particle speed up.  It is possible, of course, that a fast particle may just happen to bounce off faster,  and the slow one slower, but it is unlikely.

     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, or one in a million.  The chance of 96 fast particles all bouncing off faster at the same time from 96 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 of the hot, very-fast moving particles in the hot gasses of the fire might strike the kettle and bounce off moving still faster.  In that case, the water in the kettle would get cooler while the fire got hotter.  The Second Law would be violated.  From a philosophical viewpoint one can argue that this process is possible and that the Second Law is no law at all—just a tendency that is more likely to be followed than violated.  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. 

     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.  This statement originally applied to the order and disorder in physical systems, and it can be related to their heat and energy content.  But with a little extension we can apply it to a lot of common everyday situations.

Disorder is so easy; order is so hard

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 of clubs).  Even if you put the four suits together differently, or arrange each suit in a sequence that runs from king down to ace, they still represent order.

     We might also arrange the cards so that they are alternately red and black, but without any consideration for numbers or suits.  If I am shown the seven of clubs, I can predict that the next card will be a red card, but that is all.  Red-and-black-in-alternation still represents some order, then, but not much.      It should be obvious, though, that if you consider all the possible arrangements of the 52 cards in a deck, the number of arrangements that allow you to make predictions about a card from the preceeding one is a small, a very small, portion of the whole.

     Suppose you shuffle a deck in such a way that it can fall into 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, are not great.

     That is why, when you shuffle cards thoroughly, you would be most astonished to find, when you are through, that the cards have ended up with each suit in a perfect sequence—ace of spades, two of spades, and so on—or even red-black, red-black all the way to the end.  Let us take another example.  When a platoon of soldiers marches past four abreast and in perfect step, that represents a high degree of order.  When we see one rank of four soldiers move by, we can predict exactly what the next rank will pass by, how many will be in it, whether they will be moving their right feet or left at the moment of passing, and so on.  Other examples of order would have soldiers moving two abreast or in single file or one rank marching and the next skipping, in alternation.

     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 higher than the number of ways with order.

     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 become disorderly.  In short, in every possible situation you can think of, the number of ways of being disorderly is much, much greater than the number of ways of being orderly.

     This is exactly comparable to the fact that the number of ways in which extremes get choopped off in the random collisions of particles is much, much greater than the number of ways in which extremes get more extreme.

     Another way of stating the Second Law, then, is: “The universe is constantly getting more disorerly.”

     Viewed that way, we can see the Second Law all around 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 workding order; how easy to let them deteriorate.  In fact, all we have to do is nothering, and everything dteriorates, collapses, breaks down, wears out, all by itself—and that is what the Second Law is all about.

Maybe life is the great exception

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, more orderly, over the billions of years of the planet’s existance.  From no life at all, living molecules were developed, then living cells, then living conglomerates of cells, 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 place?

     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; far, far greater than the decrease that is represented by the evolution required to develop the human 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 chipped away?

     Scientists are still arguing the point.  Some think the universe originally had its matter and energy all smashed together into one huge “comic 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 is some process in the universe that spontaneously decreases entropy, some naural process that unshuffles and reorders 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 some unimaginable span of years—just happen to bring about an at-least-partial unshuffling.  After all, if  you shuffle and reshuffle cards ceaselessly for a trillion years, you may violate the Second Law and end  up with an arrangement possessing at least some 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 restored to order after a quadrillion years of having been run down.  We are now running down again.  After the unvierse is compeltely run down, another quadrillion years or so may see a section of it ushuffled once more.

     Stars and galaxies will then form again, 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 all will end.