Introduction: A powerful law

The second law of thermodynamics is based on our common human experience. It didn't begin with complicated apparatus or complex theories, but rather with thinking about how old-fashioned steam engines worked. The first important equation to emerge from this work appeared to be very simple: just q/T.

Yet the second law is probably our most powerful aid in helping us understand why the world works as it does both in simple and in complex ways: why hot pans cool down, why ping pong balls don't bounce forever when they are dropped, why gasoline (plus the oxygen in air) makes engines run, why our 'engines' — our bodies — run and we continue to live and our bodies stay warm even when it's cold, but also why we die when some chemical reactions within us fail. In fact, the second law helps to explain everything that happens in our physical world. In chemistry, it's especially important because it can tell us whether any chemical reaction that we write on paper will probably be spontaneous and go as we have written it.

The big problem for anyone who wanted to understand the second law since 1865

Unfortunately, for almost a century and a half, the second law has been expressed by experts in ways that a beginner in chemistry could not possibly understand without a great deal of additional explanation. Here are just three of many such definitions of entropy:

• "The entropy of the universe increases toward a maximum" (Clausius)

• "It is impossible in any way to diminish the entropy of a system of bodies without thereby leaving behind changes in other bodies" (Planck)

• "In any irreversible process the total entropy of all bodies concerned is increased." (Lewis)

Entropy, entropy, entropy! But what is entropy? Unfortunately, some professors and textbooks still have the attitude of "Don't ask about understanding it. Just work the problems that have entropy in them and you'll gradually understand it because you will be able to work problems"!  That's the old way which fortunately has been discarded by most US general chemistry texts. (See list at entropysite.com/#whatsnew.) The good news of the twenty-first century is that now entropy can be described as a simple idea (no matter how complex to calculate and deal with in advanced courses and research.)  Because of our new conceptual approach, a basic version of the second law can be understood easily.

A modern version of the second law

"Energy of all types changes from being localized to becoming dispersed or spread out, if it is not hindered from doing so. Entropy change is the quantitative measure of that kind of a spontaneous process: how much energy has flowed or how widely it has become spread out at a specific temperature."

(A detailed exposition, primarily for chemistry instructors, is at entropy_isnot_disorder.html)

What does that "energy of all types" and "becoming dispersed" mean? Let's first think about light (which technically is electromagnetic radiation). Does the radiation from a light bulb stay inside that glass of the bulb? Of course not. It spreads out just as far as it can, hindered from dispersing to miles and even farther only by dust or air density differences. What about the sound from a stereo speaker -- does it stay inside a dorm room or a car? It disperses farther than other people want to hear it, usually! And what happens to the kinetic energy of a fast moving car if the car should hit a brick wall? It spreads out in a crashing sound, in twisting metal and heating it while tearing apart the bricks of the wall so that they fly around, slightly warmer than they were. Those are just a few examples of different types of energy and some ways in which they become dispersed, or spread out. 

Energy of all types disperses...if it is not hindered from doing so.

[We will come back to talk about entropy, the measure of how much and how spread out the dispersed energy is, near the end of this Section, and in the next.]

The importance of the second law in chemistry

In chemistry, the type of energy in which we are most often interested is the kinetic energy of molecules, molecular motional energy. We know from kinetic molecular theory that molecules are in constant motion if they are above 0 K. In gases like nitrogen and oxygen, they are moving at an average speed of around a thousand miles (1600 km) an hour at 298 K and go about 200 times their diameter before bumping into another molecule. The molecules in liquids may be moving approximately as fast even though they are constantly hitting one another as they move a little here and there. In solids, the particles, molecules or atoms or ions, can only 'dance in one place' (vibrating in coordination with the other particles in the solid). This is a kinetic energy of vibration that is equivalent to the motional energy of gases or liquids at the same temperature.

The motional energy of molecules consists of their translation, rotation, and vibration (Figure 1 of 2ndlaw.com/entropy.html.) Note that this vibration is vibration inside a molecule and by itself, as though the chemical bonds between atoms were like springs. The vibration in a crystal that we were just talking about is a vibration of a whole molecule or other particle in one place and coordinated with the other molecules in the crystal.)

Examples from everyday life, and one in chemistry

Let's see how the second law helps us to understand our common experience better, to see how so many totally different events really are just examples of energy dispersing or spreading out, i.e, of the second law. A rock will fall if you lift it up and then let go. Hot frying pans cool down when taken off the stove. Iron rusts (oxidizes) in the air. Air in a tire is at a high pressure and shoots out even from a small puncture to the lower pressure atmosphere. Ice cubes melt in a warm room.

(We'll also learn about essential descriptions of 'system' and 'surroundings' that are used in thermodynamics.)

A rock has potential energy (PE) localized in it when you lift it up above the ground. The rock is the 'system'; everything else it encounters is the 'surroundings'. Drop the rock and its PE changes to kinetic energy (energy of movement. KE), pushing air aside as it falls (therefore spreading out the rock’s KE a bit) before it hits the ground, dispersing a tiny bit of sound energy (compressed air) and causing a little heating (molecular motional energy) of the ground it hits and in the rock itself. The rock is unchanged (after a minute when it disperses to the air the small amount of heat it got from hitting the ground). But the potential energy that your muscles localized in by lifting it up is now totally spread out and dispersed all over in a little air movement and a little heating of the air and ground. (System: rock above ground, then on ground. Surroundings: air plus ground.)

A hot frying pan? The iron atoms in a hot frying pan (system) in a room (surroundings) are vibrating very rapidly, like fast ‘dancing in place’. Therefore, considering both the pan and the room, the motional energy in the hot pan is localized. Its motional energy will disperse — if it can and is not hindered from spreading out, according to the second law. Whenever the less rapidly moving molecules in the cooler air of the room hit the hot pan, the fast-vibrating iron atoms transfer some of their energy to the air molecules. The pan’s localized energy thus becomes dispersed, spread out more widely to molecules in the room air. (System: pan. Surroundings: room air.)

In a chemical reaction such as iron rusting, i.e., iron plus oxygen to form iron oxide or rust, the reactants of iron and oxygen don't have to be at a high temperature to have energy localized within them. Iron atoms (as -Fe-Fe-Fe-) plus oxygen molecules of the air (O-O) have more energy localized within their bonds than does the product of their reaction, iron rust (iron oxide).

(That’s why iron reacts with oxygen — to release energy from their combined total of higher energy bonds and form the lower energy bonds in iron oxide. Then, all that difference in energy becomes dispersed to the surroundings as ‘heat’ i.e., the reaction is exothermic and makes molecules in the surroundings move faster. But remember how chemical reactions occur! Remember that it requires energy to break bonds and therefore to start any reaction there must be some extra energy, an activation energy supplied somehow to break a bond or many bonds in the reacting substances. (For information about activation energies, see 2ndlaw.com/obstructions.html.) Then, if the bonds that are being formed in the product are much stronger than those being broken in the reactants, that difference in energy (which usually causes greater motional energy of all the molecules) can feed back to break more bonds in the reactants.

However, in the case of iron reacting with oxygen at normal room temperature around 298 K, the process is very slow because only a few oxygen atoms are moving exceptionally fast and hit the iron just right so an iron-iron bond and an O-O bond are broken and an iron-oxygen bond can form. There isn't enough heat (motional energy) localized in nearby iron atoms and no other unusually fast-moving oxygen molecule at that instant hitting the iron so that many other iron-iron bonds in the pan can be broken to form iron oxide. It's a slow process depending on collision of the small amount of fast moving oxygen atoms in the surroundings to make it happen.

Therefore, even in moist air (that speeds up another process yielding iron oxide), iron doesn't react very rapidly with oxygen but it steadily does so and in time, both the iron atoms and the oxygen molecule spread out to the surroundings the portion of their bond energy that iron oxide doesn't need for its existence at that temperature. (System: Reactants:iron and oxygen, product: iron oxide. Surroundings: the nearby air or any object in contact with the rusting iron.)

Air in a tire is at a higher pressure than the atmosphere around it and so it shoots out even from a small hole. What could that have to do with a big deal like the second law of thermodynamics? (Every spontaneous physical or chemical process involves the second law!) Those nitrogen and oxygen molecules in the tire each have motional energy but it is far more 'localized', compressed in the small volume of the tire, than it would be in the huge volume of the atmosphere. Thus, the second law explains why punctures or blowouts occur: the motional energy of those localized/forced together molecules will become dispersed and spread out to the lower pressure, larger volume atmosphere if it is no longer hindered by the tire walls from becoming so. (System: air in tire; surroundings: atmosphere.)

An ice cube melts in a big warm room. How can the melting of a little ice cube in a warm room maybe 200,000 times bigger than it is be an example of the second law: i.e., how could that possibly be a spreading out of energy? But the second law has to do with energy dispersal and there's a little spreading out in that 200,001st part of that total of system plus surroundings! As we learn more quantitatively about entropy, we will easily prove that motional molecular energy is always more dispersed when that energy moves from a warmer surroundings or system to a cooler surroundings or system. Hotter goes to cooler spontaneously. Always.

Lots of things are happening when molecules in the warm air disperse some of their energy to the molecules that are vibrating (like dancing rapidly in one place) in the ice cube. Right at the surface many hydrogen bonds between the water molecules of the ice are being broken by the motional energy of the air molecules being transferred to those surface molecules. (This doesn't change the amount of motional energy of those molecules and therefore their temperature doesn't change. They increase in potential energy due to the hydrogen-bond breaking.) Now, because the water molecules whose hydrogen bonds to other molecules in the rigid ice structure are broken, they are freer to form hydrogen bonds to other water molecules that are liquid — they can exchange partners and move from one to another. The vibrational energy that allowed them to dance in place in the crystal is changed to translational energy in the liquid and the molecules can move just a bit every trillionth of a second.

Thus, although the true picture is just a bit more complex (i.e., it is the closer energy levels in translation than in solid vibration that make the energy far more dispersed in liquid than solid), we can sense that the movement of molecules in liquid water allows the energy to be more spread out even than in crystalline ice, even at melting temperature. It is not a matter of order and "disorder"! (That's as misleading as magic and as obsolete as 1898 fashions. order_to_disorder.pdf)

The second law tells us about energy dispersal and entropy is the word for how that energy dispersal is measured — how spread out the energy becomes in a system, how much more dispersed it has become compared to how localized it was.  Such energy changes and consequent entropy changes are the focus for understanding how and why spontaneous events occur in nature. Only sometimes do the structures or arrangements of molecules in an object help us to see greater or lesser localization of energy (that used to be called ‘order to disorder’). (System: ice cube; surroundings: warm room.)

NOW we can understand what thermodynamicists have been talking about the last century and a half when they spoke in apparently mysterious sentences like "The entropy of the universe increases toward a maximum."  All they meant was simply that energy, everywhere, spreads out as much as it can (and that spreading out of energy is measured by entropy).

Recap and Conclusion

All the rocks falling down mountains, hot pans cooling in cool rooms, anything made of iron rusting, anything burning or reacting with oxygen — all spontaneous events and chemical reactions that occur by themselves  -- are due to energy dispersing or spreading out. Entropy is the quantitative measure of how much energy and how much dispersal occurs in a process or reaction. Therefore, entropy is constantly increasing because spontaneous events continue to occur in our energy-rich universe. Thus we can decipher the following statement of the second law:

'In any irreversible process the total entropy of all bodies concerned is increased.'

That just means: "In any process in which energy becomes spread out, the measure of that spreading out or dispersing (i.e., the total entropy) increases when you include both what happens in the system AND its surroundings.”

Now we can translate ‘second law language’! It seems very confusing if you read it rapidly, but taking it a few words at a time and knowing what we have just reviewed, the ideas are not complicated.

Next, let's see how entropy helps us understand more about things in our world.