AP Chemistry - Entropy: Spontaneous Change
One of the main goals of thermodynamics is to understand the relationships among the factors that control whether events are possible. Many such possible events are part of our every day lives all of the time, and they occur without outside help. A book slips from your hand and will start to fall. The ice cubes in a cold drink will gradually melt. Such events are examples of spontaneous change - they occur by themselves without outside assistance. Once conditions are right for them to begin, they proceed on their own.

Some spontaneous changes occur rapidly. An example is the set of biochemical reactions that take place when you accidently touch something hot. Other spontaneous events, such as the gradual erosion of a mountain, occur slowly and many years pass before a change is noticed. Still others occur at such an extremely low rate under ordinary circumstances that they appear not to be spontaneous at all. Gasoline-oxygen mixtures appear perfectly stable indefinitely at room temperature because they react so slowly. If heated, their rate of reaction increases and they can react explosively until all of one or the other is totally consumed.

Each day we also witness many events that are not spontaneous. We may pass a pile of bricks in the morning and later in the day find that they have become a brick wall. You should know from experience that the wall did not form by itself. A pile of bricks becoming a brick wall is not spontaneous.

Once a spontaneous event begins, it has a tendency to continue until it is finished. A nonspontaneous event, on the other hand, can continue only as long as it receives some sort of outside assistance.

Nonspontaneous changes have another common characteristic. They can occur only when some spontaneous event has occurred first.


Enthalpy, Entropy and Spontaneity

Exothermic reactions tend to be spontaneous.

Because spontaneous reactions are so important, it is necessary for you to understand the factors that favour spontaneity. Think about a skier going downhill, a waterfall and a fuel fire at a gasoline refinery. If you study these events all of them involve a lowering, or decrease, in the energy of a system. Because these events are spontaneous, we can conclude that when a change lowers the energy of a system, it tends to occur spontaneously. Since a change that lowers the energy of a system is exothermic then we can come up with the opening sentence generalization. Exothermic changes have a tendency to proceed spontaneously.

The word tendency should be emphasized. There are some exothermic reactions that are not spontaneous, nor is every nonspontaneous endothermic.

The dissolving of salts such as NaI in water is just one example of a change that occurs spontaneously even though it is endothermic. It is a universal phenomenon that something that brings about randomness is more likely to occur than something that brings about order. Think about your room at home. It does not spontaneously get more organized. But clean it up and wait a few days and it will look like a hurricane went through it. There is a tendency for things to become more disorganized and random. Another example to think about is playing cards. Take out a deck of cards, that are in order. Throw them up in the air. What are the chances that they will land on the floor perfectly lined up and still in order. (The orders are so high that we don't make a number big enough to describe the event).

We expect this disordering of the cards because there are so many ways for them to become disordered and only one way for them to fall and still stay in order.

The term entropy, S, is used to describe the degree of randomness in a system. The larger the value of the entropy, the larger is the degree of randomness of the system. Like enthalpy, entropy is a state function. It depends only on the state of the system, and therefore a change in entropy, Δ S, is independent of the path from start to finish. Δ S is defined as Δ S = Sfinal -Sinitial    or, for chemical systems as Δ S = Sproducts - Sreactants

As you can see, if the Sproducts is larger than Sreactants then the value of Δ S is positive. A positive value of Δ S means an increase in the randomness of the system during the change, and we have seen that this kind of change tends to be spontaneous. This leads to a general statement about entropy:

Any event that is accompanied by an increase in the entropy of the system tends to occur spontaneously.

Predicting Δ S for Physical and Chemical Changes

It is often a relatively simple matter to predict whether a particular change will become more or less random. One of the things to look for is the state of the reactants and products. Gases have more entropy than liquids which have more than solids. During chemical reactions, the freedom of movement of the atoms often changes because of changes in the complexity of the molecules. For example, consider the reaction

                                     2 NO(g) -----> N2O4(g)

Among the reactants are six atoms combined into two molecules of NO2. Among the products, these same six atoms are confined to one molecule. In the reaction vessel, dividing the six atoms between two molecules allows them to spread out more ad gives greater freedom of movement than when the atoms are combined into just one molecule. Therefore, we can conclude that as this reaction occurs, there is an entropy decrease.

Two general rules for predicting entropy changes.

1.   Look at the states first. (gases > liquids > solids)

2.   If  both states are the same then look at the number of moles of reactants and products and decide if there has been an increase in the number of moles or a decrease.


The Second Law of Thermodynamics

"Whenever a spontaneous event takes place in the universe, it is accompanied by an overall increase in entropy."

Note that the increase in entropy that's referred to here is for the universe, not just the system. This means that a system's entropy can decrease, just as long as there is a larger increase in the entropy of the surroundings so that the net entropy change is positive. Because everything that happens relies on spontaneous changes of some sort, the entropy of the universe is constantly increasing.

The Third Law of Thermodynamics

It is often a relatively simple matter to predict whether a particular change in a reaction will cause the energy of the reactants to become more spread out (have greater entropy) or less spread out (have lesser entropy).  One of the things to look for is the state of the reactants and products. Gases have more entropy than liquids which have more than solids. During chemical reactions, the freedom of movement of the atoms often changes because of changes in the complexity of the molecules. For example, consider the reaction
 
2 NO2(g) ----- N2O4(g)

Among the reactants are six atoms combined into two molecules of NO2. Among the products, these same six atoms are confined to one molecule. In the reaction vessel, dividing the energy of the six atoms between two molecules allows their energy to be  spread out more in their free movement than when the atoms are combined into just one molecule. Therefore, we can conclude that as this reaction occurs, there is an entropy decrease.
 
Two general rules for predicting entropy changes.
 
1.   Look at the states first. (gases liquids solids)
 
2.   If  both states are the same then look at the number of moles of reactants and products and decide if there has been an increase in the number of moles or a decrease.
 
The entropy of a pure crystal is zero at absolute zero.
 
The entropy of a substance (i.e; the extent of its dispersal of energy at a given temperature) varies with the temperature of the substance. The lower the temperature, the lower the entropy.
 
For example, at a pressure of 1 atm and a temperature above 100oC, water exists as a highly disordered gas with the energy of its molecules widely spread out: a very high entropy. If confined, the molecules of water vapour will be spread evenly throughout their container, and they will be in constant motion. When the system is cooled, the water vapour eventually condenses to form a liquid. Although the molecules can still move somewhat freely, their lesser energy is less widely dispersed; they are now confined to the bottom of the container. Their energy is not as great nor as widely spread out as in the gas and thus the entropy of the liquid is lower. Further cooling decreases the entropy even more, and below 0oC, the water molecules join together to form ice, a crystalline solid. The molecules are now not at all free to move, particularly in comparison to that of the gas, and the entropy of the system is very low.
Yet even in the crystalline form, the water molecules still have some entropy. There is enough thermal energy left to cause them to vibrate within the general area of their lattice sites. Thus at any particular instance, we would find the molecules near, but probably not exactly at, their lattice positions. If we cool the solid further, we decrease the thermal energy and the molecules spend less time away from their lattice positions. The amount of energy and its spreading out decreasese and the entropy decreases also. Finally, at absolute zero, the ice will be in a state of absolutely minimal energy of molecular movement and its entropy will be zero. This leads us to the statement of the Third Law of Thermodynamics. At absolute zero, the entropy of a pure crystal is also zero.
 
 i.e.     S = 0   at     T = 0K
 
Because we know the point at which entropy has a value of zero, it is possible by measurement and calculation to determine the actual amount of entropy that a substance possesses at temperatures above 0 K. If the entropy of one mole of a substance is determined at a temperature of 298 K (25oC) and a pressure of 1 atm, we call it the standard entropy, So. In your databook there is a listing of standard entropies next to the standard enthalpies.
 
                                    ********* IMPORTANT *********
                      Entropy has units of J/K degree J/K not kJ/K!!!!!
 
Once we know the entropies of a variety of substances we can calculate the standard entropy change, Δ So, for chemical reactions in much the same way that we calculated Ho.
 
Δ So = (sum of So of products) - (sum of So of reactants)
 
The values of Sfo have not been calculated for you. If you need them, then you must calculate then from the values of So.
 
Sample problem
Urea (from urine) hydrolyzes slowly in the presence of water to produce ammonia and carbon dioxide.
 
CO(NH2)2(aq) + H2O(l) ---- CO2(g) + 2 NH3(g)

 
What is the standard entropy change, in J/K, for this reaction when 1 mole of urea reacts with water?
 
  Δ So = [CO2(g) + (2)NH3(g)] - [CO(NH2)2(aq) + H2O(l)]
          = [213.6 J/K + (2)192.5 J/K] - [173.8 J/K + 96.96 J/K]
          = (598.6 J/K)-(243.8 J/K)
          = 354.8 J/K

Go to the Entropy Third Law Calculations Worksheet

Entropy: In Depth
A special thanks to:
Frank L. Lambert, Professor Emeritus (Chemistry)
Occidental College, Los Angeles
for his permission to reproduce this work.
Introduction
       The second law of thermodynamics is a powerful aid to help us understand why the world works as it does -- why hot pans cool down, why our bodies stay warm even in the cold, why gasoline makes engines run.  Entropy also is simple to describe and explain qualitatively.  However, to begin our qualitative approach we must avoid the briar patches involving the second law and entropy that have been planted all over acres of book pages and Web sites.
 
For those who prefer conclusions before explanations:
The second law of thermodynamics says that energy of all kinds in our material world disperses or dissipates if it is not hindered from doing so. Entropy is the quantitative measure of that kind of spontaneous process: how much energy has flowed from being constricted or concentrated to being more widely spread out (at the temperature in the process).

        From the 1860s until now, in physics and chemistry (the two sciences originating and most extensively using the concept) entropy has applied only to situations involving energy flow that can be measured as "heat" change, as is indicated by the two-word description, thermodynamic ("heat action or flow") entropy. 
 
     Entropy is not disorder, not a measure of chaos, not a driving force. Energy's diffusion or dispersal to more microstates is the driving force in chemistry. Entropy is the measure or index of that dispersal. In thermodynamics, the entropy of a substance increases when it is warmed because more thermal energy has been dispersed within it from the warmer surroundings. In contrast, when ideal gases or liquids are allowed to expand or to mix in a larger volume, the entropy increase is due to a greater dispersion of their original unchanged thermal energy. From a molecular viewpoint all such entropy increases involve the dispersal of energy over a greater number, or a more readily accessible set, of microstates. 
 
For several years students were taught that "Entropy is disorder," Entropy is NOT disorder! This confusion about disorder and entropy comes from 1895 before an adequate understanding of the details of energy change in atoms and molecules was possible. At that time even the existence of molecules was not acknowledged by some of the most prominent scientists in physics and chemistry. Those who proposed and elaborated the second law had no better catchall phrase to describe to others what they believed was happening. Order/disorder became increasingly obsolete to apply to entropy and the second law when the existence of quantized energy levels in physics and chemistry began to be understood in the early twentieth century.
 
       Although order/disorder is still present in some elementary chemistry texts as a gimmick for guessing about entropy changes, it is both misleading and an anachronism today and will be phased out of future textbooks. In the humanities and popular literature, the repeated use of entropy in connection with "disorder" (in the multitude of its different common meanings) has caused enormous intellectual harm. Entropy has been thereby dissociated from the quintessential connection with its atomic/molecular energetic foundation. The result is that a nineteenth century error about entropy's meaning has been generally and mistakenly applied to disorderly parties, dysfunctional personal lives, and even disruptions in international events. This may make pages of metaphor but it is totally unrelated to thermodynamic entropy in physico-chemical science. It is as ridiculous as talking about how Einstein's relativity theory can be applied to a person's undesirable relatives in Chicago.



The Second Law of Thermodynamics
A special thanks to:
Frank L. Lambert, Professor Emeritus (Chemistry)
Occidental College, Los Angeles
for his permission to reproduce this work.
 
        The Second Law of Thermodynamics -- what a forbidding group of words! However, any fear of the phrase or what lies behind it disappears when we realize that we already know the second law well from our everyday experience. We just haven't recognized that such varied happenings as the following are all examples of the second law: hot pans cool; water spontaneously flows down Niagara Falls; tires under high pressure blow out forcefully if their walls are damaged; if gasoline is mixed with air in a car's cylinders, it explodes when a spark is introduced. How are all these different events described by just one law, especially a law with a complicated name?
 
      In a hot metal pan the atoms are very rapidly vibrating (because heat has been dispersed to them from a hotter flame). They will disperse their energy to any less rapidly moving molecules -- to those in a cool counter top or those in the atmosphere of a cool room. Molecules of water atop Niagara Falls have relatively great potential energy; they disperse it if they fall far down to the river below. Molecules of air (that is composed of nitrogen and oxygen) in a pressurized tire on a car have great potential energy because those molecules were forced close together by air dispersed from a higher pressure source. The air molecules in the tire will spontaneously (and vigorously!) spread out their energy to the atmosphere if the tire is punctured or the tread separates from the walls.
 
        Molecules of gasoline with oxygen (from air) have greater energy in the internal bonds that hold their atoms together than do the carbon dioxide and water that gasoline forms when it reacts with oxygen. Therefore, gas and oxygen spontaneously tend to react and make carbon dioxide and water because then energy would be dispersed in the process. However, just as compressed air in a tire is physically blocked from dispersing its potential energy to the atmosphere by the strong tire walls and tread, gasoline and air are chemically blocked from dispersing their energy by a barrier called an activation energy.  Thus, gasoline and the oxygen of air can remain unchanged for years and centuries. Nevertheless, given a spark to overcome the activation energy blocking the reaction, gasoline and oxygen will violently react to spread out large quantities of heat from their bonds while forming lower-energy carbon dioxide and water.
 
       All of the minute particles, the atoms and molecules, in these examples will spread out their energy if they possibly can. The second law of thermodynamics is merely the summary of all the preceding statements that have a single theme: energy disperses if it is not hindered from doing so. Always. This generality is far more extensive than those five examples. All spontaneous happenings in the material world (those that occur by themselves without outside pushing or help, except perhaps for a spark to start, or an initial shock [that starts nitroglycerin exploding]) are examples of the second law because they involve energy dispersing. Energy that is in the rapidly moving, ceaselessly colliding minute particles of matter (many kinds of which, like gasoline with oxygen, contain higher-energy bonds within them than their possible products) will diffuse, disperse, dissipate if there is some way for that to occur without hindrance.
 
       The second law of thermodynamics is so much a part of our everyday experience that it is adequately summarized in the simple examples we have seen, the two archetypes being:

 "hot pans cool down", the case of an immediate dissipation of energy,

because they tend to disperse the energy of their fast moving particles [that we commonly call heat] in their metal or glass to anything they contact, such as the cooler room air [slower moving molecules that then increase their speed somewhat],
or "gasoline explodes", the case of an obstructed dissipation of energy,
because it tends to react with the oxygen in air, but does so only if the mixture is ignited. Then, the gasoline and oxygen can spread out some of the energy in their bonds (chemical bonds hold atoms together in molecules) in forming carbon dioxide and water that have lesser energy in their bonds -- but the rest of the energy is dispersed to all the molecules in the gaseous vapor (left-over oxygen, nitrogen, carbon dioxide, CO, etc.). This makes them move extremely fast (characteristic of the molecules/atoms in anything that is very hot) and the pressure in a confined space immediately increases. Such a high pressure in the small cylinder volume, amounting to a very large potential energy, further dissipates (second law again) by pushing the car's pistons down forcefully and they disperse their kinetic energy by turning the crankshaft…etc., etc.
       The word "tends" in the foregoing cannot be overemphasized. It is omission of "tends" or "tendency" and their implications that leads most non-scientists astray in their reading or writing about the second law. So much stress is usually placed on the inevitability of dire effects of the second law (and its supposed complexity) that it seems immediately threatening to almost every aspect of our lives.
 
        The second law of thermodynamics is by no means an instantaneously obeyed edict. Admittedly, it accurately predicts the probability of the dispersal of energy that is localized or "concentrated" in a group of molecules or atoms -- and that can result in undesirable events ranging from serious accidents to disastrous forest fires or to our ultimate death. In this sense, the second law is our "baddest bad". However, the law is completely silent about two factors, namely:
(1) what will allow the second law's prediction of energy dispersal to be carried out (because many natural processes cannot occur as rapidly as a hot pan cooling down; gasoline plus oxygen or a tree plus oxygen cannot start to react without a spark or hot flames to activate them to begin their oxidation (burning) and thereby disperse part of their internal bond energy);

(2) over what span of time will the whole dispersal process extend (hot pan, slow (minutes); gasoline + oxygen + spark, fast (fractions of a second).

 
Spontaneity
A special thanks to:
Frank L. Lambert, Professor Emeritus (Chemistry)
Occidental College, Los Angeles
for his permission to reproduce this work.
 
Entropy  increase without energy increase?
     Many everyday examples of entropy increase involve a simple energy increase. This energy increase is usually evident from a rise in temperature. 
 
        We can analyze many simple situations in terms of energy and entropy. Why does ice melt in a warm room? A first approximation is easy. The faster moving ("hotter") molecules in the room can disperse their energy by making the slower moving ("colder") molecules in the ice speed up. This would be a following of the second law and therefore it should be a spontaneous process involving an increase in entropy in the ice as it melts to form water. A more sophisticated view includes the fact that liquid water can have many more ways of dispersing energy than ice -- water molecules in the liquid form can rotate and move far more freely than in ice. Therefore, if water more effectively disperses energy than ice, when they are together at an equilibrium temperature, liquid water will be favored because it better disperses the energy available in the system.
 
       Conversely, why do snowflakes form when moisture (water) is in air that is colder than water's freezing temperature? The water will disperse its energy to the colder air and then the water's temperature will drop to freezing and the water will begin to form crystals of ice that we recognize as snowflakes.
 
       Some more difficult evaluations of energy and entropy are involved even in mundane situations encountered daily. However, with a few hints we can arrive at general answers for all such events.
 
1. Why do gases mix spontaneously? The same basic question is expressed in "Why could you quickly smell perfume that is released in one corner of a large room in the far corner even if the room air could be 'absolutely perfectly' still?" (There is NO change in energy in the process and yet it is spontaneous. Where is any energy dispersal here that the second law says is characteristic of all spontaneous happenings?)

2. Why do liquids mix spontaneously? Same question, "Why does cream mix with coffee at the same temperature?" (NO change in energy. Where is any kind of energy dispersal?!)

3. Why would perfume vapor or oxygen or nitrogen or helium spontaneously and instantly flow into an evacuated chamber? (NO change in energy. Where's the second law here?)
 

        There is a broad range of speed and kinds of motion in any group of molecules that is above absolute zero. Molecules move (translate), tumble around (rotate) and vibrate (atoms in the molecules act as though they were connected with springs, back and forth, or wig-wag vibration). All of these motions increase as energy content increases (indicated by the temperature). Each type of motion is associated with specific energy levels ranging from lower to higher energy content.  These levels are discrete, i.e., molecules cannot be in any in-between energy state. Energy is "quantized" and treating their energy relationships is part of quantum mechanics.
 
       The more energy levels that are occupied by energetic molecules, the more widely energy can be dispersed and the greater is the entropy. But in the many cases we have talked about, additional energy levels could only be occupied if the system were heated so the slower molecules would be speeded and there would be many more fast moving molecules to occupy the possible higher levels. However, this is not the only way that additional energy levels can be made available.
 
       When molecules are allowed to expand into a larger volume (in three-dimensional space) , quantum mechanics shows that an interesting change in possible energy levels takes place: the energy levels become closer together. (Technically, we must say that the density of occupiable levels in any selected energy range is greater.) This means effectively that molecules, if allowed to occupy a larger volume even without any increase in their energy, can spread out to occupy many more energy levels. This means greater dispersal of energy and an increase in entropy simply by there being a greater three-dimensional volume in which the molecules can move. (Further, because any change in which entropy increases is a spontaneous change. It happens without any outside aid, energy input, etc.)
 
        How does that apply to (1), perfume in a room? It spontaneously mixes with the gases in the large room because its energy is redistributed among more energy levels than in the small vapor space of the bottle. This is the same as having greater energy dispersal = an increase in entropy = spontaneity.

         And (2), cream in coffee? (Or any other kinds of liquids mixing?) Same as above. Because of an increase in volume, the energy of the cream, or of any liquid mixing with another, is redistributed among more energy levels in the greater volume than alone by itself = greater energy dispersal = increase in entropy = spontaneous mixing.

         (3) A gas spontaneously rushing in to a space that was a vacuum? Same explanation as above. Increase in volume = more energy levels available for a substance with the same energy as in a smaller volume = redistribution of energy among more energy levels = increased energy dispersal = increase in entropy = spontaneous process.
 

         In this example of a gas being "allowed" to go into an evacuated bottle, box, or chamber, our feelings are that this should not only be spontaneous (happen by itself) but instantaneous (happen very fast). But feelings aren't reliable. Science demands reasons (and, as we are aware, the second law makes predictions only about the spontaneity of events, not about their rates or speed of their taking place). Fortunately, there is now a firm theoretical basis for our practical gut feeling that "of course a gas would automatically and instantly fill a vacuum!". Quantum mechanics provides unquestionable calculations that are the reasonable basis, not just for a gas expanding into a vacuum, but for all the results of the second law presented in this article. In science, that's even better than feeling.

FAQs About Entropy
A special thanks to:
Frank L. Lambert, Professor Emeritus (Chemistry)
Occidental College, Los Angeles
for his permission to reproduce this work.
Q. What is entropy? How is it related to the second law?
A.      Entropy is not a complicated concept qualitatively. Most certainly, entropy is not disorder nor a measure of chaos!  Entropy measures how much energy is dispersed in a particular process (at a specific temperature). 
 
Q:  So, what IS the second law of thermodynamics? Well, wait a minute, what's the first law?
A: The first law is very simple.  You can't create or destroy energy.

You can just change it from one form to another, for example, electricity to heat, heat that will boil water and make steam, hot steam to push a piston (mechanical energy) or turn a turbine that makes electricity which can be changed to light (in a light bulb) or, using only a tiny quantity changed to sound in an audio speaker system, and so forth. 

    The second law of thermodynamics looks mathematically simple but it has so many subtle and complex implications that it makes most chem majors sweat a lot before (and after) they graduate. Fortunately its practical,down-to-earth applications are easy and crystal clear. These are what we'll talk about. From them we'll get to very sophisticated conclusions about how material substances and objects affect our lives.

Looking at the direction of energy flow in any happening/process/event is the first step to understanding what the second law of thermodynamics is and what it applies to.

Energy spontaneously tends to flow only from being concentrated in one place to becoming diffused or dispersed and spread out.

  The perfect illustration is: A hot frying pan cools down when it is taken off the kitchen stove.
 

Q. Come on. All this build up for that dumb example?
A:  I could have snowed you with differential equations and diagrams instead of that. We're being practical and visual rather than going the math route, essential as that is in chemistry.

    The big deal is that all types of energy behave like the energy in that hot pan unless somehow they are hindered from spreading out. They tend not to stay concentrated; they flow toward becoming dispersed -- like electricity in a battery or a power line or lightning, wind from a high pressure weather system or air compressed in a tire, all heated objects, loud sounds, water or boulders that are high up on a mountain, your car's kinetic energy when you take your foot off the gas. All these different kinds of energy spread out if they can. The reason for their occurring is the same, the tendency for concentrated energy not to stay localized, to disperse if it has a chance and isn't hindered somehow.  The direction of energy flow is just a tip of the iceberg of that law.
 

Q. Iceberg? 
A.    Come on now. You know that's just a figure of speech to give a feeling for the size of this principle. But... OK, let's get literal: Run that Titanic movie as the ship hits the iceberg. See those steel plates ripped open and the ship begin to sink. Realistic, right? Can you imagine a real happening in which the reverse occurs? A sinking ship whose steel side heals up as it comes up out of the water and floats? Ridiculous. Too stupid to think about. But why is it stupid? Because it is so improbable from your and my experience. Only a movie run backward would show that kind of unrealistic fantasy. The second law isn't some weird scientific idea. It fits with everything common happening that we know.

Our psychological sense of time is based on the second law.  It summarizes what we have seen, what we have experienced, what we think will happen.

Sinking ships are like rocks rolling down a mountain -- as they sink, their potential energy due to being high above sea-bottom is diffused, spread out to the water that they push aside (or, in the case of mountain rocks, diffused as they roll down to the valley and hit other rocks, give them a bit of kinetic energy, and warm them slightly by friction.)

    In a video that is run backward, you may have laughed at some diver who zooms up from the water to a ten-meter diving board, but you're never fooled that the video is going forward, i.e., that you are seeing an event as it actually happened in real time. Unconsciously, you are mentally comparing what you see now with your past practical experience -- and that has all followed the second law. Even though you may never have heard of the law before, in the years of your everyday experience you have seen thousands and thousands of examples of energy flowing from being concentrated to becoming diffused.

    A swimmer doesn't come shooting up out of the water to the diving board, rocks in a valley don't
suddenly roll up a mountain, outside air doesn't rush into a flat tire, batteries don't get charged by sitting around. We sense that videos -- or any sequences of photographs -- are arranged in the right order of showing time going forward only if the events in them agree with our lifetime experience about the direction of energy flow: concentrated to diffused. The second law points the direction of how we feel time goes.
 

Q: You mentioned those tricky words, "spontaneously" and "tends"?
A:  In the second law "spontaneously" means only that any energy which is available in the object or substance for diffusing will spread out from it -- if given a chance. It doesn't have anything to do with how fast or slow that occurs after the dispersal of energy starts, or even when it might start. That's why "tends" is so important to understand as part of the second law.

    The energy available in a hot frying pan or in a loud BOOM from a drum immediately and rapidly begins to spread out to their environments. Nothing hinders them from happening. Lots of unhappy events are like that. But there are an enormous number of "energy diffusing" second-law happenings that are hindered so they don't occur right away. Here's a simple illustration: If I hold a half-pound rock in my fingers so it is ready to fall, it has potential energy concentrated in it because it is up above the ground.   If the second law is so great and powerful, why doesn't the energy that has been concentrated in the rock spread out? Obviously, it can't do that because my fingers are "bonding" to it, keeping it from falling. The second law isn't violated. That rock tends to fall and diffuse its energy to the air and to the ground as it hits -- and it will do so spontaneously by itself, without any help -- the second I open my fingers and "unbond" the rock.
 

Q: Is this understanding of "tends" really so important?
A: Yes, it is. Many philosophers and novelists learned about the second law only from physicists.  The writers pass too quickly over the fact that it is a tendency rather than a prediction of what will happen right away.

    In many real-world chemicals and things the second law can be obstructed or hindered for millions of years. Certainly, the mountains of the world haven't all slid down to sea level in the last several hundred centuries! Similar to my fingers holding the small rock (but millions of times more tightly), even overhanging stone in cliffs or mountains is bonded, chemically bonded, to adjacent atoms of stone and so the stone can't obey the second law tendency for it to fall to a lower level. Here, as in countless other examples, the second law is blocked by chemical bonds. It takes a huge number of repetitions of outside energy input like freezing and thawing and earthquakes and windy rainstorms to break the bonds along a weak bond-line, make a crack, and free particles or pebbles or rocks so they can follow the second law by falling to a lower level. 

    Blockage of the second law is absolutely necessary for us to be alive and happy. Not one of the complex chemical substances in our body and few in the things we enjoy would exist for a microsecond if the second law wasn't obstructed. Its tendency is never eliminated but, fortunately for us, there are a huge number of compounds in which it is blocked for our lifetimes and longer.
 

Q Isn't it about time we got to something human rather then rocks?
A:      Chem profs approach the second law the other way around, starting with atoms and molecules first.  Professors rightfully avoid much talk about the behavior of big visible things at all. In the limited time of a chemistry course they can only develop the nature of atoms and molecules and of chemical substances. Objects made from chemicals like a gear or a bridge or a wooden house or a book or a bone just have to be assumed to behave like their constituent substances. 

       Wood and paper are both primarily cellulose. Paper is easier to experiment with so let's think about its burning. When paper catches fire and burns, there's a lot of energy given out as heat and some as yellow light. It's well known now that the products of the combustion of cellulose with the oxygen of the air are carbon dioxide and water. (The slight amount of black ash is due to the clay that was on the paper adsorbing a small amount of carbon.) Once started, the burning is spontaneous --i.e., the process goes on by itself without any further help after a match starts it -- and also burning is really fast. Now, if energy is flowing out in this reaction of paper with oxygen, the paper and oxygen must have had a lot more energy inside them before the reaction than do the carbon dioxide and water after the reaction .

    What's happening here is a beautiful illustration of the predictions of the second law. Systems (groups) of chemicals -- or objects made from them (like sheets of paper or houses) -- tend to react if they have more energy bound inside their molecules than do the reaction products that they can form. Then, when they react, they are spontaneously spreading out their internal energy in two ways: 1) only a part to each molecule of the products because each has lesser energy concentrated in it than was in the starting materials, and 2) giving those product molecules much more kinetic energy (making them move much faster) than the original cellulose and oxygen. These fast molecules show a high temperature on a thermometer; we say they are hot, not because heat is a "something" but because heat is the process of energy transfer from one kind of matter to another -- from fast molecules of gas to the thermometer bulb or to one's hand if you're so foolish as to put it in a flame.
 

Q:  You had to put a match to that paper to start it burning! What's spontaneous or second law about that??
A: Have you already forgotten that essential word "tends" in the second law?

    All the paper and wood and things made from them in the entire world tend right now to react with the oxygen in the air and form one gigantic fireball. Why don't they? Well, why don't all the mountains on earth spread out the potential energy in their high stone cliffs this second and collapse into spread out much-lower mounds of sandy particles? It's the strength of the chemical bonds (between silicon, oxygen, potassium, aluminum and other atoms and ions) that holds stone together and acts as an obstacle to the second law's immediate execution. The potential energy of high rocks/mountains is hindered from spreading out instantly.

    Just so, the strength of the chemical bonds (between carbon, hydrogen and oxygen) in cellulose holds it together and obstructs the instant spreading out of the energy inside the cellulose in air. This strength prevents oxygen from instantly breaking into the cellulose molecules to form even stronger bonds (of carbon dioxide and water) and to release large amounts of energy (because the stronger the chemical bond, the less energy is contained within the molecule). However, it takes just a little extra push of energy from the match flame to start to break a few sextillion bonds in the cellulose of paper or wood.

The initial energy push (usually from heat), the small energy "hill" in the diagram below, is the activation energy, Ea, that is necessary to overcome the bond-strength obstacle to the second law in most chemical reactions. Thus, this requirement for input of an initial energy, the energy of activation, hinders both desirable and undesirable reactions from occurring.
An important idea is "Activation energies protect substances from change."

As these first "heated up" bonds are breaking, the oxygen from the air begins to grab carbon and hydrogen atoms to form carbon dioxide and water molecules. But the formation of new strong bonds in the CO2 and water gives out a lot of energy -- enough to start to break many many more sextillions of bonds of cellulose (no bond being totally broken before oxygen has simultaneously begun to form a new CO2 and water molecule from the developing fragments). These new molecules of CO2 and water also absorb some of the energy from the new bonds as they are formed and many move faster than    twice the speed of sound. We sense those fast moving molecules as hot gas and we call it "heat".
 

Q.   I remember that in the Malibu fires a couple of years ago some houses started to blaze from the inside because heat from the nearby burning trees and brush ignited the cloth drapes inside the picture windows. Then there were others with big windows that didn't catch fire because they had aluminum blinds which were closed. That involved activation energy, right? Cotton cloth is cellulose, isn't it?
A. Yes to both questions. First of all, the glass of the windows probably got extremely hot, both from the heated air of the fire and the fire's infrared radiation. In addition, as you suggest, the intense IR radiation went right through the windows and heated the fabric drapes even more -- enough to exceed their activation energy that normally hinders their oxidation in air. They began to burn and this gave out enough energy to ignite the whole interior -- by exceeding the activation energy of oxidation of all the other flammable materials in the house.

    Just as does every idea that we've been talking about, the concept of activation energies gives us tremendous power in understanding how the world works, even in unusual events. For instance, you've heard about the dangers of nitroglycerin, a liquid that explodes violently just from being shaken hard or jarred sharply. Do you think that its energy diagram would look like the one for cellulose above? Of course not. It must have a very low activation energy, Ea.  That leads to an extremely fast formation of hot gaseous products, an explosion (despite the  relatively small difference in energy between "nitro" and the products).  Explosives form hot gases so rapidly because they all have oxygen atoms as part of their molecules. Thus, they are not limited in their reaction rate by access to atmospheric oxygen as are most substances.  Alfred Nobel was driven to invent a safer explosive when four workers and his brother were killed in the family nitroglycerin plant. He made what he called "dynamite" when he mixed oily nitroglycerin with some powdery silica material to form a seemingly dry solid that could be pressed into stick shape. They didn't detonate just from being hit or dropped. Obviously, therefore, a considerably higher Ea indicating that more energy must be put in, e.g., by a blasting cap, to initiate the spontaneous decomposition of the nitroglycerin. (TNT, used in armor piercing shells, is about six times more resistant to shock than nitroglycerin. Thus, you can guess at TNT's activation energy for reaction.)  Dynamite has been mainly replaced by other explosives for excavation, etc., today.

    There. We've seen some substances with low activation energies but we don't often run into nitro or TNT! 
 

Q: What about the flow of enegy? and the waste from this energy flow?
A.  Nature's second law predicts that the energy concentrated inside a chemical like oil or coal (or food) will spread out. It will, if the proper other chemical (usually oxygen) and if that necessary little energy push to overcome an activation energy barrier are also present.  We make our whole technological world run by grabbing as much as we can of the energy flow available from concentrated energy sources like fuels to run an infinite variety of machines, electrical generators and vehicles. (Our bodies, as we have said, use second-law energy flow from the oxidation of food for the synthesis of essential compounds and for all activity, from biochemical to muscular to mental.) However, when we change energy from one form to another it is impossible for us to get to use all of the energy in the concentrated energy source for the jobs we want it to do. Some always must be wasted, mainly as unusable heat to the environment, a sort of necessary 'energy friction' in every real-world energy transfer. That's where our body gets heat to maintain our 37.0ºC.

    This fact of some unavailable, unusable energy when it is transferred is really a hint about the ultimate basis of the scientific statement of the second law -- of what can be considered the ultimate cause for energy to flow in one direction only. I have avoided mentioning it until now because it is very abstract compared to its practical, down-to-earth results of lightning, explosions, engines running and flat tires. It's entropy.
 

Q: Are you serious?
A:  Let's look at the mining of  iron ore. It's scattered all over the earth, sometimes in big pockets that are very valuable because they have an especially large concentration of iron oxide.

    This minute all around the world there are tens of thousands of people who are "using" (transforming to mechanical work, losing some to waste heat spread to the environment) the concentrated energy in coal, oil and gas to dig up the ore with giant scoops and transport it via trucks, trains, and ships from different mines to steel mills. Then, more energy is used by more thousands of people to change it into iron and finally to shiny steel...What a long parade of actions based on using the second law to get what we want!

Every step from the original rusty dirt in the ground requires transformation of concentrated energy (in coal, oil, gas) to do a lot of mechanical work (along with that dispersing of less concentrated energy in the hot exhaust gases of CO2 and water). Then bringing together thousands and thousands of tons of ore, coal and limestone to one place, the steel mill, is another enormous expenditure of concentrated energy in fuels (not counting the human effort in muscle and brain). Next, a totally different variety of energy transformation is done, changing the iron (oxide) ore to iron metal that has a larger internal energy content in its bonds that does the oxide. Wait a minute! Doesn't it seem against the second law to force a dispersed-energy chemical like iron oxide to change into a concentrated-energy chemical like nearly pure iron? Sure it is, but there's no problem -- if we are willing to pay the second-law price of loss of some of the energy as wasted heat. Just as in running all those truck, train and ship engines, we can take energy flow from a spontaneous process (here in this case, from two chemical processes):
    The spontaneous reaction of carbon from coal with a little oxygen to form CO and a lot of heat, followed by
    the spontaneous reaction of CO with iron oxide to form CO2 plus pure iron and some more heat)
and cause the nonspontaneous change of iron oxide to iron. Of course, in doing that we will lose a large flow of energy as waste heat. To give an idea of the size of it in iron making, a ton of near-pure carbon (coke from coal) reacts with four tons of air at around 1000 C in a blast furnace to form a ton of pig iron from two tons of ore. The energy price is six tons of hot flue gas that the process spews out as energy that is mainly not available for more changing of iron oxide to iron. Pretty big operation.

    Did we beat the second law? No way. But by using the second law (taking the energy from two spontaneous "downhill" reactions and transferring much of it to force a nonspontaneous process to go "uphill" energy-wise and make something), just as we take gasoline energy and change some of its energy into mechanical energy (to make nonspontaneous engines turn the car wheels), we got what wanted: iron from which we can produce steel, the structural material for a near-infinite number of useful objects. 
 

Q: Are there more examples? 
A:  Lot's of them.  Let’s finish this recap of human use of the second-law energy flow: Besides making concentrated-energy chemicals like iron, copper, chromium and silver from their diffused-energy ores, we make thousands of other high energy substances for our pleasure or our needs. Minor things like flavors for foods. Important pharmaceuticals that save millions of lives. It may take dozens of reactions (milder than that violent one for iron from iron oxide!) to change starting materials stepwise to the final chemical product, but the overall process involves diverting energy from spontaneous reactions to make the substance we want.

Of course, this is the kind of coupled process (i.e., a spontaneous + a non-spontaneous) that nature uses – taking a tiny bit of sunlight energy and, with the aid of extremely complex processes in organisms like plants, changing lower-energy carbon dioxide and water and traces of minerals into thousands of higher-energy substances. But don’t think that "natural" or "from natural materials" has something to do with good or harmless! There are hundreds of harmful or even poisonous chemicals in nature – from strychnine to the extremely deadly compound in simple castor beans. Also usually omitted when someone extols the beneficial qualities of everything "natural" is the fact that all terribly toxic viruses and bacteria are totally natural!
 

Q: You're using doublespeak on me! First you said it was bod for us and now you show that the second law is a good buddy because we can use it to get energy to do what we want.  What's the story?
A:  You're not naive so stop acting like it. . Life is full of stuff that can be good and bad. But stand back now:

The second law is the biggest good and the biggest bad on earth.

    The good: Because of the second law about the direction of energy flow, life is possible.
 

 We can eat concentrated energy in the form of food and process that energy (using  some, losing some) unconsciously for synthesizing complex biochemicals and running our organism, consciously for mental and physical labor, excreting diffused energy as body heat and lesser concentrated energy substances.
 We can use concentrated energy fuels (most frequently, plus oxygen) to gather all kinds of materials from all parts of the world and, without any energetic  limitation, arrange them in ways that please us. Similarly, we can effect a near-infinite variety of non-spontaneous reactions such as getting pure metals from ores, synthesizing curative drugs from simple compounds, and altering DNA.
  We can make machines that make other machines, machines that mow lawns, move mountains, and go to the moon. We can make the most complex and intricate and beautiful objects imaginable to help or delight or entertain us.


The bad: Because of the second law about energy flow's direction, life is always threatened.
 

Every organic chemical of the 50,000 different kinds in our bodies is metastable, synthesized by a nonspontaneous reaction and only kept from instant oxidation in air by activation energies. (Loss or even the radical decrease of just a few chemicals could mean death for us.)

Living creatures are essentially energy processing systems that cannot function unless a multitude of "molecular machines", biochemical cycles, operate synchronically to use (process) energy to oppose second law predictions. All of the thousands of biochemical systems that run our bodies are maintained and regulated by feedback subsystems, many composed of complex substances.

Most of these compounds as well as the rest of the 50,000 are synthesized internally by thermodynamically nonspontaneous reactions, effected by  utilizing energy ultimately transferred from the metabolism (slow oxidation) of food.  These metabolic and synthetic processes are also governed by feedback subsystems.

When these feedback subsystems fail -- due to inadequate energy inflow, malfunction from critical errors in synthesis, the presence of toxins or competing agents such as bacteria or viruses -- dysfunction, illness, or death results: energy can no longer be processed to carry out the many reactions we need for life that are contrary to the direction predicted by the second law.


How's that for starters? You can't get any better for good -- that living is possible due to the second law. And you can't get much worse for bad -- that death is always possible too, due to the second law.
 

Q: Aren't Murphy's Law and the second law related?  Murphy's Law isn't about death, just about less bad things that hit us?
A:  Murph doesn't get that serious very often, but there are at least five thousand illnesses, diseases, "things that can go wrong" with our bodies that may not kill us. That's 5K of Murphs. These are biochemical problems that humans suffer from. But how many do most people have? Did you ever see a PDR Medical Dictionary or an AMA Home Med Encyclopedia? They'll make you very thankful for activation energies and feedback systems that keep your bod working as well as it does (and long as it will) to counter the second law, using food intake as your energy source.

    However, let's look at the other annoyances (and disasters) that the mother of all Murphys is responsible for when things that are around us have energy concentrated inside them. That's always potential big trouble. All that has to happen, somehow, sometime, is for a little energy push -- a spark, a flame, an impact -- to get up over that activation energy hill. 

First, problems caused by the thing or material having concentrated energy inherent in its chemicals:.
        Trees catching fire                              a house struck by lightning
                a curtain too near a candle...              the forgotten cigarette left on a sofa
                        Mrs. O'Leary's cow kicking over a lantern in straw and burning half of Chicago
                            the spark from a bulldozer that started a grass fire and then a forest fire
        These are all cases of an activation energy being exceeded and a spontaneous reaction resulting.

        And, of course, there are many less (or equally) dramatic examples in the oxidation of metals
                Rust on a tool, disfiguring or damaging it         rust in a machine, hindering operation
                        copper oxide in an electrical socket, causing overheating and then a fire
                                battery cable corrosion in Chuck Yeager's X-1 that almost killed him.

Second, annoyances (or worse) due to concentrated energy in the object being present or flowing by it, but not inherent or part of its nature:
        Tires that blow out              hydraulic brake systems that leak suddenly under pressure
                audio speakers that are fed high wattage signals      230 volts into a 115 V house circuit
                        winds in the air.....from gales to hurricanes, from windstorms to tornadoes.
        A car going 80 around a 30 mph curve, a 747 hitting a mountain, an Indy car into the wall.
 

Q: Fine.  I get the point. Or points. Know too much about car crashes. New to me, before we began to talk, was to hear that burnable stuff, wood or paper or cloth, in my room is basically made of concentrated energy chemicals. But I don't have sparks or candles around to give them an activation energy kick. Breaking things is more of a problem to me. Is there energy locked inside a skateboard or a ski that wrecks me because it tends to diffuse or spread out?
A: Good comment and good question. It's great that you now understand why certain things can react with oxygen and why a spark or low flame sets off a spontaneous reaction. You also know now that all of these kinds of problems from plane and car crashes to lightning to tornadoes and fires are related by the second law of thermodynamics: concentrated energy tends to spread out. (A fast moving car is a "reely big" bundle of concentrated kinetic energy.)

    Your question about breakage is just as important because that kind of incident or accident happens to us more often than "Murphy problems" of fire from energy concentrated inside the object.

    Breaking things  involves concentrated energy that is initially outside the thing that gets broken. It's the second law working in the environment of the object -- energy flowing around or through it for some reason or other and hitting it with enough energy and of the right kind to tear it apart. (Right kind? Right amount? Heat won't make a concrete bridge shatter into fragments in thirty seconds, but a strong earthquake will.) Chemists never talk about breaking things because they don't consider that to be a chemical process. The chemical nature of a ski that gets broken, for example, isn't changed. It's just two skis so far as the chemicals in it are concerned. (Try to tell that to the skier.) Technically, the energy content of the two pieces of ski has not been appreciably altered so chemists call a fracture a physical process.

    However, in a micro sense it is a chemical process because in any break chemical bonds are ruptured all along the line of the break as well as complexly broken and reformed near that break line. It's just that the number of bonds altered is extremely small compared to all the others in the ski that are not affected and therefore a chemist would never be able to measure any energy change. Also, where and when the break will occur depends on so many factors that aren't what chemists call fundamental, such as: how the object was made, its shape, its ratio of surface area to volume, the strains and defects present in it, whether it is brittle or ductile and even the rate of application of energy to it.

You are probably aware that microparticles continually change speeds when they collide, but they average roughly around a thousand miles an hour at ordinary temperatures. When they are in a gas, they go a little distance before colliding, not so far when as a liquid, and as a solid they can only vibrate that fast.

Fast-moving atoms and molecules incessantly run into one another, tending to become as scattered as they can be, and in this way energy is transferred and spread out in any way available to them. This is what entropy measures. (That "available to them" phrase means that they may be held in place by chemical bonds until these are broken, that they can’t magically go through walls or to physically improbable locations, and their energy content limits them to being in probable energetic levels, not improbably high ones, under ordinary conditions.)
 

Q: Watch it! That's too big a jump -- from concrete chunks to atoms and molecules!
A: You're right. You're keen to sense instantly what many non-scientists miss: big pieces of matter are made of tiny particles, atoms or molecules or ions, but obviously they don't behave as does a single small particle. (More about that error in a minute.)

    I jumped that way in talking with you just because those drastically broken bridge bits that once moved all around randomly allowed me to bring in entropy's relation to the atoms and molecules that are always moving to all kinds of locations "available to them". Why and how microparticles move to all positions in their available space is vital in understanding the scientific details of the second law in chemistry. But I think that it is better to keep to generalities rather than introducing too many chemical details in our talking together here. 

    The remainder of this section will straighten out some of the confusion that popular and scientific writers have created around the word "entropy".

    Frequently, outside of chemistry, physics or molecular biology, entropy has had its relation to its scientific roots of heat and temperature ignored. The results are disastrous for nonscientists trying to get a feeling for how the world works. Instead of correctly applying entropy to the normal behavior of energetic atoms and molecules, many authors have misled their readers by saying thermodynamic entropy explains the mixing up of all kinds of ordinary things like books or clothes in a dorm room or playing cards that are immobile non-energetic objects or even people's relationships. Maybe it's stupid to say, but even though sheets of paper and books and decks of cards often get all mixed up, they don't go flying around by themselves like molecules in a gas.
 

Q. Of course that's stupid to say. Why tell me that?
A. Because of quotations like those in the next paragraph. Don't they give you the feeling that the clutter and the messes have occurred by themselves, just like molecules spontaneously move all around randomly without any outside influences? Couldn't readers who weren't as analytical and science-minded as you begin to wonder if some weird unseen force called entropy was always lurking in the dark, ready to push things here and there and everywhere?

    In a textbook there is a picture of Einstein's desk taken the day he died with a statement, "Desktops illustrate the principle that there is a spontaneous tendency toward disorder in the universe..." Wow! Stay away from desktops -- you don't want to get caught by the scary spontaneous tendency that happens there! Here's a quote and a photo that really deceives a reader by the first four words that I've italicized: "If left to themselves, the books and papers on the top of my desk always tend to the most mixed-up, disordered possible state." Wasn't the writer ever near the desk? Some mysterious alien force from outer space did it? Another, from a book that sold over a million copies: "Anyone who has ever had to take care of a house, or work in an office, knows that if things are left unattended, they soon become more and more disorderly..." Unattended usually means nobody around, doesn't it?. Isn't that writer implying that things all by themselves cause this disorderliness, rather than people? (He should be told that King Tutankhamen's tomb was left unattended -- really unattended -- for 3274 years and its arrangement of things was found to be totally unchanged, though dusty, when the tomb was finally opened in 1922.)
 

Q: Why be so critical? Those writers just failed to say that they or somebody else was messing things up. What's this got to do with entropy?
A: That's not a minor omission! It's like a guy outside a bank telling you (as police were running toward you two), "Look at all this money that the nice bank teller shoved at me" and just failed to say, "I had a gun pointed at him." Don't you think the gun had something to do with the money-shoving?

    As I said a minute ago, reading statements like these in books gives many people who aren't as sophisticated as you a strange idea about entropy: it's a mysterious force that makes ordinary things jump around and is at work to mix up the world. That's nonsense.  Remember that the authors are writing about the second law of thermodynamics, but using the word entropy for it (in sentences near the above quotes). In only a few minutes together by looking at examples of energy flow in the world, we have found that seeing the second law act that way is not at all mysterious. In fact, it erases all the mystery from dozens of everyday happenings.

    BUT -- and I put that in capitals to warn you about the most frequent error of scientific as well as popular writers -- even texts "leave out the gun" when they start talking about the ordinary world getting mixed up and "going toward disorder". It's people who mess up desks and dorm rooms (and much of the environment), it's hurricanes and tornadoes that tear houses and trees to pieces and scatter the bits; it's earthquakes that can even fracture a concrete freeway and topple a whole building. What's common to all those examples? The flow of energy going from concentrated to dispersed, of course. As a result of that process, solid things get scattered all over and mixed up. The objects do NOT, by themselves, become disordered or random. There isn't any "tendency of objects to become disorganized" in nature any more than bank tellers have a "tendency to give money to robbers" -- without a gun. Energy flow of many kinds is the driving force, the gun, for the world's macro objects tending to become disorderly.

      Whenever an adequate* amount of energy flows through a system of objects, it tends to scatter them. (The energy flow, if adequate*, can break bonds and disperse the resulting object parts.) They will be strewn to random, statistically probable locations consistent with all applicable factors of the objects and their flight paths or those for their fragments. In this process the concentrated energy in the energy flow becomes diffused in imparting kinetic energy to the objects; its entropy is increased. Unless the original objects (or an appreciable part of them) are ground into a fine powder, their energy and their entropy contents are essentially unchanged a short while after the process of movement and scattering  has stopped. (This time period allows temporary heating effects to come to equilibrium with the atmosphere.)
 

Q: Then is this OK? Fast-moving microparticles tend toward randomness, because they thereby can spread out any energy in the system better. Ordinary non-moving solid objects don't tend to go anywhere by themselves (the mobile atoms inside the objects don't make them jump around!)  But if solid things are hit from the outside by energetic winds (or people) of course they get shoved into mixed-upness or randomness.  But I'm uncomfortable with that "No change in entropy in macro objects if they get all mixed up and scattered".
A: Great summary. Here's more of the whole picture of why there is zero entropy change in shuffled cards or messed up rooms. (Zero change in cards or rooms, but there IS entropy increase in the card shuffler's muscles or the room trasher's!).

    Too many writers say that the same is true of large ordinary solid things,when they talk like this: "A disorderly and mixed-up bunch of a number of solid objects has a higher entropy than those same objects in an orderly pattern." This doesn't make sense. Inside disorderly, scattered solid objects -- whose molecules aren't changing at all-- there is exactly the same number of microenergetic states for those molecules as there is in a pretty patterned arrangement of the objects. Whatever pattern the big visible objects are lined up in, it is totally external to the molecules and their behavior. So it is absurd to talk about an entropy change in a group of random solid objects versus the same ones when they were put in some neatnik pattern. NO entropy change occurs in macro objects when they are altered from ordered to disordered or vice versa. ZERO, zilch, zip, nada entropy change because the number of microenergetic states within them is completely unaffected.

    Excuse me for being so repetitious but textbook authors rarely take the space to make this important point clear to students. (Just wait until you see some horrors in the next paragraph. Most books for nonscientific readers are even worse.).

    A typically erroneous quote from a high school chem text is: "The law of disorder states that things move spontaneously in the direction of maximum chaos or disorder." First of all, there is no such law of disorder for things. But the worst here is how the sentence misleads students about things moving by themselves when the author puts in that word "spontaneously". That defeats understanding of how the second law works. Molecules tend to become random spontaneously by themselves, but things do NOT. Every movement toward disorder of a solid object involves an energy flow of some sort from outside it that pushes it. The entropy increase in the energy flow as it becomes more dissipated while moving the object is interesting. The zero entropy change in the object is a scientific bore.

    "Scattered marbles have a higher entropy than gathered marbles." Here is another example of dozens you could see in texts and articles -- totally erroneous because it refers to big visible things rather than microparticles. Marbles aren't molecules, constantly moving at a thousand miles an hour in many different translational and rotational microstates! And, of course, the same is true of a card deck or of clothes and all the stuff in a dorm room: the shuffled deck or the new deck each has the same entropy; the messy room and the neat room likewise.

We are not talking here about human judgement of patterns or preferences or esthetics, just about thermodynamic entropy. A sparkling and neat Martha Stewart bedroom may look much better than the same room after a slob has lived there a month, but the entropy change is zero -- even though that kind of guy could be thrown out legally in less than a week. Any entropy change that occurs when things are moved occurs in the person (or wind, or earthquake) that messes it up.
 

Q: So what?
A: So everything! This is the payoff.
    People from the beginning of history have worried about material things going wrong in their lives. About why bones break, why shiny copper jewelry (valuable in antiquity) turns green, why tools wear out, why rivers of mud rush down the hills and wreck the village, why people get sick, why they die. Fate and karma and spiteful gods have been just a few of the infinity of inaccurate solutions to the threatening problem of seemingly erratic nature. "Why me?" has probably been a human feeling before the invention of language. It is common today in any catastrophe. Is it justified?

    You now know the basic cause of every material/physical event that we think is bad: It is the second law or, more accurately, what the second law describes: the behavior of energy in our real world. All the structures that we prize -- from our own bones to our artifacts like chairs or houses, skyscrapers, bridges or jet planes -- are subject to being broken or destroyed by adequate energy flow moving from being concentrated to becoming spread out and diffused. The distressing results of forceful impacts on bones and cars and buildings are simply manifestations of this tendency of concentrated energy.

(Quakes and violent winds are temporary and coincidental accumulations from less concentrated energy sources).

     Further, you know now that all the chemical catastrophes that hit us are similarly caused because the substances involved in the disaster obey the second law. Whether forest fire, or Hindenburg explosion, or dangerous corrosion of a car part, blocking of brain patterns by Alzheimer's factors, or bacteria that interfere with a critical feedback system in the body -- these are just examples of concentrated energy spreading out contrary to our human preferences.

     As one of our major goals, we humans want order and organization of many different varieties. An equally important goal is our desire for concentrated energy substances as materials in our artifacts and as totally controllable power sources in our machines. Neither goal is consistent with the second law. Yet we are surprised when, against our naive wishes, the predictions of the law actually come about. Murphy's Law (speaking only of matter-related events) fits an emotional human need when we are frustrated; it is humorous because it is such a gigantic exaggeration.

    However, we may subconsciously let its humor make us concentrate on things going wrong and blind us to the most amazing fact in our second-law world: Usually things do NOT go wrong. There are three major reasons that they don't: First, constant human care and caution in protecting against second law predictions. (Two mundane examples: actions that reduce the possibility of fire in industry and the home, painstaking design for safety and the continued careful inspection of airplanes.) Second, the existence of activation energies that obstruct and block the second law from milliseconds to millennia. Third, the literally incredible organization in living things: from simple amebas to humans, from primitive grasses to complex plants, all those energy processing systems live and procreate because they are protected from failure by an enormous variety of feedback mechanisms.

It is often the failure of only one activation energy out of billions, or one feedback loop out of thousands, that makes Murphy's Law seem valid. A fractured leg in a ski accident, a spark in the fuel tank of TWA Flight 800, a broken timing gear in a Corvette, a fire in a fraternity house started by a forgotten cigarette, a California freeway collapse in an earthquake, a fall from a horse that results in a broken spine and quadriplegia -- all these are examples of activation energies being exceeded, whether in chemical reactions or physical fractures. Together with the thousands of illnesses that can destroy our functioning as whole persons, they constitute "things going wrong" in people's lives.

     But activation energies that obstruct undesirable chemical and physical events almost always protect us and our prized objects even from disastrous change that the second law predicts. Bodily feedback systems almost always protect us from bacteria and malfunctionintg human biochemistry.

Almost always.


Entropy and Biological Systems
A special thanks to:
Frank L. Lambert, Professor Emeritus (Chemistry)
Occidental College, Los Angeles
for his permission to reproduce this work.
 Our greatest good, the second law of thermodynamics
       The second law is a constant threat to us. Our bodies are made up of tens of thousands of chemical substances ("compounds") that are essential to our functioning. However, the oxygen that we need to live also tends to destroy almost every one of those essential biochemical compounds. Why? Oxygen plus any of our essential organic compounds have a higher energy content than the oxidized compounds that would be formed from them. Thus, if the second law were not somehow obstructed, the substances of our bodies would all spread out some of their energy when they encountered oxygen because chemical reactions would occur to allow that energy to be dispersed. Concentrated energy to diffused or dispersed energy. That's the pattern in nature that the second law sums up.

This is exactly similar to gasoline and oxygen having higher energy in their bonds than do their products, carbon dioxide and water. However, a superficial reason that we could never spontaneously oxidize ("combust") as rapidly as does gasoline in oxygen is the large amount of water throughout our cells restraining such a process. (Wood in the trunks of living trees burns (oxidizes) slowly and with difficulty because it is both solid and wet -- in contrast to faster burning leaves and branches.) Admittedly, even if our whole body didn't quickly oxidize, we could have a sufficient number of cells in us, say a hundredth of a percent of our total of critical cells, that could randomly oxidize and follow the second law of dispersing concentrated energy. That could be enough to cause serious dysfunction and death.

       Fortunately, there is a profound reason that our cells and their chemical constituents resist the threat of the second law (that they "must" react with oxygen because then they would disperse their energy) The reason is the existence of activation energies, an innate obstacle to the second law of thermodynamics in chemical reactions. We have seen it present in our oft-used illustration of gasoline and oxygen: no reaction occurs until a spark or flame is first injected in the mixture to give a little energy "push" to start the reaction. This is typical of almost all biochemical reactions. Even though the second law is a fundamental threat to our lives, it is equally fundamentally obstructed.
 
       In a sense, a greater hazard posed to us by the second law than the foregoing is caused by our being energy-processing machines. To live, we must follow the second law. There is no alternative. We must continually have energy supplied us from outside ourselves (from oxygen and food, or from energy-storage substances such as ATP that we had formed from oxygen and food) for our thinking, sensing, and moving every moment. Our chemical substances and the complex cells from which they are made must continually be destroyed and the residues excreted as new ones are synthesized. (For one example, there are about 250 million hemoglobin molecules in each red blood cell. Every hemoglobin has four iron atoms that are responsible for capturing oxygen in our lungs, transporting it to all the cells of our bodies and releasing it there. A person of average weight synthesizes approximately 500 trillion molecules of iron-containing hemoglobin per second in the bone marrow. The same number of hemoglobin molecules are destroyed each second and then excreted as part of fecal matter giving it the color of one form of iron oxide rust.) There cannot be minutes in which oxygen is not supplied to the energy-requiring heart or pumped to the energy-requiring brain: we die from a heart attack if adequate oxygen isn't given to its cells and the brain will either be permanently damaged or, if too many minutes elapse, death will result. The normal second law direction of energy flow from concentrated to dispersed, from activity in brain and muscle and every cell to waste heat that keeps us near 37°C must be followed by all of us in order to continue living.
 
       At the same time that we realize the second law of thermodynamics to be a constant threat, we could also say that it is our "greatest good": What if the direction of energy flow were not always from concentrated to dispersed? What if the process were often erratic or if it were precisely 50-50 -- with energy flowing in reverse from dispersed to concentrated half the time? It is the always-dependable direction of spontaneous energy dispersion that makes possible the total range of our energy-demanding activities as well as our very lives themselves.  Thousands of times a day in our normal activities (and untold trillions times trillions of times in the biochemistry of our bodies), we unknowingly use the second law's directionality of energy flow to our great advantage.
 
       Among a multitude of different automatic biochemical processes in our body, we use inhaled oxygen to react spontaneously with chemicals in our food, from carbohydrates to fats. This oxidation process occurs in astoundingly complex ways and in many steps (so any energy that is spread out as heat is slowly and moderately released, unlike the seemingly "one-step" instant dispersal of energy when gasoline reacts with oxygen). Furthermore, the heat that is dispersed in our bodies is not wasted because it keeps our bodies warm to function optimally even in a cold environment. Some of the energy is stored in energetic bio molecules like ATP in the muscles (and in every cell in our bodies). This storage obstructs the second law. The energy within the bonds of those ATP molecules and similar varieties is kept from being dispersed by activation energy barriers until, unknown to us, our cells need it for some action. ATP and similar energy-storage sources are what give us the instant conscious choice of using our arm muscles for work or our eye muscles for looking in a particular direction -- or for using our brain for thought. (As mentioned before, the mechanism of brain action, although far from completely understood, is known to require a constant supply of oxygen for the production of energy -- "slow combustion"!) Some of the energy being spread out from the oxidation of our food is diverted to our useful biochemical processes that synthesize approximately 30,000 different compounds within each of us that we need for optimal physical life. The second law -- or better, the energy flow predicted by the second law -- is essential to all life.
 
       In our open system of earth and sun and outer space we have the enormous privilege of taking advantage of the second law for human benefit, as does nature for maintenance of its high-energy-content ecology on the earth. We do this by diverting part of the energy to our purposes as it is dispersing when a spontaneous process follows the second law. The preeminent example is our use of combustion or oxidation. Combustion is the spontaneous reaction of carbon-containing substances like wood, coal, gas or oil with oxygen -- after the reaction has been initiated with a flame or spark. Because it is spontaneous according to the second law, in addition to the new lower-energy chemical compounds formed (mainly carbon dioxide and water), oxidation dissipates a great deal of energy in the form of heat (that is actually very rapidly moving molecules of the carbon dioxide + water + air) and some light. Then comes the payoff: our use of the second law for our human goals. Today, it is not just diverting some of that dissipating energy from the burning wood of a campfire for warming ourselves and cooking our food as has been done for millennia, but diverting the energy flow of fossil fuel to make engines and machines that function to transform our material world.
 
      Obviously, if we think of being grateful for natural phenomena such as the glory of the warm sun each day and the benefit of rain on fertile soil, we should be grateful indeed for the second law. But also, how could we overvalue the enormous diversion of energy that we are able to achieve from the dispersal of energy that the second law favors when we burn fossil fuels? Coal, and especially petroleum-sourced fuel in cars, planes, trucks, earth-movers, trains, ships and electrical power plants are the life-blood, arms, and legs and support the nervous system of modern life. Of course, we are not able to divert more than a portion of the energy obtained from combustion for our use. Some of any energy dispersion continues immediately on its way to complete dissipation in the environment and ultimate loss to outer space. Most energy not "dammed" by synthesis of new higher energy long-lived compounds (as in photosynthesis) but just used in moving cars or similar temporary functions is merely dispersed later than the waste heat lost from the tailpipe following the initial explosion of the fuel. The second law may be delayed but it is never violated.
 
      Equally obviously, our truly greatest gratitude for the second law should be for the continued dispersal of the sun's energy that long ago aided the various life-forms that ultimately yielded fossil fuels like petroleum and coal -- the same solar energy-dispersing-process that makes possible plant and human life today. Of the enormous amount of solar energy dispersed to outer space, just one-billionth of it strikes the tiny volume of the earth. About 30% of this is immediately reflected and dispersed to outer space and 70% is temporarily absorbed by clouds and the earth's surface. Only about 0.02% of the one-billionth of the sun's energy coming to the earth is captured for photosynthesis. (These figures set in context the irrationality of writers who say, in essence, that the universe is moving toward "a flowering of increased life and complex organization [of plants and animates]". Such flowering, though all-important to us, is ultramicroscopic so far as the universe is concerned.)
 
       In nature, the sun's radiant energy disperses as it strikes water molecules in the ocean and causes them to move more rapidly, i.e., the water becomes warmer and evaporates more readily. In this process of dissipating the sun's energy, untold tons of water are raised in the air, creating clouds as some of the water molecules spread out part of their energy to the cooler upper atmosphere. When the sun's energy is dispersed in striking the earth's surface and heating it, some of it is shadowed by clouds. The uneven warming of land and water causes variable columns of warm air rising and increases random air motion. The results are winds that further diffuse the original energy of the massive air movement. Water in the air, that was in the form of clouds, cools radically as it starts to flow over high mountains or encounters cold air and precipitates as rain, adding to lakes and creating stream sources at high elevations. Of course, this gives potential energy to such streams because they are far above sea level. Water flowing from heights dissipates its potential energy (if it is not dammed, and the second law thus obstructed) by flowing downward, cutting ravines and, with uplift of the earth (caused by the dispersal of energy deep beneath the surface), forming small, as well as grand, canyons. 
 
       We take advantage of water movement in rivers (dispersing their potential energy as they flow down toward sea level) to turn turbines connected to electrical generators that produce electrical power for us (further diffusing the potential energy of the flowing water). Winds dissipating their energy in turning windmills attached to generators also produce some electrical power. These are a few of the actions by which nature, in exemplifying the second law, provides us with fresh water, with variable breezes, and with higher-than-sea-level water that drives our turbines and generates electricity. 
 
      Occasionally and coincidentally, movements of wind and warm moisture from a tropical ocean can cause a concentration of energy to form a hurricane. (Hurricanes are no more a violation of the second law than a car going uphill. More heat from the warm ocean surface has been fed into the incipient circling wind pattern than is present in the final huge vortex. Of course, the observer of a destructive hurricane cannot sense the basic contributions of solar energy nor the complex energy dissipation that coincidentally formed it.) The "death" of a hurricane is a more obvious example of the second law in action: Unless this kind of ocean-originated storm is continuously fed thermal energy from warm waters to maintain its high-energy existence, a hurricane dissipates its energy just as any wind "blows itself out". The second law always is a valid tendency and -- in dynamic cases like this -- demonstrates that tendency in a relatively short time rather than years or eons.
 
Photosynthesis, another example of the coupling of energy dispersal with diversion of part of that energy flow to yield a more desirable or more concentrated energy state

       In general the photosynthetic process uses second law dispersal of the sun's energy similarly to what we humans do with fossil fuels. We take the energy in the chemical bonds of the fuel and oxygen to make engines accomplish what we want -- at the expense of spreading out some of the chemical energy in the fuels and oxygen as waste heat to the atmosphere. Plants take some wavelengths of the sun's dispersing energy (plus carbon dioxide from the air and water from the air or earth) and make new chemical compounds in the plant that are more complex and more energy-containing than the original carbon dioxide and water. (Meanwhile oxygen is released and that most of that solar energy striking the plant is diffused as heat).
 

       Subsequently those new active chemical substances in the plant, in breathtakingly complicated processes form carbohydrates, some amino acids, fatty acids and thousands of other compounds by a myriad of other reactions -- but also dissipate energy in all of these secondary processes as heat. Overall in the plant, the "downhill" process of energy being dispersed from the sun is diverted and then coupled with an "uphill" process of concentrating energy in new plant substances but there is no violation of the second law: only about 30% of the downhill solar energy has been captured in the primary process of photosynthesis. The net overall dispersion, "loss", of energy (70%) is still greater than the concentration, "gain", of energy (30%).
 
(The overall energy pattern is similar to our driving a car uphill. This may seem to be contrary to the second law for a moment because we have "created" great potential energy by having a heavy car at the top of a hill. However, calculations quickly show that far more energy has been dispersed from changing the chemical bonds in the gasoline and oxygen to carbon dioxide, water and heat (to make the pistons, gears, and wheels move) than the potential energy that the car acquires by being at the top of the hill. In the huge number of processes more complex than driving a car up a hill, photosynthesis uses or diverts only some of the downhill second-law energy flow to create the "uphill" substances and supply the energy for the growing plant to continue to function.

       It is accurate to say that we use or take advantage of the second law by diverting energy from its "downward" (dispersing) flow to run engines that aid our transportation across the earth and into space, to change the earth's topography for our pleasure and for our increased safety (dikes, levees, water diversion), to make useful things from skis to skyscrapers, or simply to rearrange small and massive objects to please our sense of beauty or order. However, neither we nor nature's photosynthesis ever are actually defeating the second law. Energy spontaneously disperses if it is not obstructed -- or diverted by us or nature from doing so immediately.


Activation Energy: 
Obstructions to the Second Law
A special thanks to:
Frank L. Lambert, Professor Emeritus (Chemistry)
Occidental College, Los Angeles
for his permission to reproduce this work.
       Energy dispersal can be delayed for microseconds to millennia or eons by barriers that are described in chemistry texts  or are obvious. Objects that are high above ground level have potential energy. The second law predicts that they tend to disperse that energy by falling to ground level. Obviously, mountains do not rapidly carry out this prediction of the second law. No change occurs in high mountain stone until external energy sources such as extremely violent windstorms or many freezing and thawing cycles first physically break or crack rock portions and pieces of the mountain so that they can disperse their potential energy by falling to lower levels. 
 
       We humans devise all sorts of methods for obstructing or "damming" the second law for considerable periods of time.  Painting is effective in this way not for any sophisticated chemistry but simply because it keeps the oxygen away from iron so reaction can't occur.  Chrome plating of steel and anodizing of aluminum are other methods of hindering the second law by interfering with the oxidation of steel and aluminum to form their less energy-containing oxides. A Thermos bottle for hot or cold liquids  is a simple example of obstructing the rapid dissipation of heat that is predicted by the second law. 
 
       Some systems spread out their energy rapidly, e.g., the thermal energy in hot objects to a cooler room, as we have been discussing. However, some disperse their energy very slowly, e.g., the potential energy of the mass of ice in a glacier as it moves downward over centuries.  The energy within cellulose and other chemical substances in trees, surrounded by the oxygen in air, remains unchanged for years or centuries, but in a short while hot flames can start the release of that energy in the form of heat and carbon dioxide and water -- and the amount of energy released can be enough to spread a forest fire. 
 
         Chemical bonds are the forces that hold atoms together in a molecule.  Most bonds between atoms in molecules are quite strong; it usually takes a great deal of energy to break them. (Conversely, when bonds are formed between individual atoms to yield a molecule, much energy is usually evolved.) 
 
         In a chemical reaction, say of hydrogen with oxygen to produce water (H-H and O-O yielding H-O-H), the bonds between hydrogen atoms in two molecules and that between oxygen atoms must be broken and new bonds between hydrogen and oxygen must be formed to yield two molecules of water. The breaking of bonds and the forming of new ones occur almost simultaneously when rapidly moving hydrogen and oxygen collide with one another -- almost simultaneously but not quite!
 
        This is why most reactions require a relatively small energy "push" to start. For example, a spark has to be introduced into a mixture of hydrogen and oxygen before the reaction begins to form water, but then immediately it becomes an explosion. Why this strange combination of molecular recalcitrance followed by fantastically rapid reaction? Breaking the old bonds (requiring energy) normally must occur slightly before the formation of new ones (evolving energy). Thus, even though water has lower energy in its bonds than hydrogen plus oxygen in theirs so that a large amount of energy is evolved overall when a reaction occurs, none of that energy can be released without an initial "push" to aid the break of a few hydrogen and oxygen bonds just before they form a few water molecules. Once that "push" occurs, the energy evolved as the water is formed feeds back to make many of the unreacted hydrogen and oxygen molecules move far more rapidly and collide forcefully so they react to evolve more energy and so on and on.
 
       The "push" described in the preceding paragraph is what chemists call an activation energy. Most spontaneous reactions require this initial input of a small amount of energy, activation energy, to aid the first few molecules to react so they feed back their evolved energy to serve as activation energy for succeeding molecules to repeat the cycle. 
 
         It is this "minor" detail of chemical reactions, the activation energy, that obstructs the instant carrying out of second law predictions and thus protects our bodily biochemicals and our degradable artifacts from instant oxidation and other deleterious reactions.