|AP Chemistry - Entropy: Spontaneous Change|
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
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.
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
|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
|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.
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
|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.
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.
|Urea (from urine) hydrolyzes
slowly in the presence of water to produce ammonia and carbon dioxide.
|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.
| 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.
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
"hot pans cool down", the case of an immediate dissipation of energy,
or "gasoline explodes", the case of an obstructed 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],
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,
(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);
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
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
| 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||
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
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.
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
|Q: You mentioned those tricky words, "spontaneously"
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
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.
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
|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):
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.
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.)
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.
|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:.
And, of course, there
are many less (or equally) dramatic examples in the oxidation of metals
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:
|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.
|Entropy and Biological Systems||
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
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.
Obstructions to the Second Law
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
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.)
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.|