S
= q(rev)/TQ: That's gibberish. About IT? About what?
A: About ENTROPY! Scientifically, qualitatively, entropy is simple -- entropy
change is just a way of measuring exactly what we have been talking about, how
much change occurs at a specific temperature when energy spreads out according to the second law.
But that word entropy has been so erroneously defined and so misused by so many people that I'm sorry that I got trapped into talking about it when were thinking about what a city looks like after a huge earthquake! That mess of broken buildings and busted bridges would be foolishly called "an example of entropy increase" by many people who aren't scientists -- and even by some chemistry teachers.
Q: What's wrong with that? My chem text says that "Entropy is disorder"
and a mess is disorder, isn't it?
A: Your text may be excellent in other topics, but it's just plain dumb wrong
where it says that! Entropy only involves energy and its spreading out (and
temperature), not appearance or neat patterns. Even when considering molecules
precisely arranged in a crystal, any question about entropy must be like "What
is the energy distribution here? How is the crystal vibrating and the molecules
moving fast but almost staying in one place," not "How orderly is
this pattern?" Energy, energy, energy!
Entropy is not "disorder". No way. No how. That's an old 1890s idea that was obsolete after statistical and quantum mechanics became fully developed in chemistry. However, it hasn't yet been eliminated from a few textbooks. They may be good in other parts but they simply don't tell you the straight stuff about entropy if they use that old obsolete definition with "disorder".
Q: Hey! You can't just say a text is wrong and expect me to believe you! You'd
better give me solid evidence that "entropy is not disorder" if my
chem book says it is.
A: Of course. Your text is out of date because most new editions of college/university
general chemistry textbooks have deleted "entropy is disorder" and adopted
my approach.
Click on entropysite.com to ‘what’s new’ and scroll down to May 2009 to see the list of new editions that have thrown out “disorder” and now define entropy in terms of energy dispersal. (Your professor can check cracked_crutch.html. This is the article that helped convince textbook authors to delete “disorder”. Also for your professor, the article at entropy_is_simple describes the bases for interpreting entropy as energy dispersal and an improved approach to microstates.)
Q: OK. What IS entropy, really?
A: It's simple basically because you know about the second law -- that energy
spreads out and disperses rather than staying concentrated, i.e., localized
in one place. Entropy just measures what happens in that kind of process of
energy dispersing. And that's why your text says that entropy is always increasing
in the world -- it's because spontaneous reactions/events are what are always
happening and they happen because then energy spreads out!. (Actually, we should
always say "entropy change" because we're measuring
the difference in energy distribution "after" some happening versus
the "before".)
More precisely: Entropy (change) in chemistry measures either by
1) how much molecular motional energy has been spread out in a reversible process divided by the constant absolute temperature, T
S
= q(rev)/T
[ q is the amount of energy (motional energy, thermal energy, "heat")
that is dispersed to a system at T from the surroundings at a very very slightly
higher temperature than T, or vice versa, from the system at a tiny bit higher
temp than the surroundings at T. Because the temperature differences are so
small, this gradual dispersal of motional energy ("heat") in either direction
is essentially reversible. This is the case in phase changes, at the melting
point or the boiling point. (As some more advanced texts state, when you heat
a system - i.e., increasing the "how much" motional energy is in a system - by
calculus you can find the S change )];
or (2) how spread out the original molecular motional energy (i.e. no change in q) of a system becomes (e.g, when an ideal gas spontaneously expands into a vacuum and increases in volume or when different ideal gases or liquids mix. (No change in temperature in the processes.)
Entropy change doesn't measure "disorder"! (What are the dimensions of "disorder"? Malarkeys per minute or some such nonsense? The scientific dimensions of entropy change are joules/Kelvin.) Entropy change in chemistry measures the spreading of molecular motional ENERGY. (For more details of that kind of energy of molecules moving ["translating"] and rotating and vibrating, see 2ndlaw.com/entropy.html. Your professor could check the site for instructors at entropy_isnot_disorder.html)
Q: If entropy measures how much energy has been dispersed in a bunch of chemicals,
and that's q, why bother with dividing by T?
A: Because you don't really have entropy (or entropy change) if you don't include
that absolute temperature, T. With entropy properly defined that way you have
immense power in understanding how important is any energy change to that "bunch
of chemicals". Entropy change, S,
doesn't merely measure energy spreading out, it shows us exactly how important
to a system is the dispersion of a given amount of energy in that system or
substance at a particular temperature.
How's this for an analogy: If a quiet library represents a low temperature system (relatively small number for T), and you yelled "HEY, YOU!" there, everybody would jump and the librarian would turn purple. However, in a football game at touchdown time (like a high temperature system, very large number for T), if you yelled "HEY, YOU!" just as loudly, nobody would notice it. The effect of the "energy spread out in your yelling" is a lot different in a library than in a stadium!
The scientific application is this: an amount of energy dispersed, say a q of 10 joules, from the surroundings (that are just infinitesimally warmer than 100 K) to a cold 100 K system would certainly be important (q/T = 10 J/100 K= 0.1 J/K) while the same amount of 10 joules spread out from different surroundings (just infinitesimally warmer than 1000 K) to a 1000 K system would be relatively trivial. (q/T = 10 J/1000 K = 0.01 J/K)
Now, you know that a hot pan will cool down if the room is cooler than the pan -- we started with that -- it's our lifetime experience -- it's what we called the second law and we interpreted it as energy spreading out if it can. But is there any quantitative way that we can show that the second law "works"? Yes! That's where the power of entropy comes in! Entropy measures energy's spreading out; the larger the entropy increase, the greater the spreading out and the more probable is the event. Just look at that preceding paragraph: If a 1000 K and a 100 K system are in contact and 10 joules of motional energy were allowed to flow from one to the other, which direction would the energy flow? Only if energy flowed from the 1000 K system to the 100 K system would there be any entropy increase -- (the calculation that you will learn from your text and class is not as simple as the arithmetic for the reversible transfer in the preceding paragraph, but the direction of the process is adequately indicated by that easy arithmetic.).
So entropy increases when "heat" (transfer of energy) spontaneously flows from something hot to something colder. (Same as "entropy change is positive in sign.")
Q : So that's all?? Just hot pans cooling down again? And that one little q(rev)/T
is entropy change?
A: ALL? HOLD IT now!! That's just like your question "Is that all?"
when we first talked about the second law. And then we went on to see the amazing
implications of the second law -- that it's the greatest generality in all of
science -- that it's incredibly important for your understanding of how the
world works -- that it's the greatest good and baddest bad for your own being
alive. Ya can't have anything more important than that! Exactly parallel, entropy
is of enormous importance in ANY serious understanding of chemistry and chemistry
is central to everything in this universe.
The words and meaning of "entropy" and "second law" are so closely related (entropy being the quantitative measure of the qualitative law) that they are often used interchangeably. Never never forget that entropy MUST always be connected with ENERGY in general, and specifically with ENERGY that is being or has been dispersed.
[Entropy is more fully discussed in 2ndlaw.com/entropy.html . In the Appendix to the site you are now reading (accessible from the Last Page) are given some details of processes in which q is zero --i.e., the original ENERGY of the system is unchanged but it is more spread out over more volume; thus entropy increases. Those processes include a gas expanding into a vacuum, or two or more ideal gases or liquids mixing. An ideal solute dissolving in a solvent also involves no change in original ENERGY but the entropy of the solution increases because an added solute allows that energy to be more spread out.]
Q: You sure are yelling LOUD and long about energy being connected to entropy!
A: Absolutely!! THAT'S the big mistake that popular writers and even some teachers
make about entropy. They've heard that antique erroneous statement about "entropy
is disorder" so often that they too say that anything you can see in the
world as mixed-up or messy is an example of an entropy increase. Nonsense. Total
nonsense. You have to focus on how much and how widely is energy
dispersed in their examples. When and how and what kind of energy
got spread out has to be the first question in any example they talk about or
we think about. Here, look at some horrible actual quotes.
In a textbook, there is a picture of Einstein's desk taken the day he died. Like most desks where scientists have been working hard, it looks messy. But the textbook says "Desktops illustrate the principle that there is a spontaneous tendency toward disorder in the universe..." Wow! Stay away from desktops -- you don't ever 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." (And that was written by a scientist!) Wasn't he ever near that desk of his? Some mysterious alien force from outer space did it? Another, from a book about entropy 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 means that nobody is 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 seemingly unchanged, though dusty, when the tomb was finally opened in 1922.)
You get the point. The messy appearance of a bunch of visible objects (and even the neat molecular order in an x-rayed crystal) have nothing to do with entropy. The only questions are "what is the energy process that made the objects that way? In what way was energy dispersed and how much energy change at what T occurred? In the usual dumb examples like those quotes in the paragraph above, it is in the ATP of the muscles of the people who pushed the papers/books/clothes/pizza plates around where energy has been dispersed and so only there has the entropy increased.