An armchair scientist's question - Thermodynamics

[faster]

I love reading Asimov's monologues on sciences, as well as his fiction. Some of the books I have are crumbling with age, and I keep piecing them together. That's devotion, chum.

I'm confused, though, about the laws of Thermodynamics. Maybe someone can easily answer it here, if they'd be willing.

As I understand it, the First law says that energy can change form, but that there's a fixed amount in the cosmos, and that that is unchangeable.

How, then, can that comport with the concept of entropy? Isn't entropy involved with the Second Law, which tells us that no use of energy can ever be 100% efficient, that some energy will always be lost and can never be recovered?

Don't these two things conflict? How can the universe "wind down" (entropy) when it has a fixed amount of energy that is static and unchangeable?

Probably a first year college Physics major could answer that one in a coma. I'd ask Mr. A. if he were still alive and was online answering basic and inane questions like mine.

I'm not a student, though I'd like to be. But I'd be too sexy and old for it; the students wouldn't be able to resist me and would flunk because they couldn't pay attention in class. I wouldn't want to jeopardize the next generation's intellectual achievements.

Thanks,
Holly B.

 

[Bystander]

Simple, hand-waving version? E_Universe = T_UniverseS_Universe. That is, the relationship among energy, entropy, and temperature for the universe is hyperbolic; T drops, S increases, and E is constant.

Second law can be stated many ways; the physical chemist's favorite statement is, "For any spontaneous process, the entropy of the universe increases." The "universe" is the sum of any system of interest and its surroundings.

 

[LURCH]

An even simpler way of putting it; entropy is energy lost from a particular system. For example, if your system is a battery-powered toy car then energy is intended to move from the battery in the toy to the tires, to drive them forward. But not all of the energy from the batteries will actually make it to the tires; some of that energy is lost fighting friction between the axle and its mounting. This is energy that left the battery, but never made it to the tires. Instead, it became heat and was radiated out of the car and into the room. The energy still exists, but is no longer in the system (the car).

 

[Pythagorean]

I think what they're saying is that the total energy in the universe doesn't change, but right now it is heterogenoeus. It's not uniform: there's 'chunks' of high energy here, and 'chunks' of low energy there.

I assume entropy is that energy wanting to spread out and be uniform throughout the whole universe, but don't quote me.

 

[Danger]

I'd be too sexy and old for it

I believe that this would be the appropriate time for you to post a shot in the 'Members Photos' section of GD. :tongue2:
Essentially, as Pyth mentioned, the total energy content of the universe is constant. Entropy is the desire of that energy to become homogenous throughout the universe.
Something to keep in mind, as well, when reading Asimov's essays... (at the risk of being considered blasphemous)... his PhD was in biochemistry, and that's what he taught at university. However brilliant he might have been, he was not an expert at other branches of science and did indeed publish a couple of inaccurate views about subjects that he didn't fully understand.

 

[3trQN]

As I understand it, the First law says that energy can change form, but that there's a fixed amount in the cosmos, and that that is unchangeable.

How, then, can that comport with the concept of entropy? Isn't entropy involved with the Second Law, which tells us that no use of energy can ever be 100% efficient, that some energy will always be lost and can never be recovered?

Ive seen the second law stated in many forms, some better thanothers, the one you use there doesn't really cover all possible circumstances so you have found an apparent contradiction between the two statements.

The second law states that the most probable state for any isolated system left to its own devices is a state of maximum entropy.

Another way of stating it, i think a quote from Max Plank ( i doubt i recall it correctly ):

"It is impossible to lower the entropy of a system of bodies without also causing a corresponding increase in the entropy of another system of bodies."

Which is maybe easier to relate to your efficiency of energy transffer problem. What is implied by your statement of the second law is that the energy is lost from "System" and not from the "Cosmos". The system would be a proper subset of the cosmos.

 

[Sojourner01]

In my understanding, energy can be concentrated into arrangements of matter which not only bring a lot of potential energy together, but present it in a form which lends itself to being transferred to something else. That's 'order' - energy locked into a specific arrangement.

As entropy increases, energy becomes less 'useful' as it has less tendency to transfer from one form to another and undergo some useful process inbetween. And, when you reach maximum entropy, the energy's still there, it's just sitting around in this lukewarm featureless soup that's utterly useless for anything. There's as much energy as there always was, it's just impossible to gather it up and use it for anything without expending more energy to do so.

 

[Andrew Mason]

I'm confused, though, about the laws of Thermodynamics. Maybe someone can easily answer it here, if they'd be willing.

As I understand it, the First law says that energy can change form, but that there's a fixed amount in the cosmos, and that that is unchangeable.

I don't think that is a fair statement of the first law. The first law was developed before Einstein, who discovered that matter could be converted into energy (and vice-versa). So the energy in the universe CAN and does change. It is not fixed.

The first law deals with energy in thermodynamic processes. It says that the energy is conserved in any process: Energy in = Increase in Energy stored + Energy out; heat added = change in internal energy + work done or: dQ = dU + PdV.

In that last expression, PdV (pressure x change in volume, as in a car engine when the hot gas expands and pushes a piston) is the useful work done in a thermodynamic process. The second law says essentially that you cannot convert heat entirely into useful work - some of the heat has to change the internal energy of the thermodynamic system.

How, then, can that comport with the concept of entropy? Isn't entropy involved with the Second Law, which tells us that no use of energy can ever be 100% efficient, that some energy will always be lost and can never be recovered?

It is not that the energy cannot be recovered. It is still there, but it is just not in a useable form. It cannot be used to perform useful work. 1 gram of water at 100 degrees C can mix with 100 grams of water at 0 degrees C and result in 101 grams of water at about 1 degree C. The energy content before and after is the same but the entropy has increased (the energy has become more disperse).

Don't these two things conflict? How can the universe "wind down" (entropy) when it has a fixed amount of energy that is static and unchangeable?

The universe is not really winding down, energy-wise, because matter is constantly being transformed into energy. So the energy content of the universe is increasing (although you could think of mass as a concentrated form of energy, in thermodynamics matter and energy are distinct). Energy is becoming more disperse, but at the same time, new low entropy energy is being created.

AM

 

[Farsight]

faster, you probably don't need any more input, but here's a little more:

There's a whole pile of confusing terms in colloquial use when it comes to energy. People talk about things like "energy production" or "energy consumption" or "pure energy", and it creeps into popular physics. One useful way of thinking about it is in terms of money. If you spend some, it has gone from your "local system", but it hasn't gone from the Cosmos.

 

[actionintegral]

Everybody is going to snub my simple-minded approach, but here goes.

Entropy had nothing to do with energy per se. It is a statement about statistics.

How many ways can you roll a 12? Only 1. 12 is low entropy.

How many ways can you roll a 6? 5. High entropy.

 

[masudr]

As far as I know, the best operational definition of entropy is this:

1. For any process that gets your system from one state to another, find a reversible path to get to the final state from the initial state
2. At each infinitesimal step of this reversible process, calculate the heat given up by/given to the system divided by the temperature at which this occurs, call it A
3. Add up (i.e. integrate) all these values of A over the path.

That is the change in entropy of the system. More formally, it is often given as:

$$S=\int_{reversible} \frac{dQ}{T}$$

A simple consideration of this definition along with Clausius' theorem demonstrates in an ireversible cycle the entropy increases, and in a reversible cycle it stays constant: http://theory.ph.man.ac.uk/~judith/stat_therm/node31.html .

Clausius' theorem itself follows from Clausius' formulation or Kelvin's formulation (which are equivalent to the OP's phrase "energy can ever be 100% efficient, that some energy will always be lost and can never be recovered?") of the second law to this above definition. See: http://theory.ph.man.ac.uk/~judith/stat_therm/node30.html

 

[actionintegral]

Heat? Temperature? Infinitesimals? In order to understand Entropy, you need to start by understanding macrostates and microstates!

 

[masudr]

hah! well tell me the entropy change of the gas in your room when you turn the heater on using microstates and macrostates.

Remember, I said "operational definition".

 

[3trQN]

In order to understand entropy, you need only see my room, in timelapse mode maybe.

 

[faster]

I'm back - the armchair scientist

Although my devotion to Asimov is indeed strong, and thus my emotions want me to regard as blasphemy of a sort any criticism of him, I must concur that he was human and able to err, especially outside of his field of biochemistry (which, it might be noted, my father, Olaf Bergeim, pioneered early in the 1900's, and Dr. Asimov certainly earned his own PhD through having read my father's textbook, since there were no others back then), I still have a level of certainty about most of what "The Great Explainer" said. Had he blooped, he'd have made a large retraction somewhere, as his readers would be quick to point out his errors to him. Even without capability to be a scientist, I still do think in scientific terms - my daddy saw to that! Nobody is beyond scrutiny, nor are ideas. It is narrowness of thought (religion, orthodoxy, prejudice, et al) which has always cramped science, not openness.

I'm gathering that entropy is a "concept" which only means anything when referring to a closed system. So would it have any effect on an open, i.e. infinite, one? Or would it simply take more time? No, I don't suppose it could, since an infinite universe would take infinite time for entropy to treat it as a closed system and affect the whole in any meaningful way.

Masudr, my dove, you flatter my intellect. I don't know that big mathematical symbol "S" any better than I know Osama. It's kinda cute, though, which is one aspect that is different from Osama, at least, and handy, too, if I ever want to awe someone when I don't really know jack, and don't stick at duplicity. Which is, for me, never; I'm relatively guileless. I can fully understand science though - as long as I don't have to get into the math part. I'm a word person. That's my excuse. My irresistible beauty would not garner me an A in physics, sorry to say.

Actionintegral, you pique my curiosity. What are macro- and microstates? I was pretty smug about a year ago when I read about string theory and actually comprehended most of it. I thought I was keeping pretty up to date. But now you've shown me that my smugness was inapt. I grovel.

Have you read "The Final Question" that he wrote? If you haven't, do. It's a treat. Read it when you won't be interrupted. It's one of the great sci-fi short story classics, and not a tentacle to be seen. It is often remembered mostly for the punch of the story itself, and people often forget its title and author - to the good Dr. A's chagrin. That story is a medium through which he explained what entropy was, how the universe is gradually winding down, and will, one day, be empty, dark and cold. Well, maybe not cold, but without matter, so it might as well be arctic, for all that all that loose energy can achieve. Unless other factors as yet unknown change the scenario. We don't have a Multivac yet, and if Bill Gates has his way, it would, if it ever could exist, be forever based on DOS.

Though fiction, the story was not attempting to present entropy as anything but what it was. To the best of his knowledge, and to the best of knowledge of his own day, that is, of course. Misrepresenting it would never be his style, even in fiction. He was the "Great Explainer," not the "Great Misleader" and always corrected his flubups, however it dented his oft-proclaimed great humility! My papa held the opinion he was bastardizing or prostituting science. It was one point on which I disagreed with him. Asimov was able to kindle my interest in science by proving to me that I could comprehend even some really difficult stuff. My dad didn't have the gift of words, and couldn't accomplish it, though he truly tried. He was human; maybe he resented that Asimov could do what he couldn't for me. Not his fault, though, and I couldn't have loved him more, despite that. Asimov opened doors of understanding to many people who later chose science. Making it understandable instead of esoteric can't help but be inspiring, and thus of great value. Explaining to the novice, making it understandable, takes the fear of it away, and replaces it with hungry curiosity. That's very good. My dad would have been right, only if Dr. A had been a pseudoscientist. He was anything but that. It was Dr. A's book, "The Universe, from Flat Earth to Quasar," which inspired my interest in all sciences, thus making me the "armchair scientist" that I am today. It made me realize I wasn't as stupid as I'd thought - I can't deny that I appreciated that. I'd give anything to have another copy of it - the original was lost, and I can't buy another, since I'm disabled and retired in Mexico now. It was a wonderful book. I recommend it.

Given, then, that entropy is as described in that tale, how can the universe have a fixed amount of energy? Energy, once loose in the universe, is incapable of making itself turn back into some form of matter. Something that has no matter and has no ability to affect anything at all might be said not to exist at all, mightn't it? The worst effect it could have would be to make the empty universe hot as blazes. But even then, how hot is a hot vacuum (assuming the vacuum to be total)? It needs matter in order for the actual heat to be perceivable at all, or to DO anything at all. Isn't it true that energy can NOT make heat without some kind of matter to act upon? A hot "nothing" is still a "nothing." Who could describe the nature of a complete cosmos which is empty of anything but energy? Eventually, all interstellar atoms would be burned up - nothing left. At such time how could it be said the universe could continue existing at all, much less that it contained something massless? The tree that falls in the forest where nobody is able to hear it still made a noise. That's not the same thing, you know, as a completely empty universe which "doesn't exist" simply because WE can't detect it, or aren't there to do so. In this case, its nonexistence would indeed still be real and total. Surely, once the last speck of matter was burned up and became loose energy, the universe itself would have "winked out of existence."

Is it possible that entropy only applies to our universe IF the universe is a great big, humungous CLOSED system? By "universe," I am referring to all that is, not all that we perceive of it. By today's knowledge, there is reason to believe there probably is more than we can perceive, but nobody knows how much. The issue of "dark matter" within the perceivable part of the cosmos is still being pursued to determine whether it will collapse and rebound in a new Big Bang or not. (See? I've read more than Asimov; I read all I can that's on my level of comprehension of science.) But there could be a whole lot of matter so distant that it is beyond the reach of our technical ability to detect. After all, if the cumulative rate of expansion which we have detected exists between us and the other objects we can see is so, and is consistent, then the most distant quasar that we can see becomes separated from us by this expansion, cumulatively, and when that rate of cumulative separation becomes equal to the speed of light, it wouldn't matter how much matter is beyond that quasar; we'd never see it because the light would never catch up to us, ever. For our practical purposes, it might as well not exist, but its existence could still be real, and could still make it part of an infinite cosmos, or even a closed-system cosmos which is simply larger than we can detect.

And if the entire cosmos is determined to be closed, the chicken/egg question nags, whether we like it or not - what exists beyond the parts that participated in the collapse? Nothing at all? Then would it be an infinitum of nothingness, or would there be some point at which matter might be encountered anew? It's almost impossible to comprehend infinity, but when looked at in this manner, it's almost impossible to imagine that the entire cosmos can be anything else. Whether we comprehend it or not, the cosmos almost must be infinite, whether it is empty of "stuff" or not. Even granting relativity, consisting of folded space, oughtn't there be room to ask what lies beyond even that? If donut-shaped or shaped like a mobius, it's still valid to ask whether there is something beyond it. Wouldn't even a mobius-shaped cosmos still be somewhat finite, and thus with a likelihood that something else lies beyond it? Or at least there ought to be. Maybe only Stephen Hawking can explain it, but I might need an Asimov to make it comprehensible to the likes of me. And Hawking's another dude whom I hold in great reverence. He's a bit harder to understand, though. I admire him for his grit, in staying alive at all - that's enough for a kind of reverence, right there. But that guy has a MIND. An awesome one. Hope he lives forever...

Couldn't entropy then be a means of determining whether the universe (that which we perceive and that which we cannot perceive) is a limited one or an infinite one? If we could somehow determine, say, that entropy will CERTAINLY proceed to maximum in the universe, we'd know for sure that the universe is a closed system, no matter how vast. I don't know what means might be used to test it, but couldn't such a thing be a test of the true nature of our universe's extent? Limited or infinite? Without our having to actually travel to what is our presently-perceived "end" of the universe to do more tests and find out? That could be - tedious.

If entropy will indeed proceed to maximum here, then we'd know the universe is limited, a closed system. As long as we know our test will absolutely prove it if it is so that entropy will proceed to maximum, then, if it would not yield a positive a result, and NOT proceed to maximum, we'd have no alternative but to conclude the cosmos to be an infinite one. Because if it was closed, we'd certainly have our proof of it. Since, by Planck's Law, entropy would affect the entire cosmos, we could test its ability to maximize just as well in our own part of the cosmos as in any other. As long as Planck's Law was true, and consistent everywhere. Unless there is some third option, about which we have no knowledge.

Even if, through the process, the total amount of the energy in the cosmos (closed or infinite) will remain the same, maximum entropy would literally wipe out all matter it contained, with what little residue that remained incapable of turning any part of itself into energy. Crumbs, in other words. Result: a dead universe with lots of energy bouncing around, signifying nothing. No way to make new stars, nebulas, etc. With all that energy about, eager to make something good and hot, though, I'd bet even those crumbs wouldn't last long. Can a truly empty universe still BE a universe, simply because it still contained pure energy? Energy is massless. How can a universe exist without mass somewhere? Isn't it mass which gives any kind of cosmos its existence?

It would be harder to devise a test to determine that entropy will NOT proceed to maximum. That's like trying to prove that God doesn't exist; an exercise in futility. It's hard to prove a negative, so it probably can't be done. But surely someone could devise a test to tell us for SURE that entropy will maximize, if, in fact, that is so? Therefore, a result that isn't positive would perforce prove that entropy will not maximize, and that the whole universe is therefore infinite. I know I'd like to know which it is, and I'd bet most other people would, too. If our segment of the whole universe can be shown to rebound into a new Big Bang, that doesn't necessarily mean the whole thing will participate. There could be other sectors too distant to be affected by the forces of physics bringing it about, either way, whether it's expanding or contracting. Gravity is pervasive and strong in large areas, but even so, since it diminishes as the square of distance, there'd be matter outside of gravity's ability to pull it into the mass contraction our area is undergoing. Which probably means that when our area contracts, the matter within it will likely be roughly spherical. Well, if shaped like a mobius, maybe not. There could still be matter outside of the ability of any physical laws coming from our area to affect it in any way.

If the universe is a closed system, that would argue much more for the rebounding universe. If an open (infinite) system, it would argue more in the direction of a universe expanding forever. Max Planck's theorem would only extend the conclusion we had reached, since entropy affecting one part of the universe would inevitably affect ALL other parts of the universe, however remote they may be. Thus concluding openness or closed-ness for even a part of the universe-system would apply to any other parts we cannot perceive - it would, by Planck's Law, be a measurement of the whole kaboodle. A closed system would perforce be completely affected by entropy, no matter how much is beyond our ability to perceive. It would still be a limited cosmos. An infinite system, however diligently pursued by the effects of Planck's Law, would never be completely affected by entropy, try as it might. Or is it possible even an infinite universe could be decaying, winding down, all at once? If so, how might we make that determination?

I guess my question also must involve the questions of "what happens to loose energy that gets lost in our part of the universe? Where does it go, what forms might it take on its own, what effects can it have? Does it relate to the 3K temperature of space left over from the Big Bang? Can it, given enough time, actually raise that temperature? If so, might the 3K temp have been lower a few hundred billion years ago? If not, why not?"

With apologies to Andrew Mason, I was not saying the energy of the universe cannot change, but that, whatever changes might occur, the quantity of that energy remains fixed, not the forms in which it exists. Do I gather, Mr. Mason, that, rather than meaning the universe's energy is winding down, that entropy means it is the universe's MATTER which is doing so? In other words, the things in the universe will go byebye, as they turn themselves, inexorably, into loose energy? Should it get to a point where there no longer is matter, it would mean there is no universe, either, I should think. The universe can only "exist" by containing matter. A nothing containing nothing is still just a nothing, even if that nothing contains energy. The energy is still a nothing at such an ultimate point, isn't it? What is energy except something with a capacity to DO something? For that, it needs a thing to DO something TO. Without it, energy alone is a nullity. Energy IS massless, isn't it? Am I getting close?

Farsight, you need not chide yourself; all input is welcome. Always. When I did some teaching, I always told people that there's no such thing as a dumb question. There's also no such thing as a too-redundant answer. One such may contain a kernel the others lacked, one which can inspire great thoughts and ideas. Input is always innocent. It is what one does with it which can make any difference at all. Your intent is good, and good intentions, contrary to Milton, DO matter, very much indeed. August he may have been, but even Milton could be wrong - and he was. If my child was run over and killed, the intentions of the driver would matter hugely - a sober, conscientious driver makes it a tragedy, a thing over which nobody could have had any control; a drunken, reckless driver makes it a crime, something avoidable, which need not have happened, and a life which might have continued. Oh, yes, intentions matter a whole lot, and yours were good ones.

I'm gleaning that energy in the universe does remain in the same quantity (the universe, meaning the whole thing, perceived or not), but that entropy is what will, eventually, turn virtually all matter into energy, leaving the universe one day with a vacuum filled with virtually all the energy that ever existed, having squeezed it out of the matter which no longer, for practical purposes, exists any longer. But ONLY if the total cosmos is a closed system. If not, entropy will not affect the fate of the cosmos; it'll only affect closed thermodynamic systems - of any size, but not be able to affect the cosmos itself, and thus the cosmos would NOT "wind down". Is that getting closer?

Sorry I can't supply the picture. It would be simply too disruptive for all you busy people working hard to learn and achieve. I have, at least, some mercy... Besides, I'm like the kid who sat at the front of the class, always raising an arm and asking questions that made everyone scowl at me, including the teacher. You weren't supposed to "What if?" or "Ah, but..." the teach. It's probably for the best that I'm no longer a student, because I'd probably still do it. Hardly conducive to romance, so you won't really need that photo. A pest is still a pest, however irresistible, right?

I'm even more of a nuisance on the subject of cosmology. Of course, what we're discussing here bears heavily on cosmology, doesn't it? I just love the way all sciences are gradually melding almost into one, where one must know an awful lot about other disciplines in order to make progress in one's own. I like that; it shows great progress and flexibility, and it forces all scientists to be more well-rounded, the results of which can only be good. We need all we can get of that, to counter the creationists who are slathering to legally stifle all science and all inquiry (except to make more bombs and such), and who may already constitute a majority. The consequences of that are too horrible to contemplate, but counter it, we must. Still, pity those in the astronomical forums. Well, at least I'm not rude about it. I'm not only irresistible, I'm polite. Isn't that grand? I'm so nice that I can genuinely hope that this discussion might get some scientist here to thinking along new lines somehow, often with innovations as the result. Amateurs have been known to do that at times, often without realizing it. It'd be a real hoot if I knew I'd started something like that.

Thanks to all, and keep it coming, if so inclined,
Holly B.

 

[actionintegral]

hah! well tell me the entropy change of the gas in your room when you turn the heater on using microstates and macrostates.

Remember, I said "operational definition".

I don't know what "operational definition" means. My point is that understanding the statistical definition of entropy is very easy. After that
concept is understood, then you carefully map those parts onto a "real system" like an ideal gas or something.

 

[actionintegral]

Have you read "The Final Question" that he wrote? Holly B.

Yes, I did. My favorite story by Asimov is "Profession". Understand that story, and understand me.

Most people think that in knowledge you start with the simple and end up with the advanced. I disagree. You start with the advanced and whittle away and whittle away until it becomes simple. Then you retrace your steps back to the advanced.

I recommend the berkley series on statistical mechanics. The teach entropy in the manner I describe. Once you realize how simple it is, it makes full-blown thermodynamics less intimidating.

Let me know when you have acquired a copy on amazon.com
[/QUOTE]

 

[Farsight]

You start with the advanced and whittle away and whittle away until it becomes simple...

Talking my language there, actionintegral.