advanced thermodynamics

May 31, 2008 4:52 PM

explain further The Second Law of Thermodynamics

I asked a few months ago for the good members of Metafilter to explain to me the 2nd Law and I got a great response.

But the more I learn about the second law the more confused I seem to became.

I understand the 2nd law to be this: expression of the universal law of increasing entropy,

or to put it more simply

"energy is moving about"

basicly meaning:

"nothing is free" or more correctly "profit can never be made"

is there anthing wrong with what I understand?

posted by complience to science & nature (17 comments total)

Nope, you've got it. There will always be a loss to waste heat. You can never have a system which converts one form of energy to another perfectly. Note that potential energy can be stored losslessly (e.g. carrying a rock uphill) but you lose energy storing it and removing it again. Per your profit comparison, there's always a transaction cost.

The three laws in a nutshell: you can't win, you can't even break even and you can't quit playing.
posted by GuyZero at 5:03 PM on May 31, 2008 [2 favorites has favorites]

Er, the 2nd law of thermodynamics doesn't extend to any notion of profit. It's a physical law that has many different ways of being stated. Some of the more intuitive are:

- a process cannot convert heat to usable work with 100% efficiency
- it takes work to move heat from cold to hot
- every process increases the entropy of its [isolated] system
- and more generally, any 'order' in the universe is at the expense of disorder somewhere else.

Now real physicists can come in and disagree with me :)
posted by devilsbrigade at 5:06 PM on May 31, 2008 [1 favorite has favorites]

Also, for what its worth, you can convert work (energy) into heat with 100% efficiency via electric resistance.
posted by devilsbrigade at 5:09 PM on May 31, 2008

Um, sorta. GuyZero is closer. Example: As energy transfers, there are always "leaks" caused in the process of transferring that prevent 100% transfer. One ball hits another: the energy is transferred by physical impact, which also compresses and thus heats both balls - perhaps 98% of ball A's energy is now in ball B, but 2% was lost to waste heat. Thus, given time, every system will wind down eventually since it loses a bit of energy every cycle.
More like Nothing is Perfect, and It Gets Worse Over Time.
posted by bartleby at 5:24 PM on May 31, 2008

Yeah I had trouble getting head around this law and entropy at first because there were so many ways to describe or explain it. But it seems the most updated view is that energy will always tend to disperse, to reach equilibrium. It can also be seen in terms of probability and microstates; systems tend towards more probable states.

A seemingly more common, and outdated, way of seeing it is everything (order) tends towards disorder, randomness and mixedness.
posted by gttommy at 6:07 PM on May 31, 2008

Lets not forget the "in a closed system" thingy.
posted by francesca too at 6:12 PM on May 31, 2008

GuyZero's summaries are a classic joke in the field, but I'm afraid they're not really correct. The Third Law doesn't say "You can't get out of the game." It describes what zero entropy would look like. (A perfectly regular crystal at absolute zero temperature.)

I think you'd do well to read the Wikipedia articles.

First Law
Second Law
Third Law
Zeroth Law

Attempts to summarize the laws of thermodynamics through use of pithy analogies will ultimately lead you to confusion and mistake, because they'll make you think you understand it when you don't really. (As the bard said, it ain't the things you don't know that get you into trouble, it's the things you know that ain't so.)

The Second Law isn't words, it's a formula which describes the theoretical maximum efficiency that a heat engine can achieve. A different way to say it is that it describes the guaranteed minimum fraction of energy that a heat engine will waste.

It's better to dive in and really understand them for real, really.
posted by Class Goat at 6:15 PM on May 31, 2008 [1 favorite has favorites]

Whenever you get confused about entropy, go back to what entropy means: it's the number of microscopic states your system has that look the same to your experiment. (More strictly, it's how many digits that number has, multiplied by some dimensionful constant. That definition has nice mathematical properties, but from a conceptual standpoint it doesn't add much.) You have lots of good examples in your previous question, but it's easier for me to add another one than find the one in my head and link to it.

Remember that the second law of thermodynamics isn't really something that's inevitable in the usual cause-and-effect sense of the word. The second law generally works because (i) probability theory isn't complete hogwash and (ii) systems big enough for you to notice tend to have an enormous number of degrees of freedom, so all the murky bits of probability theory that come from undersampling (which is the problem that makes political statistics so worthless) go away.

The classic tractable example is the boxful of pennies: if I put N pennies in a box, shake the box, and look inside, how many pennies will I find heads up? The average answer is easy enough: N/2. The statistical approach tells you how close you get to the average answer, over many trials: about two-thirds of the time, the number of heads showing will differ from N/2 by less than √(N/2). If I have a box with two pennies, this method tells me to expect 1±1 heads --- hardly predictive. If my box has 200 pennies, I should expect 100±10 heads. I'd have to shake the box and check a thousand times to get fewer than 70 or more than 130 heads to show, and I'd have to try 2²⁰⁰=10²¹ times before I expect to see a box with 200 heads. You're welcome to figure up how long this would take, for any sensible time to shake up the box.

nerdfilter technical note: actually the number of heads is binomial- rather than poisson-distributed, so this is wrong for N<30 or so. heavens!

If, instead of 200, I have 2×10²⁰ pennies, I can expect to find 10²⁰±10¹⁰ heads up, and 10²⁰±10¹⁰ heads down. Whatever those two numbers are, they agree to nine or ten decimal places. One way to state the second law of thermodynamics is that ten decimal places is quite plenty, thank you: unless you do something very special to your box the number of heads and tails will be "exactly" equal. If instead of pennies you have 10²⁰ noninteracting electron spins, you have a good handwavy reason why you don't find magnetized chunks of copper: unless something that makes the electron spins "want" to point the same direction, you'll always find "exactly" half of them going each way.

To do an example with temperature, you have to be a little cleverer about counting the microscopic states. It isn't inevitable that your bathwater will come to thermal equilibrium with the rest your bathroom. But there are so many more equilibrium states than nonequilibrium states that no bathwater in history has ever failed to cool off, and even if you bathed until the sun ran out of fuel, none would.
posted by fantabulous timewaster at 7:08 PM on May 31, 2008 [6 favorites has favorites]

at the risk of a pithy analogy :)

you'll never get the eggs and flour back out of the cake you made


lock your cake in a universe sized vacuum and return at infinity -1 years, your cake will have evaporated throughout the vacuum and the molecules and atoms will have collided and spread the average energy throughout the system - or so I would guess. Sort of like energy osmosis? :)

less seriously:
The Last Question
posted by clanger at 7:09 PM on May 31, 2008

There is no such thing as cold.

Only heat.

And less heat.
posted by wfrgms at 10:13 PM on May 31, 2008

This doesn't really answer your question directly, but it's an interesting sidenote to the 2nd Law:
The Second Law is often used as an anti-evolution argument. (Example)
Here's why that's just not true.
posted by The Esteemed Doctor Bunsen Honeydew at 12:15 AM on June 1, 2008

Fantabulous timewaster explains it very well, and wfrgms explains it very poorly (or not at all, as far as I can tell).

_{for one thing neither 'heat' nor 'cold' actually exist, simply kinetic energies of various particles. Thermodynamics is formulated using heat and energy, but it could be reformulated using the amount of 'cold' if you wanted too. But that has nothing to do with the second law.}
posted by delmoi at 2:44 AM on June 1, 2008

Your confusion may also stem from the fact there's a lot of ways to describe the second law, all of which are equivalent but not obviously so. I'd personally opt to explain the probabilistic approach of things moving always to more likely states, unless someone's trying to actually do thermodynamics in which case I'd start with more classical statements about heat engines or something and link the others to that as they progress. If you try to take in all the different ways of stating it at once, without trying to see the connections, you'll understandably become confused.
posted by edd at 4:36 AM on June 1, 2008

Book recommendation: "Warmth Disperses and Time Passes" by Hans Christian von Baeyer
posted by fantabulous timewaster at 5:00 AM on June 1, 2008

So Class Goat and fantabulous timewaster have given two different descriptions of the second law. CG's description is based on classical thermodynamics while ft's is based on statistical mechanics. It is one of the most remarkable results of modern physics that these two descriptions refer to the same physical quantity: entropy. I do have to quibble with one thing in ft's description, though. He describes the relation S=klogW as a "definition [that] has nice mathematical properties, but from a conceptual standpoint it doesn't add much"; I disagree. Conceptually, it is this definition that connects the statistical view of entropy to the classical view of entropy. It makes possible the connection between statistical mechanics and classical thermodynamics, and it makes the conclusions of statistical mechanics experimentally accessible.
posted by mr_roboto at 1:04 PM on June 1, 2008 [1 favorite has favorites]

Along the lines of fantabulous timewaster's recommendation:

Into the Cool: Energy Flow, Thermodynamics, and Life .
posted by psyche7 at 3:26 PM on June 1, 2008 [1 favorite has favorites]

You don't mention what about entropy is confusing you. One thing to notice is the "isolated system" clause of the law.

Where is the profit from? It's from localized pockets of high order.

It's like some Bizarro Marxism where the poor get paid by the rich who have so much capital that its ignited into a huge flaming ball of hydrogen... humm, I mean:

Many situations that you might be thinking about are not closed systems. Earth, over any sort of time scale short of astronomical(and the long end of astronomical at that), looks like a system that is getting a huge in flux of energy from the Sun.
posted by bdc34 at 8:32 PM on June 2, 2008