# 2nd law of thermodynamics

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our teacher was explaining the equivalence of kelvin plank & clausius statement of 2nd law. i would like to know if there is any proof of them individually. thaks in advance.

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The various statements are equivalent.

There is ample evidence that they are true, e.g. the lack of overunity perpetual motion machines.

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what is over unity perpetual machine?

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A machine that generates more energy than it consumes.

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but why cant it be just equal? over unity wont be possible for it would break energy conservation law.

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True. Perpetual motion of that kind is also impossible.

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If you use the concept of entropy, then all the statements are equivalent. There is a site explains the 2nd law quite well.

http://www.panspermia.org/seconlaw.htm

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I found a website (below) that discusses entropy.

http://www.chiark.greenend.org.uk/~sbleas/creative/entropy/#11

Consider a box of small magnets. If the small magnets are lined up in the same direction, as a group they can attract other metal objects. If they are not lined up in the same direction, individual magnets cancel each other's effect and cannot do useful work. The same is true of energy - it is useful when it is ordered, but when it is disordered, its effects cancel each other out.

........

When there is zero entropy, all the energy can be used. As the entropy increases, available energy decreases until, with maximum entropy, no useful energy is available.

Continuing with the concept of the magnets, imagine you must move them to a different box in order to use them. As you are moving them, you may put some into the new box the wrong way round - the useful energy will then have decreased. Of course, the slower and more carefully you make the exchange, the fewer mistakes you will make. The same is true of energy - the entropy in the system always increases, unless the rate of change is infinitesimally small.

But why doesn't entropy (the disorder) decrease? What prevents only those magnets facing the wrong way being turned round? This could happen in two ways -

1. The first possibility is that someone decides to increase the order in the system. However, as anyone tries to order the system, that person is doing work - and so the system's entropy decrease would be balanced by a hefty increase in that person's entropy. Thus entropy would increase on the whole.

2. Otherwise it could happen by chance. This is very unlikely because, for both magnets and energy, there are a lot more ways in which things can be disordered than ways in which they can be ordered. This means it is practically impossible an ordered arrangement will appear by accident and practically certain any ordered arrangement will become less ordered. With one hundred magnets, it is more likely that you win the national lottery jackpot four times in a row than that they all point the same way by chance. With the many millions of atoms in any system, for all intents and purposes, entropy will never decrease.

For #2, is that a good analogy for why entropy tends to occur? If so, the reasoning has a flaw.

It would be just as unlikely for the magnets to all end up facing opposite ways in a perfectly even distribution. Not to mention, wouldn't it be order to have such an even distribution?

Take a checkers board.

If you separated the colors so that each side of the board were a solid color, you'd have order.

And if each square moved randomly here and there, you'd get disorder.

But if all the random-moved squares became evenly distributed, you'd have order again.

It'd be a lot easier to go from a totally even distribution to a messy one.

Wouldn't it?

And so shouldn't a completely even distribution be the same as a completely ordered non-distribution?

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I've found that one way to better comprehend the 2nd Law is to 'blend' (Macroscopic)Thermodynamics with (Microscopic)Statistical Mechanics. Thermo. states that, for a closed system, the entropy can either remain constant or increase. Shift to SM for the definition of entropy, S=k(logW), and the 2nd Law can be expressed as: dS/dt>0, or dS/dt=0. The tricky and rather tedious part is that 'W' is the total # of ALL POSSIBLE (quantum) states of the system.

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i havent done statistical mechanics yet so pls explain

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• 2 weeks later...
i havent done statistical mechanics yet so pls explain

Well, basically. . .you can't get more out than you put into the system because you're always going to lose some energy to heat or friction. Neither of these 'drags' on your system will come without a cost, in energy.

So unless you can remove both heat and friction (including air), you will never balance your system.

Without balance you will never have perpetual motion. Let alone a system that produces more energy than it consumes.

You have to equal before you can exceed. Nobody has reached equal status, yet. So--by definition--nobody has exceeded the energy input.

It's a bugaboo, it doesn't exist without 'free' energy input. Kind of like a Hydroelectric dam where the rain falls upstream (after a lot of evaporation downstream) but it doesn't cost you--as the producer of hydro power--anything to make this happen.

It still takes a lot of energy to get those rain clouds upstream from the dam, but it doesn't cost anyone anything to make it happen.

Not the same--by a long shot--as perpetual motion, but it works kinda' the same when you realize that all the work of getting the water above the generator is free.

Something to think about, once you've given-up on the whole 'free' energy thing.

It ain't gonna work. Newton was right.

Sorry.

There is a reason we call these things 'Laws' instead of 'theories.'

Bill Wolfe

Edited by StrontiDog
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It would be just as unlikely for the magnets to all end up facing opposite ways in a perfectly even distribution. Not to mention, wouldn't it be order to have such an even distribution?

Actually, no, it wouldn't. Exactly half and half is far, far more probable than all one way or all the other. If you expand that to "approximately half and half," it becomes extremely likely, and more and more so the more entities you add.

Coin flips are probably a simpler example. No matter how many times you flip, there are always only two ways for "order" (all heads or all tails), but the total number of possibilities doubles with each additional flip, so order becomes less and less likely. And half and half is always the single most probable outcome, with probability of heads vs. tails ratios looking like a bell curve, that gets steeper and steeper the more coins you flip. (There are vastly more ways to get 51-49 than 99-1, etc.)

Take a checkers board.

If you separated the colors so that each side of the board were a solid color, you'd have order.

And if each square moved randomly here and there, you'd get disorder.

But if all the random-moved squares became evenly distributed, you'd have order again.

It'd be a lot easier to go from a totally even distribution to a messy one.

Wouldn't it?

And so shouldn't a completely even distribution be the same as a completely ordered non-distribution?

A precise even distribution like that would also be extremely unlikely, yes. However, again, the vast majority of "messy" configurations are approximately evenly distributed, and become more so the bigger the checkerboard you have.

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our teacher was explaining the equivalence of kelvin plank & clausius statement of 2nd law. i would like to know if there is any proof of them individually. thaks in advance.

One cannot prove scientific theories - they are models of systems after all, and to prove them would require looking at every single system, which is of course impossible.

Evidence we can find can support the theory, and even to the point where we are so certain of its truth that it would be ridiculous to think otherwise, but you only need a single verifiable contradiction, and the theory is wrong and may need wholescale changing, or refinement.

Theories however can be disproven of course, as many have - such as the lumiferous aether, young earth creationism, phrenology, homeopathy and so on.

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