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- Thread starter The_Brain
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jcsd

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marcus

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Originally posted by jcsd

jcsd here's a question that might interest you to think about:

in the example you offer here,

what would happen to the size of the universe and

to the amount of entropy in it

if one of the stars in it collapsed

to form a black hole?

I hope this extra wrinkle fits into the context of

what you were describing and is a meaningful question.

not sure how "size" is measured in this discussion,

I guess volume? The_Brain was talking about volume

and entropy.

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jcsd

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Yes,I was just using size as synonym for volume.

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marcus

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Originally posted by jcsd

Yes,I was just using size as synonym for volume.

so as long as there is one black hole in the universe, the entropy of the universe cannot be defined?

you have to wait 10

every black hole time to evaporate and then finally you can

have a state of thermodynamic equilibrium and define the entropy?

I had the notion that one could say something at least approximately correct about this in the short run.

It seemed to me that when a star collapses to form a black hole there is at that moment quite a substantial increase in entropy.

If you can, please elaborate. Several of us might benefit from

more discussion of this.

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jcsd

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marcus

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Originally posted by jcsd

No, the entropy of a black hole is well defined and is a function of the surface area of the event horizon, so the more massive the black hole the higher it's entropy. .....

That is what I thought, jcsd.

So now I am back to my original question.

You seem able to imagine defining the entropy of the universe.

What happens to the entropy of the universe

when a star collapses to form a black hole?

Does it change, by a lot, by a little? Does it stay the same?

Can you discuss this a bit for us?

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jcsd

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Of course in these models we're just viewing the universe as a closed system of finite and fixed volume.

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marcus

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Originally posted by jcsd

Of course in these models we're just viewing the universe as a closed system of finite and fixed volume.

I believe your intuition is absolutely right here! A black hole has an enormous amount of entropy per unit volume, within its event horizon. Far more than any star.

We might be able to make a rough order-of-magnitude estimate.

edit: Bravo! jcsd, I just came back to this thread and saw that you have in fact does this for 5 solar masses. Good show---nice to have a definite number in the picture

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jcsd

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Originally posted by jcsd

Of course in these models we're just viewing the universe as a closed system of finite and fixed volume.

Ok, so what if the model we used was one such as when a certain limit is reached, the system expands in volume? 2nd Law says that entropy can never decrease, so after the system expands it can only gain more entropy which would require more volume at a critical limit.

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jcsd

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You have to realize entropy, though it works with almost no exception (actually I should say scientists have observed decreases in entropy on a minute scale over a short period of time) are not absolute, they are statistical. This is why the law is phrased "The entropy of a closed system

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Originally posted by jcsd

infact after an arbitarily long period of time you would (statistically) expect to see a huge decrease at some stage in the total entropy of a closed system of fixed volume.

I thought the entropy of a closed system could never decrease?

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jcsd

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No, they're is always a very tiny chance that it will decrease, as I said before it is statistical.

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vedder

Lets say we have a closed system defined as one liter of 100 degree H^2O in a perfect container(one that does not allow diffusion from it to it's surroundings). The information in that container will not become less organized will it? It seems to me that the information needs an area to spread into for it to become less organized. That would mean that The_Brain was pretty right on when he said "an increase in entropy over a certain limit could necessitate an increase in area".

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jcsd

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vedder

The point is the 2nd law of thermodynamics only works because the universe is not in a state of thermal equilibrium

Of course if we look at the equation for entropy it does not imply an increase in area. What i mean to say is that here, in this universe which is not in thermal equilibrium, entropy is the only thing i can think of, as a law, that would necessitate the expansion we observe.

I do think you are very correct to say this...

The conclusion should be that the 2nd law of thermodynamics will cease to hold at this point

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vedder said:What i mean to say is that here, in this universe which is not in thermal equilibrium, entropy is the only thing i can think of, as a law, that would necessitate the expansion we observe.

Yes, this is exactly what I am led to think. However there are people here who know much more about physics than I do so please, if anybody can, tell us why this might be false?

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