Hello:
I'm a sort of self-educated physics dork, and I would have expected myself to understand something as fundamental as entropy. But after reading the Wikipedia article, I still don't understand it. Then I ran into this article on Physorg, which has me even more confused. Can someone dumb down entropy for me?
QUOTE (siouxdax+Aug 27 2009, 02:41 PM)
I'm a sort of self-educated physics dork, and I would have expected myself to understand something as fundamental as entropy. But after reading the Wikipedia article, I still don't understand it. Then I ran into this article on Physorg, which has me even more confused. Can someone dumb down entropy for me?
It might make more sense if you think of entropy in terms of "energy diversity."
Having both a heater and an ice cube in the same room would be an example of energy diversity.
A room with everything the same exact temperature would have low energy diversity, but high entropy.
Entropy is the lack of energy diversity.
At maximum entropy, the entire universe would exist at the same temperature, and no particle would have more energy than any other particle.
This doesn't mean that all energy is exhausted, it means that there are no energy differences.
It might make more sense if you think of entropy in terms of "energy diversity."
Having both a heater and an ice cube in the same room would be an example of energy diversity.
A room with everything the same exact temperature would have low energy diversity, but high entropy.
Entropy is the lack of energy diversity.
At maximum entropy, the entire universe would exist at the same temperature, and no particle would have more energy than any other particle.
This doesn't mean that all energy is exhausted, it means that there are no energy differences.
Likewise, entropy in other contexts is also related to diversity.
1111111111 - no diversity, lowest entropy
1010101010 - very limited diversity, low entropy
6ceae12be3 - higher diversity, more entropy
utoAT80gHH - highest (on this example) diversity, most (on this example) entropy
1111111111 - no diversity, lowest entropy
1010101010 - very limited diversity, low entropy
6ceae12be3 - higher diversity, more entropy
utoAT80gHH - highest (on this example) diversity, most (on this example) entropy
QUOTE (rpenner+Aug 27 2009, 11:35 PM)
Likewise, entropy in other contexts is also related to diversity.
1111111111 - no diversity, lowest entropy
1010101010 - very limited diversity, low entropy
6ceae12be3 - higher diversity, more entropy
utoAT80gHH - highest (on this example) diversity, most (on this example) entropy
I could have sworn that entropy and diversity were inverses of each other. High entropy being low diversity and vice versa.
1111111111 - no diversity, lowest entropy
1010101010 - very limited diversity, low entropy
6ceae12be3 - higher diversity, more entropy
utoAT80gHH - highest (on this example) diversity, most (on this example) entropy
I could have sworn that entropy and diversity were inverses of each other. High entropy being low diversity and vice versa.
It's about information, not just temperature.
Take a box of atoms. At low energies (quantum effect) the box can only be in a finite basis of states (like my lower-case base-16) string. At high energies, the box can be in a much larger number of states (like my base-64 string).
To the macroscopic observer all these states look the same -- they all have about the same energy. So the equilibrium box has more possibilities -- and more entropy. Also there are many, many more states available to the box at higher temperature. (It's this number of indistinguishable states which is close to the information theory definition of information entropy.)
Now cut the box into two. How much entropy does each half have? Each half has half the entropy.
Now cool one box off to the low temperature, and it has half the entropy of the whole box, when the box was at low temperature.
So now we can see why a box half-high and half-low has less entropy than the same box at equilibrium. All the energy that flows to the low temperature side increases the entropy of the cold side faster than it decreases the entropy of the warm side. In fact, the entropy change for a small amount of energy is proportional to 1/T and proportional to the amount of energy.
Take a box of atoms. At low energies (quantum effect) the box can only be in a finite basis of states (like my lower-case base-16) string. At high energies, the box can be in a much larger number of states (like my base-64 string).
To the macroscopic observer all these states look the same -- they all have about the same energy. So the equilibrium box has more possibilities -- and more entropy. Also there are many, many more states available to the box at higher temperature. (It's this number of indistinguishable states which is close to the information theory definition of information entropy.)
Now cut the box into two. How much entropy does each half have? Each half has half the entropy.
Now cool one box off to the low temperature, and it has half the entropy of the whole box, when the box was at low temperature.
So now we can see why a box half-high and half-low has less entropy than the same box at equilibrium. All the energy that flows to the low temperature side increases the entropy of the cold side faster than it decreases the entropy of the warm side. In fact, the entropy change for a small amount of energy is proportional to 1/T and proportional to the amount of energy.
QUOTE
δS = δE/T
Yikes. After reading rpenner's post I'm even more confused. (No offense)
If you recall that the entropy S of a system can be defined in terms of the number of microstates Ω associated with the arrangement of the system (this sounds confusing but maybe it'll be more clear with an example).
The relation between the two is S = k ln Ω.
The relation between the two is S = k ln Ω.
QUOTE (O_o+Aug 28 2009, 01:54 PM)
If you recall that the entropy S of a system can be defined in terms of the number of microstates Ω associated with the arrangement of the system (this sounds confusing but maybe it'll be more clear with an example).
The relation between the two is S = k ln Ω.
What you have described is absolutely Greek to me. I can't even do long division by hand (LOL), so the equation you provided went way over my head.
The relation between the two is S = k ln Ω.
What you have described is absolutely Greek to me. I can't even do long division by hand (LOL), so the equation you provided went way over my head.
QUOTE (siouxdax+Aug 28 2009, 07:53 PM)
What you have described is absolutely Greek to me. I can't even do long division by hand (LOL), so the equation you provided went way over my head.
Well, hate to say this, but if you can't do long division by hand, you may as well give up on Entropy, at the very least until you get to 7th grade or so math level....
By the way, some of that actually IS Greek!
Well, hate to say this, but if you can't do long division by hand, you may as well give up on Entropy, at the very least until you get to 7th grade or so math level....
By the way, some of that actually IS Greek!
siouxdax
Don't be discouraged by Quantum_Conundrum's comment. He has not a shred of credibility here (or likely anywhere else) and feels that he needs to push others around to compensate. Most here are likely to tell you that Quantum has not likely completed the 7th grade himself.
Entropy
It rather depends if you are talking about general entropy or entropy as it relates to thermodynamics.
My favorite bit on entropy is this particular little ditty.
The 3 laws of thermal entropy.
1. You can't win.
2. You can't break even.
3. You can't quit the game.
Here's a good bit on it that starts with that ditty...
Entropy
I hope that helps.
Don't be discouraged by Quantum_Conundrum's comment. He has not a shred of credibility here (or likely anywhere else) and feels that he needs to push others around to compensate. Most here are likely to tell you that Quantum has not likely completed the 7th grade himself.
Entropy
It rather depends if you are talking about general entropy or entropy as it relates to thermodynamics.
My favorite bit on entropy is this particular little ditty.
The 3 laws of thermal entropy.
1. You can't win.
2. You can't break even.
3. You can't quit the game.
Here's a good bit on it that starts with that ditty...
Entropy
I hope that helps.
QUOTE (RobDegraves+Aug 29 2009, 01:17 AM)
siouxdax
Don't be discouraged by Quantum_Conundrum's comment. He has not a shred of credibility here (or likely anywhere else) and feels that he needs to push others around to compensate. Most here are likely to tell you that Quantum has not likely completed the 7th grade himself.
Just to make a point.
Derivative of X^3 + 3X^2 + 4x + 5 = 3X^2 + 6X + 4
I'm also pretty sure they still don't teach series, multiple-integrals, or determinants in 7th grade, or 12th for that matter.
Don't be discouraged by Quantum_Conundrum's comment. He has not a shred of credibility here (or likely anywhere else) and feels that he needs to push others around to compensate. Most here are likely to tell you that Quantum has not likely completed the 7th grade himself.
Just to make a point.
Derivative of X^3 + 3X^2 + 4x + 5 = 3X^2 + 6X + 4
I'm also pretty sure they still don't teach series, multiple-integrals, or determinants in 7th grade, or 12th for that matter.
They do in good schools.
Honestly, I re-invented enough of multi-variable calculus to pass my 3 hour final exam without opening the book, attending a lecture or taking the mid-term exam. My high school gave me enough tools to coast through that class with nothing more than perspiration.
And that was a state-funded education in the US at a school known mostly for its unbroken history of (American) football victories -- a school whose head administrator refused to let students enter a contest to win a computer for the school because in the remote chance that the grand prize was won, there was no foreseeable provision to find a place for said computer.
Honestly, I re-invented enough of multi-variable calculus to pass my 3 hour final exam without opening the book, attending a lecture or taking the mid-term exam. My high school gave me enough tools to coast through that class with nothing more than perspiration.
And that was a state-funded education in the US at a school known mostly for its unbroken history of (American) football victories -- a school whose head administrator refused to let students enter a contest to win a computer for the school because in the remote chance that the grand prize was won, there was no foreseeable provision to find a place for said computer.
QUOTE (RobDegraves+Aug 29 2009, 06:17 AM)
siouxdax
Don't be discouraged by Quantum_Conundrum's comment. He has not a shred of credibility here (or likely anywhere else) and feels that he needs to push others around to compensate. Most here are likely to tell you that Quantum has not likely completed the 7th grade himself.
Entropy
It rather depends if you are talking about general entropy or entropy as it relates to thermodynamics.
My favorite bit on entropy is this particular little ditty.
The 3 laws of thermal entropy.
1. You can't win.
2. You can't break even.
3. You can't quit the game.
Here's a good bit on it that starts with that ditty...
Entropy
I hope that helps.
Thanks for letting me know to ignore his comment. I was rather offended, which is odd since little gets to me. Yes, I cannot do long division by hand, I don't need to, I'm an artist by blood and by choice. Still, I am able to grasp a lot of physics, otherwise I wouldn't be here on this forum. I read about particle physics, etc, for pleasure (I hate fiction with the exception of William S Burroughs and Ray Bradbury). At any rate, I very much appreciate your concise descriptions of entropy. I have come to accept that I can't understand every facet of physics. Oh, and Conundrum: I DO know that some of that was Greek. But thanks anyway for attempting to correct me.
Don't be discouraged by Quantum_Conundrum's comment. He has not a shred of credibility here (or likely anywhere else) and feels that he needs to push others around to compensate. Most here are likely to tell you that Quantum has not likely completed the 7th grade himself.
Entropy
It rather depends if you are talking about general entropy or entropy as it relates to thermodynamics.
My favorite bit on entropy is this particular little ditty.
The 3 laws of thermal entropy.
1. You can't win.
2. You can't break even.
3. You can't quit the game.
Here's a good bit on it that starts with that ditty...
Entropy
I hope that helps.
Thanks for letting me know to ignore his comment. I was rather offended, which is odd since little gets to me. Yes, I cannot do long division by hand, I don't need to, I'm an artist by blood and by choice. Still, I am able to grasp a lot of physics, otherwise I wouldn't be here on this forum. I read about particle physics, etc, for pleasure (I hate fiction with the exception of William S Burroughs and Ray Bradbury). At any rate, I very much appreciate your concise descriptions of entropy. I have come to accept that I can't understand every facet of physics.
Oh, and Conundrum: I DO know that some of that was Greek. But thanks anyway for attempting to correct me.
Rob:
I haven't seen the word "ditty" in quite a long time. Thanks for making me smile; I needed it.
I haven't seen the word "ditty" in quite a long time. Thanks for making me smile; I needed it.
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