Entropy

[Eelpie]

In "wonders of the universe" I was slightly confused by the description of entropy. Prof Cox used the example of a low energy sand castle and a high entropy pile of sand in a cone. Can the grains of sand in the sand castle really only be arranged in that order to create a sand castle? Surely there are many ways the grains could be ordered to create a sand castle; and is this number really massively less than the cone of sand which he claimed was high entropy? I also wondered if Prof Cox's hairstyle was low or high entropy? At first sight it looks like a high entropy system but I would imagine over the course of the day it flattens out....so presumably it is actually intially low entropy? I am also confused by salad dressing again on Cox's ordering example mixed salad dressing is high entropy yet this would imply that once the vinegar and the oil seperated out it would have lower entropy.

 

Looking for a better description please!

[swansont]

If you lower the number of available states, you lower the entropy — so any restriction on where a grain of sand can be lowers its entropy. The sand castle will spontaneously slump into a pile, but the reverse will not happen.

[Zarnaxus]

The amount of entropy in the entire universe is always increasing due to thermodynamics.

 

Entropy is the amount of energy in a system that is no longer able to do work. When something can be done, there is entropy. When nothing can be done, there is no entropy.

 

I've always thought of it like this: the amount of potential energy in the universe is always decreasing. Entropy is kind of the opposite of potential energy, I suppose.

[Eelpie]

If you lower the number of available states, you lower the entropy — so any restriction on where a grain of sand can be lowers its entropy. The sand castle will spontaneously slump into a pile, but the reverse will not happen.

 

 

Thanks swansont....I see that there is more potential energy in a sand castle than a cone of sand although I doubt very much that a sand castle could collapse into a smooth pile that looks like a cone either, although I guess that wind etc could then erode it into a smooth structure. I can accept that there are probably marginally more ways to order the cone than the castle but it didn't seem like a great example.... the cynic in me wondered if the choice of the example was driven more by wanting to go to a tropical beach than whether it was the best way of demonstrating the concept...anyway my main problem is that it doesn't seem to describe other increases in entropy like salad dressing separating out?

 

Is the best description of entropy in physics really the number of ways that a system can be ordered?

[swansont]

S =k ln(N) in statistical mechanics

[Eelpie]

S =k ln(N) in statistical mechanics

 

Not sure I follow.....I got this from wikipedia Is the point that having the oil and vinegar seperated out is much more likely than them being mixed and hence the entropy still increases even though it appears more ordered?

 

Cheers.

[swansont]

Not sure I follow.....I got this from wikipedia Is the point that having the oil and vinegar seperated out is much more likely than them being mixed and hence the entropy still increases even though it appears more ordered?

 

Cheers.

 

In thermal equilibrium all states are equally accessible, and the sum just becomes the number of states.

 

I haven't seen the show, so I don't know how he lays out the example, but it's an example of why the naive application of order vs disorder isn't always an accurate proxy for entropy.

[Eelpie]

In thermal equilibrium all states are equally accessible, and the sum just becomes the number of states...it's an example of why the naive application of order vs disorder isn't always an accurate proxy for entropy.

 

 

 

 

Thanks very much. I thought that it had to be a over simplification. Googling had turned this up on: ehow.com which still seems to focus on the number of different ways a system can be ordered (to me a mixed mixture can be ordered in far more ways than a separated mixture):

Energy and Entropy

• Mixing oil and water would break hydrogen bonds, which takes up energy and is therefore unfavorable. Moreover, mixing oil and water results in decreased entropy. (Entropy basically measures the number of different ways you can arrange the components of a system to get the same state). As we know from the laws of thermodynamics, nature always tends toward lower energy and higher entropy; the only way we can reverse this trend is by doing work, putting energy into a system--as when you shake a bottle of dressing to mix the oil and vinegar. Ultimately, however, given time the system will slowly revert to the higher-entropy, lower-energy state.

Still don't think I fully understand entropy but nice to know that's my previous understanding, which was closer to Zarnaxus' description, is a better "approximation" than the ordering example.

 

 

I haven't seen the show, so I don't know how he lays out the example

 

Great disappointment, massive budget BBC/Discovery channel production which is long on panoramic shots and uplifting music but doesn't really teach anything to anyone who has read a couple of pop science books on cosmology.

Edited April 21, 2011 by Eelpie

[James Putnam]

I viewed this at:

 

http://lcni.uoregon.edu/~mark/Stat_mech/thermodynamic_entropy_and_information.html

 

Excerpt: "The bottom line is that thermodynamic entropy is best understood not as a property or macroscopic state of matter (like mass, temperature, or pressure), but as a lack of knowledge of the detailed configuration of matter. In particular, thermodynamic entropy is a measure of our lack of information about the microstate of a closed system of matter near equilibrium. To make this concrete, I'll compare two similar simple systems, one of particles and one of bits. Although the concept of entropy in classical thermodynamics was elucidated long before information theory was developed, thermodynamic entropy can be viewed as a straight-forward application of information theory to a physical problem."

 

Interesting. I see this opinion as clearly, scientifically evasive. Something that was precisely defined in terms of temperature, energy transiting into or out of a system in thermal equilibrium, and something that required the passage of time, is dismissed as being a counting problem unrelated to the definition of thermodynamic entropy. This appears to be an example of avoiding answering a fundamental question before racing off into an unrelated area. Thermodynamic entropy was defined long before space-cells were defined for reasons of sort-kinda calculating thermodynamic entropy, or long before microstates were discovered. Clausius discovered thermodynamic entropy, a macroscopic thermodynamic property. If one does not know what it is, then, one should admit that and not divert attention to something else. That is what I think.

 

James