Of sand mixtures and thermodynamics!
Hope you all are familiar with the common experience with haldiram bhujia...The big chunks of the yummy stuff is always on the top and separates out from the rest of the smaller sized bhujia. I say this because, we always had a fight at home as to who gets to open the pack! Similarly...if you shake a mixture of sand, you will find the bigger sized stones always on top.
Now the question is: Since shaking is a random process, we should expect the particles to be randomly distributed (to have more disorder, increase in entropy) but we have an apparent order (separation of particles into different sizes). Isn't it a against our second law of thermodynamics? Where is the catch? :)
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Now the question is: Since shaking is a random process, we should expect the particles to be randomly distributed (to have more disorder, increase in entropy) but we have an apparent order (separation of particles into different sizes). Isn't it a against our second law of thermodynamics? Where is the catch? :)
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posted by atma_tripta at 10/09/2005 11:50:00 AM
7 Comments:
Though shaking produces randomly distributed particles, the small particles can slide through the space inbetween large particles. This produces a larger density of small particles down and a larger relative density of larger particles on top.
This is not against the second law since the law states that "the total entropy in the universe never decreases". But to shake itself takes energy (which comes from the hand which shakes it, that gives out heat in the process, that in turn excites the surrounding molecules thereby increasing entropy outside the can/bottle). Thus, this process only reduces the entropy within the packet/bottle but not the total entropy (which will always increase).
As for the mechanism, in addition to what bal said, drag could also be an issue (especially if the particle sizes are small). After a shake, the particles fall down through the air. Since the drag on a larger particle is more, it takes a while longer to fall. Before the larger particle has the time to reach its position, a smaller particle is already there (possibly by sliding from the neighborhood). This incremental effect accumulates and finally results in a gross difference in distribution between the two sizes.
On the right track libran. Little cow, your are right in saying that entropy should always increase. Now combine this with what libran is saying...how do you define randomness....whats its connection to volumes...Well Iam giving it away here, if I say anything more!
Little cow..its not that hard and Noooo..there is no fluid mech in this! :)
So to continue, the smaller pieces fall down through the space inbetween larger pieces. As it falls down it's potential energy gets converted to kinetic energy which gets converted to heat. This heat escapes to the surroundings and the entropy of the surroundings increase. So, the overall entropy of the universe increases while the entropy of the jar decreases.
Also, because the particles go down, they get more and more dense. As a result, the volume available to the surroundings increase. This implies that the entropy of the surroundings increase due to the additional volume and the heat energy. So, the overall entropy of the universe increases even thought the entropy of the sand decreases.
The answer to this was on lines of what BAL said. Entropy is a measure of randomness (disorder) of the system. Now if the smaller particles separate from the larger ones, then the specific free volume (i.e space available for the particles to move around) increases for the smaller ones and this increases the disorder(because, the spatial distribution of the particles is more random now) and is more than offset by the separation of the larger particles. And hence, within the system the entropy increases and there is no contradiction.
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I think we can give BAL 0.5 points (Iam being a miser here!!)
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