Separation of differently sized particles

[Xtrem]

If we had a mixture of particles of different sizes and we run it through a sifter of various sizes we would be able to sort our different sized particles. How does this relate to entropy? Initially, I would think the entropy of the system is high because of a mixture, but then it becomes separated. I'm not sure what I'm asking, but what do you think? Is the entropy of the system decreased or increased? If decreased, how? Is there energy added by "shaking" the sifter?

 

[CycloWizard]

This is essentially what is done in size exclusion chromotography (SEC) or entropic interaction chromatography (EIC). I think you're right that the entropy in the solution would decrease as the entropy of mixing is essentially taken out of the system. I think the energy is added to the system in SEC/EIC by mechanical work done on the system via an applied pressure gradient or, in your example, shaking.

 

[Xtrem]

This is essentially what is done in size exclusion chromotography (SEC) or entropic interaction chromatography (EIC). I think you're right that the entropy in the solution would decrease as the entropy of mixing is essentially taken out of the system. I think the energy is added to the system in SEC/EIC by mechanical work done on the system via an applied pressure gradient or, in your example, shaking.

This is exactly my thought, but shaking can be done "without friction" theoretically... so there would not be energy input?

 

[CycloWizard]

This is exactly my thought, but shaking can be done "without friction" theoretically... so there would not be energy input?

The shaking is still an applied load which has an associated quantity of work. How this work might be transferred to the particles depends on the particulars of the system but in the end separation relies on friction. In SEC, the solids are dissolved in a liquid; viscous stresses in the liquid transfer the input energy to the polymer chains forcing them to deform and travel through pores (in porous SEC anyway). In solid sifting of the sort I think you're describing, friction isn't essential but you are still doing work to translate/rotate the particles to bring them into appropriate position to pass through the sieve. If it were perfectly frictionless then I don't know if a separation could be achieved.

 

[Xtrem]

The shaking is still an applied load which has an associated quantity of work. How this work might be transferred to the particles depends on the particulars of the system but in the end separation relies on friction. In SEC, the solids are dissolved in a liquid; viscous stresses in the liquid transfer the input energy to the polymer chains forcing them to deform and travel through pores (in porous SEC anyway). In solid sifting of the sort I think you're describing, friction isn't essential but you are still doing work to translate/rotate the particles to bring them into appropriate position to pass through the sieve. If it were perfectly frictionless then I don't know if a separation could be achieved.

Perhaps let's think about particles that are perfectly spherical but of different diameter, there is no need to rotation or translation. Each particle may have to be moved to a hole to see if they can fall through, but this should not add to the energy of each particle. Or if we think about it differently, consider a sifter with NO holes, if we were to "shake" it, then the system would not have added energy because... nothing is changed, entropy is the same.

 

[edcarman]

Or if we think about it differently, consider a sifter with NO holes, if we were to "shake" it, then the system would not have added energy because... nothing is changed, entropy is the same.

Surely this is then just another form of perpetual motion machine? In these cases, violations of the second law are often possible once you ignore friction.

 

[Xtrem]

Surely this is then just another form of perpetual motion machine? In these cases, violations of the second law are often possible once you ignore friction.

I suppose you would be adding energy into the kinetic energy of the particles and it will perpetually move but that is besides the point because you cannot infinitely extract energy from it... Second law of thermodynamics will still be valid. My point was separation of the particles would not require work (I think?).

 

[Paperdoc]

Friction is involved, I believe, in an interesting way, and there is no doubt the shaking action does work on the particles being sorted.

First of all, I see friction as the reason that the initial array of particles does NOT sort itself through the sieve(s). If it weren't for friction, they would all slide over and around each other and fall through the sieves without any shaking.

What does shaking do? It adds to the particles an Activation Energy - that is, a small amount of additional energy that allows the particles to "escape" their initial stable state and move around to do something else. The particles certainly gain Enthalpy because they begin to move - they have acquired translation energy. But they also have acquired Entropy - more disorder - because they no longer are resting securely against each other in a well-defined arrangement, but are now separated from each other slightly by a thin film of some fluid like air or a carrier solvent. The minute separations reduce the effect of friction so that the main forces inhibiting movement of particles past each other becomes short-lived impacts, and the new translational (and rotational) energy of the particles allows them to move around each other. The result is the the particles at the bottom of the array and in contact with the sieve wires can move to the holes and re-orient themselves as necessary to fit through the holes (provided the holes are larger that the particle).

Now, what happens to all that added Activation Energy? Some of it is dissipated into the surroundings as sound because particle impacts with each other and with the sieves cause vibrations. Some of it is retained in the particles as minutely increased temperature - heat, really - as the atoms and/or molecules of the particles increase their own vibrational and rotational energy states. I agree with others that, at the end, the overall system would appear to have reduced disorder - reduced Entropy - but I think it also has increased Enthalpy. However, as I said, some of that Enthalpy has been lost to the surroundings, too.

 

[Rakehellion]

Each particle may have to be moved to a hole to see if they can fall through

Bingo.

I suppose you could make a sifter styled like a pachinko machine so they all just fall through without any effort, but there's still friction on all of the moving parts, which is overcome by gravity, which is overcome when you expend energy by llifting the particles into the machine.

 

[CycloWizard]

I think Paperdoc and Rakehellion covered this pretty well but I'll try to generalize. Motion of the particles must occur if they are to separate. The energy from this motion must come from somewhere. If you use gravity sifting, potential energy is added to the particles to lift them above the sieve. If you use SEC or other flow-driven methods, pumping work is added. If you use a manual shaking method, then you are applying the work. The closest possible case I can think of would be if you wanted to separate microparticles using Brownian motion in the presence of a membrane but even then the random fluctuations of the solvent molecules which cause movement in the microparticles require thermal energy (i.e. the solvent would actually cool very slowly over time if it were in a truly closed system).

 

[DrPizza]

Regardless, one way or another, the sifting is done by gravity. Work is done by gravity on the particles that fall through the sifter.

 

[Paperdoc]

Let me correct the end of my previous post (4 up). The Activation Energy (both Enthalpy and Entropy) added by shaking becomes just a part of the total Energy of the particles system as the process starts and continues. BUT at the end when shaking is shut off and the sorting has been done, all the particles have fallen due to gravity to a state of lower potential energy. That is, the total Energy of the particles system is now lower than before the process started. It is true that gravity does do work on the particles as they fall - it is a force acting through a distance, producing an acceleration resulting in kinetic energy in the particles. When a particle hits bottom, though, and stops falling, it transfers that kinetic energy it gained from gravity (equal to the potential energy change in the fall), plus the Activation Energy input from shaking, to the surroundings and other particles as sound, heat in the particles and sieves, etc.The particles may have lost Entropy and gained a little in temperature, but overall they have lost energy. I'm making a reasonable guess, I think, to suggest that the Activation Energy input from shaking is less than the loss of Potential Energy from falling. That may not be the case, though, in SEC or reverse osmosis separation systems for liquids.

 

[colonelciller]

This is exactly my thought, but shaking can be done "without friction" theoretically... so there would not be energy input?

shaking coud not be done "without friction"

try to shake something (anything) and unless it is completely wrapped in your hand it would slide right out instantly... in fact you would never be able to pick it up... and you would slide across the floor like you were standing on a greased block of ice... and all nearby objects would slide to the lowest points at incredible speeds...

 

[Xtrem]

Ah ok, I was not thinking the hands but the plate

 

[Revolution 11]

Even if there was no friction and the particles moved to the correct holes without energy input, you are still using potential energy (height of particles) and converting that into kinetic energy (particles moving through filter), ending up with reduced potential energy (lower height) to reduce entropy. The particles have less entropy but not the system.