wdog

this is more or less what I think is right, but it is not really a law that system evolution must procede along maximal entropy rate of change, I believe it is a tendency

http://members.tripod.com/spacetimenow/section6.html

oh and be sure to back up a few pages on the 'previous' button at the bottom of the page to get full context, the picture of the Bernard Cell is really neat.

Jesse

I believe there actually are more possible microstates available to the system when the oil and water molecules are separated than when they're mixed. This is because a system's microstate includes both the position and the momentum of each particle, and potential energy is minimized when the molecules are separated, so the system has more total kinetic energy and thus more possible ways to distribute this as momentum among all the different particles. There would presumably be a bit of a trade-off between more possible arrangements of position when oil and water are mixed and more possible arrangements of momentum when they're separated, but the highest-entropy state will be the one that balances this in such a way that the most microstates are available. I have read in a few places that oil and water would separate even in a totally isolated system.

A similar account would tell you why a cold distributed nebula may actually increase in entropy when it condenses into a hotter sphere due to gravity--again, less potential energy = more possible microstates available in momentum-space.

HRG

Quite possible - and the system would heat up at the same time.

Quote:

A similar account would tell you why a cold distributed nebula may actually increase in entropy when it condenses into a hotter sphere due to gravity--again, less potential energy = more possible microstates available in momentum-space.

All what you said is perfectly correct, IMHO. Many people forget that states are to be counted in phase space: position and momentum.

Still, in an isothermal situation, the extra energy gained by rearrangements in position space (which make the system appeare more "orderly") will be taken up by the environment, such that the temperature remains constant. That's why in this case equilibrium is a minimum of free energy, and not necessarily a maximum of entropy.

Regards,
HRG.

wdog

jesse,

yes, entropy should be looked at in phase space with full accounting of all the degrees of freedom (a point particle has 6). And a system will tend to maximize its phase volume, correct?

In regard to the oil and water system though, might it also be that the system could simply have a stronger tendency to minimize energy? In the Helmholtz potential U-TS, entropy can go down as long as the energy U goes down even more, in accordance with the second law for closed systems. I don't know, just musing... hasn't someone done a complete analysis somewhere? this is such an old problem

edited to add: Lol, HRG and me are at the same point in pahse space

Jesse

Yeah, we're just talking about the difference between isolated and non-isolated systems, I think. If I'm remembering right from thermodynamics, one of the cases where you minimize free energy is when you have a small system which can exchange heat with a larger heat sink. In this case the state of maximum entropy for the combined small system + heat sink system will be the one where the free energy of the small system is minimized. So situations where entropy is not maximized for a system are the ones where the system is not isolated but is in contact with some other system; if the combined system is isolated from external influences, the whole thing will go to a state of maximum entropy.

I would say it's a little easier to make the point that "lower entropy != more disordered" by considering simpler cases of truly isolated systems, like oil and water in isolation or a nebula in isolation. In these cases we can see that a system can become more ordered in position-space as a consequence of becoming more disordered in the total position-momentum phase space (which in a way is similar to the case of a combined system where the total entropy of small system + heat sink goes up while the entropy of the small system itself goes down).

Jesse

wdog:
jesse,

yes, entropy should be looked at in phase space with full accounting of all the degrees of freedom (a point particle has 6). And a system will tend to maximize its phase volume, correct?

If it's isolated, yes.

wdog:
In regard to the oil and water system though, might it also be that the system could simply have a stronger tendency to minimize energy? In the Helmholtz potential U-TS, entropy can go down as long as the energy U goes down even more, in accordance with the second law for closed systems. I don't know, just musing... hasn't someone done a complete analysis somewhere? this is such an old problem

If the oil and water system is truly isolated, entropy will always rise. If it is closed but not isolated (capable of exchanging heat, but nothing else, with the external environment), then it may be that entropy will drop while some other quantity like the free energy is minimized or maximized (I've forgotten a lot of the details here, I'd have to look them up). Not sure where you could find a complete analysis of the oil and water problem, though.

Supramolecular

Actually KC, you are correct.
When an oil molecule is introduced into water, it causes the water molecules surrounding it to have a more ordered state than they otherwise would have in the bulk liquid (due to the non-covalent interactions between the oil molecule and the water molecule). This is obviously a decrease in entropy.

Image two oil molecules placed into water and each having 5 water molecules surrounding them in their 'more ordered state'. When the two oil molecules come together they have a smaller surface area and so fewer water molecules surround them in an ordered state (lets say 7 instead of 10). The release of the 3 ordered water molecules back in to bulk solution increases the entropy of the system.
When many oil molecules come together (i.e. form a separate layer), many water molecules are released into bulk water and so the system has a higher entropy as a whole.

KC

But I was saying that the separated state was more 'ordered', which was incorrect.

KC

Jesse

KC:
But I was saying that the separated state was more 'ordered', which was incorrect.

It's correct in one sense--if you consider only the position of the center of mass of each molecule, there are more possible arrangements of positions where the oil and water are mixed than there are arrangements where they're separated, so in this restricted phase space the separated state is more ordered. But if you consider the full phase space, including the momentum of each particle as well as each particle's orientation (water molecules have less rotational freedom on the boundary of oil molecules, as this page points out...I forgot about this in my earlier explanation), there are fewer configurations where they're mixed than when they're separated, so in the full phase space it's the mixed state that's more ordered.

Supramolecular

KC,

I was basically agreeing with your statement that order does not necessarily mean low entropy, which is correct. This is the case in the oil/water system.

Contrary to non-praying Mantis's statement, the group of oil and water particles have more possible states that they could exist in when they are separated into layers. The water molecules have more degrees of freedom.
The enthalpy component of this process (separation) is close to zero due to the few electrostic interactions between oil and water, but the entropic component is positive. Due to deltaG = deltaH-TdeltaS, this results in a negative free energy, hence the process occurs spontaneously.

I think confusion arises because order/disorder and entropy are often thought as being exactly the same thing. As HRG basically said, it's the free energy change of the process that's important.

Regards