Why is Entropy Always Increasing in Closed Systems?

[Terdbergler]

The most common illustration of entropy is the box with the partition and the two gases on either side. It took energy to separate the gases on either side of the partition, but if we remove the partition, no additional work needs to be done in order to get them to mix. We must expend more energy if we want to separate the gases again. So it's concluded that entropy is always on the rise, since no work needs to be done in order to sustain it.

But what about oil and water. In fact, we don't even have to bring up oil and water. Let's consider the gases. Which gases are they? Helium and argon perhaps? Both are noble so they won't interact, and one has a higher atomic mass than the other, so one will settle in the middle of the box (assuming the box is in free fall) while the other rests beyond it. The gases will naturally separate themselves, just as the iron of a molten planet sinks to the bottom and the water floats to the top.

Like oil and water, many admixtures of elements and compounds naturally tend toward heterogeneity. The longer a rock has to cool, the larger its constituent crystals are.

Anyways, my question is "Why do we really believe that entropy is on the rise?"

 

[DrClaude]

Deep down, the 2nd law is basically a law of probability: we observe the most probable outcome. For any large enough system (thermodynamic limit), the fluctuations around the most probable outcome are themselves so tiny that they are not observable. That's why we are very confident that entropy always increases, as it corresponds to a change towards a more probable situation.

Be careful about the "order/disorder" analogies that are often used to portray entropy, as they can be misleading. In the case of water and oil, for instance, you have to consider that the interaction between two water molecules is so much more favorable than between a water molecule and an oil molecule, that it is worth it to have a reduced entropy due to the separation of the mixture, as much more entropy will be gained by the lower energy situation of water with water and oil with oil. By considering order only, you could never explain the phase transitions gas → liquid and liquid → solid.

Note also that gravity has a lot to do with the fact that iron is found at the center of the Earth.

 

[Hornbein]

The most common illustration of entropy is the box with the partition and the two gases on either side. It took energy to separate the gases on either side of the partition, but if we remove the partition, no additional work needs to be done in order to get them to mix. We must expend more energy if we want to separate the gases again. So it's concluded that entropy is always on the rise, since no work needs to be done in order to sustain it.

But what about oil and water. In fact, we don't even have to bring up oil and water. Let's consider the gases. Which gases are they? Helium and argon perhaps? Both are noble so they won't interact, and one has a higher atomic mass than the other, so one will settle in the middle of the box (assuming the box is in free fall) while the other rests beyond it. The gases will naturally separate themselves, just as the iron of a molten planet sinks to the bottom and the water floats to the top.

Like oil and water, many admixtures of elements and compounds naturally tend toward heterogeneity. The longer a rock has to cool, the larger its constituent crystals are.

Anyways, my question is "Why do we really believe that entropy is on the rise?"

Entropy never decreases in a closed system. These systems you are discussing are not closed. Usually the ringer is that the process that increases order gives off heat, and this heat increases the entropy of the surrounding materials more than the order results in a decrease.

In the case of the crystallizing rocks the heat given off is called the "heat of fusion." If the rock cannot give off this heat, it will not crystallize.

Suppose one puts oil and water into a system and mixes them vigorously. One may use these facts to predict that the process of the oil and water separating will produce heat that more than makes up for the decrease in entropy due to the separation of the materials. But I'm not certain: if that's wrong I'd like to know about it.

 

[DrClaude]

Entropy never decreases in a closed system. These systems you are discussing are not closed.

Sorry, but this is wrong on two levels. First, I think you mean isolated, not closed. When talking about a box containing gases, or a mixture of oil and water, we are definitely considering closed systems, with no exchange of matter with the outside. Even then, what you said is not correct. Any closed and isolated system that is not in internal equilibrium will move towards equilibrium and will see its entropy increase.

Usually the ringer is that the process that increases order gives off heat, and this heat increases the entropy of the surrounding materials more than the order results in a decrease.

In cases where additional heat is produced, that heat can be used to raise the temperature of the system itself. It corresponds to what I was mentioning above: the lowering of entropy due to the segregation is compensated by an increase of entropy elsewhere, in this case due to the increase in kinetic energy. Your statement to that effect was correct.

 

[Hornbein]

Sorry, but this is wrong on two levels. First, I think you mean isolated, not closed. When talking about a box containing gases, or a mixture of oil and water, we are definitely considering closed systems, with no exchange of matter with the outside. Even then, what you said is not correct. Any closed and isolated system that is not in internal equilibrium will move towards equilibrium and will see its entropy increase.

I mean closed in the sense that nothing whatsoever enters or leaves the system. No matter, no energy, no exchange at all.

Also, perhaps "never decrease" threw you off. Entropy may increase or remain constant.

 

[Chestermiller]

I agree with Dr Claude. You are confusing a closed system with an isolated system. In an isolated system, entropy cannot decrease, but, in a closed system, entropy can definitely decrease.

Closed System: No exchange of mass with the surroundings

Isolated System: No exchange of mass, heat, or work with the surroundings.