# Law of Thermodynamics only applies on large particle system?

1. Apr 22, 2013

### alexay95

Assume I got a box full with four particals two of them cold and two other hot.
This system got entropy s0
Now I got a button that in activation divides the box to two boxes.
I push it without even look at my system
And I can get a situation where the cooler particals in one side and hotter in other.
There's a large chance for that to happen.
So if I understand right, Entropy now decrees?
So, I don't understand entropy? or the law of Thermodynamics only applies on large particals system?

2. Apr 22, 2013

### Crazymechanic

you can't have two cold and two hot particles in the same room because thermodynamics one of most basic principles is that systems tend to go to equilibrium.That means if you have two cold particles and two hot ones and you let them to interact them the twp hot one will get colder and he cold ones will get a little hotter and in the end there will be four particles with the same temperature.

Now this happens to air all the time the only difference is that normally a jar of air or any amount of air is far far more than just 4 particles but if you break it down you can go to any number of particles you like but the basic thing doesn't change.Whenever you open up your window in a winter time the hit air rushes out and the cold one in.Until they mix that the temperatures match.

All systems tend to go towards disorder with time or they increase in entropy , just like the universe which started from a much smaller hot "place" and has expanded ever since and cooled down.
The only difference is that in your scenario with the particles if they are perfectly isolated then they count as isolated system and before they have been put together they have a different state now among interaction their total entropy is maximized at the exact moment upon interaction and it stays that way for ever as long as the system is isolated.
Because you have only 4 particles , two were hot two were cold now that they have interacted there is nothing more to happen if they are isolated and that's why entropy stops and stays the same.

3. Apr 22, 2013

### alexay95

Why would they interact with each other so fast?
They change Tempature when they collide and I can activate my button before they interact?

4. Apr 22, 2013

### Crazymechanic

Now before you have put them together in a perfect theoretical system they don't interact the hot ones are hot the cold one are cold , I hope you understand that hot and cold is a measure of temperature which is a measure of the kinetic energy of the particles or their "bouncing"

Now when you put them together in a box they will interact and the hot ones or the fast ones will collide and give off some energy to the cold ones and so they will get to equilibrium.
Now ofcourse if your thought experiment box is as big as the universe with only 4 particles in all that vast space the chance for them to collide is extremely small but in an ordinary box with a human scale size they would interact pretty quickly.

Why would they interact?
Hmm let me put it this way.You have a hungry tiger and a fresh peace of meat.When you keep the tiger in a cage and the meat outside nothing happens , when you put the meat in the cage or let the tiger out or do both at the same time what do you think happens?
And believe me in the case of tiger and fresh meat it happens extremely quick.

5. Apr 22, 2013

### alexay95

It can be some balls with car velocities. So that the collation happens once in a while. By the time of the first interaction I'll will push the button.
So is the law of Thermodynamics applies on specific systems?

6. Apr 22, 2013

### Staff: Mentor

The second law is a statement on the statistics of a thermodynamic system. With only four particles, the fluctuations in entropy are indeed quite big, because the different macrostates (1 hot and 1 cold in each box, 2 hot in one 2 cold in the other, all 4 in one box, etc.) have very similar probabilities. It is only in the termodynamic limit (big system) that you can state the second law as finding the system in the most probable macrostate, with fluctuations being too small to measure.

Note that even if the particle collide and thermal equilibrium is reached (which would take an extremely long time with only four particles), you still have entripy corresponding to density, or how many particles you will find in each box.

7. Apr 22, 2013

### Staff: Mentor

How can you compare particles such as atoms and molecules to a conscious animal?

Last edited: Apr 22, 2013
8. Apr 22, 2013

### Crazymechanic

DrClaude I didn't compare animals to particles , you just didn't understand the analogy , it was meant to represent the fact that hungry animal interacts with food , just as "hot"particles interact with "cold" ones if brought together in a single "box"
The key here is interaction not consciousness or something other.
Not to mention that the level of consciousness in animals compared to that in humans is an open question but well that's not the subject here.

Another fact that the probability of interaction and change in entropy given the OP conditions of the 4 particles and a box depends on the size of the box , considering the density is only 4 particles no matter how big the box , so the bigger the "space" the less the chance of interaction.

I suggest reading up on entropy

http://en.wikipedia.org/wiki/Entropy

9. Apr 22, 2013

### Staff: Mentor

"
Indeed, I do not understand your analogy, which is why I asked the question. Maybe "conscious" was not the right word, what about "cognitive" or "intelligent"? My point is that an animal will see or smell the food. Comparing the interaction of particles in a gas and a tiger with meat is, if not completely wrong, at least unhelpful.

but you are the one who said
Please define quickly, because even in a trap of μm size, 4 atoms will not collide very frequently.

10. Apr 22, 2013

### Staff: Mentor

This thread may have started off on the wrong foot with the specification of "hot particles" and "cold particles".

Those terms are only meaningful if each particle has a large number of internal states, and this is neither what most people mean by the word "particle" nor consistent with the way that we're characterizing the state of the box just by the positions of the particles.