Exploring Entropy and Chaos Theory: Insights from My Chemistry Teacher

[alias25]

my chemistry teacher was talking about how strange it is that the general law of entropy is that any system over time becomes more disordered however the universe seems to be becoming more orderly from the big bang, but then I am thinking does't a chemical reaction go through a similar route, when 2 reactants are in transition state...theyre in like a state of disorder and usually the products formed are more stable and ordered, and I am thinking prephaps the universe is becoming more stable?
also i heard that the 'arrow of time' flows in the direction of increasing entropy, so if our universe is becoming more orderly doesn't that suggest that the 'arrow of time' is flowing backwards. I am really interested in learning more.
I'd appreciate any clarification and suggested websites that include
entropy
chaos theory
anything you think maybe related and helpful.

thanks!
btw I am a second year 6th form student, not too complicated websites please :)

 

[Libertine]

How does the universe seem to be becoming more orderly since the Big Bang?

 

[gulsen]

How do you know there's something such as "Big Bang"?

 

[alias25]

well hmm thinking about it of the universe came from a singularity, where everything was confined it probably is more ordered than all matter and energy just being scattered everywhere, although its not just everywhere is it they seem to be localised in galaxies and clusters etc
big clarification needed here...what exactly is disorder/order how would u define, is it just a visual/spatial thing? involving notable patterns in a system? and how can u measure it?

 

[ptabor]

Your chemistry teacher has somewhat mislead you.
Entropy, per se, is not defined as the amount of disorder in the system. Nor does the second law itself state that disorder increases.

the second law states that for an irreversible process the entropy of the universe must always increase.

Entropy itself is defined as the product of the Boltzmann constant and the natural logarithm of the multiplicity.

to understand multiplicity, consider the flipping of three coins - for which we have the following outcomes:
HHH
HHT
HTH
THH
HTT
THT
TTH
TTT
each one of these outcomes is defined as a microstate. A macrostate is when you ask how many states correspond to having only 2 Heads? HHT, THH, HTH - 3 possible ways to obtain a state with two heads. Hence, the multiplicity of state 2H is 3.

for two coins, we have:
HH
HT
TH
TT
here the macrostate with the greatest multiplicity is 1H (or 1T) - ie there are two ways to get this macrostate. There is only 1 way to get HH and only one way to get TT - hence you would expect that given a fair coin heads would come up half the time, as would tails.

So you can see that the second law is a statement of statistics, it simply means that a) multiplicity tends to increase in any irreversible process, and b) a system in equilibrium will tend to be found in the state with the highest multiplicity. This last statement is verified by your ordinary experience: when you leave out a cup of coffee, it tends to transfer heat to the air until it reaches equilibrium.

This is the reason you do not suffocate sitting in your chair. In equilibrium, the air molecules tend to be more or less uniformly distributed throughout the volume of the room. They could be all in one corner, but this state has a very low multiplicity and hence we do not observe it.

What does this imply? This implies that, among other things, the total amount of work available in any system will tend toward zero (ie energy is dissipated as heat in any process).

At this point you can probably see the flaw in your teacher's question. As stars radiate away energy, a portion of this is irretrievably lost (for instance, sunight warms the sidewalk, which then radiates this heat at night back into the atomsphere) - the entropy of the universe increases.
Thus, the evolution of the universe serves to increase the total entropy - there is no violation of the second law.

 

[alias25]

o wow thanks! seems so easy when u read, hard to think up something like that, wanns see what my chemistry teacher's face would look like when i tell him that, lol. He's one of those people who doesn'y like being wrong.

 

[Azael]

If you have a box filled with atoms the entropy might very well increase if the atoms form molecules. The molecules is more ordered, but energy is released in the process of bonding and that energy release increase the systems total entropy more than the bonding of the atoms decrease it.

Its the same with stars and galaxies as ptabor say.

 

[alias25]

what about endothermic reactions that energy is taken in from surroundings to form products that are usually less stable...are they more ordered then? what if it was an irrevesible reaction then its entropy actually decreased there? or can it be revesible because it's entropy decreased? so any system that undergoes decrease in entropy has! to be reversible?
sorry for any stupid questions
hang on isn't every process irrevesible because time flows in one direction...u could never go back to exact conditions etc so entropy is always increasing no matter what? full stop?

 

[Azael]

You can decrease the entropy in one system by using energy from another system. But the total entropy of both system always increase(or stay constant).

I can't answere if a system that gets decreased in entropy is reversible or not.

But think of diamond and graphite. If you have a system consisting of graphite you can make it into diamond by some process unknown to me(pressure??, heat??). After you have made the diamond close the system. The diamond will be stable forever(as far as I know) even though the entropy of the system would be higher if the diamond turned back to graphite.

A systems entropy always increase or stay constant. But the entropy doesn't always have to be maximised(atelast not during our lifetime) depending on the configuration of the system.

I don't know if that was the answere to your question though...

Entropy is just defined as Ln(g) where g is the multiplicity(number of possible quantum states). A system always strives toward the configuration that maximises the amount of possible quantum states. You can do a lot of neat tricks and calculations with that. But that's all entropy is.