h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Actually, I have a question.

Why do things diffuse? I know that diffusion is things moving from where they are more concentrated to where they are less concentrated, and the explanation is that they "want" to spread themselves out. Why do they do this?

Imagine a football crowd - 2000 Man U supporters (red), and 200 Man City supporters (blue). Fence them all in on a football pitch. Put all the City supporters in the six yard box at one end, all together.

People being people, you'll observe 2 effects.

1. Most people will stay standing more or less where they are, and won't randomly bump into other people.

2. The City supporters will tend to stay together, because they are able to think about things. They really do WANT to stay together - there is a definite will involved.

Now contrast that with the behaviour of atoms. Atoms:

1. Assuming they're in a gas phase, jiggle about randomly and bump into each other randomly all the time and DON'T MIND.
2. Don't have any particular attachment to other atoms like themselves, at least when they're in the form of a gas. They don't WANT to do anything in particular.

So to more accurately model atoms you must change how your footie fans behave.

1. Blindfold them - they mustn't know where they are or who they're next to.
2. Put them all in those big comedy inflatable sumo suits so they can't hurt each other and bounce off each other entertainingly.
3. Tell them each to take one step in any random direction they choose, once per minute.

Now - put all your City fans in one corner together. How long do you think it will take for them to be more or less evenly spread across the pitch? Maybe an hour? Maybe, a day? But it will happen. And it depends on how often they all take a step. If they take a step once per minute, it'll take quite a while. If they take a step once per SECOND, it'll happen much quicker. How often they take a step - how "jiggly" they are - is analogous to the temperature of the gas they represent.

The crucial thing is, they won't end up evenly spread out because they WANT to be - volition has nothing to do with it at all.

They won't even KNOW they're evenly spread - they're blindfolded remember. But it will happen, just be the application of the very, very simple rules, i.e. "move randomly, don't look round, bounce off things you hit".



Just how spread out they are at any given time is known as the "entropy" of the system, and the second law of thermodynamics states that this will tend to a maximum.

It's important to realise, though, that this is a statistical prediction ONLY, not an immutable law like, say, conservation of momentum.

The practical upshot of that is that it's POSSIBLE, in principle, that all your City fans could, at some point in the future, end up purely by accident all standing next to one another in the centre circle. There's nothing stopping them. It's incredibly unlikely, but it's statistically possible.

It's also important to realise that while the entropy of the WHOLE system tends to a maximum, the entropy of individual bits of the system can go DOWN.

Consider - the six yard box may at time t=200 contain just 2 City fans. But purely at random, at time t=400, there might be 10 City fans in there. So the entropy of that particular bit of the pitch has gone DOWN, even though the entropy of the pitch as a whole has gone up.

Inadequately educated creationists often think that the second law of thermodynamics somehow means that things ALWAYS become more disordered, and use that as a "disproof" of evolution (without realising it's also a disproof of reproduction - dullards). What they've failed to understand is that the law applies only to CLOSED systems such as our football pitch, and only applies to the system *as a whole*. Individual bits of the system need not comply - indeed, *probably* won't comply - even if they're behaviour is entirely random.

If it's NOT random - if there's a chemical reaction happening, say, which constrains atoms to behave in specific ways, isolated areas of reduced entropy should be EXPECTED.

Hope that helps...

H.

Thanks Hoo.

The reason I used the word "want" is because it's what you get taught up to GCSE- which is where my chemistry stopped (thankfully). What I was getting at was, though the football fans are now blindfolded and comically attired, the point is that you have told them to move. I was wondering if you could tell me (in idiot- terms, it's all I can deal with at the moment) what gets the atoms to move- what, if you like, is the equivalent of someone yelling "RIGHT, ALL MOVE AROUND ONE PACE ANY DIRECTION ONCE A MINUTE. SILENCE!" to the atoms.

Is it something to do with atoms being, when y'get right down to it, these balls of energy or string or whatever the current fasion is?

Yeah, the whole "want" thing is a bit confusing, because it's difficult to let go of later. We conceptualise the world based on what we know, and the thing we know best is ourselves. So we anthropomorphise things - attribute human motivations to them, in order to understand them better. The trouble is, if you overdo it, you understand them LESS.

As for why atoms jiggle - this is one of those slightly circular definitions, which basically comes down to - jiggling about is something atoms just DO, all the time. It's one of their basic defining characteristics.

Atoms jiggle about because they contain energy. How do we know they contain energy? Because they're jiggling. Tautologous, I know. But there you are.

The measure of how much jiggling they're doing is something you use every day - temperature. Measure it in Kelvin, and it's an absolute measure of jiggling. Get a substance down to zero Kelvin, and in theory at least, all jiggling stops - that's what zero Kelvin IS, what it's defined as. (It's not actually true, but never mind.)

For solids, they just jiggle in place - jogging on the spot, because they've not the energy to do any more. Picture your fans all freezing cold and too tired to move, huddled behind a rope barrier across the half way line in nicely ordered lines. They're jumping up and down on the spot and shifting from foot to foot, but they've not got the energy to do much else.

Liquids maintain a surface, but are able to move within that surface. So feed all your fans a pie and a nice cup of Bovril, and watch as they move away from where they were standing and start to mill about, staying all the while behind the rope barrier across the half way line. You'll probably find you need to move the barrier a few yards to make a bit of extra space (most liquids are less dense than the corresponding solid - this isn't the case for water, for complex reasons...). Watch as the rope, previously static, now bends outwards as people move against it. See as individual fans move around within the whole, going where they like, within their own half. Note that there's even some "evaporation" - occasionally the odd fan will work up enough energy to jump the rope and wander off into the other half.

Note that the more pies and Bovril (energy) you give them, the more will jump the rope, until eventually, the rope might as well not be there... the crowd has "boiled", and you have...

A gas, they go where they like ANYWHERE on the pitch... every now and then one will bang against the fence. This will happen a bit at first, but the more energy (the higher the temperature), the more it happens. Things hitting the sides are what generates PRESSURE. That's what pressure IS - atoms hitting the sides of the container. The more impacts per second, the higher the pressure.

Is this all making sense?

H.

Sadly, yes.



You can expand this analogy to explain partial pressure too - the counterintuitive effect that says why you should squeeze the air out of a bottle (obviously not glass ) of lemonade to stop it going flat.

If we have a mixture of City and United fans representing lemonade and carbon dioxide the more volatile United fans - no offense - will be more likely to jump the rope, in either direction, when they encounter it than the City fans. The space 'above' the rope will be partly filled with a lot of United fans and one or two City fans. In real life (how did that creep in?) it would be filled with air too - lets say a load of shoppers from the nearby Trafford Centre.

In a full bottle of lemonade there is very little air and lots of carbon dioxide - lots of United fans and very few shoppers. The United fans can keep hopping backward and forward over the rope and an equilibrium is reached - just as many United fans hop back into the crowd than hop out - and the crowd stays fizzy. An odd shopper may hop over the rope into the crowd, indeed an odd shopper may turn out to be a United fan, but this has almost no effect on the level of United fans in the crowd.

If you increase the amount of space 'above' the rope (by pouring out some of the lemonade), although a lot of shoppers will now enter this space there is still plenty of room for the United fans; a lot of whom will be lost from the crowd until equilibrium is again reached where as many hop back into the crowd as hop out. The shoppers don't affect this process but they do give us something amusing to watch as they struggle with their carrier bags and crash into loads of United supporters.

Similarly the air in a lemonade bottle doesn't prevent the carbon dioxide diffusing out of the drink, other than the tiny amount of carbon dioxide in the air itself. Only once the equilibrium level of carbon dioxide is reached - called the partial pressure - does the drink stop losing its fizz. The more space there is for the gas to move into the more is lost before equilibrium is reached. Consequently squeezing the bottle to reduce the air space will help prevent the drink going flat.

Sorry to interfere Hoo but this is one of my favourite counterintuitivities.

F

Thanks very much. If I compress it all (I love the analogies, thanks so much), basically, the atoms jiggle, and based on the amount of jiggle energy they have, the jiggle moves them around a bit. And they sort of randomly move out.

I found it really interesting too, thanks.