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Macrostates and Microstates : The difference between macrostates and microstates. Thermodynamic equilibrium.
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- SAL: I've done a bunch of videos where I use words like
- pressure and-- let me write these down-- pressure and
- temperature and volume.
- And I've done them in the chemistry and physics
- playlist. Especially the physics playlist, but even in
- the chemistry playlist, I also use words like kinetic energy.
- I'll just write e for energy.
- Or I use force and velocity.
- And you know, a whole bunch of other types of, I guess,
- properties of things, for better or for worse.
- And in this video what I want to do is I want to make a
- distinction.
- Because it becomes important when we start getting a little
- bit more precise, especially when we get more precise in
- thermodynamics, or, I guess, you know, the study of how
- heat moves around.
- So these properties right here, these are
- properties of a system.
- Or we could call them macrostates of a system.
- And these could be macrostates.
- So for example, let me make it clear, when I call a system,
- if I have some balloon like this, and it has a little tie
- there and, you know, maybe it has a string.
- This has these macrostates associated with it.
- There is some pressure in that balloon.
- Remember that's force per area.
- There is some temperature for that balloon.
- And there's some volume to the balloon, obviously.
- But all of these, these help us relate what's going on
- inside that balloon, or what that balloon is doing in kind
- of an every day reality.
- Before people even knew about what an atom was, or maybe
- they thought that there might be such an atom but they had
- never proved it, they were dealing with these
- macrostates.
- They could measure pressure, they could measure
- temperature, they could measure volume.
- Now we know that that pressure is due to things like, you
- have a bunch of atoms bumping around.
- And let's say that this is a gas-- it's a balloon- it's
- going to be a gas.
- And we know that the pressure is actually caused-- and I've
- done several, I think I did the same video in both the
- chemistry and the physics playlist. I did them a year
- apart, so you can see if my thinking has evolved at all.
- But we know that the pressure's really due by the
- bumps of these particles as they bump into the walls and
- the side of the balloon.
- And we have so many particles at any given point of time,
- some of them are bumping into the wall the balloon, and
- that's what's essentially keeping the balloon pushed
- outward, giving it its pressure and its volume.
- We've talked about temperature, as essentially
- the average kinetic energy of these-- which is a function of
- these particles, which could be either the molecules of
- gas, or if it's an ideal gas, it could be just the
- atoms of the gas.
- Maybe it's atoms of helium or neon, or something like that.
- And all of these things, these describe the microstates.
- So for example, I could describe what's going on with
- the balloon.
- I could say, hey, you know, there are-- I could just make
- up some numbers.
- The pressure is five newtons per meters squared, or some
- number of pascals.
- The units aren't what's important.
- In this video I really just want to make the
- differentiation between these two ways of describing
- what's going on.
- I could say the temperature is 300 kelvin.
- I could say that the volume is, I don't know,
- maybe it's one liter.
- And I've described a system, but I've described in on a
- macro level.
- Now I could get a lot more precise, especially now that
- we know that things like atoms and molecules exist. What I
- could do, is I could essentially label every one of
- these molecules, or let's say atoms, in the gas that's
- contained in the balloon.
- And I could say, at exactly this moment in time, I could
- say at time equals 0, atom 1 has-- its momentum is equal to
- x, and its position, in three-dimensional coordinates,
- is x, y, and z.
- And then I could say, atom number 2-- its momentum-- I'm
- just using rho for momentum-- it's equal to y.
- And its position is a, b, c.
- And I could list every atom in this molecule.
- Obviously we're dealing with a huge number of atoms, on the
- order of 10 to the 20 something.
- So it's a massive list I would have to give you, but I could
- literally give you the state of every atom in this balloon.
- And then if I did that, I would be giving you the
- microstates.
- Or I would give you a specific microstate of the
- balloon at this time.
- Now when a system-- and I'm going to introduce a word
- here, because this word is important, especially as we
- go-- is in thermodynamic equilibrium.
- So let me write that down.
- Equilibrium.
- We learned about equilibrium from the
- chemistry point of view.
- And that tells you, that the amount of something going into
- forward reaction is equivalent to the amount going in the
- reverse reaction.
- And when we talk about macrostates, thermodynamic
- equilibrium essentially says that the
- macrostate is defined.
- That they're not changing.
- If this balloon is in equilibrium, at time 1 its
- pressure, temperature, and volume will be these things.
- And if we look at it a second later, its pressure,
- temperature, and volume will also be these things.
- It's in equilibrium.
- None of the macrostates have changed.
- And actually, I'll talk about in a second, in order for
- these macrostates to even be defined, to be well defined,
- you have to be in equilibrium.
- I'll talk about that in a second.
- Now, at second number, at time equals 0, you might have this
- whole set of-- I went and I listed 10 to the
- 20th-something microstates of all the different atoms in
- this molecule.
- But then if I look at these gases a second later, I'm
- going to have a completely different microstate right?
- Because all of these guys are going to have bumped into each
- other, and given each other their momentum.
- And all sorts of crazy things could have happened in a
- second here, so I would have a completely different
- microstate.
- So even though we're at thermodynamic equilibrium, and
- our macrostate stayed the same, our microstates are
- changing every gazillionth of a second.
- They're constantly changing.
- And that's why, for the most part, in thermodynamic, we
- tend to deal with these macrostates.
- And actually most of thermodynamics, or at least
- most of what you'll learn in a first-year chemistry or
- physics course, it was devised or it was thought about well
- before people even had a sense of what was going on at the
- macro level.
- That's often a very important thing to think about.
- And we'll go into concepts like entropy and internal
- energy, and things like that.
- And you can rack your brain, how does it relate to atoms?
- And we will relate them to atoms and molecules.
- But it's useful to think that the people who first came up
- with these concepts came up with them not really being
- sure of what was going on at the micro level.
- They were just measuring everything at the macro level.
- Now I want to go back to this idea here, of equilibrium.
- Because in order for these macrostates to be defined, the
- system has to be in equilibrium.
- And let me explain what that means.
- If I were to take a cylinder.
- And we will be using this cylinder a lot, so it's good
- to get used to this cylinder.
- And it's got a piston in it.
- And that's just, it's kind of the roof of the cylinder can
- move up and down.
- This is the roof of the cylinder.
- The cylinder's bigger, but let's say this is a, kind of a
- roof of the cylinder.
- And we can move this up and down.
- And essentially we'll just be changing the volume of the
- cylinder, right?
- I could have drawn it this way.
- I could have drawn it like a cylinder.
- I could have drawn it like this, and then I could have
- drawn the piston like this.
- So there's some depth here that I'm not showing.
- We're just looking at the cylinder front on.
- And so, at any point in time, let's say the gas is between
- the cylinder and the floor of our container.
- You know, we have a bunch of molecules of gas here, a huge
- number of molecules.
- And let's say that we have a rock on the cylinder.
- We're doing this in space so everything above
- the piston is a vacuum.
- Actually just let me erase everything above.
- Let me just erase this stuff, just so you see.
- We're doing this in space and we're doing it in a vacuum.
- Just let me write that down.
- So all of this stuff up here is a vacuum, which essentially
- says there's nothing there.
- There's no pressure from here, there's no particles here,
- just empty space.
- And in order to keep this-- we know already, we've studied it
- multiple times, that this gas is generating, you know things
- are bumping into the wall, the floor of this
- piston all the time.
- They're bumping into everything, right?
- We know that's continuously happening.
- So we would apply some pressure to offset the
- pressure being generated by the gas.
- Otherwise the piston would just expand.
- It would just move up and the whole gas would expand.
- So let's just say we stick a big rock or a big weight on
- top of-- let me do it in a different color-- We put a big
- weight on top of this piston, where the force-- completely
- offsets the force being applied by the gas.
- And obviously this is some force over some area-- right,
- the area of the piston-- over some areas so that we could
- figure out its pressure.
- And that pressure will completely offset the pressure
- of the gas.
- But the pressure of the gas, just as a reminder, is going
- in every direction.
- The pressure on this plate is the same as the pressure on
- that side, or on that side, or on the bottom of the container
- that we're dealing with.
- Now let's say that we were to just evaporate this-- well
- let's not say that we evaporate the rock.
- Let's say that we just evaporate half of the rock
- immediately.
- So all of a sudden our weight that's being pushed down, or
- the force that's being pushed down just goes to half
- immediately.
- Let me draw that.
- So I have-- maybe I would be better off just cut and
- pasting this right here.
- So if I copy and paste it.
- So now I'm going to evaporate half of that rock magically.
- So let me take my eraser tool.
- And I just evaporate half of it.
- And now what's going to happen?
- Well, this piston is now applying half the force.
- It can't offset the pressure due to this gas.
- So this whole thing is going to be pushed upwards.
- But I did it so fast. I did it so fast. And you could try it.
- I mean, this would be truth of a lot of things.
- If you had a weight hanging from a spring, and you would
- just remove half the weight, it wouldn't just go very, you
- know, nice and smoothly to another state.
- What's going to happen is-- and let me see if I can do
- this using their cut and paste tool-- it'll essentially,
- right when I evaporate half of it, the gas is going to expand
- a bunch, and then this weight is going to come back down,
- it's going to spring and go down.
- So let me do it again.
- It's going to expand, because that gas is going to push up,
- and then it's going to come back down.
- And then, it's just going to oscillate a little bit.
- And then eventually it'll come back to some stable and maybe
- it'll go back.
- It'll look, like right about there.
- And let me fill this in.
- This shouldn't be white, it should be black.
- Let me put some walls on it, on the container.
- So if we wait long enough, eventually we'll get to
- another equilibrium state, where this thing, the piston
- on top isn't, or the ceiling isn't moving anymore.
- And now the gas has filled this container.
- Now, at this point in time we were in equilibrium.
- The pressure throughout the gas was the same.
- The temperature throughout the gas was the same.
- The volume was in a stable situation.
- It wasn't changing from second to second.
- So because of that, our macrostates were well defined.
- Now, when we wait long enough, this thing will get to some
- stability where this thing stops moving.
- When this thing stops moving our volume stops changing.
- And hopefully our pressure will start to become uniform
- throughout the container.
- And our temperature will become uniform.
- And we'll now be a higher volume or lower pressure,
- probably a lower temperature if we assume that there's no
- other heat being added to the system.
- And then we'll be well defined again.
- So we could say what the pressure, and the volume, and
- the temperature's going to be.
- But what about right when I removed this rock?
- And this thing flew up and it oscillated, and for a while
- the pressure at the top was lower than the
- pressure down here.
- Maybe the temperature at the top was lower than the
- temperature down here.
- The whole thing was in a state of flux.
- It was not an equilibrium.
- And at that point, when we're-- let me let me draw
- that really-- so you know, when we were in that state,
- where everything was just crazy, right when we
- evaporated the rock.
- You know, we have a little rock up here.
- Everything is going up and down.
- Maybe the pressure up here was lower than the
- pressure down here.
- Everything did not have a chance to reach an
- equilibrium.
- At this state-- and this is important, especially as we go
- into talking about things like reversible reactions, and
- reversible processes, and quasi-static processes.
- At this point in the reaction, when we just did this, none of
- these macrostates were well defined.
- You couldn't tell me what the volume of this system is,
- because it's changing for every second to second, or
- microsecond to microsecond, it's fluctuating.
- You couldn't tell me what the pressure of the system is,
- because it's changing every second.
- You couldn't tell me what the temperature is.
- Maybe the temperature could be something there.
- It could be something there.
- All sorts of crazy things are happening.
- So when the system is in a state of flux, your
- macrostates are not well defined.
- And I really want to hit that point home.
- So me just draw that in a diagram.
- Let me draw that in a PV diagram.
- And we're going to use these fairly heavily.
- So on my y-axis I'm going to put pressure.
- In my x-axis I'm going to put volume.
- So our initial state here, when we had the rock sitting
- on top of the ceiling, this movable ceiling or this
- piston, maybe we had some well-defined
- pressure and volume.
- So my y, this is pressure and this is volume.
- So this is where we started off.
- So it was well defined.
- This is state 1.
- Let me label it right there.
- Now when we evaporated half the rock, we eventually waited
- long enough, and this got to an equilibrium.
- We got to state 2, and our pressure volume and out
- temperature was well defined.
- And I'll just put it on this pressure volume.
- So maybe this is state 2.
- We got down here.
- And just as an aside, I could maybe put temperature as an
- extra dimension, but temperature is completely
- determined by pressure and volume, especially if we're
- dealing with an ideal gas.
- Remember, and we did this in multiple videos, you have PV
- is equal to nRT.
- These are constants.
- The number of moles isn't changing.
- This is the universal gas constant, not changing.
- So if you know P and V you know T.
- So that's the only two things we have to plot.
- But I'll talk a lot more about that in future videos.
- But the important thing to realize is, I started off at
- this state, where pressure and volume were well defined.
- I finished in this state, where pressure and volume were
- well defined.
- But how did I get there?
- And because this reaction I did, all of a sudden it
- happened super fast, and it was essentially thrown out of
- equilibrium.
- I don't know how I got here.
- The pressure and volume were not well defined from going
- from that state to this state.
- Pressure, volume, and temperature are only well
- defined if every intermediate step is still almost in
- equilibrium.
- And we'll talk a lot more about that in the next video.
- But I want to really make this point home.
- It would be nice if we could draw some path.
- We could say, we moved from some pressure and volume to
- some other pressure and volume, and we moved along a
- well-defined path.
- But we cannot say that.
- Because when we went from there there, our definitions
- just disappeared for pressure and volume.
- We cannot define those macrostates in these
- intermediate non-equilibrium states.
- Now, just as a little aside, we could have defined the
- microstates.
- The microstates never change.
- At any given snapshot in time, I could have listed every
- particle that's in this thing.
- And I could have given you its kinetic energy.
- I could have given you its position.
- I could have given you its momentum.
- And there's no reason why I couldn't have done that.
- So I could have actually made a plot of
- one particular particle.
- And I could have said what its kinetic energy, and over a
- course of time, is at any given moment in time.
- And this is really important.
- So microstates are always well defined.
- The microstate is what's exactly happening to the atom
- in terms of its force and its velocity and its momentum.
- While macrostates are only defined, I should say well
- defined, when the system-- in this case it's the balloon, in
- this case it's this piston on top of this cylinder, this
- movable ceiling-- the macrostates are only well
- defined when the system is in equilibrium, or when you can
- essentially say, the pressure is x, the pressure is the same
- throughout.
- Or the volume isn't changing from moment to moment.
- Or the temperature is the same thing throughout.
- Anyway, I'll leave you there and we'll talk more about why
- I went through all this pain in the next video.