Macrostates and Microstates

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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.