Main content
Physics library
Course: Physics library > Unit 10
Lesson 3: Laws of thermodynamics- Macrostates and microstates
- Quasistatic and reversible processes
- First law of thermodynamics / internal energy
- More on internal energy
- What is the first law of thermodynamics?
- Work from expansion
- PV-diagrams and expansion work
- What are PV diagrams?
- Proof: U = (3/2)PV or U = (3/2)nRT
- Work done by isothermic process
- Carnot cycle and Carnot engine
- Proof: Volume ratios in a Carnot cycle
- Proof: S (or entropy) is a valid state variable
- Thermodynamic entropy definition clarification
- Reconciling thermodynamic and state definitions of entropy
- Entropy intuition
- Maxwell's demon
- More on entropy
- Efficiency of a Carnot engine
- Carnot efficiency 2: Reversing the cycle
- Carnot efficiency 3: Proving that it is the most efficient
© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice
Macrostates and microstates
In physics, a microstate is defined as the arrangement of each molecule in the system at a single instant. A macrostate is defined by the macroscopic properties of the system, such as temperature, pressure, volume, etc. For each macrostate, there are many microstates which result in the same macrostate. Created by Sal Khan.
Want to join the conversation?
- At, sal said at the Micro state is changing gazillion of a second but at last few minutes sal said "Micro state never changes , I don't get it , please tell me if I am missing something . 6:35(52 votes)
- He means microstate is defined every instant, not that it doesn't change. On the other hand, we cannot talk about macrostate in every instant since it's not well defined.(76 votes)
- At, why does the piston oscillates when the rock's mass is halved? 11:44
Thanks. :)(32 votes)- If you're asking why it goes through a bit of harmonic motion (oscillation), it's because the top has momentum after it is pushed up by the pressure of the gas so that when gravity takes over it is a little above the level that it reaches equilibrium. Then gravity brings it down and gives it momentum so that it is a little below the equilibrium level and the gas pressure takes over again. This process of oscillation continues until damping allows the piston to reach equilibrium.(55 votes)
- At about, in discussing microstates, Sal says that we can know the position and the momentum. I thought that, because of the uncertainty principle, we can never know both the position and the momentum of any given particle. Is he just simplifying things so that we understand the difference between microstates and macrostates, or am I missing something? 4:30
Thanks.(29 votes)- According to the Heisenberg Uncertainty Principle, you cant know both the location and momentum of a particle so you are correct. I believe it is a simplification.(14 votes)
- what sal had told at, an ideal gas is always single atomic molecule gas? 2:56(8 votes)
- An ideal gas is modelled as a monatomic gas.(15 votes)
- why do we express temperature in Kelvin?,why not in degree celsius?(3 votes)
- Temperatures like Celsius have an arbitrary placement of 0. 0 degrees C was decided to be the freezing point of pure water and 100 is the boiling point of water at standard pressure. The Kelvin scale has 0 set to be the lowest possible temperature. Since temperature is basically the average random kinetic energy by placing the base of the scale at 0 then you have a direct relation between this random kinetic energy and temperature.(21 votes)
- The product of the pressure and volume is equal to the product of the pressure and volume in the second case, right ? Thanks ! :)(9 votes)
- NO:). Its a constant as long as the temperature is constant. But in this case its doing some work (against the rock though its in space and i dont know how it affects the system). That implies that it's going lose some energy beacuse there's nothing else that is going to help the gas. This in turn means that the temperature of the gas drops. If the temperature drops, then the product of pressure and the volume becomes something else. I hope I've been coherent:)(11 votes)
- When Sal says he's using rho for momentum at, he means p, right? I'm pretty sure the momentum formula uses p rather than rho. 4:37(4 votes)
- The Greek alphabet and the English alphabet have similarities and differences.
Some examples:
If you look at a written or printed version of the Greek alphabet, you will see that the Greek letter "rho" looks just like the English letter "p." The only way to tell which you have is from context.
We don't have any difficulty recognizing the Greek letter "pi" because no English letter looks like it.
An upper case "Alpha" looks just like a capital "A," but a lower case "alpha" does not look like a lower case "a."
Hope this helps.(14 votes)
- I'm confused as to when the equilibrium took place, was it after the rock's weight was split in half? At that moment, did all the molecules shoot upward? That too and what is ideal gas?
I'm a 7th grader working for SciOly and these parts are rather confusing. I would appreciate any help. :)(4 votes)- CRUX of the video :
1. macrostates : are the parameters which helps you quantitatively measure the properties of matter. you dont need to know much about atoms while measuring.
2. microstates : are parameters which helps in qualitative study of the properties of the material(gas) inside the cylinder which are in this case atoms / molecules.
3 Equilibrium : it is a state when everything settles means the macrostate & microstate properties do not change at different point of time.
4. the rock put on the pistin was halved . before, it was in equilibrium means pressure exerted by gas was constant . but when rock was halved the force exerted by rock also halved but pressure was contant in the gas so that means the force exerted by pressure of gas will dominate the rock force and move the pistin up. It is same as TUG of WAR game
5.ideal gas is a gas which will show behavior(macrostates) as predicted theoretically . in that case no friction air resistance an other external forces are considered. but it fails on earth to show the predicted values so on earth its called real gases.(11 votes)
- could u please elaborate on "When the atoms are all in equilibrium with the same microstates, then the macrostate becomes constant. That is what gives us a measurable, stable volume."(5 votes)
- That is not completely true, as there is no way to keep the "same microstates" as they are constantly changing. In this micro world, everything is "on average", so a stable and measurable macrostate means a "stable average of the microstates". In a stable macrostate, a single atom can experience drastic variations of its kinetic energy, but the average kinetic energy will be constant (until a certain level of precision).(9 votes)
- what is the meaning of thermal contact?(4 votes)
- a thermal contact is established when the transfer of heat can take place from one body to another(7 votes)
Video transcript
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.