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SAL: In the last video, where
we talked about macrostates,

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we set up this situation where
I had this canister, or the

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cylinder, and had this
movable ceiling.

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I call that a piston.

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And the piston is being kept
up by the pressure from the

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gas in the canister.

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And it's being kept down by, in
the last example I had, a

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rock or a weight on top.

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And above that I had a vacuum.

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So essentially there's some
force per area, or pressure,

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being applied by the
bumps of the

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particles into this piston.

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And if this weight wasn't here--
let's assume that the

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piston itself or this movable
ceiling itself, it has no

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mass-- if that weight wasn't
there it would just be pushed

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indefinitely far, because
there'd be no pressure from

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the vacuum.

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But this weight is applying
some force on

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that same area downwards.

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So we're at some equilibrium
point, some stability.

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And we plotted that on this
PV diagram right here.

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I'll do it in magenta.

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So that's our state 1 that
we were in right there.

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And then what I did in the last
video, I just blew away

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half of this block.

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And as soon as I blew away half
of this block, obviously

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the force that's being applied
by the block will immediately

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go down by half, and so the
gas will push up on it.

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And it happened so fast that,
al of a sudden the gas is

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pushing up.

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Right when it happens, the gas
near the top of the canister

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is going to have lower pressure,
because it has less

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pushing up against it.

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The molecules that are down here
don't even know that I

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blew away this block yet.

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It's going to take some time.

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And essentially the gas is going
to push it up, and then

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maybe it'll oscillate down,
and then push it up, and

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oscillate down a little bit.

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It'll take some time eventually
until we get to

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another equilibrium state, where
we have a new, probably,

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or definitely lower pressure.

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We definitely have
a higher volume.

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I won't talk too much about it
yet, but we probably have a

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lower temperature as well.

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And this is our new state.

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And our macrostate's pressure
and volume are defined once

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we're at the new equilibrium,
so we're right here.

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So my question in the
last video was,

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how did we get here?

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Is there any way to have defined
a path to get from our

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first state-- where pressure and
volume were well defined,

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because the system wasn't
thermodynamic equilibrium-- to

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get to our second state?

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And the answer was no.

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Because between this state
and this state

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all hell broke loose.

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I had different temperatures
at different

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points in the system.

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I could have had a different
pressure here

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than I had up here.

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The volume might have
been fluctuating

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from moment to moment.

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So when you're outside of
equilibrium-- and I had

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written it down over there--
you cannot define, or you

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can't say that those macro
variables are well defined.

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So there was no path that you
could say how we got from--

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erase this-- how we got from
state 1 to state 2.

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You could just say, OK, we
were in some type of

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equilibrium.

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So we were in state 1.

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Then I blew away
half the rock.

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The pressure went down,
the volume went up.

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The temperature also
probably went down.

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And so I ended up in this other
state once I reached

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equilibrium.

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And that's all fair and good,
but wouldn't it have been nice

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if there was some way?

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If we could have said, look,
you know, there's some way

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that we got from this
point to this point?

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If we could perform my little
rock experiment in a slightly

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different manner, so that all
this hell didn't break loose,

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so that maybe at every point in
between my macro variables

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are actually defined?

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So how could I do that?

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Remember, I said that the
macro variables, the

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macrostates, whether it's
pressure, temperature, volume,

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and there are others, but I said
these are only defined

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when we are in a thermodynamic
equilibrium.

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And that just means that
things have reached a

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stability point.

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That, for example, the
temperature is consistent

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throughout the system.

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If it's not consistent
throughout the system, I

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shouldn't be talking about it.

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If the temperature is different
here than it is up

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here, I shouldn't say that
the temperature of

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the system is x.

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It's different at different
points.

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I really can't make a
well-defined statement about

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temperature, similar for
pressure or for volume,

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because the volume is
also fluctuating.

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But what if I perform that
same experiment?

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That same process,
I should call it.

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Let me draw it again.

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So I have my canister.

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And instead of starting with a
rock, just one big rock-- let

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me draw, this is my piston right
here, at the top of the

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movable ceiling of
the cylinder.

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And I have some gas
inside of it.

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Instead of having just one big
rock like I had over here, how

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about I start with an equal
weight of rock?

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But let's say I have a bunch of
small pebbles that add up

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to that same rock.

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So just a bunch of, well, you
know, just a pile of pebbles.

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You know, maybe they're sand.

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They're super duper small.

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Instead of just blowing away
half of the sand all at once,

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like I did with that rock over
there, and immediately jumping

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to that state and throwing the
whole system into this

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undefined state of
non-equilibrium.

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Instead of doing that, let me
just do things very slowly and

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very gently.

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Let me just take out one grain
of sand at a time.

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So if I just take out
one grain of sand.

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And so I took out an

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infinitesimal amount of weight.

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So what's going to happen?

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Well this piston's going to
move up a little bit.

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And let me draw that.

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So let me copy and paste it.

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So I just took out one
little piece of sand.

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The force pushing down will
be a little bit less.

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The pressure pushing down
will be a little less.

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And so my piston-- let me see
if I can draw this-- it will

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have moved up-- let me erase
it-- it will have moved up a

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very infinitesimal--
infinitesimal means an

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infinitely small amount-- it
would have moved an infinitely

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small amount of time.

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And so you wouldn't have thrown
that system into this,

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you know, havoc that I
did this last time.

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Of course, we haven't moved
all the way here yet.

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But what we have done is, we
would have moved from that

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point maybe to this other point
right here that's just a

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little bit closer to there.

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I've just removed a little
bit of the weight.

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So my pressure went down
just a little bit.

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And my volume went up
a just a little bit.

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Temperature probably
went down.

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And the key here is I'm trying
to do it in such small

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increments that as I do it, my
system is pretty much super

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close to equilibrium.

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I'm just doing it just slow
enough that at every step it

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achieves equilibrium
almost immediately.

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Or it's almost in equilibrium
the whole time I'm doing it.

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And then I do it again,
and do it again.

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And I'll just draw my drawings
a little less neat, just for

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the sake of time.

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Let's say I remove another
little dot of sand that's

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infinitely small mass.

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And now my little piston will
move just a little bit higher.

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And I have, remember I have one
less sand up here than I

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had over here.

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And then my volume in my gas
increases a little bit.

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My pressure goes down
a little bit.

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And I've moved to
this point here.

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What I'm doing here is I'm
setting up what's called a

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quasi-static process.

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And the reason why it's
called that is

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because it's almost static.

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It's almost in equilibrium
the whole time.

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Every time I move a grain of
sand I'm just moving a little

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bit closer.

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And obviously even a grain of
sand, the reality is if I were

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to do this in real life, even
a grain of sand on a small

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scale is going to reek
a little bit

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of havoc on my system.

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This piston is going to
go up a little bit.

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So say, let me just do even a
smaller grain of sand, and do

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it even a little bit slower
so that I'm always in

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equilibrium.

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So you can imagine this is kind
of a theoretical thing.

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If I did an infinitely small
grains of sand, and did it

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just slow enough so that it's
just gently moved from this

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point to this point.

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But we like to think of it
theoretically, because it

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allows us to describe a path.

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Because remember, why am I
being so careful here?

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Why am I so careful to make
sure that the state, the

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system is in equilibrium the
whole time when I get from

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there to there?

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Because our macrostates, our
macro variables like pressure,

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volume, and temperature, our
only defined when we're in

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equilibrium.

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So if I do this process super
slowly, in super small

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increments, it allows me to keep
my pressure and volume

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and actually my temperature
of macrostates at

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any point in time.

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So I could actually
plot a path.

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So if I keep doing it small,
small, small, I could actually

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plot a path to say, how did I
get from state 1 to state 2 on

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this on this PV diagram.

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And you might say, hey, you
know, Sal, this is all-- And

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I'll take a little
step back here.

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I always found this
really confusing.

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You know, you'll see a lot of
talk in thermodynamic circles,

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or even in your book about--
it has to be a quasi-static

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process, and I always used to
wonder, why are people going

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through these pains to describe
this process where

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you're removing sand
after sand?

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And the whole point is because
you want to get as close to

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equilibrium the whole time
you're doing it as possible so

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that your pressure and volume
are defined the whole time.

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The reality is, in the real
world you can never get

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something that's continuously
defined, but you can just do

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really, really, really
small increments.

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So that at each small increment
you're at some

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equilibrium.

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And if you're not happy with
that, you can do even smaller

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increments.

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So at some point, at some
limiting point, you do have

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some type of continuous state
change, while you're always in

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equilibrium.

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It's almost an oxymoron, because
you're saying you're

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static, you're saying that
you're in equilibrium the

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whole time, but clearly you're
also changing the whole time.

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You keep removing little
pieces of sand.

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But you're moving them just
slowly enough that all that

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crazy up and down motion, and
all of the flux, and all of

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the weird temperature changes
don't happen.

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And it just, you know, just
that it slowly, slowly,

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slowly creeps up.

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The reason why I'm even going
through this exercise is

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because it's key when we start
talking about thermodynamics

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and these PV diagrams, and
we'll start talking about

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carnot engines and all of that,
that we be able to at

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least theoretically describe the
path that we take on this

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PV diagram.

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And we wouldn't have been able
to do that if we can't assume

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that we're dealing with a
quasi-static process.

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Now there's another term that
you'll hear in thermodynamic

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circles that really, I mean, to
me it really, I don't know,

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I had trouble comprehending it
the first time I heard it,

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called reversible.

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And sometimes these terms
quasi-static and reversible

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are used interchangeably, but
there is a difference.

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Reversible processes are
quasi-static, and most

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quasi-static processes are
reversible, but there are a

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few special cases that aren't.

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But the idea of a reversible
process is something that

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happens so slowly.

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So in this example I took off
a grain of sand and I got to

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the state, but if I assume that
no friction when, you

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know, when this piston moved up
a little bit, in the real

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world, let's say if this piston
was metal, when this

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rubs against the canister,
there'd be a little bit of

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friction generated and a little
bit of energy would be

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dissipated as friction
or heat.

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But in a reversible process,
we're assuming that, look,

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this is frictionless.

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When anything happens in the
system, when we go from this

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state right here-- let's
say this the state a,

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this is state b.

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So this is state a,
this is state b.

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When we go from this state
to this state, one, we're

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infinitesimally close to
equilibrium the whole time, so

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all of our macrostates
are well defined.

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And even more, when we move from
one state to the other,

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there's no loss or dissipation
of energy.

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So those are two important
characteristics.

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One, infinitely close to
equilibrium at all times, and

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no loss of energy.

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And the reason why that matters
for a reversible

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process is because if we wanted,
if we were sitting in

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state b, we could just add
another grain of sand back in,

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push down this piston infinitely
slowly, at an

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infinitely small increment,
and get back to state a.

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So that's why it's called
reversible.

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You could be at this point right
here, and take out a

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little bit of sand, and get
to this point right here.

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But if you want, since no energy
was lost, you could add

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a little bit of sand, and get
back to this point right here.

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Now the reality in the real
world is, there is no such

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thing as a perfectly
reversible process.

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There will always be, whenever
you do anything, there will

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always be some energy or heat
lost to the process.

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In the real world, if I moved
down here, if I tried to put

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the sand back I would lose some
energy and probably get

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to a little slightly
different point.

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But you don't have to
worry about that.

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The important takeaway from
this video is that, in the

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situation I described there,
there was no intermediate

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macrostate variables, because
our system was in flux, it

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wasn't in equilibrium.

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So if we wanted to get
intermediate states, we just

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have to essentially do
this process slower.

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And so slow, I mean, it
theoretically would take you

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forever, so we can only
approximate it.

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But the sand gives you an idea
of what we're talking about.

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And if we did it slowly with
these infinitesimally small

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particles of sand, then we can
define the state at every

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point along the process.

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And that's why we call it
quasi-static, because at any

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point it's almost static.

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It's almost in equilibrium.

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So our pressures, volumes, and
temperatures can be defined.

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And if we add to that the notion
that we haven't lost

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00:13:51,890 --> 00:13:55,510
any heat when we're going in one
direction or another, we

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00:13:55,510 --> 00:13:57,420
could say it's reversible,
because if we took a piece of

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00:13:57,420 --> 00:14:02,050
sand away, we can always add
a little bit of sand next.

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00:14:02,050 --> 00:14:04,280
Now, actually, with that said,
let me give you the one

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00:14:04,280 --> 00:14:07,440
example of maybe a
quasi-static-- no, actually

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00:14:07,440 --> 00:14:08,910
I'll save that for
future video.

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00:14:08,910 --> 00:14:11,370
Anyway, hopefully you understand
that these are two

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00:14:11,370 --> 00:14:14,560
concepts that used to really
confuse me, and hopefully this

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00:14:14,560 --> 00:14:15,670
clears it up a little bit.

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00:14:15,670 --> 00:14:18,180
And I think more than what it
is, I think the first time I

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00:14:18,180 --> 00:14:20,210
read about them I'm like, OK,
well what's the big deal?

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00:14:20,210 --> 00:14:25,130
The big deal is, it allows you
to define your macrostates for

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00:14:25,130 --> 00:14:27,770
every state in between
these two states

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00:14:27,770 --> 00:14:28,540
that you care about.

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00:14:28,540 --> 00:14:30,880
When you just did it as
a regular kind of

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00:14:30,880 --> 00:14:34,040
non-quasi-static process,
in between you

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00:14:34,040 --> 00:14:35,980
don't know what happened.

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