PV-diagrams and expansion work

WEBVTT
Kind: captions
Language: en

00:00:00.510 --> 00:00:02.820
In the last video, we
saw that a system

00:00:02.820 --> 00:00:04.970
could do work by expanding.

00:00:04.970 --> 00:00:08.710
And in the situation we drew,
we had a situation where the

00:00:08.710 --> 00:00:09.880
ceiling was movable.

00:00:09.880 --> 00:00:14.790
We had this piston and we, like
in our process video, we

00:00:14.790 --> 00:00:15.660
had a bunch of pebbles.

00:00:15.660 --> 00:00:19.370
We removed a pebble, so the
pressure in our system, if we

00:00:19.370 --> 00:00:21.480
assume that it was just so small
that the pressure was

00:00:21.480 --> 00:00:25.600
constant, it pushed up on the
piston with some force.

00:00:25.600 --> 00:00:28.280
We figured out that that force,
since pressure is force

00:00:28.280 --> 00:00:31.865
per area, we just multiplied
pressure times the area of our

00:00:31.865 --> 00:00:35.300
piston, and we got the amount
of force we're applying.

00:00:35.300 --> 00:00:37.530
We apply that, and then we
multiply that times the

00:00:37.530 --> 00:00:40.730
distance that we push the piston
up, and then we get the

00:00:40.730 --> 00:00:42.950
amount of work that it
did by expansion, or

00:00:42.950 --> 00:00:44.310
the expansion work.

00:00:44.310 --> 00:00:45.780
We said, well, you know we could
have rewritten that.

00:00:45.780 --> 00:00:50.760
If you said pressure times our
area, times our distance, we

00:00:50.760 --> 00:00:54.440
could instead write that as
pressure, times the area,

00:00:54.440 --> 00:00:55.210
times the distance.

00:00:55.210 --> 00:00:56.780
And the area times
the distance is

00:00:56.780 --> 00:00:58.380
the change in volume.

00:00:58.380 --> 00:01:00.780
And so we came up with a neat
little formulation, that the

00:01:00.780 --> 00:01:05.260
work done by a system could be
written as the pressure times

00:01:05.260 --> 00:01:06.590
the change in volume.

00:01:06.590 --> 00:01:09.620
So in this case, I wrote the
internal energy formula, where

00:01:09.620 --> 00:01:11.400
it's the work done
by the system.

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So I did a minus, right?

00:01:13.120 --> 00:01:16.210
Because when you do work, you
are giving energy away to

00:01:16.210 --> 00:01:17.720
someone else.

00:01:17.720 --> 00:01:20.500
So in that situation,
we did a minus.

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And so instead of writing work,
we could say, minus the

00:01:22.940 --> 00:01:25.370
pressure, times the
change in volume.

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And remember this is a
quasi-static process.

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And we're doing it at very
small increments.

00:01:30.590 --> 00:01:33.190
We're assuming that this change
in volume is very

00:01:33.190 --> 00:01:37.010
small, and that the pressure
is roughly constant while

00:01:37.010 --> 00:01:37.840
we're doing this.

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And of course that's not
the case, right?

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If we did this, if this was a
large change in volume, or if

00:01:42.780 --> 00:01:44.910
this happened all of a sudden,
if these were really big

00:01:44.910 --> 00:01:48.090
pebbles, then our pressure
will change as we expand.

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So it's hard to say what
the pressure times the

00:01:50.540 --> 00:01:52.050
change in volume is.

00:01:52.050 --> 00:01:54.890
But if we assume things are
really, really being done in

00:01:54.890 --> 00:01:57.300
very, very small increments,
we could say, OK, let's say

00:01:57.300 --> 00:02:00.140
the pressure was constant over
that small increment, and then

00:02:00.140 --> 00:02:02.760
we can multiply it by the
change in volume.

00:02:02.760 --> 00:02:05.460
Now let's see how this can
relate to some of what we've

00:02:05.460 --> 00:02:07.980
done before with
the PV-diagram.

00:02:07.980 --> 00:02:11.900
And so far, all we've seen the
PV-diagram, or what I used it

00:02:11.900 --> 00:02:15.110
for, is to kind of help explain
the difference between

00:02:15.110 --> 00:02:18.060
quasi-static processes,
or to say when

00:02:18.060 --> 00:02:20.080
macrostates are defined.

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But let me now do something
more useful with it.

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And this will give you an idea,
or start giving you an

00:02:25.120 --> 00:02:28.870
idea of why people who
study thermodynamics

00:02:28.870 --> 00:02:30.480
love these so much.

00:02:30.480 --> 00:02:33.555
So before I did anything, when
my canister was just here, I

00:02:33.555 --> 00:02:34.510
had all the pebbles on it.

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And we were in a state
of equilibrium.

00:02:36.290 --> 00:02:39.520
I could describe all of its
macrostates, its pressure, its

00:02:39.520 --> 00:02:42.000
volume, its temperature.

00:02:42.000 --> 00:02:44.802
I could describe its internal
energy as well.

00:02:44.802 --> 00:02:46.170
So let me draw it here.

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So let's say I was
at this state.

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This was state number 1.

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State number 1 was
right there.

00:02:55.180 --> 00:02:57.150
And then, let's say I just
start removing pebbles.

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Remember, if I just remove all
the pebbles at once, the

00:03:00.370 --> 00:03:02.290
system's going to
go into flux.

00:03:02.290 --> 00:03:06.025
We wouldn't be doing a
quasi-static process, or a

00:03:06.025 --> 00:03:08.140
reversible process, which isn't
always the same thing.

00:03:08.140 --> 00:03:10.810
But for our purposes, we
wouldn't be in equilibrium the

00:03:10.810 --> 00:03:11.170
whole time.

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And we would have to wait
to get to equilibrium.

00:03:12.475 --> 00:03:15.560
And at some point we'd have
some pressure and volume

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that's down here.

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This is if we weren't doing it
as a quasi-static process.

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Now we are, what I showed in the
last video, we are doing

00:03:23.140 --> 00:03:26.640
it as a, or we're trying to get
close to a quasi-static

00:03:26.640 --> 00:03:28.410
process, because we're doing it
in small increments, with

00:03:28.410 --> 00:03:29.180
these little pebbles.

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And if these aren't small enough
for you, you could do

00:03:30.760 --> 00:03:32.320
it in smaller pebbles.

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So we're moving incrementally.

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So, for example, in that
last video, we

00:03:35.170 --> 00:03:36.380
maybe moved from there.

00:03:36.380 --> 00:03:38.950
We removed one pebble and
we got right there.

00:03:38.950 --> 00:03:40.920
You remove another pebble
and you go right there.

00:03:40.920 --> 00:03:42.880
You remove another pebble
and you go right there.

00:03:42.880 --> 00:03:45.630
And the benefit of doing these
quasi-static processes is you

00:03:45.630 --> 00:03:49.820
really get a path going from
one state to the next.

00:03:49.820 --> 00:03:53.340
Let's say when you remove all
but one of the pebbles, just,

00:03:53.340 --> 00:03:55.870
you know, this describes
our path.

00:03:55.870 --> 00:03:59.020
So let's say we are in state 2
and we've removed all but one.

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Let me draw that.

00:04:00.870 --> 00:04:03.705
So state 2 will look something
like this.

00:04:03.705 --> 00:04:06.850
I'll draw it really quick.

00:04:06.850 --> 00:04:08.900
So that's our container.

00:04:08.900 --> 00:04:10.070
That's our piston.

00:04:10.070 --> 00:04:12.730
We only have one pebble
left on top.

00:04:12.730 --> 00:04:17.430
And then of course we
have the gas now.

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Let me write this down.

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This is state 2.

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And let me write state 1 was
something like this.

00:04:23.860 --> 00:04:26.600
State 1, the ceiling
was lower.

00:04:26.600 --> 00:04:28.570
We had a bunch of pebbles
on top of it.

00:04:31.670 --> 00:04:34.400
And we had a smaller volume,
and so the gas was bumping

00:04:34.400 --> 00:04:37.750
into the ceiling and the walls
and the floor a lot more.

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I'll just draw the
same number.

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So we had a higher pressure.

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So pressure was high
and volume low.

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Now in state 2-- so this
is pressure high.

00:04:50.590 --> 00:04:52.610
This pressure is this axis.

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This is volume.

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So we had high pressure,
low volume.

00:04:55.760 --> 00:04:57.310
And we got to a situation after

00:04:57.310 --> 00:04:59.145
removing all but one pebble.

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And we're doing it slowly, so
we're always in equilibrium.

00:05:01.940 --> 00:05:02.910
So we have a path.

00:05:02.910 --> 00:05:05.660
This is after removing each of
the pebbles, so that our

00:05:05.660 --> 00:05:07.450
pressure and volume
macro states

00:05:07.450 --> 00:05:08.360
are always well defined.

00:05:08.360 --> 00:05:14.270
But in state 2, we now
have a pressure low

00:05:14.270 --> 00:05:17.150
and volume is high.

00:05:17.150 --> 00:05:19.810
The volume is high, you can just
see that, because we kept

00:05:19.810 --> 00:05:22.760
pushing the piston up slowly,
slowly, trying to maintain

00:05:22.760 --> 00:05:24.170
ourselves in equilibrium so our

00:05:24.170 --> 00:05:26.180
macrostates are always defined.

00:05:26.180 --> 00:05:28.740
And our pressure is lower just
because we could have the same

00:05:28.740 --> 00:05:30.260
number of particles, but they're
just going to bump

00:05:30.260 --> 00:05:32.640
into the walls a little bit
less, because they have a

00:05:32.640 --> 00:05:35.550
little bit more room
to move around.

00:05:35.550 --> 00:05:36.770
And that's all fair and dandy.

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So this describes the path of
our system as it transitioned

00:05:41.440 --> 00:05:45.260
or as it experienced this
process, which was a

00:05:45.260 --> 00:05:46.910
quasi-static process.

00:05:46.910 --> 00:05:48.560
Everything was defined
at every point.

00:05:48.560 --> 00:05:51.910
Now we said that the work done
at any given point by the

00:05:51.910 --> 00:05:55.760
system is the pressure times
the change in volume.

00:05:55.760 --> 00:05:57.210
Now, how does that
relate to here?

00:05:57.210 --> 00:05:58.810
Change in volume is
just a certain

00:05:58.810 --> 00:06:01.350
distance along this x-axis.

00:06:01.350 --> 00:06:03.220
Along, more like I should
call it the volume-axis.

00:06:03.220 --> 00:06:05.660
This is a change in volume.

00:06:05.660 --> 00:06:07.690
We started off at this volume,
and let's say when we removed

00:06:07.690 --> 00:06:10.260
one pebble we got
to this volume.

00:06:10.260 --> 00:06:12.390
Now, we want to multiply that
times our pressure.

00:06:12.390 --> 00:06:15.370
Since we did it over such a
small increment, and we're so

00:06:15.370 --> 00:06:17.840
close to equilibrium, we could
assume that our pressure's is

00:06:17.840 --> 00:06:20.150
roughly constant over
that period of time.

00:06:20.150 --> 00:06:21.820
So we could say that this
is the pressure over

00:06:21.820 --> 00:06:23.950
that period of time.

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And so how much work we did,
it's this pressure over here,

00:06:28.370 --> 00:06:35.820
times this volume, which is
the area of this rectangle

00:06:35.820 --> 00:06:37.030
right there.

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And for any of you all who've
seen my calculus videos, this

00:06:39.830 --> 00:06:41.490
should start looking a
little bit familiar.

00:06:44.400 --> 00:06:46.880
And then what about when we
could take our next pebble?

00:06:46.880 --> 00:06:48.950
Well now our pressure is
a little bit lower.

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This is our new pressure.

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Our pressure is a little
bit lower.

00:06:53.560 --> 00:06:57.440
And we multiply that times our
new change in volume-- times

00:06:57.440 --> 00:07:01.390
this change in volume-- and we
have that increment of work.

00:07:01.390 --> 00:07:05.040
Once again, this is the area
of this rectangle.

00:07:05.040 --> 00:07:09.440
And if you keep doing that, the
amount of work we do is

00:07:09.440 --> 00:07:13.700
essentially the area of all of
these rectangles as we remove

00:07:13.700 --> 00:07:14.670
each pebble.

00:07:14.670 --> 00:07:16.640
And now you might say,
especially those of you who

00:07:16.640 --> 00:07:19.500
haven't watched my calculus
videos, gee, you know, this

00:07:19.500 --> 00:07:22.140
might be getting close, but the
area of these rectangles

00:07:22.140 --> 00:07:25.120
isn't exactly the area
of this curve.

00:07:25.120 --> 00:07:26.010
It's a little inexact.

00:07:26.010 --> 00:07:26.970
There's a little error here.

00:07:26.970 --> 00:07:29.880
And what I would say is, well if
you're worried about that,

00:07:29.880 --> 00:07:34.630
what you should do is use
smaller increments of volume.

00:07:34.630 --> 00:07:36.730
And if you want to have smaller
changes in volume

00:07:36.730 --> 00:07:39.260
along each step, what
you do is you remove

00:07:39.260 --> 00:07:40.520
even smaller pebbles.

00:07:40.520 --> 00:07:43.790
And this goes back to trying
to get to that ideal

00:07:43.790 --> 00:07:45.900
quasi-static process.

00:07:45.900 --> 00:07:48.630
So if you did that of,
eventually the delta V's would

00:07:48.630 --> 00:07:51.430
get smaller and smaller and
smaller, and the rectangles

00:07:51.430 --> 00:07:53.350
would get thinner and
thinner and thinner.

00:07:53.350 --> 00:07:55.710
You'd have to do it over
more and more steps.

00:07:55.710 --> 00:07:58.730
But eventually you'll get to a
point, if you assume really

00:07:58.730 --> 00:08:02.150
small changes in our delta V.

00:08:02.150 --> 00:08:05.370
In calculus world, that
infinitely small changes, you

00:08:05.370 --> 00:08:08.040
write it as dV.

00:08:08.040 --> 00:08:11.940
So if you take a sum of all the
pressures, times the dV's

00:08:11.940 --> 00:08:14.780
you get the area under
this curve.

00:08:14.780 --> 00:08:16.880
So the way to think about it
when you're looking at this

00:08:16.880 --> 00:08:19.480
PV-diagram, if someone says,
you're going from this point

00:08:19.480 --> 00:08:22.130
to this pressure and this
volume, to this pressure and

00:08:22.130 --> 00:08:23.010
this volume.

00:08:23.010 --> 00:08:24.380
And they say, how much
work did you do?

00:08:24.380 --> 00:08:26.690
You say, oh, well I just had to
figure out the area under

00:08:26.690 --> 00:08:27.770
this curve.

00:08:27.770 --> 00:08:30.540
If you want to know the real
math behind it, if you could

00:08:30.540 --> 00:08:33.120
get your pressure as a function
of volume-- and if

00:08:33.120 --> 00:08:35.820
you haven't watched the calculus
videos you can ignore

00:08:35.820 --> 00:08:39.010
this little aside I'm
going to do here.

00:08:39.010 --> 00:08:42.169
This is this curve right here.

00:08:42.169 --> 00:08:44.450
If you could write it this way,
let's say you could write

00:08:44.450 --> 00:08:47.370
pressure as a function
of volume.

00:08:47.370 --> 00:08:51.290
When you're in algebra, you
learn a curve is, you know, y

00:08:51.290 --> 00:08:52.150
is a function of x.

00:08:52.150 --> 00:08:55.000
But here, y is the pressure
and x is volume, so its

00:08:55.000 --> 00:08:56.920
pressure is a function
of volume.

00:08:56.920 --> 00:09:01.780
So the area under this curve
is the integral of the

00:09:01.780 --> 00:09:04.580
pressure as a function of
volume, that's the height at

00:09:04.580 --> 00:09:10.850
any point, times our very
small change in volume.

00:09:10.850 --> 00:09:14.480
So times our very small
change in volume.

00:09:14.480 --> 00:09:18.910
And you take the sum from our
starting volume, so volume

00:09:18.910 --> 00:09:21.280
initial to volume final.

00:09:21.280 --> 00:09:24.130
And we'll do this in the future,
especially when we

00:09:24.130 --> 00:09:25.230
start touching on entropy.

00:09:25.230 --> 00:09:26.650
But this is a neat result.

00:09:26.650 --> 00:09:28.575
Even if you don't know the
calculus, or if this confuses

00:09:28.575 --> 00:09:30.870
you, if you've never seen
an integral before, you

00:09:30.870 --> 00:09:31.850
could ignore it.

00:09:31.850 --> 00:09:34.020
But you could look at this
intuitively and see the work I

00:09:34.020 --> 00:09:37.500
did is the area under
this curve.

00:09:37.500 --> 00:09:39.860
Now, let me ask you
one more thing.

00:09:39.860 --> 00:09:42.700
Let's say some work is being
done to the system.

00:09:42.700 --> 00:09:46.690
So we start adding some
marbles back.

00:09:46.690 --> 00:09:48.300
So let's say-- actually,
let's say we're

00:09:48.300 --> 00:09:49.350
going from this direction.

00:09:49.350 --> 00:09:52.880
Let's say we start at state 2
and we go in that direction.

00:09:52.880 --> 00:09:54.680
So direction matters.

00:09:54.680 --> 00:09:57.010
So let's say we go in that
direction right there.

00:09:57.010 --> 00:09:58.370
So I should put some arrows.

00:09:58.370 --> 00:10:01.410
And I'm overloading this
picture so much.

00:10:01.410 --> 00:10:03.140
Actually let me just do a new
picture, that's probably the

00:10:03.140 --> 00:10:05.490
best thing to do.

00:10:05.490 --> 00:10:10.966
So it's pressure, volume-- I'm
actually going to do two.

00:10:10.966 --> 00:10:16.000
Let me just do pressure,
volume.

00:10:16.000 --> 00:10:17.320
I'm going to do two
graphs here.

00:10:20.240 --> 00:10:21.170
All right.

00:10:21.170 --> 00:10:23.070
So in the first one
it's pressure,

00:10:23.070 --> 00:10:25.510
volume, pressure, volume.

00:10:25.510 --> 00:10:31.220
We started here at 1, and
we went here to 2.

00:10:31.220 --> 00:10:34.950
So our system was essentially
pushed up on the piston.

00:10:34.950 --> 00:10:37.160
And it could be a curve or a
line, I'm not going to get too

00:10:37.160 --> 00:10:40.450
particular right now, but it was
going in this direction.

00:10:40.450 --> 00:10:42.960
And so we can say that the work
done was the pressure

00:10:42.960 --> 00:10:45.980
times the increase in volume
at any moment.

00:10:45.980 --> 00:10:49.610
So the work done was the
area under this curve.

00:10:54.660 --> 00:11:02.300
Now, if we started at position
2 and we go to position 1.

00:11:02.300 --> 00:11:04.430
2 to 1.

00:11:04.430 --> 00:11:05.260
Now what's happening?

00:11:05.260 --> 00:11:06.250
Now we're compressing.

00:11:06.250 --> 00:11:08.885
So if we're going in that
direction, you might say, oh

00:11:08.885 --> 00:11:11.220
OK, maybe the work done by
the system is still the

00:11:11.220 --> 00:11:12.490
area under the curve.

00:11:12.490 --> 00:11:13.480
Well you'd be close.

00:11:13.480 --> 00:11:14.280
Because what's happening now?

00:11:14.280 --> 00:11:15.780
We're now compressing
the system or

00:11:15.780 --> 00:11:17.440
adding the marbles back.

00:11:17.440 --> 00:11:19.680
We're putting energy
into the system.

00:11:19.680 --> 00:11:23.310
So if we do that, remember, your
work done by the system

00:11:23.310 --> 00:11:26.880
was pressure times an
increase in volume.

00:11:26.880 --> 00:11:28.710
Now it's going to be
your pressure times

00:11:28.710 --> 00:11:30.360
a decrease in volume.

00:11:30.360 --> 00:11:35.870
So when you go back in this
direction, the area is not the

00:11:35.870 --> 00:11:40.225
work done by the system, it's
the work done to the system.

00:11:40.225 --> 00:11:43.630
And maybe I'll do that in a
different color, so green for

00:11:43.630 --> 00:11:46.090
work done to the system.

00:11:46.090 --> 00:11:50.840
Now let me throw you another
little interesting idea.

00:11:50.840 --> 00:11:53.330
And this is actually
a key idea.

00:11:53.330 --> 00:11:54.850
It's good to get the
intuition here.

00:11:54.850 --> 00:11:58.470
So let me just draw a very
simple PV-diagram again.

00:12:04.320 --> 00:12:07.450
So let's say we start
at some state here.

00:12:07.450 --> 00:12:08.540
State 1.

00:12:08.540 --> 00:12:13.640
And I do something, you know,
I'm in a quasi-static process

00:12:13.640 --> 00:12:16.450
and it, you know, it's doing
something weird, and I get to

00:12:16.450 --> 00:12:19.230
state 2 here.

00:12:19.230 --> 00:12:22.370
And it's going in
this direction.

00:12:22.370 --> 00:12:24.470
So my volume is increasing.

00:12:24.470 --> 00:12:27.720
So in this situation, what is
the work done by the system?

00:12:27.720 --> 00:12:29.890
Easy enough, it's the area
under this curve.

00:12:32.970 --> 00:12:38.770
Now let's say that I keep
doing some type of

00:12:38.770 --> 00:12:41.340
quasi-static process, but it
takes a different path.

00:12:41.340 --> 00:12:43.370
I'm doing something else, other
than adding the marbles

00:12:43.370 --> 00:12:44.670
directly back.

00:12:44.670 --> 00:12:51.110
So my new path looks something
like this to get

00:12:51.110 --> 00:12:52.360
back to state 1.

00:12:55.290 --> 00:12:57.150
So these arrows are
going back.

00:12:57.150 --> 00:13:00.440
So now what is the work
done to the system?

00:13:00.440 --> 00:13:03.230
well my volume is decreasing,
so it's the area under the

00:13:03.230 --> 00:13:05.090
second curve.

00:13:05.090 --> 00:13:06.700
The area under the second
curve is the

00:13:06.700 --> 00:13:09.650
work done to the system.

00:13:09.650 --> 00:13:12.420
So if I want to know what the
net work the system did, going

00:13:12.420 --> 00:13:16.110
from state 1 to state 2, and
then going back to state 1--

00:13:16.110 --> 00:13:17.640
remember, this is a pressure
and volume

00:13:17.640 --> 00:13:19.550
diagram-- what is it?

00:13:19.550 --> 00:13:22.380
Well the work that the system
did was this whole area under

00:13:22.380 --> 00:13:23.630
this brown curve.

00:13:23.630 --> 00:13:27.790
And then it had some work done
to it, which is the area under

00:13:27.790 --> 00:13:29.010
this magenta curve.

00:13:29.010 --> 00:13:32.150
So the net work it did is
essentially the white, the

00:13:32.150 --> 00:13:34.730
whole area, minus
this red area.

00:13:34.730 --> 00:13:38.620
So the net work it did would be
essentially just the area

00:13:38.620 --> 00:13:39.960
inside this loop.

00:13:42.830 --> 00:13:44.660
And hopefully you don't have to
know calculus to do this,

00:13:44.660 --> 00:13:46.120
although calculus you would
actually use to

00:13:46.120 --> 00:13:49.140
compute these areas.

00:13:49.140 --> 00:13:52.530
But I just want to give you that
intuition, that the area

00:13:52.530 --> 00:13:56.720
inside this closed loop is
actually the amount of work

00:13:56.720 --> 00:13:59.740
that our system has done.

00:13:59.740 --> 00:14:02.560
And what's important is the
direction that it's going.

00:14:02.560 --> 00:14:05.705
So it increased volume, then
decreased volume, so it's kind

00:14:05.705 --> 00:14:07.770
of this clockwise motion.

00:14:07.770 --> 00:14:12.690
This is the work that our system
has done, which, I

00:14:12.690 --> 00:14:14.430
don't know, to me is a pretty
interesting thing.

00:14:14.430 --> 00:14:16.900
And later we can use this notion
to come up with some

00:14:16.900 --> 00:14:20.230
other ideas behind our
state variables

00:14:20.230 --> 00:14:22.060
I'll make one little
aside here.

00:14:22.060 --> 00:14:25.880
Remember, our state variable
pressure volume, we did stuff

00:14:25.880 --> 00:14:27.230
to it then we went back
to that state.

00:14:27.230 --> 00:14:28.330
That stayed the same.

00:14:28.330 --> 00:14:29.550
And I want to say
another thing.

00:14:29.550 --> 00:14:33.280
For our purposes, when we're
dealing with ideal gases,

00:14:33.280 --> 00:14:36.080
where the internal energy is
essentially the kinetic energy

00:14:36.080 --> 00:14:39.440
of the system, if we go and do
all sorts of crazy stuff and

00:14:39.440 --> 00:14:43.230
come back, our internal
energy hasn't changed.

00:14:43.230 --> 00:14:45.580
So the internal energy is always
going to be the same at

00:14:45.580 --> 00:14:46.190
this point.

00:14:46.190 --> 00:14:48.840
So if I said, I did all of this
stuff and came back here,

00:14:48.840 --> 00:14:50.660
what is my change in
internal energy?

00:14:50.660 --> 00:14:51.245
It's 0.

00:14:51.245 --> 00:14:52.780
The change is 0.

00:14:52.780 --> 00:14:55.040
Now if I said I went from here
to here, I would have a

00:14:55.040 --> 00:14:56.570
different internal energy
and my change would

00:14:56.570 --> 00:14:57.900
be something real.

00:14:57.900 --> 00:15:00.670
But since this is a state
function, it doesn't care how

00:15:00.670 --> 00:15:01.330
I got there.

00:15:01.330 --> 00:15:03.450
If I took all these loops and
got back there, it just says,

00:15:03.450 --> 00:15:07.220
look, if I'm at this point in
the PV-diagram, my internal

00:15:07.220 --> 00:15:09.200
energy is the same thing.

00:15:09.200 --> 00:15:11.890
So if I start at this point,
and I finish again at this

00:15:11.890 --> 00:15:14.890
point, I have had no change
in internal energy.

00:15:14.890 --> 00:15:17.120
And we'll talk more about
that in the next video.

00:15:17.120 --> 00:15:18.910
But I just wanted to leave you
there and get you this

00:15:18.910 --> 00:15:21.620
intuition behind the areas
under the curves in the

00:15:21.620 --> 00:15:22.870
PV-diagram.


Work from expansion

WEBVTT
Kind: captions
Language: en

00:00:00.620 --> 00:00:03.750
I've talked a lot about how our
change in internal energy

00:00:03.750 --> 00:00:07.830
of a system can be due to some
heat being added to the

00:00:07.830 --> 00:00:12.530
system, or some work being added
to the system, or being

00:00:12.530 --> 00:00:13.840
done to the system.

00:00:13.840 --> 00:00:15.700
And I'm going to write it again
the other way, just

00:00:15.700 --> 00:00:16.900
because you see it both ways.

00:00:16.900 --> 00:00:19.370
You could say that the change
in internal energy could be

00:00:19.370 --> 00:00:22.900
the heat added to the
system minus the

00:00:22.900 --> 00:00:25.500
work done by the system.

00:00:25.500 --> 00:00:27.820
So there's two questions
that might naturally

00:00:27.820 --> 00:00:29.000
spring up in your head.

00:00:29.000 --> 00:00:33.250
One is, how is heat added to or
taken away from a system?

00:00:33.250 --> 00:00:38.000
And how is work done, or done
by, or done to a system?

00:00:38.000 --> 00:00:40.370
The heat, I think, is
fairly intuitive.

00:00:40.370 --> 00:00:44.720
If I have a-- and we'll be a
little bit more precise in the

00:00:44.720 --> 00:00:46.510
future of this, but I just want
to give you the sense of

00:00:46.510 --> 00:00:50.500
what we're talking about-- if I
have some system here, some

00:00:50.500 --> 00:00:56.560
particles in some type
of a canister.

00:00:56.560 --> 00:00:59.650
And it's at temperature, I don't
know, let's say it's a

00:00:59.650 --> 00:01:02.820
temperature T1.

00:01:02.820 --> 00:01:10.170
I'll even give it a-- say
it's at 300 kelvin.

00:01:10.170 --> 00:01:13.860
If I want to add heat to this
system, what I can do is I can

00:01:13.860 --> 00:01:18.010
place another system right
next to it, maybe

00:01:18.010 --> 00:01:20.900
right next to it.

00:01:20.900 --> 00:01:22.610
Who knows what size it is.

00:01:22.610 --> 00:01:26.280
And it's got some
particles there.

00:01:26.280 --> 00:01:29.610
But its temperature is much,
much, much higher.

00:01:33.620 --> 00:01:37.095
So this system's temperature,
I'll say temp T2 is equal to,

00:01:37.095 --> 00:01:39.210
I don't know, let's say
it's 1000 kelvin.

00:01:39.210 --> 00:01:40.810
I'm just making up numbers.

00:01:40.810 --> 00:01:42.900
So what's going to happen in
this situation, you're going

00:01:42.900 --> 00:01:46.880
to have heat transferred from
this second system to the

00:01:46.880 --> 00:01:47.560
first system.

00:01:47.560 --> 00:01:50.780
So you're going to have heat
going into the system.

00:01:50.780 --> 00:01:55.870
Now, heat and, work and even
internal energy, this goes

00:01:55.870 --> 00:01:58.290
back to our conversation
of macrostates versus

00:01:58.290 --> 00:01:59.240
microstates.

00:01:59.240 --> 00:02:02.620
Heat is changing the macrostate
of our systems.

00:02:02.620 --> 00:02:05.120
This system is going to
lose temperature.

00:02:05.120 --> 00:02:06.750
This system's going to
gain temperature.

00:02:06.750 --> 00:02:09.110
But we know what's happening
on a micro level.

00:02:09.110 --> 00:02:11.650
These molecules are going
to lose kinetic energy.

00:02:11.650 --> 00:02:13.665
These molecules are going
to gain kinetic energy.

00:02:13.665 --> 00:02:15.600
How is that actually
happening?

00:02:15.600 --> 00:02:19.040
Well, we assume that there's
some type of a container here.

00:02:19.040 --> 00:02:21.170
Maybe it's a solid wall.

00:02:21.170 --> 00:02:23.320
These molecules are going to
bump into that wall, and are

00:02:23.320 --> 00:02:26.260
going to make the particles in
that wall vibrate, and then

00:02:26.260 --> 00:02:29.350
they're going to make the
particles in the green

00:02:29.350 --> 00:02:31.150
container's walls vibrate.

00:02:31.150 --> 00:02:33.860
And so when the green
container's molecules touch

00:02:33.860 --> 00:02:35.960
the wall, they're going to
bounce off with even more

00:02:35.960 --> 00:02:38.250
kinetic energy, with even more
velocity, because of that

00:02:38.250 --> 00:02:41.300
vibration in the wall will push
them back even further.

00:02:41.300 --> 00:02:45.090
So that's essentially how you
get this transfer of kinetic

00:02:45.090 --> 00:02:46.690
energy, or this transfer
of heat.

00:02:46.690 --> 00:02:47.820
I think that's fairly
intuitive.

00:02:47.820 --> 00:02:52.240
If we put this next to a cooler,
a system with lower

00:02:52.240 --> 00:02:54.330
temperature, we would
lose kinetic energy,

00:02:54.330 --> 00:02:55.120
or would lose heat.

00:02:55.120 --> 00:02:56.390
And there's other ways
that we can do it.

00:02:56.390 --> 00:02:58.580
We could compress the-- well,
I don't want to talk about

00:02:58.580 --> 00:03:01.050
that just now, because that'll
be touching on work.

00:03:01.050 --> 00:03:04.740
So, how can we add or subtract
work to a system?

00:03:04.740 --> 00:03:06.420
And this one's a little
bit more interesting.

00:03:06.420 --> 00:03:08.255
Let's go back to our
piston example.

00:03:11.185 --> 00:03:14.280
Let me just draw some
lines here.

00:03:14.280 --> 00:03:16.680
So I have my container.

00:03:16.680 --> 00:03:17.580
There you go.

00:03:17.580 --> 00:03:21.240
It's got a little movable
ceiling to it.

00:03:21.240 --> 00:03:22.930
That's my piston.

00:03:22.930 --> 00:03:25.150
And go back to the example.

00:03:25.150 --> 00:03:27.530
Because what we're going to be
dealing with-- especially once

00:03:27.530 --> 00:03:31.810
I go into the pressure volume
diagram, the PV diagram that

00:03:31.810 --> 00:03:33.610
I'm about to go into--
we want to deal with

00:03:33.610 --> 00:03:35.270
quasi-static processes.

00:03:35.270 --> 00:03:38.440
Processes that are always close
enough to equilibrium

00:03:38.440 --> 00:03:41.990
that we feel OK talking
about macrostates like

00:03:41.990 --> 00:03:43.110
pressure and volume.

00:03:43.110 --> 00:03:46.020
Remember, that if we just did
something crazy and the whole

00:03:46.020 --> 00:03:48.040
system is in flux,
those macrostates

00:03:48.040 --> 00:03:50.260
aren't defined anymore.

00:03:50.260 --> 00:03:52.140
So we want to do a quasi-static
process.

00:03:52.140 --> 00:03:54.660
So I'll have pebbles instead
of one big rock.

00:03:54.660 --> 00:03:57.280
I'll draw the pebbles a little
bigger this time.

00:03:57.280 --> 00:03:59.270
And I have some pressure.

00:03:59.270 --> 00:04:02.250
So that's my piston and
it's being kept

00:04:02.250 --> 00:04:04.120
down by these rocks.

00:04:04.120 --> 00:04:06.430
It's being kept up by the
pressure of the gas.

00:04:06.430 --> 00:04:08.700
The gas is bumping into
this ceiling.

00:04:08.700 --> 00:04:09.770
It's bumping into everything.

00:04:09.770 --> 00:04:12.310
The pressure at every point in
the container is the same.

00:04:12.310 --> 00:04:14.110
It's at equilibrium.

00:04:14.110 --> 00:04:21.300
Now, what happens in that
example where I removed one

00:04:21.300 --> 00:04:22.350
rock from that?

00:04:22.350 --> 00:04:24.445
So let me copy and paste that.

00:04:24.445 --> 00:04:29.270
So if I remove one rock from
this thing right here.

00:04:32.130 --> 00:04:35.000
Copy and paste.

00:04:35.000 --> 00:04:36.910
So that's the same thing.

00:04:36.910 --> 00:04:41.060
Now let me remove a rock.

00:04:41.060 --> 00:04:43.900
I'll remove this top
one, was removed.

00:04:43.900 --> 00:04:45.220
What's going to happen?

00:04:45.220 --> 00:04:48.150
Well I now have less weight
pushing down on the piston,

00:04:48.150 --> 00:04:50.600
and I have a certain amount
of pressure pushing up.

00:04:50.600 --> 00:04:53.620
The system, it'll very
temporarily go out of

00:04:53.620 --> 00:04:57.220
equilibrium, but it'll be a very
small difference in how

00:04:57.220 --> 00:05:00.120
much we're pressing down on it,
so hopefully it won't be a

00:05:00.120 --> 00:05:01.940
huge change in our
equilibrium.

00:05:01.940 --> 00:05:04.500
We'll stay pretty close to it.

00:05:04.500 --> 00:05:06.790
But we know from the previous
example, instead of this thing

00:05:06.790 --> 00:05:10.390
flying up, it's going to
shift up a little bit.

00:05:10.390 --> 00:05:13.300
This is just going to shift
up a little bit.

00:05:13.300 --> 00:05:16.690
Right when we do it it's going
to be like that, right there.

00:05:16.690 --> 00:05:20.150
And let me fill in that part
with black, because it's not

00:05:20.150 --> 00:05:23.553
like the space disappeared.

00:05:23.553 --> 00:05:26.450
So let me fill that
in right there.

00:05:26.450 --> 00:05:31.570
So our little piston will move
up a very small amount.

00:05:31.570 --> 00:05:35.040
And what I claim is, when this
happened, when I removed this

00:05:35.040 --> 00:05:39.110
little pebble from here, the
system did some work.

00:05:39.110 --> 00:05:41.010
And let's just think
about that.

00:05:41.010 --> 00:05:43.800
So work, according to the
definitions that you learned

00:05:43.800 --> 00:05:48.810
in first-year physics, and when
you're using classical or

00:05:48.810 --> 00:05:52.200
dealing with classical
mechanics, you learn that work

00:05:52.200 --> 00:05:57.160
is equal to force
times distance.

00:05:59.780 --> 00:06:02.910
So if I'm claiming that when
this piston moved up a little

00:06:02.910 --> 00:06:05.570
bit, when I removed that pebble,
I'm claiming that this

00:06:05.570 --> 00:06:07.420
system here did some work.

00:06:07.420 --> 00:06:09.820
So I'm claiming that it applied
a force to this

00:06:09.820 --> 00:06:13.200
piston, and it applied
that force to the

00:06:13.200 --> 00:06:16.160
piston for some distance.

00:06:16.160 --> 00:06:18.660
So let's figure out what that
is, and if we can somehow

00:06:18.660 --> 00:06:21.380
relate it to other macro
properties that we know

00:06:21.380 --> 00:06:22.890
reasonably well.

00:06:22.890 --> 00:06:25.940
Well we know the pressure
and the volume, right?

00:06:25.940 --> 00:06:29.760
We know the pressure that's
being exerted on the piston,

00:06:29.760 --> 00:06:31.070
at least at this
point in time.

00:06:31.070 --> 00:06:31.750
And what's pressure?

00:06:31.750 --> 00:06:36.845
Pressure is equal to
force per area.

00:06:42.720 --> 00:06:45.420
Remember, this piston, you're
just seeing it from the side,

00:06:45.420 --> 00:06:48.630
but it's a kind of a flat plate
or a flat ceiling on top

00:06:48.630 --> 00:06:49.800
of this thing.

00:06:49.800 --> 00:06:52.330
And at what distance
did it move it?

00:06:52.330 --> 00:06:55.860
You know I could blow
it up a little bit.

00:06:55.860 --> 00:06:59.980
It moved it some-- I didn't draw
it too big here-- some x,

00:06:59.980 --> 00:07:01.230
some distance x.

00:07:03.800 --> 00:07:10.520
So this change, it moved it up
some distance x there, right?

00:07:10.520 --> 00:07:13.640
So what is the force that
it pushed it up?

00:07:13.640 --> 00:07:16.300
Well, the force, we know
its pressure, the

00:07:16.300 --> 00:07:17.720
pressure's force per area.

00:07:17.720 --> 00:07:20.550
So if we want to know the force,
we have to multiply

00:07:20.550 --> 00:07:22.020
pressure times area.

00:07:22.020 --> 00:07:27.370
If we multiply both sides of
this times area, we get force.

00:07:27.370 --> 00:07:29.620
So we're essentially saying
the area of this little

00:07:29.620 --> 00:07:32.025
ceiling to this container right
there, you know, it

00:07:32.025 --> 00:07:34.060
could be, I could draw with some
depth, but I think you

00:07:34.060 --> 00:07:34.800
know what I'm talking about.

00:07:34.800 --> 00:07:36.032
It has some area.

00:07:36.032 --> 00:07:39.870
It's probably the same area as
the base of the container.

00:07:39.870 --> 00:07:43.450
So we could say that the force
being applied by our system--

00:07:43.450 --> 00:07:48.280
let me do it in a new color--
the force is equal to our

00:07:48.280 --> 00:07:57.580
pressure of the system, times
the area of the ceiling of our

00:07:57.580 --> 00:07:59.470
container of the piston.

00:07:59.470 --> 00:08:00.950
Now that's the force.

00:08:00.950 --> 00:08:02.080
Now what's the distance?

00:08:02.080 --> 00:08:05.390
The distance is this
x over here.

00:08:05.390 --> 00:08:09.680
The distance is-- I'll do it
in blue-- it's this change

00:08:09.680 --> 00:08:10.090
right here.

00:08:10.090 --> 00:08:13.510
I didn't draw it too big,
but that's that x.

00:08:13.510 --> 00:08:15.850
Now let's see if we can
relate this somehow.

00:08:15.850 --> 00:08:18.190
Let me draw it a little
bit bigger.

00:08:18.190 --> 00:08:20.035
And I'll try to draw in
three dimensions.

00:08:20.035 --> 00:08:21.650
So let me draw the piston.

00:08:21.650 --> 00:08:23.100
What color did I do it in?

00:08:23.100 --> 00:08:24.460
I did it in that brown color.

00:08:24.460 --> 00:08:27.480
So our piston looks something--
I'll draw it as a

00:08:27.480 --> 00:08:31.300
elipse-- the piston
looks like that.

00:08:31.300 --> 00:08:33.679
And it got pushed up.

00:08:33.679 --> 00:08:36.130
So it got pushed up
some distance x.

00:08:36.130 --> 00:08:39.669
Let me see how good
I can-- whoops.

00:08:39.669 --> 00:08:44.400
Let me copy and paste
that same--

00:08:44.400 --> 00:08:48.503
So the piston gets pushed
up some distance x.

00:08:48.503 --> 00:08:51.711
Let me draw that.

00:08:51.711 --> 00:08:54.217
It got pushed up some
distance x.

00:08:56.900 --> 00:08:59.930
And we're claiming that our--
oh sorry, this is the force.

00:08:59.930 --> 00:09:01.180
Sorry, let me be clear.

00:09:01.180 --> 00:09:04.700
This is the force, and
this is the distance.

00:09:04.700 --> 00:09:09.650
So work is equal to our force,
which is our pressure times

00:09:09.650 --> 00:09:16.670
our area, times the distance.

00:09:16.670 --> 00:09:17.870
I want to be very
clear with that.

00:09:17.870 --> 00:09:19.990
Because when I wrote this I
said, OK, the force that we're

00:09:19.990 --> 00:09:22.430
applying is the pressure we're
applying, times the area of

00:09:22.430 --> 00:09:23.670
our cylinder.

00:09:23.670 --> 00:09:26.620
This is the area of our
cylinder right here.

00:09:26.620 --> 00:09:29.130
That's the area of our
cylinder right there.

00:09:29.130 --> 00:09:33.880
So if you do the pressure
times this

00:09:33.880 --> 00:09:35.610
area, you get the force.

00:09:35.610 --> 00:09:39.940
And then we moved it
some distance x.

00:09:39.940 --> 00:09:42.800
Now, we could rearrange this.

00:09:42.800 --> 00:09:48.230
We could say that the work is
equal to our pressure times

00:09:48.230 --> 00:09:50.480
our area, times x.

00:09:50.480 --> 00:09:51.660
What's this?

00:09:51.660 --> 00:09:57.620
What's this area, this area
right here, times x?

00:09:57.620 --> 00:10:01.420
Well that's going to be our
change in volume, right?

00:10:01.420 --> 00:10:04.530
This area times some height
is some volume.

00:10:04.530 --> 00:10:07.090
And that's essentially how
much our container

00:10:07.090 --> 00:10:08.210
has changed in volume.

00:10:08.210 --> 00:10:11.060
When we pushed this piston up,
the volume of our container

00:10:11.060 --> 00:10:11.760
has increased.

00:10:11.760 --> 00:10:13.610
You can see that, even looking
from the side.

00:10:13.610 --> 00:10:15.760
Our rectangle got a
little bit taller.

00:10:15.760 --> 00:10:17.500
When you look at it with a
little bit of depth, you see

00:10:17.500 --> 00:10:19.450
the rectangle also didn't
get taller.

00:10:19.450 --> 00:10:21.240
We have some surface area.

00:10:21.240 --> 00:10:23.560
Surface area times
height is volume.

00:10:23.560 --> 00:10:25.840
So this right here, this
term right here,

00:10:25.840 --> 00:10:28.820
is a change in volume.

00:10:28.820 --> 00:10:33.000
So we can write work now in
terms of things that we know.

00:10:33.000 --> 00:10:37.220
We can write work done
by our system.

00:10:37.220 --> 00:10:42.985
Work done is equal to pressure
times our change in volume.

00:10:46.840 --> 00:10:50.560
Now this has a very interesting
repercussion here.

00:10:50.560 --> 00:10:53.800
So we could-- actually many--
we can rewrite our internal

00:10:53.800 --> 00:10:56.050
energy formulas.

00:10:56.050 --> 00:10:58.970
So, for example, we can write
internal change and internal

00:10:58.970 --> 00:11:03.640
energy is now equal to heat
added to the system, plus the

00:11:03.640 --> 00:11:08.565
work-- let me say minus the
work done by the system.

00:11:12.450 --> 00:11:14.430
Well what is the work
done by the system?

00:11:14.430 --> 00:11:18.010
Well it's the pressure of the
system times how much the

00:11:18.010 --> 00:11:19.990
system expanded.

00:11:19.990 --> 00:11:25.470
In this case, the system is
pushing these marbles, or

00:11:25.470 --> 00:11:26.940
these pieces of sand up.

00:11:26.940 --> 00:11:28.470
It's doing work.

00:11:28.470 --> 00:11:30.140
If we were doing it the other
way, if we were adding the

00:11:30.140 --> 00:11:33.430
sand, and we were pushing down
on our little canister, we

00:11:33.430 --> 00:11:35.300
would be doing work
to the system.

00:11:35.300 --> 00:11:37.460
So this is the situation where
I'm doing here, where I'm

00:11:37.460 --> 00:11:39.880
removing the sand and the piston
goes up, essentially

00:11:39.880 --> 00:11:43.300
the gas is pushing up on
the piston, the system

00:11:43.300 --> 00:11:44.880
is doing the work.

00:11:44.880 --> 00:11:48.000
So if we go back to our little
formula, that internal energy

00:11:48.000 --> 00:11:54.170
is heat minus the work done by
a system, so done by, then we

00:11:54.170 --> 00:11:58.430
can write this as, this is equal
to the heat added to the

00:11:58.430 --> 00:12:05.460
system minus this quantity, the
pressure of the system,

00:12:05.460 --> 00:12:07.565
times the change in volume.

00:12:07.565 --> 00:12:11.020
And it's interesting, if the
volume is increasing, then the

00:12:11.020 --> 00:12:12.520
system is doing work.

00:12:12.520 --> 00:12:14.230
And this applies-- we're going
to talk a lot more about

00:12:14.230 --> 00:12:16.640
engines in the future-- but
that's how engines do work.

00:12:16.640 --> 00:12:19.410
They have a little explosion
that goes on inside of a

00:12:19.410 --> 00:12:22.580
cylinder that pushes up on the
piston, and then that piston

00:12:22.580 --> 00:12:25.150
moves a bunch of other stuff
that eventually turns wheels.

00:12:25.150 --> 00:12:29.850
So the volume increases, you're
actually doing work.

00:12:29.850 --> 00:12:31.590
So I'm going to leave you
there in this video.

00:12:31.590 --> 00:12:34.470
In the next video, we're going
to relate this, this new way

00:12:34.470 --> 00:12:38.780
of writing our internal energy
formula, and we're going to

00:12:38.780 --> 00:12:41.050
relate it to the PV diagram.


More on internal energy

WEBVTT
Kind: captions
Language: en

00:00:00.870 --> 00:00:04.470
In the last video we defined
internal energy as literally

00:00:04.470 --> 00:00:06.470
all the energy that's
in a system.

00:00:06.470 --> 00:00:08.340
That's kind of the most
inclusive version,

00:00:08.340 --> 00:00:09.190
at least in my head.

00:00:09.190 --> 00:00:11.840
So that's my system, it's
some type of container.

00:00:11.840 --> 00:00:15.100
And I have a bunch of
particles in here.

00:00:15.100 --> 00:00:17.630
It's literally the sum of
the kinetic energies

00:00:17.630 --> 00:00:18.820
of all these particles.

00:00:18.820 --> 00:00:20.280
If they had potential
energies, we'd

00:00:20.280 --> 00:00:21.240
throw that in there.

00:00:21.240 --> 00:00:23.260
If they have electrical
potential, we'd

00:00:23.260 --> 00:00:24.460
throw that in there.

00:00:24.460 --> 00:00:27.680
If they have bonds with each
other, the energies in that

00:00:27.680 --> 00:00:28.840
bond, we would throw
it in there.

00:00:28.840 --> 00:00:29.710
It's everything.

00:00:29.710 --> 00:00:31.540
It's all inclusive.

00:00:31.540 --> 00:00:34.550
And, I told you in the last
video it's unintuitive that U

00:00:34.550 --> 00:00:35.890
stands for internal energy.

00:00:35.890 --> 00:00:37.720
But I kind of think that, you
know, U, it contains the

00:00:37.720 --> 00:00:39.550
universe of energy.

00:00:39.550 --> 00:00:40.980
You know, that's just for
me to memorize it.

00:00:40.980 --> 00:00:43.340
Don't think too deeply into
what I just said.

00:00:43.340 --> 00:00:46.830
But this is internal energy.

00:00:46.830 --> 00:00:52.320
If you show me a system, it
has some internal energy.

00:00:52.320 --> 00:00:53.890
It's a function of its state.

00:00:53.890 --> 00:00:57.070
I don't care how it got to that
state, but if you told me

00:00:57.070 --> 00:00:59.580
a system at a certain state,
maybe with a certain pressure,

00:00:59.580 --> 00:01:02.280
or a certain volume, or at a
certain temperature-- although

00:01:02.280 --> 00:01:04.550
if you give me pressure and
volume that should be enough--

00:01:04.550 --> 00:01:06.940
I can tell you what its
internal energy is.

00:01:06.940 --> 00:01:08.840
Especially if you tell me the
type of molecule I have, and

00:01:08.840 --> 00:01:09.930
things like that.

00:01:09.930 --> 00:01:12.990
Now we also said in the last
video that because internal

00:01:12.990 --> 00:01:16.640
energy is all the energy in
the system, it can't be

00:01:16.640 --> 00:01:18.260
randomly created or destroyed.

00:01:18.260 --> 00:01:23.050
It can just be transformed
from one form to another.

00:01:23.050 --> 00:01:28.600
So if I have a change in
internal energy, it can only

00:01:28.600 --> 00:01:31.060
be due to-- well, it can be
due to more than what I'm

00:01:31.060 --> 00:01:31.620
describing.

00:01:31.620 --> 00:01:34.220
But in our simple world where
all of the energy in a

00:01:34.220 --> 00:01:36.520
system-- and maybe we're dealing
with gases, because

00:01:36.520 --> 00:01:39.080
that's normally what you deal
with in a first-year chemistry

00:01:39.080 --> 00:01:42.290
course-- it's going to be the
heat that could be added to

00:01:42.290 --> 00:01:45.860
the system, plus the work
done on the system.

00:01:48.820 --> 00:01:50.830
And like I said in the last
video, sometimes they'll say,

00:01:50.830 --> 00:01:53.260
instead of plus the work done
on the system, sometimes

00:01:53.260 --> 00:01:57.020
they'll say, minus the work
that the system does.

00:01:57.020 --> 00:01:57.970
Either way.

00:01:57.970 --> 00:02:02.680
And here I just want to make
another side discussion here,

00:02:02.680 --> 00:02:04.880
because I decided to write
it without the

00:02:04.880 --> 00:02:05.810
little deltas here.

00:02:05.810 --> 00:02:08.330
And the reason why I did that
is if you were to write this

00:02:08.330 --> 00:02:10.560
equation, which you will see,
you'll see it in textbooks,

00:02:10.560 --> 00:02:13.460
teachers will do it-- nothing
inherently criminal about

00:02:13.460 --> 00:02:17.320
that-- but I just do that
because it clears in my mind

00:02:17.320 --> 00:02:20.840
what heat and what work are
relative to internal energy.

00:02:20.840 --> 00:02:31.630
If I were to write delta U is
equal to heat delta Q plus

00:02:31.630 --> 00:02:38.340
delta W to me this implies that
at some point I had some

00:02:38.340 --> 00:02:41.330
amount of heat in my system,
and then I have a different

00:02:41.330 --> 00:02:43.860
amount of heat in my system,
and I took the difference

00:02:43.860 --> 00:02:46.780
between the two and I got
a change in heat.

00:02:46.780 --> 00:02:51.860
So this implies that heat is
somehow an inherent macrostate

00:02:51.860 --> 00:02:53.880
of the system, and that's
not the case.

00:02:57.530 --> 00:02:59.440
I can tell you what the
internal energy

00:02:59.440 --> 00:03:00.540
of this system is.

00:03:00.540 --> 00:03:02.100
I can tell you its pressure.

00:03:02.100 --> 00:03:03.600
I can tell you its volume.

00:03:03.600 --> 00:03:05.390
I can tell you its
temperature.

00:03:05.390 --> 00:03:07.340
These are all macrostates
of the system.

00:03:07.340 --> 00:03:10.040
I don't know how it got to this
situation, but I can tell

00:03:10.040 --> 00:03:10.800
you about it.

00:03:10.800 --> 00:03:14.880
I cannot tell you what the
heat is of this system.

00:03:14.880 --> 00:03:19.690
And that might be a little
unintuitive, because if I ask

00:03:19.690 --> 00:03:21.330
you, hey I have a cup of coffee,
what's the heat of it?

00:03:21.330 --> 00:03:22.920
You might say, oh, it's, you
know, you might give me the

00:03:22.920 --> 00:03:23.450
temperature.

00:03:23.450 --> 00:03:25.940
Because in our everyday language
we use things like

00:03:25.940 --> 00:03:27.790
heat and temperature
interchangeably.

00:03:27.790 --> 00:03:30.920
But in thermodynamics, heat
is a transfer of energy.

00:03:30.920 --> 00:03:34.080
A way to think about it
is, if internal energy

00:03:34.080 --> 00:03:36.510
is your bank account.

00:03:36.510 --> 00:03:38.195
So you could say change
in bank account.

00:03:45.940 --> 00:03:48.370
And it really is like
the energy bank

00:03:48.370 --> 00:03:50.690
account of a system.

00:03:50.690 --> 00:03:54.660
If you have a change in a bank
account, you had some deposits

00:03:54.660 --> 00:03:55.770
or withdrawals.

00:03:55.770 --> 00:03:59.480
And heat and work are really
just deposits or withdrawals

00:03:59.480 --> 00:04:01.550
into our energy bank account.

00:04:01.550 --> 00:04:02.570
Heat is one kind.

00:04:02.570 --> 00:04:04.790
Maybe heat is like
a wire transfer.

00:04:04.790 --> 00:04:10.640
So you could say it's wire
transfers to your account.

00:04:10.640 --> 00:04:15.570
Transfers to your account
plus check deposits.

00:04:20.399 --> 00:04:24.840
Now it makes a lot of sense to
say, you could say, what is my

00:04:24.840 --> 00:04:26.360
value of my bank account?

00:04:26.360 --> 00:04:28.630
Or you could say what is my
change in my bank account?

00:04:28.630 --> 00:04:30.860
You take two snapshots of
your bank account at

00:04:30.860 --> 00:04:32.140
two different times.

00:04:32.140 --> 00:04:35.170
But would it make sense to say--
you know, I could say I

00:04:35.170 --> 00:04:37.420
wire transferred $10, right?

00:04:37.420 --> 00:04:42.220
So I could say, this statement
would be plus $10.

00:04:42.220 --> 00:04:46.080
And I could say that I
wrote $20 in checks,

00:04:46.080 --> 00:04:47.710
minus $20 in checks.

00:04:47.710 --> 00:04:50.630
In which case, my change
in my bank account

00:04:50.630 --> 00:04:53.440
would be minus $10.

00:04:53.440 --> 00:04:55.160
Now would it make sense
for me to say

00:04:55.160 --> 00:04:56.930
change in wire transfer?

00:04:56.930 --> 00:04:59.810
That implies that when I started
off maybe my bank

00:04:59.810 --> 00:05:04.390
account had $100 in it
and now it has $90.

00:05:04.390 --> 00:05:08.240
When my bank account had $100
in it, did it have any wire

00:05:08.240 --> 00:05:10.010
transfer amount?

00:05:10.010 --> 00:05:14.000
No, wire transfer was how money
was deposited or taken

00:05:14.000 --> 00:05:14.920
away from my account.

00:05:14.920 --> 00:05:17.780
Likewise, it didn't have a
checking deposit account, so I

00:05:17.780 --> 00:05:21.080
can't really-- it just seems
weird to me to say change in

00:05:21.080 --> 00:05:25.280
wire transfer is $10, or change
in check deposits is

00:05:25.280 --> 00:05:27.340
$20 or minus $20.

00:05:27.340 --> 00:05:30.370
Would you say, I made a
$10 wire transfer and

00:05:30.370 --> 00:05:32.970
I paid $20 in checks.

00:05:32.970 --> 00:05:36.050
So I had a net change in
my bank account of $10.

00:05:36.050 --> 00:05:40.280
Likewise, I say how much work
was done to me or I did, which

00:05:40.280 --> 00:05:43.610
is essentially a deposit or
withdrawal of energy.

00:05:43.610 --> 00:05:45.900
Or I could say much heat was
given to me or how much heat

00:05:45.900 --> 00:05:48.160
was released, which is another
way of depositing or

00:05:48.160 --> 00:05:51.360
withdrawing energy from my
energy bank account.

00:05:51.360 --> 00:05:53.920
So that's why I like
to stick to this.

00:05:53.920 --> 00:05:56.400
And I like to stay
away from this.

00:05:56.400 --> 00:05:58.940
And just like I said, you can't
say how much heat is in

00:05:58.940 --> 00:05:59.920
the system.

00:05:59.920 --> 00:06:02.270
So someone will say, oh, how
much heat is in this?

00:06:02.270 --> 00:06:03.560
You cannot say that.

00:06:03.560 --> 00:06:06.460
There's no heat state variable
for that system.

00:06:06.460 --> 00:06:08.370
You have internal energy.

00:06:08.370 --> 00:06:10.150
The closest thing to heat,
we'll talk about it in a

00:06:10.150 --> 00:06:11.860
future video, is enthalpy.

00:06:11.860 --> 00:06:15.430
Enthalpy is essentially a way of
measuring how much heat is

00:06:15.430 --> 00:06:18.120
in a system, but we won't talk
about that just now.

00:06:18.120 --> 00:06:20.940
And you can't say how much
work is in a system.

00:06:20.940 --> 00:06:24.140
You can't say, oh I have x
amount of work in a system.

00:06:24.140 --> 00:06:27.190
The system can do work or have
work done to it, but there's

00:06:27.190 --> 00:06:29.710
not a certain amount of work,
because that energy in the

00:06:29.710 --> 00:06:32.180
system could be all used for
work, it could all be used for

00:06:32.180 --> 00:06:34.470
heat, it could all be used for
a ton of different things.

00:06:34.470 --> 00:06:35.760
So you can't say those things.

00:06:35.760 --> 00:06:38.030
And that's why I don't like
treating them like state

00:06:38.030 --> 00:06:39.940
variables, or state functions.

00:06:39.940 --> 00:06:42.530
So with that said, this
is our definition.

00:06:42.530 --> 00:06:44.760
Let's do a couple of
simple problems,

00:06:44.760 --> 00:06:45.840
just to give you intuition.

00:06:45.840 --> 00:06:49.040
And I really want to make
you comfortable.

00:06:49.040 --> 00:06:52.560
My real goal is to make you
comfortable with, when to know

00:06:52.560 --> 00:06:54.320
to use plus or minus
on the work.

00:06:54.320 --> 00:06:57.000
And the best way to do it is not
to memorize a formula, but

00:06:57.000 --> 00:06:59.520
just to kind of think about
what's happening.

00:06:59.520 --> 00:07:02.490
So let's say that I have some
system here and, I don't know,

00:07:02.490 --> 00:07:03.540
it's a balloon.

00:07:03.540 --> 00:07:09.770
And let's say that I have no
change in internal energy.

00:07:09.770 --> 00:07:10.990
Internal energy is 0.

00:07:10.990 --> 00:07:13.100
And for our purposes we can kind
of view it as the kinetic

00:07:13.100 --> 00:07:15.350
energy of the particles
haven't changed.

00:07:15.350 --> 00:07:20.200
And let's say by expanding a
bit, by my balloon expanding a

00:07:20.200 --> 00:07:21.420
bit-- I did some work.

00:07:21.420 --> 00:07:25.730
I'll do this in more detail
in the next video.

00:07:25.730 --> 00:07:35.940
So the system does 10
joules of work.

00:07:35.940 --> 00:07:39.840
My question is, how much heat
was added or taken away from

00:07:39.840 --> 00:07:41.090
the system?

00:07:45.190 --> 00:07:46.615
So the way I can think about
it-- you don't even have to

00:07:46.615 --> 00:07:49.160
write the formula down, or you
can write it-- you could say,

00:07:49.160 --> 00:07:52.370
look, the internal energy, the
amount of energy in the system

00:07:52.370 --> 00:07:53.050
hasn't changed.

00:07:53.050 --> 00:07:56.430
The system did 10
joules of work.

00:07:56.430 --> 00:07:58.510
So that's energy going
out of the system.

00:07:58.510 --> 00:08:00.100
It did 10 joules.

00:08:00.100 --> 00:08:03.980
So 10 joules went out
in the form of work.

00:08:03.980 --> 00:08:08.640
If the internal energy did not
change, then essentially 10

00:08:08.640 --> 00:08:11.790
joules of energy had to
go into the system.

00:08:11.790 --> 00:08:13.800
10 joules had to go
into the system.

00:08:13.800 --> 00:08:16.280
If it didn't, the internal
energy would have gone down by

00:08:16.280 --> 00:08:20.020
the amount of work we had.

00:08:20.020 --> 00:08:22.490
And the only way, if is this is
the net work, the only way

00:08:22.490 --> 00:08:24.920
that we're talking about, that
we can add energy outside of

00:08:24.920 --> 00:08:26.000
work, is through heat.

00:08:26.000 --> 00:08:28.810
So 10 joules of heat must
have been added.

00:08:28.810 --> 00:08:36.860
So we can write 10 joules
of heat added to system.

00:08:36.860 --> 00:08:38.690
Now let's look at that from
the point of view of the

00:08:38.690 --> 00:08:40.450
actual formula.

00:08:40.450 --> 00:08:49.720
If we have delta U is equal to
heat added, plus work done to

00:08:49.720 --> 00:08:53.970
the system, then we would
say, OK, this was 0.

00:08:53.970 --> 00:08:59.190
It's equal to the heat
added to the system.

00:08:59.190 --> 00:09:02.060
Remember, in this way we're
saying this is the heat done,

00:09:02.060 --> 00:09:04.610
or the work done,
to the system.

00:09:04.610 --> 00:09:06.420
W is work done.

00:09:06.420 --> 00:09:09.600
Now, the system did work
to something else.

00:09:09.600 --> 00:09:12.180
It didn't have work
done to it.

00:09:12.180 --> 00:09:17.540
So if this is work done to the
system, and it did work, then

00:09:17.540 --> 00:09:20.040
this is going to
be a minus 10.

00:09:20.040 --> 00:09:21.820
Minus 10 joules.

00:09:21.820 --> 00:09:24.260
And then you solve both
sides of this.

00:09:24.260 --> 00:09:31.220
You add 10 to both sides and
you get 10 is equal to Q,

00:09:31.220 --> 00:09:33.460
which is exactly what
we got up here.

00:09:33.460 --> 00:09:35.200
But this can get confusing
sometimes, because you're

00:09:35.200 --> 00:09:38.570
like, oh, is this heat
that the system did?

00:09:38.570 --> 00:09:43.180
Is this heat that was added to
the system or taken away?

00:09:43.180 --> 00:09:48.080
The convention tends to be
that this is heat added.

00:09:48.080 --> 00:09:49.280
But then sometimes
it's confusing.

00:09:49.280 --> 00:09:52.080
Is this the work done to the
system or work done by?

00:09:52.080 --> 00:09:53.750
And that's why I like just
doing it this way.

00:09:53.750 --> 00:09:55.660
If the system does work
it loses energy.

00:09:55.660 --> 00:09:59.330
If the system has work done
to it, it gains energy.

00:09:59.330 --> 00:10:01.280
So let's do another problem.

00:10:01.280 --> 00:10:03.350
I mean, I could have done this
exact same thing using the

00:10:03.350 --> 00:10:05.650
other formula that you'll
sometimes see.

00:10:05.650 --> 00:10:14.860
Delta U is equal to Q minus the
work that the system does

00:10:14.860 --> 00:10:18.520
by the system-- Work
done by the system.

00:10:18.520 --> 00:10:21.980
And in this case, once
again, change in

00:10:21.980 --> 00:10:23.710
internal energy was 0.

00:10:23.710 --> 00:10:27.990
That is equal to heat
added to the system,

00:10:27.990 --> 00:10:30.320
minus the work done.

00:10:30.320 --> 00:10:33.560
So minus-- I told you at the
beginning of the problem that

00:10:33.560 --> 00:10:38.590
the system did 10 joules of
work-- so minus the work done.

00:10:38.590 --> 00:10:39.790
Minus 10 joules.

00:10:39.790 --> 00:10:42.080
We get the same situation
up here from

00:10:42.080 --> 00:10:43.690
two different formulas.

00:10:43.690 --> 00:10:46.420
And we got 10 is equal to Q.

00:10:46.420 --> 00:10:49.850
Either way, the heat added to
the system is 10 joules.

00:10:49.850 --> 00:10:51.170
Let's do one more.

00:10:51.170 --> 00:11:02.370
Let's say that, I don't know,
5 joules of heat taken away

00:11:02.370 --> 00:11:03.620
from system.

00:11:09.030 --> 00:11:16.260
And let's say that 1 joule
of work done on system.

00:11:16.260 --> 00:11:20.170
So maybe we're compressing the
balloon on the system.

00:11:20.170 --> 00:11:25.150
What is our change in
internal energy?

00:11:25.150 --> 00:11:27.140
Let's just figure
out our change.

00:11:27.140 --> 00:11:30.190
So the way I think of it is 5
joules of heat taken away from

00:11:30.190 --> 00:11:31.990
the system, that's going
to reduce our internal

00:11:31.990 --> 00:11:33.930
energy by minus 5.

00:11:33.930 --> 00:11:37.070
And if 1 joule work is done onto
the system, we're putting

00:11:37.070 --> 00:11:40.740
energy into it so that'll
be plus 1.

00:11:40.740 --> 00:11:44.950
So minus 5, plus 1, is
going to be minus 4.

00:11:44.950 --> 00:11:46.780
Or enter our change in internal

00:11:46.780 --> 00:11:48.450
energy is minus 4 joules.

00:11:48.450 --> 00:11:50.970
Now we could have done that a
little bit more formally with

00:11:50.970 --> 00:11:55.400
the formula, change in internal
energy is equal to

00:11:55.400 --> 00:12:03.720
heat added to the system, plus
work done on the system.

00:12:03.720 --> 00:12:06.680
So it's equal to heat
added to the system.

00:12:06.680 --> 00:12:11.530
We had 5 joules heat taken away,
so this is minus 5, plus

00:12:11.530 --> 00:12:13.990
work done on the system.

00:12:13.990 --> 00:12:17.180
We have 1 joule of work done
on the system, and there we

00:12:17.180 --> 00:12:19.880
get, once again, minus 4.

00:12:19.880 --> 00:12:22.540
Now, I could have written that
same formula the other way.

00:12:22.540 --> 00:12:27.340
I could have said change in
internal energy is equal to

00:12:27.340 --> 00:12:31.950
heat added to the system minus
the work that the system does.

00:12:31.950 --> 00:12:33.530
I want to do this both ways,
because I don't want you to

00:12:33.530 --> 00:12:37.380
get confused, either way you
see it on problems or in

00:12:37.380 --> 00:12:39.410
school, or maybe you take one
class that does it one way and

00:12:39.410 --> 00:12:40.425
one class that does
it the other.

00:12:40.425 --> 00:12:43.210
If you use it this way,
what was the heat

00:12:43.210 --> 00:12:44.340
added to the system?

00:12:44.340 --> 00:12:47.440
We had heat taken away,
so it's minus 5.

00:12:47.440 --> 00:12:51.890
So minus the work that the
system does, how much work

00:12:51.890 --> 00:12:54.250
does the system do?

00:12:54.250 --> 00:12:58.720
Well, the system had 1 joule
of work done to it.

00:12:58.720 --> 00:13:03.550
So it did itself minus
1 joules of work.

00:13:03.550 --> 00:13:06.110
So it's minus minus 1.

00:13:06.110 --> 00:13:10.130
I want to be clear, when I use
this formula, this is work

00:13:10.130 --> 00:13:13.060
done by system, done by.

00:13:13.060 --> 00:13:16.720
This is work done to.

00:13:16.720 --> 00:13:19.000
The system had work
done to it.

00:13:19.000 --> 00:13:22.700
So it had minus 1 joules of work
done by the system, so

00:13:22.700 --> 00:13:25.970
these become pluses, and you
get back to a minus 4.

00:13:25.970 --> 00:13:27.550
Do whatever's intuitive
for you.

00:13:27.550 --> 00:13:29.510
For me, this tends to be the
most intuitive, where you

00:13:29.510 --> 00:13:30.550
don't even use a formula.

00:13:30.550 --> 00:13:33.990
We just think, if I'm doing
work, I'm using up energy.

00:13:33.990 --> 00:13:37.550
If I get work done to me, I'm
being handed over energy.

00:13:37.550 --> 00:13:40.200
If I have heat taken away from
me, I'm giving away energy.

00:13:40.200 --> 00:13:43.300
If I have heat added to me,
I'm getting energy.

00:13:43.300 --> 00:13:45.100
See you in the next video.


First law of thermodynamics / internal energy

WEBVTT
Kind: captions
Language: en

00:00:00.740 --> 00:00:04.560
I've now done a bunch of videos
on thermodynamics, both

00:00:04.560 --> 00:00:07.070
in the chemistry and the
physics playlist, and I

00:00:07.070 --> 00:00:09.750
realized that I have yet to give
you, or at least if my

00:00:09.750 --> 00:00:12.300
memory serves me correctly, I
have yet to give you the first

00:00:12.300 --> 00:00:13.550
law of thermodynamics.

00:00:13.550 --> 00:00:17.310
And I think now is as
good a time as any.

00:00:17.310 --> 00:00:19.560
The first law of
thermodynamics.

00:00:24.260 --> 00:00:26.310
And it's a good one.

00:00:26.310 --> 00:00:32.330
It tells us that energy-- I'll
do it in this magenta color--

00:00:32.330 --> 00:00:38.790
energy cannot be created or
destroyed, it can only be

00:00:38.790 --> 00:00:41.680
transformed from one
form or another.

00:00:41.680 --> 00:00:53.020
So energy cannot be created or
destroyed, only transformed.

00:00:56.930 --> 00:00:59.280
So let's think about a couple
of examples of this.

00:00:59.280 --> 00:01:02.780
And we've touched on this when
we learned mechanics and

00:01:02.780 --> 00:01:07.960
kinetics in our physics
playlist, and we've done a

00:01:07.960 --> 00:01:10.620
bunch of this in the chemistry
playlist as well.

00:01:10.620 --> 00:01:15.860
So let's say I have some rock
that I just throw as fast as I

00:01:15.860 --> 00:01:17.410
can straight up.

00:01:17.410 --> 00:01:19.800
Maybe it's a ball
of some kind.

00:01:19.800 --> 00:01:21.370
So I throw a ball straight up.

00:01:21.370 --> 00:01:24.510
That arrow represents its
velocity vector, right?

00:01:24.510 --> 00:01:25.890
it's going to go
up in the air.

00:01:25.890 --> 00:01:27.570
Let me do it here.

00:01:27.570 --> 00:01:29.760
I throw a ball and it's going
to go up in the air.

00:01:29.760 --> 00:01:31.290
It's going to decelerate
due to gravity.

00:01:31.290 --> 00:01:35.530
And at some point, up here, the
ball is not going to have

00:01:35.530 --> 00:01:36.230
any velocity.

00:01:36.230 --> 00:01:39.060
So at this point it's going to
slow down a little bit, at

00:01:39.060 --> 00:01:41.160
this point it's going to slow
down a little bit more.

00:01:41.160 --> 00:01:42.920
And at this point it's going
to be completely stationary

00:01:42.920 --> 00:01:45.040
and then it's going to start
accelerating downwards.

00:01:45.040 --> 00:01:46.690
In fact, it was always
accelerating downwards.

00:01:46.690 --> 00:01:49.130
It was decelerating upwards,
and then it'll start

00:01:49.130 --> 00:01:50.200
accelerating downwards.

00:01:50.200 --> 00:01:52.220
So here its velocity will
look like that.

00:01:52.220 --> 00:01:53.980
And here its velocity
will look like that.

00:01:53.980 --> 00:01:56.330
Then right when it gets back
to the ground, if we assume

00:01:56.330 --> 00:01:59.250
negligible air resistance, its
velocity will be the same

00:01:59.250 --> 00:02:03.360
magnitude as the upward but
in the downward direction.

00:02:03.360 --> 00:02:05.660
So when we looked at this
example, and we've done this

00:02:05.660 --> 00:02:09.810
tons in the projectile motion
videos in the physics

00:02:09.810 --> 00:02:13.240
playlist, over here we said,
look, we have some kinetic

00:02:13.240 --> 00:02:13.740
energy here.

00:02:13.740 --> 00:02:14.550
And that makes sense.

00:02:14.550 --> 00:02:18.230
I think, to all of us, energy
intuitively means that you're

00:02:18.230 --> 00:02:19.120
doing something.

00:02:19.120 --> 00:02:21.110
So kinetic energy.

00:02:21.110 --> 00:02:23.580
Energy of movement,
of kinetics.

00:02:23.580 --> 00:02:25.810
It's moving, so it has energy.

00:02:25.810 --> 00:02:29.220
But then as we decelerate up
here, we clearly have no

00:02:29.220 --> 00:02:31.880
kinetic energy, zero
kinetic energy.

00:02:34.830 --> 00:02:35.860
So where did our energy go?

00:02:35.860 --> 00:02:38.920
I just told you the first law of
thermodynamics, that energy

00:02:38.920 --> 00:02:40.860
cannot be created
or destroyed.

00:02:40.860 --> 00:02:43.520
But I clearly had a lot of
kinetic energy over here, and

00:02:43.520 --> 00:02:46.570
we've seen the formula for that
multiple times, and here

00:02:46.570 --> 00:02:48.460
I have no kinetic energy.

00:02:48.460 --> 00:02:53.470
So I clearly destroyed kinetic
energy, but the first law of

00:02:53.470 --> 00:02:55.630
thermodynamics tells me
that I can't do that.

00:02:55.630 --> 00:02:58.290
So I must have transformed
that kinetic energy.

00:02:58.290 --> 00:03:00.440
I must have transformed
that kinetic energy

00:03:00.440 --> 00:03:01.840
into something else.

00:03:01.840 --> 00:03:04.010
And in the case of this ball,
I've transformed it into

00:03:04.010 --> 00:03:05.530
potential energy.

00:03:05.530 --> 00:03:08.490
So now I have potential
energy.

00:03:08.490 --> 00:03:10.970
And I won't go into the math of
it, but potential energy is

00:03:10.970 --> 00:03:17.190
just the potential to turn into
other forms of energy.

00:03:17.190 --> 00:03:18.480
I guess that's the easy
way to do it.

00:03:18.480 --> 00:03:20.660
But the way to think about it
is, look, the ball is really

00:03:20.660 --> 00:03:24.870
high up here, and by virtue of
its position in the universe,

00:03:24.870 --> 00:03:28.120
if something doesn't stop it,
it's going to fall back down,

00:03:28.120 --> 00:03:30.890
or it's going to be converted
into another form of energy.

00:03:30.890 --> 00:03:32.520
Now let me ask you
another question.

00:03:32.520 --> 00:03:34.560
Let's say I throw this ball up
and let's say we actually do

00:03:34.560 --> 00:03:36.820
have some air resistance.

00:03:36.820 --> 00:03:38.100
So I throw the ball up.

00:03:38.100 --> 00:03:41.990
I have a lot of kinetic
energy here.

00:03:41.990 --> 00:03:46.450
Then at the peak of where the
ball is, it's all potential

00:03:46.450 --> 00:03:49.082
energy, the kinetic energy
has disappeared.

00:03:49.082 --> 00:03:50.410
And let's say I have
air resistance.

00:03:50.410 --> 00:03:53.020
So when the ball comes back
down, the air was kind of

00:03:53.020 --> 00:03:57.130
slowing it down, so when it
reaches this bottom point,

00:03:57.130 --> 00:04:01.340
it's not going as fast
as I threw it.

00:04:01.340 --> 00:04:04.910
So when I reach this bottom
point here, my ball is going a

00:04:04.910 --> 00:04:07.450
lot slower than I threw
it up to begin with.

00:04:07.450 --> 00:04:09.970
And so if you think about what
happened, I have a lot of

00:04:09.970 --> 00:04:10.890
kinetic energy here.

00:04:10.890 --> 00:04:11.890
I'll give you the formula.

00:04:11.890 --> 00:04:14.440
The kinetic energy is the mass
of the ball, times the

00:04:14.440 --> 00:04:17.500
velocity of the ball,
squared, over 2.

00:04:17.500 --> 00:04:19.950
That's the kinetic
energy over here.

00:04:19.950 --> 00:04:20.899
And then I throw it.

00:04:20.899 --> 00:04:22.160
It all turns into potential
energy.

00:04:22.160 --> 00:04:24.590
Then it comes back down, and
turns into kinetic energy.

00:04:24.590 --> 00:04:26.850
But because of air resistance,
I have a

00:04:26.850 --> 00:04:28.930
smaller velocity here.

00:04:28.930 --> 00:04:31.880
I have a smaller velocity
than I did there.

00:04:31.880 --> 00:04:33.910
Kinetic energy is only dependent
on the magnitude of

00:04:33.910 --> 00:04:34.380
the velocity.

00:04:34.380 --> 00:04:37.570
I could put a little absolute
sign there to show that we're

00:04:37.570 --> 00:04:39.570
dealing with the magnitude
of the velocity.

00:04:39.570 --> 00:04:42.810
So I clearly have a lower
kinetic energy here.

00:04:42.810 --> 00:04:50.340
So lower kinetic energy here
than I did here, right?

00:04:50.340 --> 00:04:52.370
And I don't have any potential
energy left.

00:04:52.370 --> 00:04:54.650
Let's say this is the ground.

00:04:54.650 --> 00:04:55.890
We've hit the ground.

00:04:55.890 --> 00:04:57.560
So I have another conundrum.

00:04:57.560 --> 00:05:00.380
You know, when I went from
kinetic energy to no kinetic

00:05:00.380 --> 00:05:02.365
energy there, I can go
to the first law and

00:05:02.365 --> 00:05:03.000
say, oh, what happened?

00:05:03.000 --> 00:05:05.560
And the first law says, oh,
Sal, it all turned into

00:05:05.560 --> 00:05:07.190
potential energy up here.

00:05:07.190 --> 00:05:09.510
And you saw it turned into
potential energy because when

00:05:09.510 --> 00:05:12.050
the ball accelerated back down,
it turned back into

00:05:12.050 --> 00:05:12.710
kinetic energy.

00:05:12.710 --> 00:05:17.340
But then I say, no, Mr. First
Law of Thermodynamics, look,

00:05:17.340 --> 00:05:20.390
at this point I have no
potential energy, and I had

00:05:20.390 --> 00:05:22.830
all kinetic energy and I had
a lot of kinetic energy.

00:05:22.830 --> 00:05:26.660
Now at this point, I have no
potential energy once again,

00:05:26.660 --> 00:05:27.930
but I have less kinetic
energy.

00:05:27.930 --> 00:05:30.300
My ball has fallen at
a slower rate than I

00:05:30.300 --> 00:05:31.760
threw it to begin with.

00:05:31.760 --> 00:05:33.560
And the thermodynamics
says, oh, well that's

00:05:33.560 --> 00:05:34.270
because you have air.

00:05:34.270 --> 00:05:36.200
And I'd say, well I do
have air, but where

00:05:36.200 --> 00:05:37.410
did the energy go?

00:05:37.410 --> 00:05:41.990
And then the first law of
thermodynamics says, oh, when

00:05:41.990 --> 00:05:47.970
your ball was falling-- let
me see, that's the ball.

00:05:47.970 --> 00:05:50.790
Let me make the ball yellow.

00:05:50.790 --> 00:05:52.980
So when your ball was falling,
it was rubbing

00:05:52.980 --> 00:05:54.990
up against air particles.

00:05:54.990 --> 00:05:56.990
It was rubbing up against
molecules of air.

00:05:59.920 --> 00:06:02.480
And right where the molecules
bumped into the wall, there's

00:06:02.480 --> 00:06:04.100
a little bit of friction.

00:06:04.100 --> 00:06:08.310
Friction is just essentially,
your ball made these molecules

00:06:08.310 --> 00:06:11.120
that it was bumping into vibrate
a little bit faster.

00:06:11.120 --> 00:06:13.710
And essentially, if you think
about it, if you go back to

00:06:13.710 --> 00:06:16.860
the macrostate/ microstate
problem or descriptions that

00:06:16.860 --> 00:06:20.870
we talked about, this ball is
essentially transferring its

00:06:20.870 --> 00:06:24.630
kinetic energy to the molecules
of air that it rubs

00:06:24.630 --> 00:06:26.360
up against as it falls
back down.

00:06:26.360 --> 00:06:28.910
And actually it was doing it
on the way up as well.

00:06:28.910 --> 00:06:32.100
And so that kinetic energy that
you think you lost or you

00:06:32.100 --> 00:06:34.360
destroyed at the bottom, of
here, because your ball's

00:06:34.360 --> 00:06:36.920
going a lot slower, was actually
transferred to a lot

00:06:36.920 --> 00:06:38.240
of air particles.

00:06:38.240 --> 00:06:41.200
It was a lot of-- to a bunch
of air particles.

00:06:41.200 --> 00:06:45.100
Now, it's next to impossible to
measure exactly the kinetic

00:06:45.100 --> 00:06:47.480
energy that was done on each
individual air particle,

00:06:47.480 --> 00:06:49.820
because we don't even know what
their microstates were to

00:06:49.820 --> 00:06:50.810
begin with.

00:06:50.810 --> 00:06:53.910
But what we can say is, in
general I transferred some

00:06:53.910 --> 00:06:56.070
heat to these particles.

00:06:56.070 --> 00:07:01.400
I raised the temperature of
the air particles that the

00:07:01.400 --> 00:07:05.410
ball fell through by rubbing
those particles or giving them

00:07:05.410 --> 00:07:06.000
kinetic energy.

00:07:06.000 --> 00:07:10.395
Remember, temperature is just
a measure of kinetic-- and

00:07:10.395 --> 00:07:14.530
temperature is a macrostate or
kind of a gross way or a macro

00:07:14.530 --> 00:07:17.630
way, of looking at the
kinetic energy of

00:07:17.630 --> 00:07:18.960
the individual molecules.

00:07:18.960 --> 00:07:21.090
It's very hard to measure each
of theirs, but if you say on

00:07:21.090 --> 00:07:22.890
average their kinetic energy
is x, you're essentially

00:07:22.890 --> 00:07:24.730
giving an indication
of temperature.

00:07:24.730 --> 00:07:25.770
So that's where it went.

00:07:25.770 --> 00:07:27.210
It went to heat.

00:07:27.210 --> 00:07:29.130
And heat is another
form of energy.

00:07:29.130 --> 00:07:30.500
So that the first law
of thermodynamics

00:07:30.500 --> 00:07:32.300
says, I still hold.

00:07:32.300 --> 00:07:36.000
You had a lot of kinetic energy,
turned into potential,

00:07:36.000 --> 00:07:37.860
that turned into less
kinetic energy.

00:07:37.860 --> 00:07:39.820
And where did the
remainder go?

00:07:39.820 --> 00:07:40.780
It turned into heat.

00:07:40.780 --> 00:07:44.720
Because it transferred that
kinetic energy to these air

00:07:44.720 --> 00:07:47.570
particles in the surrounding
medium.

00:07:47.570 --> 00:07:49.010
Fair enough.

00:07:49.010 --> 00:07:51.630
So now that we have that out of
the way, how do we measure

00:07:51.630 --> 00:07:54.460
the amount of energy that
something contains?

00:07:57.150 --> 00:08:00.610
And here we have something
called the internal energy.

00:08:00.610 --> 00:08:03.060
The internal energy
of a system.

00:08:03.060 --> 00:08:06.620
Once again this is a macrostate,
or you could call

00:08:06.620 --> 00:08:08.510
it a macro description
of what's going on.

00:08:08.510 --> 00:08:10.556
This is called u for internal.

00:08:10.556 --> 00:08:13.250
The way I remember that is that
the word internal does

00:08:13.250 --> 00:08:15.020
not begin with a U.

00:08:15.020 --> 00:08:16.440
U for internal energy.

00:08:25.940 --> 00:08:30.100
Let me go back to my example--
that I had in the past, that I

00:08:30.100 --> 00:08:33.299
did in our previous video, if
you're watching these in

00:08:33.299 --> 00:08:39.130
order-- of I have, you know,
some gas with some movable

00:08:39.130 --> 00:08:40.919
ceiling at the top.

00:08:40.919 --> 00:08:42.220
That's its movable ceiling.

00:08:42.220 --> 00:08:43.190
That can move up and down.

00:08:43.190 --> 00:08:44.860
We have a vacuum up there.

00:08:44.860 --> 00:08:46.350
And I have some gas in here.

00:08:50.040 --> 00:08:53.360
The internal energy literally is
all of the energy that's in

00:08:53.360 --> 00:08:54.000
the system.

00:08:54.000 --> 00:08:58.210
So it includes, and for our
purposes, especially when

00:08:58.210 --> 00:09:01.210
you're in a first-year chemistry
course, it's the

00:09:01.210 --> 00:09:07.330
kinetic energy of all the
atoms or molecules.

00:09:10.140 --> 00:09:13.820
And in a future video, I'll
actually calculate it for how

00:09:13.820 --> 00:09:16.360
much kinetic energy is
there in a container.

00:09:16.360 --> 00:09:19.100
And that'll actually be our
internal energy plus all of

00:09:19.100 --> 00:09:19.780
the other energy.

00:09:19.780 --> 00:09:22.590
So these atoms, they have some
kinetic energy because they

00:09:22.590 --> 00:09:24.610
have some translational motion,
if we look at the

00:09:24.610 --> 00:09:25.810
microstates.

00:09:25.810 --> 00:09:28.430
If they're just individual
atoms, you can't really say

00:09:28.430 --> 00:09:30.780
that they're rotating, because
what does it mean for an atom

00:09:30.780 --> 00:09:31.580
to rotate, right?

00:09:31.580 --> 00:09:34.050
Because its electrons are just
jumping around anyway.

00:09:34.050 --> 00:09:36.670
So if they're individual atoms
they can't rotate, but if

00:09:36.670 --> 00:09:38.970
they're molecules they can
rotate, if it looks

00:09:38.970 --> 00:09:40.440
something like that.

00:09:40.440 --> 00:09:43.520
There could be some rotational
energy there.

00:09:43.520 --> 00:09:44.790
It includes that.

00:09:44.790 --> 00:09:47.630
If we have bonds-- so I
just drew a molecule.

00:09:47.630 --> 00:09:49.180
The molecule has bonds.

00:09:49.180 --> 00:09:51.020
Those bonds contain
some energy.

00:09:51.020 --> 00:09:53.270
That is also included in
the internal energy.

00:09:53.270 --> 00:09:56.130
If I have some electrons, let's
say that this was not

00:09:56.130 --> 00:09:59.400
a-- well I'm doing it using a
gas, and gases aren't good

00:09:59.400 --> 00:10:03.930
conductors-- but let's say
I'm doing it for a solid.

00:10:03.930 --> 00:10:05.390
So I'm using the wrong tools.

00:10:05.390 --> 00:10:11.310
So let's say I have
some metal.

00:10:11.310 --> 00:10:16.250
Those are my metal-- let me do
more-- my metal atoms. And in

00:10:16.250 --> 00:10:21.326
that metal atom, I have, a
bunch of electrons-- well

00:10:21.326 --> 00:10:24.540
that's the same color-- I have
a bunch of-- let me use a

00:10:24.540 --> 00:10:26.760
suitably different color--
I have a bunch

00:10:26.760 --> 00:10:29.250
of electrons here.

00:10:29.250 --> 00:10:31.720
And I have fewer here.

00:10:31.720 --> 00:10:33.660
So these electrons really
want to get here.

00:10:33.660 --> 00:10:35.740
Maybe they're being stopped for
some reason, so they have

00:10:35.740 --> 00:10:37.290
some electrical potential.

00:10:37.290 --> 00:10:40.250
Maybe there's a gap here, you
know, where they can't conduct

00:10:40.250 --> 00:10:41.970
or something like that.

00:10:41.970 --> 00:10:43.610
Internal energy includes
that as well.

00:10:43.610 --> 00:10:45.500
That's normally the scope out
of what you'd see in a

00:10:45.500 --> 00:10:46.480
first-year chemistry class.

00:10:46.480 --> 00:10:47.810
But it includes that.

00:10:47.810 --> 00:10:51.920
It also includes literally
every form of energy that

00:10:51.920 --> 00:10:52.060
exists here.

00:10:52.060 --> 00:10:54.870
It also includes, for example,
in a metal, if we were to heat

00:10:54.870 --> 00:10:57.910
this metal up they start
vibrating, right?

00:10:57.910 --> 00:11:00.520
They start moving left and
right, or up or down, or in

00:11:00.520 --> 00:11:01.690
every possible direction.

00:11:01.690 --> 00:11:04.760
And if you think about a
molecule or an atom that's

00:11:04.760 --> 00:11:09.420
vibrating, it's going from here,
and then it goes there,

00:11:09.420 --> 00:11:10.960
then it goes back there.

00:11:10.960 --> 00:11:12.330
It goes back and forth, right?

00:11:12.330 --> 00:11:14.750
And if you think about what's
happening, when it's in the

00:11:14.750 --> 00:11:17.240
middle point it has a lot of
kinetic energy, but at this

00:11:17.240 --> 00:11:19.670
point right here, when it's
about to go back, it's

00:11:19.670 --> 00:11:23.550
completely stationary for
a super small moment.

00:11:23.550 --> 00:11:25.360
And at that point, all
of its kinetic energy

00:11:25.360 --> 00:11:26.590
is potential energy.

00:11:26.590 --> 00:11:27.910
And then it turns into
kinetic energy.

00:11:27.910 --> 00:11:29.490
Then it goes back to potential
energy again.

00:11:29.490 --> 00:11:30.940
It's kind of like a
pendulum, or it's

00:11:30.940 --> 00:11:33.010
actually harmonic motion.

00:11:33.010 --> 00:11:37.010
So in this case, internal
energy also includes the

00:11:37.010 --> 00:11:38.990
kinetic energy for the molecules
that are moving

00:11:38.990 --> 00:11:42.110
fast. But it also includes the
potential energies for the

00:11:42.110 --> 00:11:44.530
molecules that are vibrating,
they're at that point where

00:11:44.530 --> 00:11:45.470
they don't have kinetic
energy.

00:11:45.470 --> 00:11:47.450
So it also includes
potential energy.

00:11:47.450 --> 00:11:52.000
So internal energy is literally
all of the energy

00:11:52.000 --> 00:11:54.810
that's in a system.

00:11:54.810 --> 00:11:58.270
And for most of what we're going
to do, you can assume

00:11:58.270 --> 00:12:00.190
that we're dealing with
an ideal gas.

00:12:00.190 --> 00:12:02.710
Instead of, it becomes a lot
more complicated with solids,

00:12:02.710 --> 00:12:05.580
and conductivity, and vibrations
and all that.

00:12:05.580 --> 00:12:07.900
We're going to assume we're
dealing with an ideal gas.

00:12:07.900 --> 00:12:09.910
And even better, we're going to
assume we're dealing with a

00:12:09.910 --> 00:12:11.850
monoatomic ideal gas.

00:12:11.850 --> 00:12:15.850
And maybe this is just
helium, or neon.

00:12:15.850 --> 00:12:16.990
One of the ideal gases.

00:12:16.990 --> 00:12:18.430
They don't want to bond
with each other.

00:12:18.430 --> 00:12:21.250
They don't form molecules
with each other.

00:12:23.880 --> 00:12:25.010
Let's just assume that
they're not.

00:12:25.010 --> 00:12:32.030
They're just individual atoms.
And in that case, the internal

00:12:32.030 --> 00:12:35.340
energy, we really can simplify
to it being the kinetic

00:12:35.340 --> 00:12:37.380
energy, if we ignore all
of these other things.

00:12:37.380 --> 00:12:39.690
But it's important to realize,
internal energy is everything.

00:12:39.690 --> 00:12:44.430
It's all of the energy
inside of a system.

00:12:44.430 --> 00:12:45.880
If you said, what's the
energy of the system?

00:12:45.880 --> 00:12:48.280
Its internal energy.

00:12:48.280 --> 00:12:52.390
So the first law of
thermodynamics says that

00:12:52.390 --> 00:12:56.230
energy cannot be created or
destroyed, only transformed.

00:12:56.230 --> 00:12:59.630
So let's say that internal
energy is changing.

00:12:59.630 --> 00:13:03.140
So I have this system, and
someone tells me, look, the

00:13:03.140 --> 00:13:06.370
internal energy is changing.

00:13:06.370 --> 00:13:09.070
So delta U, that's just a
capital delta that says, what

00:13:09.070 --> 00:13:10.730
is the change an internal
energy?

00:13:10.730 --> 00:13:14.600
It's saying, look, if your
internal energy is changing,

00:13:14.600 --> 00:13:17.310
your system is either having
something done to it, or it's

00:13:17.310 --> 00:13:18.780
doing something to
someone else.

00:13:18.780 --> 00:13:20.430
Some energy is being
transferred to it

00:13:20.430 --> 00:13:22.540
or away from it.

00:13:22.540 --> 00:13:24.950
So, how do we write that?

00:13:24.950 --> 00:13:27.360
Well the first law of
thermodynamics, or even the

00:13:27.360 --> 00:13:29.920
definition of internal energy,
says that a change in internal

00:13:29.920 --> 00:13:35.810
energy is equal to heat added to
the system-- and once again

00:13:35.810 --> 00:13:40.810
a very intuitive letter for
heat, because heat does not

00:13:40.810 --> 00:13:43.380
start with Q, but the
convention is

00:13:43.380 --> 00:13:45.490
to use Q for heat.

00:13:45.490 --> 00:13:49.520
The letter h is reserved for
enthalpy, which is a very,

00:13:49.520 --> 00:13:51.530
very, very similar
concept to heat.

00:13:51.530 --> 00:13:54.720
We'll talk about that maybe
in the next video.

00:13:54.720 --> 00:13:59.250
It's equal to the heat added to
the system, minus the work

00:13:59.250 --> 00:14:00.500
done by the system.

00:14:03.790 --> 00:14:05.180
And you could see this
multiple ways.

00:14:05.180 --> 00:14:06.760
Sometimes it's written
like this.

00:14:06.760 --> 00:14:10.550
Sometimes it's written that the
change in internal energy

00:14:10.550 --> 00:14:18.440
is equal to the heat added to
the system, plus the work done

00:14:18.440 --> 00:14:19.730
on the system.

00:14:19.730 --> 00:14:21.960
And this might be very
confusing, but you should just

00:14:21.960 --> 00:14:25.020
always-- and we'll really kind
of look at this 100 different

00:14:25.020 --> 00:14:25.990
ways in the next video.

00:14:25.990 --> 00:14:27.440
And actually this
is a capital U.

00:14:27.440 --> 00:14:29.680
Let me make sure that I write
that as a capital U.

00:14:29.680 --> 00:14:31.270
But we're going to do it
100 different ways.

00:14:31.270 --> 00:14:35.400
But if you think about it, if
I'm doing work I lose energy.

00:14:35.400 --> 00:14:37.790
I've transferred the energy
to someone else.

00:14:37.790 --> 00:14:41.360
So this is doing work.

00:14:41.360 --> 00:14:45.090
Likewise, if someone is giving
me heat that is increasing my

00:14:45.090 --> 00:14:48.380
energy, at least to me these
are reasonably intuitive

00:14:48.380 --> 00:14:48.980
definitions.

00:14:48.980 --> 00:14:54.950
Now if you see this, you say,
OK, if my energy is going up,

00:14:54.950 --> 00:14:57.750
if this is a positive thing, I
either have to have this go

00:14:57.750 --> 00:15:00.340
up, or work is being
done to me.

00:15:05.730 --> 00:15:09.220
Or energy is being transferred
into my system.

00:15:09.220 --> 00:15:11.930
I'll give a lot more examples of
what exactly that means in

00:15:11.930 --> 00:15:12.880
the next video.

00:15:12.880 --> 00:15:14.030
But I just want to make
you comfortable

00:15:14.030 --> 00:15:15.120
with either of these.

00:15:15.120 --> 00:15:16.520
Because you're going to see
them all the time, and you

00:15:16.520 --> 00:15:18.200
might even get confused
even if your teacher

00:15:18.200 --> 00:15:19.970
uses only one of them.

00:15:19.970 --> 00:15:22.050
But you should always do
this reality check.

00:15:22.050 --> 00:15:25.100
When something does work, it
is transferring energy to

00:15:25.100 --> 00:15:27.310
something else, right?

00:15:27.310 --> 00:15:30.120
So if you're doing work, it'll
take away, this is taking

00:15:30.120 --> 00:15:32.340
away, your internal energy.

00:15:32.340 --> 00:15:36.780
Likewise, heat transfer is
another way for energy to go

00:15:36.780 --> 00:15:40.180
from one system to another, or
from one entity to another.

00:15:40.180 --> 00:15:45.680
So if my total energy is going
up, maybe heat is being added

00:15:45.680 --> 00:15:46.730
to my system.

00:15:46.730 --> 00:15:51.210
If my energy is going down,
either heat is being taken

00:15:51.210 --> 00:15:55.450
away from my system, or I'm
doing more work on something.

00:15:55.450 --> 00:15:57.690
I'll do a bunch of examples
with that.

00:15:57.690 --> 00:15:59.000
And I'm just going to leave you
with this video with some

00:15:59.000 --> 00:16:01.050
other notation that
you might see.

00:16:01.050 --> 00:16:05.030
You might see change in internal
energy is equal to

00:16:05.030 --> 00:16:09.850
change-- let me write it again--
change in internal

00:16:09.850 --> 00:16:11.290
energy, capital U.

00:16:11.290 --> 00:16:14.360
You'll sometimes see it as,
they'll write a delta Q, which

00:16:14.360 --> 00:16:17.060
kind of implies change
in heat.

00:16:17.060 --> 00:16:18.820
But I'll explain it in a future
video why that doesn't

00:16:18.820 --> 00:16:21.240
make a full sense, but you'll
see this a lot.

00:16:21.240 --> 00:16:24.670
But you can also view this as
the heat added to the system,

00:16:24.670 --> 00:16:28.020
minus the change in work,
which is a little

00:16:28.020 --> 00:16:30.240
non-intuitive because when you
talk about heat or work you're

00:16:30.240 --> 00:16:32.000
talking about transferring
of energy.

00:16:32.000 --> 00:16:33.790
So when you talk about change
in transfer it becomes a

00:16:33.790 --> 00:16:36.470
little-- So sometimes a delta
work, they just mean this

00:16:36.470 --> 00:16:41.580
means that work done
by a system.

00:16:41.580 --> 00:16:44.750
So obviously if you have some
energy, you do some work,

00:16:44.750 --> 00:16:46.760
you've lost that energy, you've
given it to someone

00:16:46.760 --> 00:16:48.610
else, you'd have a
minus sign there.

00:16:48.610 --> 00:16:52.060
Or you might see it written like
this, change in internal

00:16:52.060 --> 00:16:58.120
energy is equal to heat added--
I won't say even this

00:16:58.120 --> 00:16:59.860
kind of reads to me
as change in heat.

00:16:59.860 --> 00:17:06.690
I'll just call this the heat
added-- plus the work done

00:17:06.690 --> 00:17:07.630
onto the system.

00:17:07.630 --> 00:17:15.160
So this is work done to, this
is work done by the system.

00:17:15.160 --> 00:17:16.020
Either way.

00:17:16.020 --> 00:17:19.040
And you shouldn't even memorize
this, you should just

00:17:19.040 --> 00:17:20.410
always think about
it a little bit.

00:17:20.410 --> 00:17:22.349
If I'm doing work I'm going
to lose energy.

00:17:22.349 --> 00:17:24.700
If work is done to me I'm
going to gain energy.

00:17:24.700 --> 00:17:27.920
If I lose heat, if this is a
negative number, I'm going to

00:17:27.920 --> 00:17:29.290
lose energy.

00:17:29.290 --> 00:17:31.710
If I gain heat I'm going
to gain energy.

00:17:31.710 --> 00:17:33.440
Anyway, I'll leave you there
for this video, and in the

00:17:33.440 --> 00:17:37.010
next video we'll really try to
digest this internal energy

00:17:37.010 --> 00:17:39.410
formula 100 different ways.