1
00:00:00,000 --> 00:00:00,510


2
00:00:00,510 --> 00:00:02,820
In the last video, we
saw that a system

3
00:00:02,820 --> 00:00:04,970
could do work by expanding.

4
00:00:04,970 --> 00:00:08,710
And in the situation we drew,
we had a situation where the

5
00:00:08,710 --> 00:00:09,880
ceiling was movable.

6
00:00:09,880 --> 00:00:14,790
We had this piston and we, like
in our process video, we

7
00:00:14,790 --> 00:00:15,660
had a bunch of pebbles.

8
00:00:15,660 --> 00:00:19,370
We removed a pebble, so the
pressure in our system, if we

9
00:00:19,370 --> 00:00:21,480
assume that it was just so small
that the pressure was

10
00:00:21,480 --> 00:00:25,600
constant, it pushed up on the
piston with some force.

11
00:00:25,600 --> 00:00:28,280
We figured out that that force,
since pressure is force

12
00:00:28,280 --> 00:00:31,865
per area, we just multiplied
pressure times the area of our

13
00:00:31,865 --> 00:00:35,300
piston, and we got the amount
of force we're applying.

14
00:00:35,300 --> 00:00:37,530
We apply that, and then we
multiply that times the

15
00:00:37,530 --> 00:00:40,730
distance that we push the piston
up, and then we get the

16
00:00:40,730 --> 00:00:42,950
amount of work that it
did by expansion, or

17
00:00:42,950 --> 00:00:44,310
the expansion work.

18
00:00:44,310 --> 00:00:45,780
We said, well, you know we could
have rewritten that.

19
00:00:45,780 --> 00:00:50,760
If you said pressure times our
area, times our distance, we

20
00:00:50,760 --> 00:00:54,440
could instead write that as
pressure, times the area,

21
00:00:54,440 --> 00:00:55,210
times the distance.

22
00:00:55,210 --> 00:00:56,780
And the area times
the distance is

23
00:00:56,780 --> 00:00:58,380
the change in volume.

24
00:00:58,380 --> 00:01:00,780
And so we came up with a neat
little formulation, that the

25
00:01:00,780 --> 00:01:05,260
work done by a system could be
written as the pressure times

26
00:01:05,260 --> 00:01:06,590
the change in volume.

27
00:01:06,590 --> 00:01:09,620
So in this case, I wrote the
internal energy formula, where

28
00:01:09,620 --> 00:01:11,400
it's the work done
by the system.

29
00:01:11,400 --> 00:01:13,120
So I did a minus, right?

30
00:01:13,120 --> 00:01:16,210
Because when you do work, you
are giving energy away to

31
00:01:16,210 --> 00:01:17,720
someone else.

32
00:01:17,720 --> 00:01:20,500
So in that situation,
we did a minus.

33
00:01:20,500 --> 00:01:22,940
And so instead of writing work,
we could say, minus the

34
00:01:22,940 --> 00:01:25,370
pressure, times the
change in volume.

35
00:01:25,370 --> 00:01:28,265
And remember this is a
quasi-static process.

36
00:01:28,265 --> 00:01:30,590
And we're doing it at very
small increments.

37
00:01:30,590 --> 00:01:33,190
We're assuming that this change
in volume is very

38
00:01:33,190 --> 00:01:37,010
small, and that the pressure
is roughly constant while

39
00:01:37,010 --> 00:01:37,840
we're doing this.

40
00:01:37,840 --> 00:01:39,230
And of course that's not
the case, right?

41
00:01:39,230 --> 00:01:42,780
If we did this, if this was a
large change in volume, or if

42
00:01:42,780 --> 00:01:44,910
this happened all of a sudden,
if these were really big

43
00:01:44,910 --> 00:01:48,090
pebbles, then our pressure
will change as we expand.

44
00:01:48,090 --> 00:01:50,540
So it's hard to say what
the pressure times the

45
00:01:50,540 --> 00:01:52,050
change in volume is.

46
00:01:52,050 --> 00:01:54,890
But if we assume things are
really, really being done in

47
00:01:54,890 --> 00:01:57,300
very, very small increments,
we could say, OK, let's say

48
00:01:57,300 --> 00:02:00,140
the pressure was constant over
that small increment, and then

49
00:02:00,140 --> 00:02:02,760
we can multiply it by the
change in volume.

50
00:02:02,760 --> 00:02:05,460
Now let's see how this can
relate to some of what we've

51
00:02:05,460 --> 00:02:07,980
done before with
the PV-diagram.

52
00:02:07,980 --> 00:02:11,900
And so far, all we've seen the
PV-diagram, or what I used it

53
00:02:11,900 --> 00:02:15,110
for, is to kind of help explain
the difference between

54
00:02:15,110 --> 00:02:18,060
quasi-static processes,
or to say when

55
00:02:18,060 --> 00:02:20,080
macrostates are defined.

56
00:02:20,080 --> 00:02:22,910
But let me now do something
more useful with it.

57
00:02:22,910 --> 00:02:25,120
And this will give you an idea,
or start giving you an

58
00:02:25,120 --> 00:02:28,870
idea of why people who
study thermodynamics

59
00:02:28,870 --> 00:02:30,480
love these so much.

60
00:02:30,480 --> 00:02:33,555
So before I did anything, when
my canister was just here, I

61
00:02:33,555 --> 00:02:34,510
had all the pebbles on it.

62
00:02:34,510 --> 00:02:36,290
And we were in a state
of equilibrium.

63
00:02:36,290 --> 00:02:39,520
I could describe all of its
macrostates, its pressure, its

64
00:02:39,520 --> 00:02:42,000
volume, its temperature.

65
00:02:42,000 --> 00:02:44,802
I could describe its internal
energy as well.

66
00:02:44,802 --> 00:02:46,170
So let me draw it here.

67
00:02:46,170 --> 00:02:48,040
So let's say I was
at this state.

68
00:02:48,040 --> 00:02:51,030
This was state number 1.

69
00:02:51,030 --> 00:02:55,180
State number 1 was
right there.

70
00:02:55,180 --> 00:02:57,150
And then, let's say I just
start removing pebbles.

71
00:02:57,150 --> 00:03:00,370
Remember, if I just remove all
the pebbles at once, the

72
00:03:00,370 --> 00:03:02,290
system's going to
go into flux.

73
00:03:02,290 --> 00:03:06,025
We wouldn't be doing a
quasi-static process, or a

74
00:03:06,025 --> 00:03:08,140
reversible process, which isn't
always the same thing.

75
00:03:08,140 --> 00:03:10,810
But for our purposes, we
wouldn't be in equilibrium the

76
00:03:10,810 --> 00:03:11,170
whole time.

77
00:03:11,170 --> 00:03:12,475
And we would have to wait
to get to equilibrium.

78
00:03:12,475 --> 00:03:15,560
And at some point we'd have
some pressure and volume

79
00:03:15,560 --> 00:03:16,810
that's down here.

80
00:03:16,810 --> 00:03:20,180
This is if we weren't doing it
as a quasi-static process.

81
00:03:20,180 --> 00:03:23,140
Now we are, what I showed in the
last video, we are doing

82
00:03:23,140 --> 00:03:26,640
it as a, or we're trying to get
close to a quasi-static

83
00:03:26,640 --> 00:03:28,410
process, because we're doing it
in small increments, with

84
00:03:28,410 --> 00:03:29,180
these little pebbles.

85
00:03:29,180 --> 00:03:30,760
And if these aren't small enough
for you, you could do

86
00:03:30,760 --> 00:03:32,320
it in smaller pebbles.

87
00:03:32,320 --> 00:03:33,650
So we're moving incrementally.

88
00:03:33,650 --> 00:03:35,170
So, for example, in that
last video, we

89
00:03:35,170 --> 00:03:36,380
maybe moved from there.

90
00:03:36,380 --> 00:03:38,950
We removed one pebble and
we got right there.

91
00:03:38,950 --> 00:03:40,920
You remove another pebble
and you go right there.

92
00:03:40,920 --> 00:03:42,880
You remove another pebble
and you go right there.

93
00:03:42,880 --> 00:03:45,630
And the benefit of doing these
quasi-static processes is you

94
00:03:45,630 --> 00:03:49,820
really get a path going from
one state to the next.

95
00:03:49,820 --> 00:03:53,340
Let's say when you remove all
but one of the pebbles, just,

96
00:03:53,340 --> 00:03:55,870
you know, this describes
our path.

97
00:03:55,870 --> 00:03:59,020
So let's say we are in state 2
and we've removed all but one.

98
00:03:59,020 --> 00:04:00,870
Let me draw that.

99
00:04:00,870 --> 00:04:03,705
So state 2 will look something
like this.

100
00:04:03,705 --> 00:04:06,850
I'll draw it really quick.

101
00:04:06,850 --> 00:04:08,900
So that's our container.

102
00:04:08,900 --> 00:04:10,070
That's our piston.

103
00:04:10,070 --> 00:04:12,730
We only have one pebble
left on top.

104
00:04:12,730 --> 00:04:17,430
And then of course we
have the gas now.

105
00:04:17,430 --> 00:04:18,410
Let me write this down.

106
00:04:18,410 --> 00:04:20,070
This is state 2.

107
00:04:20,070 --> 00:04:23,860
And let me write state 1 was
something like this.

108
00:04:23,860 --> 00:04:26,600
State 1, the ceiling
was lower.

109
00:04:26,600 --> 00:04:28,570
We had a bunch of pebbles
on top of it.

110
00:04:28,570 --> 00:04:31,670


111
00:04:31,670 --> 00:04:34,400
And we had a smaller volume,
and so the gas was bumping

112
00:04:34,400 --> 00:04:37,750
into the ceiling and the walls
and the floor a lot more.

113
00:04:37,750 --> 00:04:39,640
I'll just draw the
same number.

114
00:04:39,640 --> 00:04:41,310
So we had a higher pressure.

115
00:04:41,310 --> 00:04:48,140
So pressure was high
and volume low.

116
00:04:48,140 --> 00:04:50,590
Now in state 2-- so this
is pressure high.

117
00:04:50,590 --> 00:04:52,610
This pressure is this axis.

118
00:04:52,610 --> 00:04:54,290
This is volume.

119
00:04:54,290 --> 00:04:55,760
So we had high pressure,
low volume.

120
00:04:55,760 --> 00:04:57,310
And we got to a situation after

121
00:04:57,310 --> 00:04:59,145
removing all but one pebble.

122
00:04:59,145 --> 00:05:01,940
And we're doing it slowly, so
we're always in equilibrium.

123
00:05:01,940 --> 00:05:02,910
So we have a path.

124
00:05:02,910 --> 00:05:05,660
This is after removing each of
the pebbles, so that our

125
00:05:05,660 --> 00:05:07,450
pressure and volume
macro states

126
00:05:07,450 --> 00:05:08,360
are always well defined.

127
00:05:08,360 --> 00:05:14,270
But in state 2, we now
have a pressure low

128
00:05:14,270 --> 00:05:17,150
and volume is high.

129
00:05:17,150 --> 00:05:19,810
The volume is high, you can just
see that, because we kept

130
00:05:19,810 --> 00:05:22,760
pushing the piston up slowly,
slowly, trying to maintain

131
00:05:22,760 --> 00:05:24,170
ourselves in equilibrium so our

132
00:05:24,170 --> 00:05:26,180
macrostates are always defined.

133
00:05:26,180 --> 00:05:28,740
And our pressure is lower just
because we could have the same

134
00:05:28,740 --> 00:05:30,260
number of particles, but they're
just going to bump

135
00:05:30,260 --> 00:05:32,640
into the walls a little bit
less, because they have a

136
00:05:32,640 --> 00:05:35,550
little bit more room
to move around.

137
00:05:35,550 --> 00:05:36,770
And that's all fair and dandy.

138
00:05:36,770 --> 00:05:41,440
So this describes the path of
our system as it transitioned

139
00:05:41,440 --> 00:05:45,260
or as it experienced this
process, which was a

140
00:05:45,260 --> 00:05:46,910
quasi-static process.

141
00:05:46,910 --> 00:05:48,560
Everything was defined
at every point.

142
00:05:48,560 --> 00:05:51,910
Now we said that the work done
at any given point by the

143
00:05:51,910 --> 00:05:55,760
system is the pressure times
the change in volume.

144
00:05:55,760 --> 00:05:57,210
Now, how does that
relate to here?

145
00:05:57,210 --> 00:05:58,810
Change in volume is
just a certain

146
00:05:58,810 --> 00:06:01,350
distance along this x-axis.

147
00:06:01,350 --> 00:06:03,220
Along, more like I should
call it the volume-axis.

148
00:06:03,220 --> 00:06:05,660
This is a change in volume.

149
00:06:05,660 --> 00:06:07,690
We started off at this volume,
and let's say when we removed

150
00:06:07,690 --> 00:06:10,260
one pebble we got
to this volume.

151
00:06:10,260 --> 00:06:12,390
Now, we want to multiply that
times our pressure.

152
00:06:12,390 --> 00:06:15,370
Since we did it over such a
small increment, and we're so

153
00:06:15,370 --> 00:06:17,840
close to equilibrium, we could
assume that our pressure's is

154
00:06:17,840 --> 00:06:20,150
roughly constant over
that period of time.

155
00:06:20,150 --> 00:06:21,820
So we could say that this
is the pressure over

156
00:06:21,820 --> 00:06:23,950
that period of time.

157
00:06:23,950 --> 00:06:28,370
And so how much work we did,
it's this pressure over here,

158
00:06:28,370 --> 00:06:35,820
times this volume, which is
the area of this rectangle

159
00:06:35,820 --> 00:06:37,030
right there.

160
00:06:37,030 --> 00:06:39,830
And for any of you all who've
seen my calculus videos, this

161
00:06:39,830 --> 00:06:41,490
should start looking a
little bit familiar.

162
00:06:41,490 --> 00:06:44,400


163
00:06:44,400 --> 00:06:46,880
And then what about when we
could take our next pebble?

164
00:06:46,880 --> 00:06:48,950
Well now our pressure is
a little bit lower.

165
00:06:48,950 --> 00:06:51,050
This is our new pressure.

166
00:06:51,050 --> 00:06:53,560
Our pressure is a little
bit lower.

167
00:06:53,560 --> 00:06:57,440
And we multiply that times our
new change in volume-- times

168
00:06:57,440 --> 00:07:01,390
this change in volume-- and we
have that increment of work.

169
00:07:01,390 --> 00:07:05,040
Once again, this is the area
of this rectangle.

170
00:07:05,040 --> 00:07:09,440
And if you keep doing that, the
amount of work we do is

171
00:07:09,440 --> 00:07:13,700
essentially the area of all of
these rectangles as we remove

172
00:07:13,700 --> 00:07:14,670
each pebble.

173
00:07:14,670 --> 00:07:16,640
And now you might say,
especially those of you who

174
00:07:16,640 --> 00:07:19,500
haven't watched my calculus
videos, gee, you know, this

175
00:07:19,500 --> 00:07:22,140
might be getting close, but the
area of these rectangles

176
00:07:22,140 --> 00:07:25,120
isn't exactly the area
of this curve.

177
00:07:25,120 --> 00:07:26,010
It's a little inexact.

178
00:07:26,010 --> 00:07:26,970
There's a little error here.

179
00:07:26,970 --> 00:07:29,880
And what I would say is, well if
you're worried about that,

180
00:07:29,880 --> 00:07:34,630
what you should do is use
smaller increments of volume.

181
00:07:34,630 --> 00:07:36,730
And if you want to have smaller
changes in volume

182
00:07:36,730 --> 00:07:39,260
along each step, what
you do is you remove

183
00:07:39,260 --> 00:07:40,520
even smaller pebbles.

184
00:07:40,520 --> 00:07:43,790
And this goes back to trying
to get to that ideal

185
00:07:43,790 --> 00:07:45,900
quasi-static process.

186
00:07:45,900 --> 00:07:48,630
So if you did that of,
eventually the delta V's would

187
00:07:48,630 --> 00:07:51,430
get smaller and smaller and
smaller, and the rectangles

188
00:07:51,430 --> 00:07:53,350
would get thinner and
thinner and thinner.

189
00:07:53,350 --> 00:07:55,710
You'd have to do it over
more and more steps.

190
00:07:55,710 --> 00:07:58,730
But eventually you'll get to a
point, if you assume really

191
00:07:58,730 --> 00:08:02,150
small changes in our delta V.

192
00:08:02,150 --> 00:08:05,370
In calculus world, that
infinitely small changes, you

193
00:08:05,370 --> 00:08:08,040
write it as dV.

194
00:08:08,040 --> 00:08:11,940
So if you take a sum of all the
pressures, times the dV's

195
00:08:11,940 --> 00:08:14,780
you get the area under
this curve.

196
00:08:14,780 --> 00:08:16,880
So the way to think about it
when you're looking at this

197
00:08:16,880 --> 00:08:19,480
PV-diagram, if someone says,
you're going from this point

198
00:08:19,480 --> 00:08:22,130
to this pressure and this
volume, to this pressure and

199
00:08:22,130 --> 00:08:23,010
this volume.

200
00:08:23,010 --> 00:08:24,380
And they say, how much
work did you do?

201
00:08:24,380 --> 00:08:26,690
You say, oh, well I just had to
figure out the area under

202
00:08:26,690 --> 00:08:27,770
this curve.

203
00:08:27,770 --> 00:08:30,540
If you want to know the real
math behind it, if you could

204
00:08:30,540 --> 00:08:33,120
get your pressure as a function
of volume-- and if

205
00:08:33,120 --> 00:08:35,820
you haven't watched the calculus
videos you can ignore

206
00:08:35,820 --> 00:08:39,010
this little aside I'm
going to do here.

207
00:08:39,010 --> 00:08:42,169
This is this curve right here.

208
00:08:42,169 --> 00:08:44,450
If you could write it this way,
let's say you could write

209
00:08:44,450 --> 00:08:47,370
pressure as a function
of volume.

210
00:08:47,370 --> 00:08:51,290
When you're in algebra, you
learn a curve is, you know, y

211
00:08:51,290 --> 00:08:52,150
is a function of x.

212
00:08:52,150 --> 00:08:55,000
But here, y is the pressure
and x is volume, so its

213
00:08:55,000 --> 00:08:56,920
pressure is a function
of volume.

214
00:08:56,920 --> 00:09:01,780
So the area under this curve
is the integral of the

215
00:09:01,780 --> 00:09:04,580
pressure as a function of
volume, that's the height at

216
00:09:04,580 --> 00:09:10,850
any point, times our very
small change in volume.

217
00:09:10,850 --> 00:09:14,480
So times our very small
change in volume.

218
00:09:14,480 --> 00:09:18,910
And you take the sum from our
starting volume, so volume

219
00:09:18,910 --> 00:09:21,280
initial to volume final.

220
00:09:21,280 --> 00:09:24,130
And we'll do this in the future,
especially when we

221
00:09:24,130 --> 00:09:25,230
start touching on entropy.

222
00:09:25,230 --> 00:09:26,650
But this is a neat result.

223
00:09:26,650 --> 00:09:28,575
Even if you don't know the
calculus, or if this confuses

224
00:09:28,575 --> 00:09:30,870
you, if you've never seen
an integral before, you

225
00:09:30,870 --> 00:09:31,850
could ignore it.

226
00:09:31,850 --> 00:09:34,020
But you could look at this
intuitively and see the work I

227
00:09:34,020 --> 00:09:37,500
did is the area under
this curve.

228
00:09:37,500 --> 00:09:39,860
Now, let me ask you
one more thing.

229
00:09:39,860 --> 00:09:42,700
Let's say some work is being
done to the system.

230
00:09:42,700 --> 00:09:46,690
So we start adding some
marbles back.

231
00:09:46,690 --> 00:09:48,300
So let's say-- actually,
let's say we're

232
00:09:48,300 --> 00:09:49,350
going from this direction.

233
00:09:49,350 --> 00:09:52,880
Let's say we start at state 2
and we go in that direction.

234
00:09:52,880 --> 00:09:54,680
So direction matters.

235
00:09:54,680 --> 00:09:57,010
So let's say we go in that
direction right there.

236
00:09:57,010 --> 00:09:58,370
So I should put some arrows.

237
00:09:58,370 --> 00:10:01,410
And I'm overloading this
picture so much.

238
00:10:01,410 --> 00:10:03,140
Actually let me just do a new
picture, that's probably the

239
00:10:03,140 --> 00:10:05,490
best thing to do.

240
00:10:05,490 --> 00:10:10,966
So it's pressure, volume-- I'm
actually going to do two.

241
00:10:10,966 --> 00:10:16,000
Let me just do pressure,
volume.

242
00:10:16,000 --> 00:10:17,320
I'm going to do two
graphs here.

243
00:10:17,320 --> 00:10:20,240


244
00:10:20,240 --> 00:10:21,170
All right.

245
00:10:21,170 --> 00:10:23,070
So in the first one
it's pressure,

246
00:10:23,070 --> 00:10:25,510
volume, pressure, volume.

247
00:10:25,510 --> 00:10:31,220
We started here at 1, and
we went here to 2.

248
00:10:31,220 --> 00:10:34,950
So our system was essentially
pushed up on the piston.

249
00:10:34,950 --> 00:10:37,160
And it could be a curve or a
line, I'm not going to get too

250
00:10:37,160 --> 00:10:40,450
particular right now, but it was
going in this direction.

251
00:10:40,450 --> 00:10:42,960
And so we can say that the work
done was the pressure

252
00:10:42,960 --> 00:10:45,980
times the increase in volume
at any moment.

253
00:10:45,980 --> 00:10:49,610
So the work done was the
area under this curve.

254
00:10:49,610 --> 00:10:54,660


255
00:10:54,660 --> 00:11:02,300
Now, if we started at position
2 and we go to position 1.

256
00:11:02,300 --> 00:11:04,430
2 to 1.

257
00:11:04,430 --> 00:11:05,260
Now what's happening?

258
00:11:05,260 --> 00:11:06,250
Now we're compressing.

259
00:11:06,250 --> 00:11:08,885
So if we're going in that
direction, you might say, oh

260
00:11:08,885 --> 00:11:11,220
OK, maybe the work done by
the system is still the

261
00:11:11,220 --> 00:11:12,490
area under the curve.

262
00:11:12,490 --> 00:11:13,480
Well you'd be close.

263
00:11:13,480 --> 00:11:14,280
Because what's happening now?

264
00:11:14,280 --> 00:11:15,780
We're now compressing
the system or

265
00:11:15,780 --> 00:11:17,440
adding the marbles back.

266
00:11:17,440 --> 00:11:19,680
We're putting energy
into the system.

267
00:11:19,680 --> 00:11:23,310
So if we do that, remember, your
work done by the system

268
00:11:23,310 --> 00:11:26,880
was pressure times an
increase in volume.

269
00:11:26,880 --> 00:11:28,710
Now it's going to be
your pressure times

270
00:11:28,710 --> 00:11:30,360
a decrease in volume.

271
00:11:30,360 --> 00:11:35,870
So when you go back in this
direction, the area is not the

272
00:11:35,870 --> 00:11:40,225
work done by the system, it's
the work done to the system.

273
00:11:40,225 --> 00:11:43,630
And maybe I'll do that in a
different color, so green for

274
00:11:43,630 --> 00:11:46,090
work done to the system.

275
00:11:46,090 --> 00:11:50,840
Now let me throw you another
little interesting idea.

276
00:11:50,840 --> 00:11:53,330
And this is actually
a key idea.

277
00:11:53,330 --> 00:11:54,850
It's good to get the
intuition here.

278
00:11:54,850 --> 00:11:58,470
So let me just draw a very
simple PV-diagram again.

279
00:11:58,470 --> 00:12:04,320


280
00:12:04,320 --> 00:12:07,450
So let's say we start
at some state here.

281
00:12:07,450 --> 00:12:08,540
State 1.

282
00:12:08,540 --> 00:12:13,640
And I do something, you know,
I'm in a quasi-static process

283
00:12:13,640 --> 00:12:16,450
and it, you know, it's doing
something weird, and I get to

284
00:12:16,450 --> 00:12:19,230
state 2 here.

285
00:12:19,230 --> 00:12:22,370
And it's going in
this direction.

286
00:12:22,370 --> 00:12:24,470
So my volume is increasing.

287
00:12:24,470 --> 00:12:27,720
So in this situation, what is
the work done by the system?

288
00:12:27,720 --> 00:12:29,890
Easy enough, it's the area
under this curve.

289
00:12:29,890 --> 00:12:32,970


290
00:12:32,970 --> 00:12:38,770
Now let's say that I keep
doing some type of

291
00:12:38,770 --> 00:12:41,340
quasi-static process, but it
takes a different path.

292
00:12:41,340 --> 00:12:43,370
I'm doing something else, other
than adding the marbles

293
00:12:43,370 --> 00:12:44,670
directly back.

294
00:12:44,670 --> 00:12:51,110
So my new path looks something
like this to get

295
00:12:51,110 --> 00:12:52,360
back to state 1.

296
00:12:52,360 --> 00:12:55,290


297
00:12:55,290 --> 00:12:57,150
So these arrows are
going back.

298
00:12:57,150 --> 00:13:00,440
So now what is the work
done to the system?

299
00:13:00,440 --> 00:13:03,230
well my volume is decreasing,
so it's the area under the

300
00:13:03,230 --> 00:13:05,090
second curve.

301
00:13:05,090 --> 00:13:06,700
The area under the second
curve is the

302
00:13:06,700 --> 00:13:09,650
work done to the system.

303
00:13:09,650 --> 00:13:12,420
So if I want to know what the
net work the system did, going

304
00:13:12,420 --> 00:13:16,110
from state 1 to state 2, and
then going back to state 1--

305
00:13:16,110 --> 00:13:17,640
remember, this is a pressure
and volume

306
00:13:17,640 --> 00:13:19,550
diagram-- what is it?

307
00:13:19,550 --> 00:13:22,380
Well the work that the system
did was this whole area under

308
00:13:22,380 --> 00:13:23,630
this brown curve.

309
00:13:23,630 --> 00:13:27,790
And then it had some work done
to it, which is the area under

310
00:13:27,790 --> 00:13:29,010
this magenta curve.

311
00:13:29,010 --> 00:13:32,150
So the net work it did is
essentially the white, the

312
00:13:32,150 --> 00:13:34,730
whole area, minus
this red area.

313
00:13:34,730 --> 00:13:38,620
So the net work it did would be
essentially just the area

314
00:13:38,620 --> 00:13:39,960
inside this loop.

315
00:13:39,960 --> 00:13:42,830


316
00:13:42,830 --> 00:13:44,660
And hopefully you don't have to
know calculus to do this,

317
00:13:44,660 --> 00:13:46,120
although calculus you would
actually use to

318
00:13:46,120 --> 00:13:49,140
compute these areas.

319
00:13:49,140 --> 00:13:52,530
But I just want to give you that
intuition, that the area

320
00:13:52,530 --> 00:13:56,720
inside this closed loop is
actually the amount of work

321
00:13:56,720 --> 00:13:59,740
that our system has done.

322
00:13:59,740 --> 00:14:02,560
And what's important is the
direction that it's going.

323
00:14:02,560 --> 00:14:05,705
So it increased volume, then
decreased volume, so it's kind

324
00:14:05,705 --> 00:14:07,770
of this clockwise motion.

325
00:14:07,770 --> 00:14:12,690
This is the work that our system
has done, which, I

326
00:14:12,690 --> 00:14:14,430
don't know, to me is a pretty
interesting thing.

327
00:14:14,430 --> 00:14:16,900
And later we can use this notion
to come up with some

328
00:14:16,900 --> 00:14:20,230
other ideas behind our
state variables

329
00:14:20,230 --> 00:14:22,060
I'll make one little
aside here.

330
00:14:22,060 --> 00:14:25,880
Remember, our state variable
pressure volume, we did stuff

331
00:14:25,880 --> 00:14:27,230
to it then we went back
to that state.

332
00:14:27,230 --> 00:14:28,330
That stayed the same.

333
00:14:28,330 --> 00:14:29,550
And I want to say
another thing.

334
00:14:29,550 --> 00:14:33,280
For our purposes, when we're
dealing with ideal gases,

335
00:14:33,280 --> 00:14:36,080
where the internal energy is
essentially the kinetic energy

336
00:14:36,080 --> 00:14:39,440
of the system, if we go and do
all sorts of crazy stuff and

337
00:14:39,440 --> 00:14:43,230
come back, our internal
energy hasn't changed.

338
00:14:43,230 --> 00:14:45,580
So the internal energy is always
going to be the same at

339
00:14:45,580 --> 00:14:46,190
this point.

340
00:14:46,190 --> 00:14:48,840
So if I said, I did all of this
stuff and came back here,

341
00:14:48,840 --> 00:14:50,660
what is my change in
internal energy?

342
00:14:50,660 --> 00:14:51,245
It's 0.

343
00:14:51,245 --> 00:14:52,780
The change is 0.

344
00:14:52,780 --> 00:14:55,040
Now if I said I went from here
to here, I would have a

345
00:14:55,040 --> 00:14:56,570
different internal energy
and my change would

346
00:14:56,570 --> 00:14:57,900
be something real.

347
00:14:57,900 --> 00:15:00,670
But since this is a state
function, it doesn't care how

348
00:15:00,670 --> 00:15:01,330
I got there.

349
00:15:01,330 --> 00:15:03,450
If I took all these loops and
got back there, it just says,

350
00:15:03,450 --> 00:15:07,220
look, if I'm at this point in
the PV-diagram, my internal

351
00:15:07,220 --> 00:15:09,200
energy is the same thing.

352
00:15:09,200 --> 00:15:11,890
So if I start at this point,
and I finish again at this

353
00:15:11,890 --> 00:15:14,890
point, I have had no change
in internal energy.

354
00:15:14,890 --> 00:15:17,120
And we'll talk more about
that in the next video.

355
00:15:17,120 --> 00:15:18,910
But I just wanted to leave you
there and get you this

356
00:15:18,910 --> 00:15:21,620
intuition behind the areas
under the curves in the

357
00:15:21,620 --> 00:15:22,870
PV-diagram.

358
00:15:22,870 --> 00:00:00,000