1
00:00:00,000 --> 00:00:00,690


2
00:00:00,690 --> 00:00:03,580
Let's start with this classic
system that I keep referring

3
00:00:03,580 --> 00:00:05,210
to in our thermodynamics
videos.

4
00:00:05,210 --> 00:00:06,910
I have a cylinder.

5
00:00:06,910 --> 00:00:10,240
It's got a little piston on the
top of it, or it's got a

6
00:00:10,240 --> 00:00:12,110
ceiling that's movable.

7
00:00:12,110 --> 00:00:16,890
The gas, and we're thinking of
monoatomic ideal gases in

8
00:00:16,890 --> 00:00:21,260
here, they're exerting pressure
onto this ceiling.

9
00:00:21,260 --> 00:00:23,220
And the reason why the ceiling
isn't moving all the way up,

10
00:00:23,220 --> 00:00:26,270
is because I've placed a bunch
of rocks on the top to offset

11
00:00:26,270 --> 00:00:29,520
the force per area of
the actual gas.

12
00:00:29,520 --> 00:00:32,229
And I start this gas when
it's in equilibrium.

13
00:00:32,229 --> 00:00:33,700
I can define its macrostates.

14
00:00:33,700 --> 00:00:35,030
It has some volume.

15
00:00:35,030 --> 00:00:37,415
It has some pressure that's
being offset by these rocks.

16
00:00:37,415 --> 00:00:40,140
And it has some well-defined
temperature.

17
00:00:40,140 --> 00:00:43,890
Now, what I'm going to do is,
I'm going to place this system

18
00:00:43,890 --> 00:00:46,830
here-- I'm going to place it
on top of a reservoir.

19
00:00:46,830 --> 00:00:49,280
And I talked about what a
reservoir was either in the

20
00:00:49,280 --> 00:00:51,040
last video or a couple
of videos ago.

21
00:00:51,040 --> 00:00:55,720
You can view it as an infinitely
large object, if

22
00:00:55,720 --> 00:00:57,460
you will, of a certain
temperature.

23
00:00:57,460 --> 00:01:00,850
So if I put it next to-- if I
put our system next to this

24
00:01:00,850 --> 00:01:03,930
reservoir-- and let's say I
start removing pebbles from

25
00:01:03,930 --> 00:01:06,290
our system.

26
00:01:06,290 --> 00:01:09,060
We learned a couple of videos
ago that if we did it

27
00:01:09,060 --> 00:01:11,270
adiabatically-- what does
adiabatically mean?

28
00:01:11,270 --> 00:01:14,230
If we removed these pebbles
in isolation, without any

29
00:01:14,230 --> 00:01:17,760
reservoir around, the volume
would increase, the pressure

30
00:01:17,760 --> 00:01:19,700
would go down, and actually
the temperature would

31
00:01:19,700 --> 00:01:20,420
decrease, as well.

32
00:01:20,420 --> 00:01:23,080
We showed that a couple
of videos ago.

33
00:01:23,080 --> 00:01:26,330
So by putting this big reservoir
there that's a lot

34
00:01:26,330 --> 00:01:29,480
larger than our actual canister,
this will keep the

35
00:01:29,480 --> 00:01:33,000
temperature in our
canister at T1.

36
00:01:33,000 --> 00:01:40,530
You can kind of view a reservoir
as-- say I had a cup

37
00:01:40,530 --> 00:01:42,230
of water in a stadium.

38
00:01:42,230 --> 00:01:46,710
And the air conditioner in the
stadium is at 60 degrees.

39
00:01:46,710 --> 00:01:49,880
Well, no matter what I do to
that water, I could put it in

40
00:01:49,880 --> 00:01:52,140
the microwave and warm it up,
but if I put it back in that

41
00:01:52,140 --> 00:01:53,850
stadium, that stadium
is going to keep

42
00:01:53,850 --> 00:01:55,480
that water at 60 degrees.

43
00:01:55,480 --> 00:01:58,610
And you might say, oh, won't
the reservoir's temperature

44
00:01:58,610 --> 00:02:00,650
decrease if it's throwing
off heat?

45
00:02:00,650 --> 00:02:03,980
Well, it would, but it's so much
larger that its impact

46
00:02:03,980 --> 00:02:04,680
isn't noticeable.

47
00:02:04,680 --> 00:02:09,690
For example, if I put a cup of
boiling water into a super

48
00:02:09,690 --> 00:02:14,360
large covered-dome stadium, the
water will get colder to

49
00:02:14,360 --> 00:02:16,140
the ambient temperature
of the stadium.

50
00:02:16,140 --> 00:02:18,770
The stadium will get warmer, but
it will be so marginally

51
00:02:18,770 --> 00:02:20,560
warmer than you won't
even notice it.

52
00:02:20,560 --> 00:02:22,200
So you can kind of view
that as a reservoir.

53
00:02:22,200 --> 00:02:24,450
And theoretically, this
is infinitely large.

54
00:02:24,450 --> 00:02:27,870
So the effect of this is, as we
remove these little rocks,

55
00:02:27,870 --> 00:02:30,390
we're going to keep the
temperature constant.

56
00:02:30,390 --> 00:02:32,030
And remember, if we're keeping
the temperature constant,

57
00:02:32,030 --> 00:02:34,090
we're also keeping the internal
energy constant,

58
00:02:34,090 --> 00:02:35,130
because we're not changing
the kinetic

59
00:02:35,130 --> 00:02:36,550
energy of the particles.

60
00:02:36,550 --> 00:02:39,130
So let me see what happens.

61
00:02:39,130 --> 00:02:41,320
So I keep doing that.

62
00:02:41,320 --> 00:02:47,220
And so I get to a point-- let
me see-- where my volume has

63
00:02:47,220 --> 00:02:52,660
increased-- so let me delete
some of my rocks here.

64
00:02:52,660 --> 00:02:54,600
Delete some of the rocks.

65
00:02:54,600 --> 00:02:57,370
So some of the rocks are gone.

66
00:02:57,370 --> 00:03:02,230
And now my overall volume
is going to be larger.

67
00:03:02,230 --> 00:03:04,980
Let me move this up
a little bit.

68
00:03:04,980 --> 00:03:08,190
And then let me color
this in black.

69
00:03:08,190 --> 00:03:09,670
Oh, whoops.

70
00:03:09,670 --> 00:03:14,670
Let me color this in, just
to give an idea.

71
00:03:14,670 --> 00:03:17,632
So our volume has gotten
a bit larger.

72
00:03:17,632 --> 00:03:21,320
And let me get my
pen correctly.

73
00:03:21,320 --> 00:03:25,620
So our volume has gotten larger
by roughly this amount.

74
00:03:25,620 --> 00:03:27,550
We have the same number
of particles.

75
00:03:27,550 --> 00:03:29,930
They're going to bump into
the ceiling a little less

76
00:03:29,930 --> 00:03:32,200
frequently, so my pressure
would have gone down.

77
00:03:32,200 --> 00:03:35,390
But because I kept this
reservoir here, because this

78
00:03:35,390 --> 00:03:40,160
reservoir was here the whole
time during this process, the

79
00:03:40,160 --> 00:03:42,210
temperature stayed at T1.

80
00:03:42,210 --> 00:03:45,860
And that was only because
of this reservoir.

81
00:03:45,860 --> 00:03:47,000
And I want to make that clear.

82
00:03:47,000 --> 00:03:50,410
And also, just as review, this
is a quasi-static process,

83
00:03:50,410 --> 00:03:51,680
because I'm doing
it very slowly.

84
00:03:51,680 --> 00:03:54,340
The system is in equilibrium
the whole time.

85
00:03:54,340 --> 00:04:02,270
So let's draw what we have so
far on our famous PV diagram.

86
00:04:02,270 --> 00:04:08,570
So this is the P-axis.

87
00:04:08,570 --> 00:04:09,820
That's the V-axis.

88
00:04:09,820 --> 00:04:12,260


89
00:04:12,260 --> 00:04:14,600
You label them.

90
00:04:14,600 --> 00:04:15,840
This is P.

91
00:04:15,840 --> 00:04:17,040
This is V.

92
00:04:17,040 --> 00:04:19,200
Let me call this-- I'm going
to do it in a good color.

93
00:04:19,200 --> 00:04:21,980
This is state A of the system.

94
00:04:21,980 --> 00:04:23,940
This is state B of the system.

95
00:04:23,940 --> 00:04:27,530
So state A starts at some
pressure and volume-- I'll do

96
00:04:27,530 --> 00:04:29,960
it like that.

97
00:04:29,960 --> 00:04:31,450
That's state A.

98
00:04:31,450 --> 00:04:33,150
And it moves to state B.

99
00:04:33,150 --> 00:04:35,030
And notice, I kept the
temperature constant.

100
00:04:35,030 --> 00:04:36,910
And what did we learn in,
I think it was one

101
00:04:36,910 --> 00:04:38,250
or two videos ago?

102
00:04:38,250 --> 00:04:40,020
Well, we're at a constant
temperature, so we're going to

103
00:04:40,020 --> 00:04:42,170
move along an isotherm,
which is just

104
00:04:42,170 --> 00:04:45,360
a rectangular hyperbola.

105
00:04:45,360 --> 00:04:48,310
Because when your temperature
is constant, your pressure

106
00:04:48,310 --> 00:04:50,600
times your volume is going to
equal a constant number.

107
00:04:50,600 --> 00:04:51,530
And I went over that before.

108
00:04:51,530 --> 00:04:53,980
So we're going to move over--
our path is going to look

109
00:04:53,980 --> 00:04:59,380
something like this, and I'll
move here, to state B.

110
00:04:59,380 --> 00:05:01,590
I'll move over here
to state B.

111
00:05:01,590 --> 00:05:04,800
And the whole time, this was at
a constant temperature T1.

112
00:05:04,800 --> 00:05:09,060


113
00:05:09,060 --> 00:05:10,660
Now, we've done a bunch
of videos now.

114
00:05:10,660 --> 00:05:13,470
We said, OK, how much work
was done on this system?

115
00:05:13,470 --> 00:05:15,160
Well, the work done on
the system is the

116
00:05:15,160 --> 00:05:16,160
area under this curve.

117
00:05:16,160 --> 00:05:19,680
So some positive work was-- not
done on the system, sorry.

118
00:05:19,680 --> 00:05:21,340
How much work was done
by the system?

119
00:05:21,340 --> 00:05:22,890
We're moving in this
direction.

120
00:05:22,890 --> 00:05:24,960
I should put the direction
there.

121
00:05:24,960 --> 00:05:26,980
We're moving from
left to right.

122
00:05:26,980 --> 00:05:28,900
The amount of work done
by the system is

123
00:05:28,900 --> 00:05:30,500
pressure times volume.

124
00:05:30,500 --> 00:05:32,000
We've seen that multiple
times.

125
00:05:32,000 --> 00:05:34,180
So you take this area of the
curve, and you have the work

126
00:05:34,180 --> 00:05:36,680
done by the system
from A to B.

127
00:05:36,680 --> 00:05:36,970
Right?

128
00:05:36,970 --> 00:05:39,590
So let's call that
work from A to B.

129
00:05:39,590 --> 00:05:42,650


130
00:05:42,650 --> 00:05:45,790
Now, that's fair and everything,
but what I want to

131
00:05:45,790 --> 00:05:47,450
think more about, is
how much heat was

132
00:05:47,450 --> 00:05:48,910
transferred by my reservoir?

133
00:05:48,910 --> 00:05:51,550
Remember, we said, if this
reservoir wasn't there, the

134
00:05:51,550 --> 00:05:54,210
temperature of my canister
would have gone down as I

135
00:05:54,210 --> 00:05:56,910
expanded its volume, and as
the pressure went down.

136
00:05:56,910 --> 00:05:58,760
So how much heat came into it?

137
00:05:58,760 --> 00:06:01,970
Well, let's go back to our basic
internal energy formula.

138
00:06:01,970 --> 00:06:07,020
Change in internal energy is
equal to heat applied to the

139
00:06:07,020 --> 00:06:10,840
system minus the work
done by the system

140
00:06:10,840 --> 00:06:12,360
Now, what is the change
in internal

141
00:06:12,360 --> 00:06:14,120
energy in this scenario?

142
00:06:14,120 --> 00:06:15,500
Well, it was at a constant
temperature

143
00:06:15,500 --> 00:06:17,520
the whole time, right?

144
00:06:17,520 --> 00:06:21,330
And since we're dealing with a
very simple ideal gas, all of

145
00:06:21,330 --> 00:06:23,340
our internal energy is due
to kinetic energy, which

146
00:06:23,340 --> 00:06:24,640
temperature is a measure of.

147
00:06:24,640 --> 00:06:26,010
So, temperature didn't change.

148
00:06:26,010 --> 00:06:28,130
Our average kinetic energy
didn't change, which means our

149
00:06:28,130 --> 00:06:29,680
kinetic energy didn't change.

150
00:06:29,680 --> 00:06:36,440
So our internal energy did not
change while we moved from

151
00:06:36,440 --> 00:06:38,490
left to right along
this isotherm.

152
00:06:38,490 --> 00:06:40,970
So we could say our internal
energy is zero.

153
00:06:40,970 --> 00:06:45,180
And that is equal to the heat
added to the system minus the

154
00:06:45,180 --> 00:06:47,610
work done by the system.

155
00:06:47,610 --> 00:06:48,340
Right?

156
00:06:48,340 --> 00:06:51,996
So if you just-- we put the work
done by the system on the

157
00:06:51,996 --> 00:06:55,250
other side, and then switch the
sides, you get heat added

158
00:06:55,250 --> 00:06:58,940
to the system is equal to the
work done by the system.

159
00:06:58,940 --> 00:06:59,740
And that makes sense.

160
00:06:59,740 --> 00:07:03,340
The system was doing some work
this entire time, so it was

161
00:07:03,340 --> 00:07:07,360
giving energy to-- well,
you know, it was giving

162
00:07:07,360 --> 00:07:08,530
essentially maybe
some potential

163
00:07:08,530 --> 00:07:10,370
energy to these rocks.

164
00:07:10,370 --> 00:07:11,910
So it was giving energy away.

165
00:07:11,910 --> 00:07:14,340
It was giving energy outside
of the system.

166
00:07:14,340 --> 00:07:17,650
So how did it maintain
its internal energy?

167
00:07:17,650 --> 00:07:19,530
Well, someone had to give
it some energy.

168
00:07:19,530 --> 00:07:24,610
And it was given that energy
by this reservoir.

169
00:07:24,610 --> 00:07:27,350
So let's say, and the convention
for doing this is

170
00:07:27,350 --> 00:07:30,400
to say, that it was given--
let me write this down.

171
00:07:30,400 --> 00:07:32,820
It was given some energy Q1.

172
00:07:32,820 --> 00:07:34,830
We just say, we just put this
downward arrow to say that

173
00:07:34,830 --> 00:07:37,610
some energy went into
the system here.

174
00:07:37,610 --> 00:07:38,820
Fair enough.

175
00:07:38,820 --> 00:07:46,050
Now let's take this state B and
remove the reservoir, and

176
00:07:46,050 --> 00:07:47,700
completely isolate ourselves.

177
00:07:47,700 --> 00:07:50,400
So there's no way that heat can
be transferred to and from

178
00:07:50,400 --> 00:07:51,150
our system.

179
00:07:51,150 --> 00:07:53,650
And let's keep removing
some rocks.

180
00:07:53,650 --> 00:07:56,375
So if we keep removing some
rocks, where do we get to?

181
00:07:56,375 --> 00:07:59,820
Let me go down here.

182
00:07:59,820 --> 00:08:03,170
So let's say we remove a
bunch of more rocks.

183
00:08:03,170 --> 00:08:07,300
So let me erase even more
rocks than we had in B.

184
00:08:07,300 --> 00:08:08,870
Maybe I only have
one rock left.

185
00:08:08,870 --> 00:08:11,880


186
00:08:11,880 --> 00:08:15,690
And obviously, the overall
volume would have increased.

187
00:08:15,690 --> 00:08:20,810
So let me make our piston go up
like that, and I can make

188
00:08:20,810 --> 00:08:24,650
our piston is maybe
a lot higher now.

189
00:08:24,650 --> 00:08:28,720
And let me just fill in the rest
of our, just so that we

190
00:08:28,720 --> 00:08:32,100
don't have some empty
space there.

191
00:08:32,100 --> 00:08:37,520
So if I fill that in right
there-- OK Let

192
00:08:37,520 --> 00:08:39,510
me fill that in.

193
00:08:39,510 --> 00:08:43,510
And then I just use the blue--
I should be talking about

194
00:08:43,510 --> 00:08:44,870
thermodynamics, not drawing.

195
00:08:44,870 --> 00:08:46,520
But you get the idea.

196
00:08:46,520 --> 00:08:48,420
And then I have some
more-- you know, I

197
00:08:48,420 --> 00:08:49,670
shouldn't add particles.

198
00:08:49,670 --> 00:08:52,480
But my volume has increased
a good bit.

199
00:08:52,480 --> 00:08:56,200
My pressure will have gone down,
they're going to bump

200
00:08:56,200 --> 00:08:57,610
into the walls less.

201
00:08:57,610 --> 00:09:02,290
And because I removed the
reservoir, what's going to

202
00:09:02,290 --> 00:09:04,430
happen to the temperature?

203
00:09:04,430 --> 00:09:06,910
My temperature is going
to go down.

204
00:09:06,910 --> 00:09:09,000
This was an adiabatic process.

205
00:09:09,000 --> 00:09:12,050
So an adiabatic just means
we did it in isolation.

206
00:09:12,050 --> 00:09:16,020
There was no exchange of heat
from one system to another.

207
00:09:16,020 --> 00:09:19,150
So let me just-- this arrow
continues down here.

208
00:09:19,150 --> 00:09:20,400
I'll say adiabatic.

209
00:09:20,400 --> 00:09:24,020


210
00:09:24,020 --> 00:09:26,040
Now, since I'm moving from
one temperature to

211
00:09:26,040 --> 00:09:27,960
another, this is at T2.

212
00:09:27,960 --> 00:09:30,540


213
00:09:30,540 --> 00:09:32,920
So I will have moved to
another isotherm.

214
00:09:32,920 --> 00:09:34,550
This is the isotherm for T1.

215
00:09:34,550 --> 00:09:36,350
If I keep my temperature
constant, I

216
00:09:36,350 --> 00:09:38,380
move along this hyperbola.

217
00:09:38,380 --> 00:09:40,560
And I would have kept moving
along this hyperbola.

218
00:09:40,560 --> 00:09:43,820
But now that we didn't keep our
temperature constant, we

219
00:09:43,820 --> 00:09:45,250
now move like this.

220
00:09:45,250 --> 00:09:47,660
We move to another isotherm.

221
00:09:47,660 --> 00:09:49,660
So let's say I have another
isotherm at T2.

222
00:09:49,660 --> 00:09:51,990
It looks something like this.

223
00:09:51,990 --> 00:09:53,410
So let me draw like that.

224
00:09:53,410 --> 00:09:58,850
So let's say I have another-- it
should actually curve up a

225
00:09:58,850 --> 00:09:59,260
little bit.

226
00:09:59,260 --> 00:10:02,430
So let's say, everything at
temperature T2, depending on

227
00:10:02,430 --> 00:10:04,450
its pressure and volume, is
someplace along this curve

228
00:10:04,450 --> 00:10:06,530
that asymptotes up like
that, and then goes to

229
00:10:06,530 --> 00:10:07,760
the right like that.

230
00:10:07,760 --> 00:10:10,940
Now, I would have moved down
to this isotherm, and my

231
00:10:10,940 --> 00:10:13,400
pressure would have kept going
down, and my volume would have

232
00:10:13,400 --> 00:10:14,560
kept going down.

233
00:10:14,560 --> 00:10:20,290
So this move, from B to state
C, will look like this.

234
00:10:20,290 --> 00:10:23,500


235
00:10:23,500 --> 00:10:24,760
Let me do to it in
another color.

236
00:10:24,760 --> 00:10:27,190
Let me do it in the orange
color of this arrow.

237
00:10:27,190 --> 00:10:30,000
So it will look like this.

238
00:10:30,000 --> 00:10:33,540
And now we're at state C.

239
00:10:33,540 --> 00:10:35,200
Now, this was adiabatic.

240
00:10:35,200 --> 00:10:38,360


241
00:10:38,360 --> 00:10:40,070
Which means, there is
no exchange of heat.

242
00:10:40,070 --> 00:10:44,010
So I don't have to figure out
how much heat got transferred

243
00:10:44,010 --> 00:10:45,060
into the system.

244
00:10:45,060 --> 00:10:46,520
Now, there's something
interesting here.

245
00:10:46,520 --> 00:10:50,650
We still did do some work.

246
00:10:50,650 --> 00:10:52,670
We can take the area
under this curve.

247
00:10:52,670 --> 00:10:54,950
And we're going to leave it to
a future video to think about

248
00:10:54,950 --> 00:11:01,010
where that work energy-- well,
the main thing is, is what was

249
00:11:01,010 --> 00:11:02,880
reduced by that work energy.

250
00:11:02,880 --> 00:11:05,380
And, well, if you think
[UNINTELLIGIBLE]

251
00:11:05,380 --> 00:11:06,510
to leave it to future video.

252
00:11:06,510 --> 00:11:09,180
Our internal energy was
reduced, right?

253
00:11:09,180 --> 00:11:10,580
Because our temperature
went down.

254
00:11:10,580 --> 00:11:12,120
So our internal energy
went down.

255
00:11:12,120 --> 00:11:14,250
We'll talk more about that
in the future video.

256
00:11:14,250 --> 00:11:18,720
So now that we're at state C,
and we're at temperature T2.

257
00:11:18,720 --> 00:11:21,670
Let's put back another
sink here.

258
00:11:21,670 --> 00:11:25,000


259
00:11:25,000 --> 00:11:31,230
But this sink, what it's going
to have is a reservoir.

260
00:11:31,230 --> 00:11:33,150
So let me put two things
right here.

261
00:11:33,150 --> 00:11:36,700


262
00:11:36,700 --> 00:11:39,650
So I'm going to add--
let me erase some of

263
00:11:39,650 --> 00:11:43,190
these blocks in black.

264
00:11:43,190 --> 00:11:45,890


265
00:11:45,890 --> 00:11:47,695
So now I'm going to
add blocks back.

266
00:11:47,695 --> 00:11:50,210


267
00:11:50,210 --> 00:11:53,600
I'm going to add little
pebbles back into it.

268
00:11:53,600 --> 00:11:56,830
But I'm going to do it as
an isothermic process.

269
00:11:56,830 --> 00:12:00,220
I'm going to do it with
a reservoir here.

270
00:12:00,220 --> 00:12:02,520
But this reservoir here, it's
not going to be the same

271
00:12:02,520 --> 00:12:04,170
reservoir that I put up there.

272
00:12:04,170 --> 00:12:05,290
I swapped that one out.

273
00:12:05,290 --> 00:12:07,910
I got rid of any reservoir
when I went from B to C.

274
00:12:07,910 --> 00:12:09,730
And now I'm going to swap
in a new reservoir.

275
00:12:09,730 --> 00:12:13,780
Actually, let me make it blue.

276
00:12:13,780 --> 00:12:15,010
Because it's going to be--

277
00:12:15,010 --> 00:12:16,180
Because here's what's
happening.

278
00:12:16,180 --> 00:12:17,450
I'm now adding pebbles in.

279
00:12:17,450 --> 00:12:20,210
I'm compressing the gas.

280
00:12:20,210 --> 00:12:22,680
If this was an adiabatic
process, the gas would

281
00:12:22,680 --> 00:12:23,960
want to heat up.

282
00:12:23,960 --> 00:12:26,730
So what I'm doing is, I need to
put a reservoir to keep it

283
00:12:26,730 --> 00:12:29,750
at T2, to keep it along
this isotherm.

284
00:12:29,750 --> 00:12:31,840
So this is T2.

285
00:12:31,840 --> 00:12:34,320
Remember, this reservoir is
kind of a cold reservoir.

286
00:12:34,320 --> 00:12:36,200
It keeps the temperature down.

287
00:12:36,200 --> 00:12:37,520
As opposed to here.

288
00:12:37,520 --> 00:12:38,575
This was a hot reservoir.

289
00:12:38,575 --> 00:12:40,420
It kept the temperature up.

290
00:12:40,420 --> 00:12:42,370
So you can imagine.

291
00:12:42,370 --> 00:12:45,160
The heat generated in the
system, or internal energy

292
00:12:45,160 --> 00:12:47,490
being generated in the
system-- well, no, I

293
00:12:47,490 --> 00:12:48,590
shouldn't say that.

294
00:12:48,590 --> 00:12:52,140
The temperature of the system
will want to go up, but it's

295
00:12:52,140 --> 00:12:55,230
being released, because it's
able to transfer that heat

296
00:12:55,230 --> 00:12:57,550
into our new reservoir.

297
00:12:57,550 --> 00:12:58,910
And that amount of heat is Q2.

298
00:12:58,910 --> 00:13:01,920


299
00:13:01,920 --> 00:13:03,970
So I move along this.

300
00:13:03,970 --> 00:13:04,700
This is right here.

301
00:13:04,700 --> 00:13:08,040
I'm moving along another
isotherm, I'm moving along

302
00:13:08,040 --> 00:13:09,250
this isotherm.

303
00:13:09,250 --> 00:13:14,580
Until I get to state D.

304
00:13:14,580 --> 00:13:17,420
We're almost there.

305
00:13:17,420 --> 00:13:21,040
This is state D.

306
00:13:21,040 --> 00:13:24,720
So state D will be someplace
here, along this isotherm

307
00:13:24,720 --> 00:13:25,670
right here.

308
00:13:25,670 --> 00:13:27,590
Maybe this is state D.

309
00:13:27,590 --> 00:13:30,720
And once again, you can make
the argument that we moved

310
00:13:30,720 --> 00:13:33,400
along an isotherm Our
temperature did not change

311
00:13:33,400 --> 00:13:35,040
from C to D.

312
00:13:35,040 --> 00:13:38,600
We know that our internal energy
went down from B to C,

313
00:13:38,600 --> 00:13:39,950
because we did some work.

314
00:13:39,950 --> 00:13:42,620
But from C to D, our temperature
stayed the same.

315
00:13:42,620 --> 00:13:47,290
It was at temperature-- let me
write it down-- T2, right?

316
00:13:47,290 --> 00:13:49,520
Because we had this
reservoir here.

317
00:13:49,520 --> 00:13:50,460
It stayed the same.

318
00:13:50,460 --> 00:13:52,440
If your temperature stays the
same, then your internal

319
00:13:52,440 --> 00:13:53,660
energy stays the same.

320
00:13:53,660 --> 00:13:56,100
At least for the system we're
dealing with, because it's a

321
00:13:56,100 --> 00:13:57,080
very simple gas.

322
00:13:57,080 --> 00:13:58,710
It's actually the system you'll
deal with most of the

323
00:13:58,710 --> 00:14:01,960
time, in an intro thermodynamics
course.

324
00:14:01,960 --> 00:14:02,550
So.

325
00:14:02,550 --> 00:14:04,640
Given our internal energy didn't
change, we can apply

326
00:14:04,640 --> 00:14:10,490
the same argument that the heat
added to the system is

327
00:14:10,490 --> 00:14:13,230
equal to the work done
by the system.

328
00:14:13,230 --> 00:14:13,650
Right?

329
00:14:13,650 --> 00:14:15,580
Same math as we did up here.

330
00:14:15,580 --> 00:14:19,390
Now, in this case, the work
wasn't done by the system.

331
00:14:19,390 --> 00:14:20,820
The work was done
to the system.

332
00:14:20,820 --> 00:14:23,370
We compressed this piston.

333
00:14:23,370 --> 00:14:25,780
The force times distance
went the other way.

334
00:14:25,780 --> 00:14:29,660
So given that work was done to
the system, the heat added to

335
00:14:29,660 --> 00:14:31,260
the system was negative,
right?

336
00:14:31,260 --> 00:14:34,190
We're just applying
the same thing.

337
00:14:34,190 --> 00:14:37,910
If our internal energy is 0, the
heat added to the system

338
00:14:37,910 --> 00:14:40,250
is equal to the work
done by the system.

339
00:14:40,250 --> 00:14:42,260
The work done by the
system is negative.

340
00:14:42,260 --> 00:14:44,110
Work was done to it.

341
00:14:44,110 --> 00:14:47,600
So the heat added to the system
would be negative.

342
00:14:47,600 --> 00:14:49,330
Or another way to think
about it is that the

343
00:14:49,330 --> 00:14:51,030
system gave away heat.

344
00:14:51,030 --> 00:14:53,950


345
00:14:53,950 --> 00:14:57,430
We put that with Q2.

346
00:14:57,430 --> 00:14:58,515
And where did it
give that heat?

347
00:14:58,515 --> 00:15:01,490
It gave it to this reservoir
that we put here, this kind of

348
00:15:01,490 --> 00:15:02,510
cold reservoir.

349
00:15:02,510 --> 00:15:05,210
You could almost view
it as a-- well, it's

350
00:15:05,210 --> 00:15:06,750
accepting the heat.

351
00:15:06,750 --> 00:15:06,890
OK.

352
00:15:06,890 --> 00:15:08,360
We're almost there.

353
00:15:08,360 --> 00:15:11,390
Now, let's say we remove this
reservoir from under our

354
00:15:11,390 --> 00:15:14,720
system again, so it's completely
isolated from

355
00:15:14,720 --> 00:15:17,080
everything else, at least
in terms of heat.

356
00:15:17,080 --> 00:15:21,830
And what we do is, we start
adding-- so state D, we still

357
00:15:21,830 --> 00:15:23,275
had a few less pebbles.

358
00:15:23,275 --> 00:15:26,290
But we start adding more
pebbles again.

359
00:15:26,290 --> 00:15:29,985
We start adding more pebbles
to get it to state A.

360
00:15:29,985 --> 00:15:32,770
So let me change my
pebble color.

361
00:15:32,770 --> 00:15:34,710
So we start adding more
pebbles again to

362
00:15:34,710 --> 00:15:38,620
get it to state A.

363
00:15:38,620 --> 00:15:40,530
So that's this process
right here.

364
00:15:40,530 --> 00:15:43,430


365
00:15:43,430 --> 00:15:46,480
Let me do a different color.

366
00:15:46,480 --> 00:15:49,280
Let's say this is green.

367
00:15:49,280 --> 00:15:52,570
So as we add pebbles, that's
this movement right here.

368
00:15:52,570 --> 00:15:55,840
We're moving from one isotherm
up to another isotherm at a

369
00:15:55,840 --> 00:15:56,800
higher temperature.

370
00:15:56,800 --> 00:15:58,520
And remember, this whole
time we went

371
00:15:58,520 --> 00:16:01,330
this clockwise direction.

372
00:16:01,330 --> 00:16:05,240
So a couple of interesting
things are going on here.

373
00:16:05,240 --> 00:16:07,990
Because we're assuming an ideal
scenario, nothing was

374
00:16:07,990 --> 00:16:09,070
lost of friction.

375
00:16:09,070 --> 00:16:11,610
This piston just moves
up and down.

376
00:16:11,610 --> 00:16:13,340
No heat loss due to that.

377
00:16:13,340 --> 00:16:17,510
What we can say is that we've
achieved-- we are back at our

378
00:16:17,510 --> 00:16:19,250
original internal energy.

379
00:16:19,250 --> 00:16:21,960
In fact, this is one of the
properties of a state

380
00:16:21,960 --> 00:16:24,520
variable, is that if we're at
the same point on the PV

381
00:16:24,520 --> 00:16:27,550
diagram, the same exact
point, we have

382
00:16:27,550 --> 00:16:28,860
the same state variable.

383
00:16:28,860 --> 00:16:31,610
So now we have the same
pressure, volume, temperature,

384
00:16:31,610 --> 00:16:33,780
and internal energy as
what we started with.

385
00:16:33,780 --> 00:16:35,820
So we've done here is
completed a cycle.

386
00:16:35,820 --> 00:16:38,990
And this particular cycle, it's
an important one, it's

387
00:16:38,990 --> 00:16:41,660
called the Carnot cycle.

388
00:16:41,660 --> 00:16:44,390
It's named after a French
engineer who was trying to

389
00:16:44,390 --> 00:16:46,780
just optimize engines
in the early 1800s.

390
00:16:46,780 --> 00:16:48,030
So Carnot cycle.

391
00:16:48,030 --> 00:16:50,810


392
00:16:50,810 --> 00:16:53,330
And we're going to study this
a lot in the next few videos

393
00:16:53,330 --> 00:16:55,860
to really make sure we
understand entropy correctly.

394
00:16:55,860 --> 00:16:57,830
Because in a lot of chemistry
classes, they'll

395
00:16:57,830 --> 00:16:58,760
throw entropy at you.

396
00:16:58,760 --> 00:17:00,060
Oh, it's measure of disorder.

397
00:17:00,060 --> 00:17:02,190
But you really don't know what
they're talking about, or how

398
00:17:02,190 --> 00:17:04,810
can you quantify it, or
measure it anyway.

399
00:17:04,810 --> 00:17:07,910
And we really need to deal with
the Carnot cycle in order

400
00:17:07,910 --> 00:17:10,650
to understand where the first
concepts of entropy really

401
00:17:10,650 --> 00:17:12,390
came from, and then relate
it to kind of more

402
00:17:12,390 --> 00:17:14,069
modern notions of it.

403
00:17:14,069 --> 00:17:19,098
Now, a system that completes
a Carnot cycle is called a

404
00:17:19,098 --> 00:17:19,949
Carnot engine.

405
00:17:19,950 --> 00:17:22,868
So our little piston here that's
moving up and down, we

406
00:17:22,868 --> 00:17:24,559
can consider this
a Carnot engine.

407
00:17:24,560 --> 00:17:25,800
You might say, oh, Sal,
this doesn't seem

408
00:17:25,800 --> 00:17:26,560
like a great engine.

409
00:17:26,560 --> 00:17:29,040
I have to move pebbles
and all of that.

410
00:17:29,040 --> 00:17:30,670
And you're right.

411
00:17:30,670 --> 00:17:33,890
You wouldn't actually implement
an engine this way.

412
00:17:33,890 --> 00:17:37,280
But it's a useful engine, or
it's a useful theoretical

413
00:17:37,280 --> 00:17:40,670
construct, in order for
understanding how heat is

414
00:17:40,670 --> 00:17:42,110
transferred in an engine.

415
00:17:42,110 --> 00:17:44,520
I mean, if you think about
what's happening here, is this

416
00:17:44,520 --> 00:17:48,680
first heat sink transferred some
heat to the system, and

417
00:17:48,680 --> 00:17:51,690
then the system transferred a
smaller amount of heat back to

418
00:17:51,690 --> 00:17:56,740
the other reservoir.

419
00:17:56,740 --> 00:17:57,290
Right?

420
00:17:57,290 --> 00:18:00,940
So this system was transferring
heat from one

421
00:18:00,940 --> 00:18:02,630
reservoir to another
reservoir.

422
00:18:02,630 --> 00:18:05,180
From a hotter reservoir
to a colder reservoir.

423
00:18:05,180 --> 00:18:07,890
And in the process, it was
also doing some work.

424
00:18:07,890 --> 00:18:09,880
And what was the work
that it did?

425
00:18:09,880 --> 00:18:13,500
Well, it's the area under this
curve, or the area inside of

426
00:18:13,500 --> 00:18:14,020
this cycle.

427
00:18:14,020 --> 00:18:19,890
So this is the work done
by our Carnot engine.

428
00:18:19,890 --> 00:18:22,890
And the way you think about it
is, when you're going in the

429
00:18:22,890 --> 00:18:24,770
rightward direction with
increasing volume, it's the

430
00:18:24,770 --> 00:18:27,850
area under the curve is the
work done by the system.

431
00:18:27,850 --> 00:18:29,560
And then when you move in the
leftward direction with

432
00:18:29,560 --> 00:18:33,350
decreasing volume, you subtract
out the work done to

433
00:18:33,350 --> 00:18:35,520
the system, and then you're
left with just

434
00:18:35,520 --> 00:18:37,170
the area in the curve.

435
00:18:37,170 --> 00:18:39,230
So we can write this Carnot
engine like this.

436
00:18:39,230 --> 00:18:41,950


437
00:18:41,950 --> 00:18:48,280
It's taking, it's starting-- so
you have a reservoir at T1.

438
00:18:48,280 --> 00:18:51,240


439
00:18:51,240 --> 00:18:55,420
And then you have your
engine, right here.

440
00:18:55,420 --> 00:18:59,360
And then it's connected--
so this takes Q1

441
00:18:59,360 --> 00:19:01,350
in from this reservoir.

442
00:19:01,350 --> 00:19:03,230
It does some work, all right?

443
00:19:03,230 --> 00:19:07,130
The work is represented by the
amount of-- the work right

444
00:19:07,130 --> 00:19:11,010
here is the area inside
of our cycle.

445
00:19:11,010 --> 00:19:14,430
And then it transfers Q2, or
essentially the remainder from

446
00:19:14,430 --> 00:19:17,190
Q1, into our cold reservoir.

447
00:19:17,190 --> 00:19:18,580
So T2.

448
00:19:18,580 --> 00:19:20,660
So it transfers Q2 there.

449
00:19:20,660 --> 00:19:22,420
So the work we did is really
the difference

450
00:19:22,420 --> 00:19:24,820
between Q1 and Q2, right?

451
00:19:24,820 --> 00:19:25,810
You say, hey.

452
00:19:25,810 --> 00:19:28,360
If I have more heat coming in
than I'm letting out, where

453
00:19:28,360 --> 00:19:29,950
did the rest of that heat go?

454
00:19:29,950 --> 00:19:32,590
It went to work.

455
00:19:32,590 --> 00:19:33,510
Literally.

456
00:19:33,510 --> 00:19:39,150
So Q1 minus Q2 is equal to the
amount of work we did.

457
00:19:39,150 --> 00:19:42,200
And actually, this is a good
time to emphasize again that

458
00:19:42,200 --> 00:19:44,650
heat and work are not
a state variable.

459
00:19:44,650 --> 00:19:48,040
A state variable has to be the
exact same value when we

460
00:19:48,040 --> 00:19:49,370
complete a cycle.

461
00:19:49,370 --> 00:19:52,610
Now, we see here that we
completed a cycle, and we had

462
00:19:52,610 --> 00:19:56,650
a net amount of work done, or a
net amount of heat added to

463
00:19:56,650 --> 00:19:57,110
the system.

464
00:19:57,110 --> 00:19:58,980
So we could just keep going
around the cycle, and keep

465
00:19:58,980 --> 00:20:00,430
having heat added
to the system.

466
00:20:00,430 --> 00:20:04,440
So there is no inherent heat
state variable right here.

467
00:20:04,440 --> 00:20:07,660
You can't say what the
value of heat is at

468
00:20:07,660 --> 00:20:08,740
this point in time.

469
00:20:08,740 --> 00:20:11,420
All you could say is what amount
of heat was added or

470
00:20:11,420 --> 00:20:14,010
taken away from the system, or
you can only say the amount of

471
00:20:14,010 --> 00:20:17,440
work that was done to, or
done by, the system.

472
00:20:17,440 --> 00:20:19,900
Anyway, I want to leave
you there right now.

473
00:20:19,900 --> 00:20:21,280
We're going to study
this a lot more.

474
00:20:21,280 --> 00:20:24,040
But the real important thing is,
and if you never want to

475
00:20:24,040 --> 00:20:25,830
get confused in a thermodynamics
class, I

476
00:20:25,830 --> 00:20:27,800
encourage you to even
go off on your

477
00:20:27,800 --> 00:20:29,820
own, and do this yourself.

478
00:20:29,820 --> 00:20:34,120
Kind of-- you can almost take
a pencil and paper, and redo

479
00:20:34,120 --> 00:20:35,430
this video that I just did.

480
00:20:35,430 --> 00:20:37,550
Because it's essential that
you understand the Carnot

481
00:20:37,550 --> 00:20:40,530
engine, understand this
adiabatic process, understand

482
00:20:40,530 --> 00:20:41,520
what isotherms are.

483
00:20:41,520 --> 00:20:43,790
Because if you understand that,
then a lot of what we're

484
00:20:43,790 --> 00:20:47,760
about to do in the next few
videos with regard to entropy

485
00:20:47,760 --> 00:20:49,320
will be a little bit more

486
00:20:49,320 --> 00:20:52,140
intuitive, and not too confusing.

487
00:20:52,140 --> 00:00:00,000