1
00:00:00,000 --> 00:00:00,500


2
00:00:00,500 --> 00:00:03,660
I've now supplied you with two
definitions of the state

3
00:00:03,660 --> 00:00:04,600
variable entropy.

4
00:00:04,600 --> 00:00:06,390
And it's S for entropy.

5
00:00:06,390 --> 00:00:09,110
The thermodynamic definition
said that the change in

6
00:00:09,110 --> 00:00:12,440
entropy is equal to the heat
added to the system divided by

7
00:00:12,440 --> 00:00:14,560
the temperature at which
the heat is added.

8
00:00:14,560 --> 00:00:16,590
So obviously, if the temperature
is changing while

9
00:00:16,590 --> 00:00:18,600
we add the heat, which is
normally the case, we're going

10
00:00:18,600 --> 00:00:20,200
to have to do a little
bit of calculus.

11
00:00:20,200 --> 00:00:22,790
And then you can view this as
the mathematical, or the

12
00:00:22,790 --> 00:00:24,700
statistical, or the
combinatorical

13
00:00:24,700 --> 00:00:26,710
definition of entropy.

14
00:00:26,710 --> 00:00:29,630
And this essentially says that
entropy is equal to some

15
00:00:29,630 --> 00:00:32,320
constant times the natural log
of the number of states the

16
00:00:32,320 --> 00:00:33,840
system can take on.

17
00:00:33,840 --> 00:00:35,990
And this is the case when all
the states are equally

18
00:00:35,990 --> 00:00:37,720
probable, which is a pretty
good assumption.

19
00:00:37,720 --> 00:00:41,180
If you have just a gazillion
molecules that could have a

20
00:00:41,180 --> 00:00:43,270
gazillion gazillion states,
you can assume they're all

21
00:00:43,270 --> 00:00:44,760
roughly equally likely.

22
00:00:44,760 --> 00:00:46,970
There's a slightly more involved
definition if they

23
00:00:46,970 --> 00:00:48,480
had different probabilities,
but we won't

24
00:00:48,480 --> 00:00:49,750
worry about that now.

25
00:00:49,750 --> 00:00:52,570
So given that we've seen these
two definitions, it's a good

26
00:00:52,570 --> 00:00:56,560
time to introduce you to the
second law of thermodynamics.

27
00:00:56,560 --> 00:01:00,000


28
00:01:00,000 --> 00:01:01,220
And that's this.

29
00:01:01,220 --> 00:01:04,959
And it's a pretty simple law,
but it explains a whole range

30
00:01:04,959 --> 00:01:06,110
of phenomena.

31
00:01:06,110 --> 00:01:16,410
It tells us that the change in
entropy for the universe when

32
00:01:16,410 --> 00:01:19,760
any process is undergone
is always greater

33
00:01:19,760 --> 00:01:22,940
than or equal to 0.

34
00:01:22,940 --> 00:01:26,530
So that tells us that when
anything ever happens in the

35
00:01:26,530 --> 00:01:30,560
universe, the net effect is that
there's more entropy in

36
00:01:30,560 --> 00:01:31,830
the universe itself.

37
00:01:31,830 --> 00:01:34,830
And this seems very deep,
and it actually is.

38
00:01:34,830 --> 00:01:38,440
So let's see if we can apply it
to see why it explains, or

39
00:01:38,440 --> 00:01:41,400
why it makes sense, relative
to some examples.

40
00:01:41,400 --> 00:01:44,970
So let's say I have two
reservoirs that are in contact

41
00:01:44,970 --> 00:01:45,610
with each other.

42
00:01:45,610 --> 00:01:49,110
So I have T1.

43
00:01:49,110 --> 00:01:52,140
And let's call this
our hot reservoir.

44
00:01:52,140 --> 00:01:53,390
And then I have T2.

45
00:01:53,390 --> 00:01:56,100


46
00:01:56,100 --> 00:01:58,290
I'll call this our
cold reservoir.

47
00:01:58,290 --> 00:01:59,720
Well, we know from experience.

48
00:01:59,720 --> 00:02:03,170
What happens if I put a hot cup
of water, and it's sharing

49
00:02:03,170 --> 00:02:07,120
a wall with a cold glass of
water, or cold cube of water,

50
00:02:07,120 --> 00:02:08,090
what happens?

51
00:02:08,090 --> 00:02:09,729
Well, their temperatures
equalize.

52
00:02:09,729 --> 00:02:11,660
If these are the same substance,
we'll end up

53
00:02:11,660 --> 00:02:13,960
roughly in between, if they're
in the same phase.

54
00:02:13,960 --> 00:02:15,960
So essentially, we have a
transfer of heat from the

55
00:02:15,960 --> 00:02:18,720
hotter substance to the
colder substance.

56
00:02:18,720 --> 00:02:23,290
So we have some heat, Q, that
goes from the hotter substance

57
00:02:23,290 --> 00:02:24,550
to the colder substance.

58
00:02:24,550 --> 00:02:27,960
You don't see, in everyday
reality, heat going from a

59
00:02:27,960 --> 00:02:29,350
colder substance to a
hotter substance.

60
00:02:29,350 --> 00:02:33,850
If I put an ice cube in, let's
say, some hot tea, you don't

61
00:02:33,850 --> 00:02:35,760
see the ice cube getting
colder and the

62
00:02:35,760 --> 00:02:36,780
hot tea getting hotter.

63
00:02:36,780 --> 00:02:39,880
You see them both getting to
some equal temperature, which

64
00:02:39,880 --> 00:02:42,550
essentially the T is giving
heat to the ice cube.

65
00:02:42,550 --> 00:02:44,490
Now in this situation there
are reservoirs, so I'm

66
00:02:44,490 --> 00:02:46,810
assuming that their temperatures
stay constant.

67
00:02:46,810 --> 00:02:49,780
Which would only be the case
if they were both infinite,

68
00:02:49,780 --> 00:02:51,300
which we know doesn't exist
in the real world.

69
00:02:51,300 --> 00:02:53,950
In the real world, T1's
temperature as it gave heat

70
00:02:53,950 --> 00:02:56,390
would go down, and T2's
temperature would go up.

71
00:02:56,390 --> 00:02:59,720
But let's just see whether the
second law of thermodynamics

72
00:02:59,720 --> 00:03:01,770
says that this should happen.

73
00:03:01,770 --> 00:03:04,010
So what's happening here?

74
00:03:04,010 --> 00:03:07,490
What's the net change
in entropy for T1?

75
00:03:07,490 --> 00:03:09,790
So the second law of
thermodynamics says that the

76
00:03:09,790 --> 00:03:13,370
change in entropy for the
universe is greater than 0.

77
00:03:13,370 --> 00:03:16,670
But in this case, that's equal
to the change in entropy for

78
00:03:16,670 --> 00:03:23,310
T1 plus the change in entropy
for-- oh, I shouldn't--

79
00:03:23,310 --> 00:03:28,150
instead of T1, let me
call it just 1.

80
00:03:28,150 --> 00:03:31,490
For system 1, that's this hot
system up here, plus the

81
00:03:31,490 --> 00:03:33,730
change in entropy
for system 2.

82
00:03:33,730 --> 00:03:35,990
So what's the change in
entropy for system 1?

83
00:03:35,990 --> 00:03:43,330
It loses Q1 at a high
temperature.

84
00:03:43,330 --> 00:03:50,850
So this equals minus the heat
given to the system is Q over

85
00:03:50,850 --> 00:03:53,690
some hot temperature T1.

86
00:03:53,690 --> 00:03:57,780
And then we have the heat being
added to the system T2.

87
00:03:57,780 --> 00:04:02,460
So plus Q over T2.

88
00:04:02,460 --> 00:04:05,230
This is the change in entropy
for the system 2, right?

89
00:04:05,230 --> 00:04:08,260
This guy loses the heat, and is
at temperature 1, which is

90
00:04:08,260 --> 00:04:09,430
a higher temperature.

91
00:04:09,430 --> 00:04:12,340
This guy gains the heat, and
he is at a temperature 2,

92
00:04:12,340 --> 00:04:13,430
which is a colder temperature.

93
00:04:13,430 --> 00:04:18,399
Now, is this going to
be greater than 0?

94
00:04:18,399 --> 00:04:19,950
Let's think about
it a little bit.

95
00:04:19,950 --> 00:04:22,070
If I divide-- let
me rewrite this.

96
00:04:22,070 --> 00:04:25,900
So I can rearrange them, so that
we can write this as Q

97
00:04:25,900 --> 00:04:28,980
over T2 minus this one.

98
00:04:28,980 --> 00:04:30,740
I'm just rearranging it.

99
00:04:30,740 --> 00:04:33,830
Minus Q over T1.

100
00:04:33,830 --> 00:04:35,520
Now, which number is bigger?

101
00:04:35,520 --> 00:04:36,720
T2 to T1?

102
00:04:36,720 --> 00:04:39,130
Well, T1 is bigger, right?

103
00:04:39,130 --> 00:04:40,380
This is bigger.

104
00:04:40,380 --> 00:04:43,310


105
00:04:43,310 --> 00:04:46,060
Now, if I have a bigger number,
bigger than this--

106
00:04:46,060 --> 00:04:47,480
when we use the word
bigger, you have to

107
00:04:47,480 --> 00:04:48,870
compare it to something.

108
00:04:48,870 --> 00:04:50,590
Now, T1 is bigger than this.

109
00:04:50,590 --> 00:04:52,340
We have the same number
in the numerator

110
00:04:52,340 --> 00:04:54,050
in both cases, right?

111
00:04:54,050 --> 00:04:58,370
So if I take, let's say, 1
over some, let's say, 1/2

112
00:04:58,370 --> 00:05:01,350
minus 1/3, we're going
to be bigger than 0.

113
00:05:01,350 --> 00:05:03,830
This is a larger number than
this number, because this has

114
00:05:03,830 --> 00:05:04,635
a bigger denominator.

115
00:05:04,635 --> 00:05:06,840
You're dividing by
a larger number.

116
00:05:06,840 --> 00:05:08,190
That's a good way to
think about it.

117
00:05:08,190 --> 00:05:11,610
You're dividing this Q by some
number here to get something,

118
00:05:11,610 --> 00:05:13,000
and then you're subtracting
this Q

119
00:05:13,000 --> 00:05:14,470
divided by a larger number.

120
00:05:14,470 --> 00:05:16,890
So this fraction is going to be
a smaller absolute number.

121
00:05:16,890 --> 00:05:20,770
So this is going to
be greater than 0.

122
00:05:20,770 --> 00:05:23,490
So that tells us the second
law of thermodynamics, it

123
00:05:23,490 --> 00:05:28,630
verifies this observation we
see in the real world, that

124
00:05:28,630 --> 00:05:32,360
heat will flow from the hot
body to the cold body.

125
00:05:32,360 --> 00:05:33,990
Now, you might say, hey, Sal.

126
00:05:33,990 --> 00:05:38,100
I have a case that will show
you that you are wrong.

127
00:05:38,100 --> 00:05:39,270
You could say, look.

128
00:05:39,270 --> 00:05:45,660
If I put an air conditioner in a
room-- Let's say this is the

129
00:05:45,660 --> 00:05:50,780
room, and this is outside.

130
00:05:50,780 --> 00:05:54,230
You'll say, look what the
air conditioner does.

131
00:05:54,230 --> 00:05:59,410
The room is already cold, and
outside is already hot.

132
00:05:59,410 --> 00:06:01,620
But what the air conditioner
does, is it makes the cold

133
00:06:01,620 --> 00:06:04,490
even colder, and it makes
the hot even hotter.

134
00:06:04,490 --> 00:06:08,680
It takes some Q and it goes
in that direction.

135
00:06:08,680 --> 00:06:09,010
Right?

136
00:06:09,010 --> 00:06:11,670
It takes heat from the cold
room, and puts it out

137
00:06:11,670 --> 00:06:12,625
into the hot air.

138
00:06:12,625 --> 00:06:14,560
And you're saying, this defies
the second law of

139
00:06:14,560 --> 00:06:15,690
thermodynamics.

140
00:06:15,690 --> 00:06:17,040
You have just disproved it.

141
00:06:17,040 --> 00:06:18,790
You deserve a Nobel Prize.

142
00:06:18,790 --> 00:06:24,460
And I would say to you, you're
forgetting one small fact.

143
00:06:24,460 --> 00:06:27,340
This air conditioner inside
here, it has some type of a

144
00:06:27,340 --> 00:06:29,470
compressor, some type
of an engine, that's

145
00:06:29,470 --> 00:06:31,210
actively doing this.

146
00:06:31,210 --> 00:06:33,600
It's putting in work to
make this happen.

147
00:06:33,600 --> 00:06:38,040
And this engine right here--
I'll do it in magenta-- it's

148
00:06:38,040 --> 00:06:40,630
also expelling some more heat.

149
00:06:40,630 --> 00:06:47,490
So let's call that
Q of the engine.

150
00:06:47,490 --> 00:06:52,970
So if you wanted to figure out
the total entropy created for

151
00:06:52,970 --> 00:07:02,870
the universe, it would be the
entropy of the cold room plus

152
00:07:02,870 --> 00:07:06,870
the change in entropy for
outside-- I'll call it

153
00:07:06,870 --> 00:07:10,050
outside, maybe I'll call
this, for the room.

154
00:07:10,050 --> 00:07:10,870
Right?

155
00:07:10,870 --> 00:07:11,590
So you might say, OK.

156
00:07:11,590 --> 00:07:14,520
This change in entropy for the
room, it's giving away heat--

157
00:07:14,520 --> 00:07:16,700
let's see the room is roughly at
a constant temperature for

158
00:07:16,700 --> 00:07:19,290
that one millisecond we're
looking at it.

159
00:07:19,290 --> 00:07:23,860
It's giving away some Q at
some temperature T1.

160
00:07:23,860 --> 00:07:26,460
And then-- so that's a minus.

161
00:07:26,460 --> 00:07:30,940
And then this the outside is
gaining some heat at some

162
00:07:30,940 --> 00:07:32,480
temperature T2.

163
00:07:32,480 --> 00:07:33,440
And so you'll immediately
say, hey.

164
00:07:33,440 --> 00:07:39,110
This number right here is a
smaller number than this one.

165
00:07:39,110 --> 00:07:39,530
Right?

166
00:07:39,530 --> 00:07:41,610
Because the denominator
is higher.

167
00:07:41,610 --> 00:07:43,570
So if you just look at this,
this would be negative

168
00:07:43,570 --> 00:07:46,300
entropy, and you'd say hey, this
defies the second law of

169
00:07:46,300 --> 00:07:47,150
thermodynamics.

170
00:07:47,150 --> 00:07:47,650
No!

171
00:07:47,650 --> 00:07:50,470
But what you have to throw in
here is another notion.

172
00:07:50,470 --> 00:07:52,660
You have to throw in here the
notion that the outside is

173
00:07:52,660 --> 00:07:58,900
also getting this heat from the
engine over the outside

174
00:07:58,900 --> 00:07:59,990
temperature.

175
00:07:59,990 --> 00:08:03,980
And this term, I can guarantee
you-- I'm not giving you

176
00:08:03,980 --> 00:08:05,460
numbers right now--
will make this

177
00:08:05,460 --> 00:08:07,330
whole expression positive.

178
00:08:07,330 --> 00:08:12,430
This term will turn the total
net entropy to the universe to

179
00:08:12,430 --> 00:08:13,770
be positive.

180
00:08:13,770 --> 00:08:17,050
Now let's think a little bit how
about what entropy is and

181
00:08:17,050 --> 00:08:18,830
what entropy isn't in
terms of words.

182
00:08:18,830 --> 00:08:22,840
So when you take an intro
chemistry class, the teacher

183
00:08:22,840 --> 00:08:28,000
often says, entropy
equals disorder.

184
00:08:28,000 --> 00:08:30,770
Which is not incorrect.

185
00:08:30,770 --> 00:08:34,210
It is disorder, but you have
to be very careful what we

186
00:08:34,210 --> 00:08:35,830
mean by disorder.

187
00:08:35,830 --> 00:08:39,429
Because the very next example
that's often given is that

188
00:08:39,429 --> 00:08:40,090
they'll say, look.

189
00:08:40,090 --> 00:08:45,090
A clean room-- let's say your
bedroom is clean, and then it

190
00:08:45,090 --> 00:08:45,920
becomes dirty.

191
00:08:45,920 --> 00:08:46,950
And they'll say, look.

192
00:08:46,950 --> 00:08:48,850
The universe became
more disordered.

193
00:08:48,850 --> 00:08:53,370
The dirty room has more disorder
than the clean room.

194
00:08:53,370 --> 00:08:56,980
And this is not a case
of entropy increase.

195
00:08:56,980 --> 00:08:58,673
So this is not a good example.

196
00:08:58,673 --> 00:09:01,230


197
00:09:01,230 --> 00:09:04,230
Why is that?

198
00:09:04,230 --> 00:09:07,670
Because clean and dirty are
just states of the room.

199
00:09:07,670 --> 00:09:11,720
Remember, entropy is a
macro state variable.

200
00:09:11,720 --> 00:09:14,600


201
00:09:14,600 --> 00:09:16,720
It's something you use to
describe a system where you're

202
00:09:16,720 --> 00:09:19,430
not in the mood to sit there and
tell me what exactly every

203
00:09:19,430 --> 00:09:20,800
particle is doing.

204
00:09:20,800 --> 00:09:23,200
And this is a macro variable
that actually tells me how

205
00:09:23,200 --> 00:09:27,430
much time would it take for
me to tell you what every

206
00:09:27,430 --> 00:09:28,290
particle is doing.

207
00:09:28,290 --> 00:09:30,610
It actually tells you how many
states there are, or how much

208
00:09:30,610 --> 00:09:32,820
information I would have
to give you to tell

209
00:09:32,820 --> 00:09:34,470
you the exact state.

210
00:09:34,470 --> 00:09:36,480
Now, when you have a clean room
and a dirty room, these

211
00:09:36,480 --> 00:09:39,590
are two different states
of the same room.

212
00:09:39,590 --> 00:09:42,800
If the room has the same
temperature, and it has the

213
00:09:42,800 --> 00:09:46,580
same number of molecules in it
and everything, then they have

214
00:09:46,580 --> 00:09:47,450
the same entropy.

215
00:09:47,450 --> 00:09:49,930
So clean to dirty, it's
not more entropy.

216
00:09:49,930 --> 00:09:55,530
Now, for example, I could
have a dirty, cold room.

217
00:09:55,530 --> 00:09:58,530


218
00:09:58,530 --> 00:10:01,630
And let's say I were to go into
that room and, you know,

219
00:10:01,630 --> 00:10:03,950
I work really hard
to clean it up.

220
00:10:03,950 --> 00:10:06,980
And by doing so, I add a lot of
heat to the system, and my

221
00:10:06,980 --> 00:10:09,810
sweat molecules drop all over
the place, and so there's just

222
00:10:09,810 --> 00:10:13,240
more stuff in that room, and
it's all warmed up to me-- so

223
00:10:13,240 --> 00:10:22,810
to a hot, clean room with sweat
in it-- so it's got more

224
00:10:22,810 --> 00:10:25,350
stuff in here that can be
configured in more ways, and

225
00:10:25,350 --> 00:10:28,620
because it's hot, every molecule
in the room can take

226
00:10:28,620 --> 00:10:29,850
on more states, right?

227
00:10:29,850 --> 00:10:32,420
Because the average kinetic
energy is up, so they can kind

228
00:10:32,420 --> 00:10:36,070
of explore the spaces of how
many kinetic energies it can

229
00:10:36,070 --> 00:10:39,700
have. There's more potential
energies that each molecule

230
00:10:39,700 --> 00:10:40,240
can take on.

231
00:10:40,240 --> 00:10:42,610
This is actually an increase
in entropy.

232
00:10:42,610 --> 00:10:45,410
From a dirty, cold room
to a hot, clean room.

233
00:10:45,410 --> 00:10:47,410
And this actually goes well
with what we know.

234
00:10:47,410 --> 00:10:50,720
I mean, when I go into room and
I start cleaning it, I am

235
00:10:50,720 --> 00:10:52,080
in putting heat into the room.

236
00:10:52,080 --> 00:10:55,140
And the universe is becoming
more-- I guess we could say

237
00:10:55,140 --> 00:10:57,720
it's the entropy
is increasing.

238
00:10:57,720 --> 00:11:00,030
So where does the term
disorder apply?

239
00:11:00,030 --> 00:11:03,110


240
00:11:03,110 --> 00:11:07,330
Well, let's take a situation
where I take a ball.

241
00:11:07,330 --> 00:11:10,520
I take a ball, and it
falls to the ground.

242
00:11:10,520 --> 00:11:12,570
And then it hits the ground.

243
00:11:12,570 --> 00:11:14,050
And there should have been a
question that you've been

244
00:11:14,050 --> 00:11:16,160
asking all the time, since the
first law of thermodynamics.

245
00:11:16,160 --> 00:11:20,170


246
00:11:20,170 --> 00:11:21,360
So the ball hits the
ground, right?

247
00:11:21,360 --> 00:11:24,520
It got thrown up, it had some
potential energy at the top,

248
00:11:24,520 --> 00:11:26,380
then that all gets turned into
kinetic energy and it hits the

249
00:11:26,380 --> 00:11:28,120
ground, and then it stops.

250
00:11:28,120 --> 00:11:30,410
And so your obvious question is,
what happened to all that

251
00:11:30,410 --> 00:11:31,880
energy, right?

252
00:11:31,880 --> 00:11:33,430
Law of conservation of energy.

253
00:11:33,430 --> 00:11:34,380
Where did all of it go?

254
00:11:34,380 --> 00:11:35,890
It had all that kinetic energy
right before it hit the

255
00:11:35,890 --> 00:11:37,350
ground, then it stopped.

256
00:11:37,350 --> 00:11:37,760
Right?

257
00:11:37,760 --> 00:11:39,290
It seems like it disappeared.

258
00:11:39,290 --> 00:11:40,950
But it didn't disappear.

259
00:11:40,950 --> 00:11:44,260
So when the ball was falling, it
had a bunch of-- you know,

260
00:11:44,260 --> 00:11:45,470
everything had a little
bit of heat.

261
00:11:45,470 --> 00:11:47,960
But let's say the ground
was reasonably ordered.

262
00:11:47,960 --> 00:11:51,380


263
00:11:51,380 --> 00:11:56,260
The ground molecules were
vibrating with some kinetic

264
00:11:56,260 --> 00:11:58,100
energy and potential energies.

265
00:11:58,100 --> 00:12:00,650
And then our ball molecules
were also

266
00:12:00,650 --> 00:12:02,480
vibrating a little bit.

267
00:12:02,480 --> 00:12:06,340
But most of their motion
was downwards, right?

268
00:12:06,340 --> 00:12:09,160
Most of the ball molecules'
motion was downwards.

269
00:12:09,160 --> 00:12:12,220
Now, when it hits the ground,
what happens-- let me show you

270
00:12:12,220 --> 00:12:14,230
the interface of the ball.

271
00:12:14,230 --> 00:12:17,790
So the ball molecules at the
front of the ball are going to

272
00:12:17,790 --> 00:12:19,400
look like that.

273
00:12:19,400 --> 00:12:20,730
And there's a bunch of them.

274
00:12:20,730 --> 00:12:21,460
It's a solid.

275
00:12:21,460 --> 00:12:24,100
It will maybe be some
type of lattice.

276
00:12:24,100 --> 00:12:25,740
And then it hits the ground.

277
00:12:25,740 --> 00:12:30,150
And when it hits the ground-- so
the ground is another solid

278
00:12:30,150 --> 00:12:35,960
like that-- All right, we're
looking at the microstate.

279
00:12:35,960 --> 00:12:37,370
What's going to happen?

280
00:12:37,370 --> 00:12:39,390
These guys are going to rub
up against these guys, and

281
00:12:39,390 --> 00:12:41,880
they're going to transfer
their-- what was downward

282
00:12:41,880 --> 00:12:45,090
kinetic energy, and a very
ordered downward kinetic

283
00:12:45,090 --> 00:12:47,510
energy-- they're going
to transfer it to

284
00:12:47,510 --> 00:12:49,110
these ground particles.

285
00:12:49,110 --> 00:12:50,950
And they're going to bump into
the ground particles.

286
00:12:50,950 --> 00:12:54,040
And so when this guy bumps into
that guy, he might start

287
00:12:54,040 --> 00:12:55,910
moving in that direction.

288
00:12:55,910 --> 00:12:57,910
This guy will start oscillating
in that direction,

289
00:12:57,910 --> 00:12:59,770
and go back and forth
like that.

290
00:12:59,770 --> 00:13:02,300
That guy might bounce off of
this guy, and go in that

291
00:13:02,300 --> 00:13:04,190
direction, and bump
into that guy, and

292
00:13:04,190 --> 00:13:05,380
go into that direction.

293
00:13:05,380 --> 00:13:09,410
And then, because that guy
bumped here, this guy bumps

294
00:13:09,410 --> 00:13:11,860
here, and because this guy bumps
here, this guy bumps

295
00:13:11,860 --> 00:13:12,760
over there.

296
00:13:12,760 --> 00:13:16,820
And so what you have is, what
was relatively ordered motion,

297
00:13:16,820 --> 00:13:19,210
especially from the ball's point
of view, when it starts

298
00:13:19,210 --> 00:13:22,280
rubbing up against these
molecules of the ground, it

299
00:13:22,280 --> 00:13:24,855
starts making the kinetic
energy, or their movement, go

300
00:13:24,855 --> 00:13:26,760
in all sorts of random
directions.

301
00:13:26,760 --> 00:13:27,090
Right?

302
00:13:27,090 --> 00:13:29,130
This guy's going to make this
guy go like that, and that guy

303
00:13:29,130 --> 00:13:30,170
go like that.

304
00:13:30,170 --> 00:13:33,570
And so when the movement is no
longer ordered, if I have a

305
00:13:33,570 --> 00:13:36,550
lot of molecules-- let me do it
in a different color-- if I

306
00:13:36,550 --> 00:13:38,520
have a lot of molecules, and
they're all moving in the

307
00:13:38,520 --> 00:13:41,910
exact same direction, then my
micro state looks like my

308
00:13:41,910 --> 00:13:42,590
macro state.

309
00:13:42,590 --> 00:13:44,850
The whole thing moves
in that direction.

310
00:13:44,850 --> 00:13:47,860
Now, if I have a bunch of
molecules, and they're all

311
00:13:47,860 --> 00:13:51,900
moving in random directions,
my ball as a whole will be

312
00:13:51,900 --> 00:13:52,320
stationary.

313
00:13:52,320 --> 00:13:54,330
I could have the exact same
amount of kinetic energy at

314
00:13:54,330 --> 00:13:56,740
the molecular level, but
they're all going to be

315
00:13:56,740 --> 00:13:58,670
bouncing into each other.

316
00:13:58,670 --> 00:14:02,520
And in this case, we described
the kinetic energy as internal

317
00:14:02,520 --> 00:14:06,140
energy, or we describe it as
temperature, where temperature

318
00:14:06,140 --> 00:14:07,980
is the average kinetic energy.

319
00:14:07,980 --> 00:14:10,500
So in this case, when we talk
about, the world is becoming

320
00:14:10,500 --> 00:14:13,650
more disordered, you think about
the order of maybe the

321
00:14:13,650 --> 00:14:16,110
velocities or the energies
of the molecules.

322
00:14:16,110 --> 00:14:18,810
Before they were reasonably
ordered, the molecules-- they

323
00:14:18,810 --> 00:14:20,210
might have been vibrating a
little bit, but they were

324
00:14:20,210 --> 00:14:22,050
mainly going down in the ball.

325
00:14:22,050 --> 00:14:24,490
But when they bump into the
ground, all of a sudden they

326
00:14:24,490 --> 00:14:26,740
start vibrating in random
directions a little bit more.

327
00:14:26,740 --> 00:14:28,760
And they make the ground
vibrate in more random

328
00:14:28,760 --> 00:14:29,600
directions.

329
00:14:29,600 --> 00:14:32,800
So it makes-- at the
microstate-- everything became

330
00:14:32,800 --> 00:14:36,010
just that much more
disordered.

331
00:14:36,010 --> 00:14:37,530
Now there's an interesting
question here.

332
00:14:37,530 --> 00:14:41,830
There is some probability you
might think-- Look, this ball

333
00:14:41,830 --> 00:14:43,250
came down and hit the ground.

334
00:14:43,250 --> 00:14:46,280
Why doesn't the ball just--
isn't there some probability

335
00:14:46,280 --> 00:14:50,950
that if I have a ground, that
these molecules just rearrange

336
00:14:50,950 --> 00:14:56,880
themselves in just the right
way to just hit these ball

337
00:14:56,880 --> 00:14:58,190
molecules in just
the right way?

338
00:14:58,190 --> 00:15:00,810
There's some probability, just
from the random movement, that

339
00:15:00,810 --> 00:15:04,520
at get some second, all the
ground molecules just hit the

340
00:15:04,520 --> 00:15:08,710
ball molecules just right to
send the ball back up.

341
00:15:08,710 --> 00:15:10,200
And the answer is yes.

342
00:15:10,200 --> 00:15:13,400
There's actually some
infinitesimally small chance

343
00:15:13,400 --> 00:15:14,340
that that happens.

344
00:15:14,340 --> 00:15:16,790
That you could have a ball
that's sitting on the ground--

345
00:15:16,790 --> 00:15:19,390
and this is interesting--
could have a ball that's

346
00:15:19,390 --> 00:15:21,990
sitting on the ground, and while
you're looking, you'll

347
00:15:21,990 --> 00:15:24,740
probably have to wait a few
gazillion years for it to

348
00:15:24,740 --> 00:15:28,440
happen, if it happens at all--
it could just randomly pop up.

349
00:15:28,440 --> 00:15:33,160
And there's some random, very
small chance that these

350
00:15:33,160 --> 00:15:36,310
molecules just randomly vibrate
in just the right way

351
00:15:36,310 --> 00:15:39,960
to be ordered for a second, and
then the ball will pop up.

352
00:15:39,960 --> 00:15:43,270
But the probability of this
happening, relative to

353
00:15:43,270 --> 00:15:46,740
everything else, is
essentially 0.

354
00:15:46,740 --> 00:15:49,520
So when people talk about
order and disorder, the

355
00:15:49,520 --> 00:15:52,040
disorder is increasing, because
now these molecules

356
00:15:52,040 --> 00:15:54,640
are going in more random
directions, and they can take

357
00:15:54,640 --> 00:15:57,770
on more potential states.

358
00:15:57,770 --> 00:15:59,460
And we saw that here.

359
00:15:59,460 --> 00:16:01,970
And you know, on some level,
entropy seems something kind

360
00:16:01,970 --> 00:16:04,630
of magical, but on some
level, it seems

361
00:16:04,630 --> 00:16:06,900
relatively common sense.

362
00:16:06,900 --> 00:16:10,210
In that video-- I think was the
last video-- I had a case

363
00:16:10,210 --> 00:16:13,580
where I had a bunch of
molecules, and then I had this

364
00:16:13,580 --> 00:16:18,000
extra space here, and then
I removed the wall.

365
00:16:18,000 --> 00:16:23,760
And we saw that these molecules
will-- we know,

366
00:16:23,760 --> 00:16:26,220
there's always some modules
that are bouncing off this

367
00:16:26,220 --> 00:16:28,430
wall before, because we probably
had some pressure

368
00:16:28,430 --> 00:16:29,640
associated with it.

369
00:16:29,640 --> 00:16:31,790
And then as soon as we remove
that wall, the molecule that

370
00:16:31,790 --> 00:16:34,910
would have bounced there
just keeps going.

371
00:16:34,910 --> 00:16:36,170
There's nothing to stop
it from there.

372
00:16:36,170 --> 00:16:37,410
In that direction, there's
a lot of stuff.

373
00:16:37,410 --> 00:16:39,180
It could bump into other
molecules, and it could

374
00:16:39,180 --> 00:16:40,410
bumping into these walls.

375
00:16:40,410 --> 00:16:42,190
But in this direction, the
odds of it bumping into

376
00:16:42,190 --> 00:16:45,020
everything is, especially for
these leading molecules, is

377
00:16:45,020 --> 00:16:45,710
essentially 0.

378
00:16:45,710 --> 00:16:48,690
So it's going to expand
to fill the container.

379
00:16:48,690 --> 00:16:50,640
So that's kind of
common sense.

380
00:16:50,640 --> 00:16:53,500
But the neat thing is that the
second law of thermodynamics,

381
00:16:53,500 --> 00:16:57,170
as we saw in that video, also
says that this will happen.

382
00:16:57,170 --> 00:17:00,520
That the molecules will all
expand to fill the container.

383
00:17:00,520 --> 00:17:05,270
And that the odds of this
happening are very low.

384
00:17:05,270 --> 00:17:11,030
That they all come back and
go into a ordered state.

385
00:17:11,030 --> 00:17:13,470
Now there is some chance, just
from the random movements once

386
00:17:13,470 --> 00:17:15,710
they fill, that they all just
happen to come back here.

387
00:17:15,710 --> 00:17:18,098
But it's a very, very
small probability.

388
00:17:18,098 --> 00:17:22,159
And even more-- and I want to
make this very clear-- S is a

389
00:17:22,160 --> 00:17:23,410
macro state.

390
00:17:23,410 --> 00:17:25,970


391
00:17:25,970 --> 00:17:28,410
We never talk about
the entropy for

392
00:17:28,410 --> 00:17:30,010
an individual molecule.

393
00:17:30,010 --> 00:17:32,310
If we know what an individual
molecule is doing, we

394
00:17:32,310 --> 00:17:33,500
shouldn't be worrying
about entropy.

395
00:17:33,500 --> 00:17:35,610
We should be worrying about
the system as a whole.

396
00:17:35,610 --> 00:17:38,270


397
00:17:38,270 --> 00:17:43,400
So even if we're looking at
the system, if we're not

398
00:17:43,400 --> 00:17:45,470
looking directly at the
molecules, we won't even know

399
00:17:45,470 --> 00:17:48,940
that this actually happened.

400
00:17:48,940 --> 00:17:50,920
All we can do is look
at the statistical

401
00:17:50,920 --> 00:17:52,110
properties of the molecules.

402
00:17:52,110 --> 00:17:54,460
How many molecules they are,
what their temperature is, all

403
00:17:54,460 --> 00:17:56,750
their macro dynamics,
the pressure, and

404
00:17:56,750 --> 00:17:57,560
say, you know what?

405
00:17:57,560 --> 00:18:01,700
A box that has these molecules
has more state than a smaller

406
00:18:01,700 --> 00:18:03,740
box, than the box when we
had the wall there.

407
00:18:03,740 --> 00:18:06,520
Even if, by chance, all of the
molecules happened to be

408
00:18:06,520 --> 00:18:08,580
collecting over there, we
wouldn't know that that

409
00:18:08,580 --> 00:18:10,920
happened, because we're not
looking at the micro states.

410
00:18:10,920 --> 00:18:13,150
And that's a really important
thing to consider.

411
00:18:13,150 --> 00:18:17,130
When someone says that a dirty
room has a higher entropy than

412
00:18:17,130 --> 00:18:20,510
a clean room, they're looking
at the micro states.

413
00:18:20,510 --> 00:18:23,070
And entropy essentially is
a macro state variable.

414
00:18:23,070 --> 00:18:24,890
You could just say
that a room has a

415
00:18:24,890 --> 00:18:26,650
certain amount of entropy.

416
00:18:26,650 --> 00:18:32,160
So entropy is associated with
the room, and it's only useful

417
00:18:32,160 --> 00:18:33,640
when you really don't
know exactly what's

418
00:18:33,640 --> 00:18:34,390
going on in the room.

419
00:18:34,390 --> 00:18:37,040
You just have a general sense of
how much stuff there is in

420
00:18:37,040 --> 00:18:39,020
the room, what's the temperature
of the room,

421
00:18:39,020 --> 00:18:40,550
what's the pressure
in the room.

422
00:18:40,550 --> 00:18:42,750
Just the general macro
properties.

423
00:18:42,750 --> 00:18:45,910
And then entropy will
essentially tell us how many

424
00:18:45,910 --> 00:18:50,120
possible micro states that
macro system can actually

425
00:18:50,120 --> 00:18:53,380
have. Or how much information--
and there's a

426
00:18:53,380 --> 00:18:56,150
notion of information entropy--
how much information

427
00:18:56,150 --> 00:19:00,970
would I have to give you to tell
you what the exact micro

428
00:19:00,970 --> 00:19:03,250
state is of a system at
that point in time.

429
00:19:03,250 --> 00:19:03,780
Well anyway.

430
00:19:03,780 --> 00:19:05,330
Hopefully you found this
discussion a little bit

431
00:19:05,330 --> 00:19:08,710
useful, and it clears up some
misconceptions about entropy,

432
00:19:08,710 --> 00:19:11,720
and gives you a little bit more
intuition about what it

433
00:19:11,720 --> 00:19:12,780
actually is.

434
00:19:12,780 --> 00:00:00,000
See you in the next video.