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PROFESSOR NELSON: So last time
we just about finished up the

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00:00:24,270 --> 00:00:26,540
discussion of thermochemisty,
and we went through a

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00:00:26,540 --> 00:00:28,600
description of calorimetry,
how we actually make

11
00:00:28,600 --> 00:00:30,500
measurements of thermodynamic
a quantities.

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00:00:30,500 --> 00:00:32,550
I should mention, which I didn't
last time, that you

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00:00:32,550 --> 00:00:35,330
know a calorimeter, apart from
measuring heats of formation

14
00:00:35,330 --> 00:00:37,650
also is used to measure
standard thermodynamic

15
00:00:37,650 --> 00:00:39,400
quantities like heat
capacities.

16
00:00:39,400 --> 00:00:42,480
You know how much heat does it
take to raise the temperature

17
00:00:42,480 --> 00:00:43,540
of something by a degree?

18
00:00:43,540 --> 00:00:47,290
Well, you put the material
inside the calorimeter, and

19
00:00:47,290 --> 00:00:50,100
you have a heater and it's
connected up to current

20
00:00:50,100 --> 00:00:52,490
source, and you can accurately
measure how much heat you're

21
00:00:52,490 --> 00:00:54,800
putting in, because you can
measure how much current is

22
00:00:54,800 --> 00:00:57,980
going into it, and you
separately are measuring the

23
00:00:57,980 --> 00:01:01,050
temperature of the material, so
it's a straightforward way

24
00:01:01,050 --> 00:01:03,310
of measuring the heat
capacities, thermodynamic data

25
00:01:03,310 --> 00:01:04,080
of this sort.

26
00:01:04,080 --> 00:01:06,590
So work on phase transitions,
just ordinary

27
00:01:06,590 --> 00:01:07,670
properties of material.

28
00:01:07,670 --> 00:01:10,880
Chemical reactions, all the
thermochemistry involved is

29
00:01:10,880 --> 00:01:14,510
done using constant pressure or
constant volume calorimetry

30
00:01:14,510 --> 00:01:16,530
in a pretty routine way.

31
00:01:16,530 --> 00:01:18,890
So we talked about how to use
the results of measurements

32
00:01:18,890 --> 00:01:23,420
like that to calculate
reaction energetics,

33
00:01:23,420 --> 00:01:25,730
enthalpies of reaction.

34
00:01:25,730 --> 00:01:29,070
And I just want to end the unit
on thermochemistry with a

35
00:01:29,070 --> 00:01:34,420
real brief discussion of an
approximate way of formulating

36
00:01:34,420 --> 00:01:38,110
heats of reaction, and that is
in terms of bond energies.

37
00:01:38,110 --> 00:01:41,920
Now you know you're probably
never going to sit down and do

38
00:01:41,920 --> 00:01:43,360
a series of thermodynamic

39
00:01:43,360 --> 00:01:45,840
calculations using bond energies.

40
00:01:45,840 --> 00:01:50,460
You could always look up heats
of formation of compounds and

41
00:01:50,460 --> 00:01:54,680
from those determine very
accurately heats of reaction,

42
00:01:54,680 --> 00:01:58,270
by looking at the heats of
formation of products and the

43
00:01:58,270 --> 00:02:00,320
heats of formation
of the reactants

44
00:02:00,320 --> 00:02:01,720
and subtracting them.

45
00:02:01,720 --> 00:02:04,480
And since that data is available
for a really wide

46
00:02:04,480 --> 00:02:07,980
range of materials, that's sort
of the simplest approach

47
00:02:07,980 --> 00:02:11,570
and the most accurate one to
determine reaction energetics.

48
00:02:11,570 --> 00:02:14,990
On the other hand, if you just
want to think about molecules,

49
00:02:14,990 --> 00:02:17,580
you know, you think
about bonds.

50
00:02:17,580 --> 00:02:20,140
You know if you say I've got
methane or ethane, I'm going

51
00:02:20,140 --> 00:02:24,390
to use a fuel and burn it
and capture the energy.

52
00:02:24,390 --> 00:02:26,260
How much energy do
we have in there?

53
00:02:26,260 --> 00:02:29,240
Well the way you want to be
thinking about that is all

54
00:02:29,240 --> 00:02:32,380
right, I'm going to take the
starting material, the fuel,

55
00:02:32,380 --> 00:02:35,170
I'm going to break bonds, and
I'm going to form some final

56
00:02:35,170 --> 00:02:36,870
product with new bonds.

57
00:02:36,870 --> 00:02:38,630
Roughly what kinds
of energetics

58
00:02:38,630 --> 00:02:40,030
are we talking about?

59
00:02:40,030 --> 00:02:42,610
In biological systems, it's
also super important.

60
00:02:42,610 --> 00:02:47,050
You know you think about
ordinary biochemical

61
00:02:47,050 --> 00:02:50,520
energetics, what's used is fuel
in biology and what are

62
00:02:50,520 --> 00:02:52,270
the products that are formed?

63
00:02:52,270 --> 00:02:56,050
And again, it's just super
important to be able to think

64
00:02:56,050 --> 00:03:00,100
sort of semi-quantitatively
in terms of bond energies,

65
00:03:00,100 --> 00:03:02,300
because you don't want to always
be going and looking up

66
00:03:02,300 --> 00:03:03,510
everything in tables.

67
00:03:03,510 --> 00:03:05,850
If you need to do an extensive
series of calculations, it's

68
00:03:05,850 --> 00:03:07,640
very useful to have
the tables.

69
00:03:07,640 --> 00:03:10,560
But if you just want to think
about how something is

70
00:03:10,560 --> 00:03:13,610
working, you know biological
or system or an engine or

71
00:03:13,610 --> 00:03:16,620
another application, it's very
useful to just be able to

72
00:03:16,620 --> 00:03:19,880
think in terms of
bond energies.

73
00:03:19,880 --> 00:03:21,510
So let's just go over
bond energies.

74
00:03:21,510 --> 00:03:25,360
And you've seen this in 5.111
and 2, so I'm not going to

75
00:03:25,360 --> 00:03:29,580
belabor it but they're just a
little bit of examples that I

76
00:03:29,580 --> 00:03:32,170
want to go through, just so
it's fresh on your mind.

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00:03:32,170 --> 00:03:40,790
So the idea, of course, is to be
able to have an idea of how

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00:03:40,790 --> 00:03:43,830
much energy is involved
in forming or

79
00:03:43,830 --> 00:03:45,880
breaking a single bond.

80
00:03:45,880 --> 00:03:52,770
So, if we just do this by
example, we can take methane

81
00:03:52,770 --> 00:03:57,840
so it's a real simple case
because we know it's just got

82
00:03:57,840 --> 00:04:03,040
four identical carbon hydrogen
bonds, and we could say OK,

83
00:04:03,040 --> 00:04:04,370
let's just break them.

84
00:04:04,370 --> 00:04:08,080
So we'll start with methane
gas and go to one atom of

85
00:04:08,080 --> 00:04:11,160
carbon in the gas phase,
plus four atoms of

86
00:04:11,160 --> 00:04:14,010
hydrogen in the gas phase.

87
00:04:14,010 --> 00:04:18,550
The energetics in this case
aren't given by the usual

88
00:04:18,550 --> 00:04:19,440
heats of formation.

89
00:04:19,440 --> 00:04:22,120
You'd just say, if I want to
know about methane, I can look

90
00:04:22,120 --> 00:04:24,620
up its heat of formation from
the elements in their

91
00:04:24,620 --> 00:04:27,020
standards states. but the
difference here is these

92
00:04:27,020 --> 00:04:30,300
elements aren't in their
standard states.

93
00:04:30,300 --> 00:04:33,010
Carbon in its standard state
at room temperature and

94
00:04:33,010 --> 00:04:36,140
pressure is graphite, a solid,
it's not carbon atoms in the

95
00:04:36,140 --> 00:04:39,270
gas phase, and hydrogen in the
standard state is hydrogen

96
00:04:39,270 --> 00:04:43,260
molecules H2, not individual
atoms.

97
00:04:43,260 --> 00:04:49,430
All right, so we'd like to
have this bond energy for

98
00:04:49,430 --> 00:04:51,510
these things.

99
00:04:51,510 --> 00:04:54,400
So let's just to make a cycle
that will allow us to

100
00:04:54,400 --> 00:04:55,550
determine this.

101
00:04:55,550 --> 00:05:02,200
So this'll be our first step in
that cycle, or one way of

102
00:05:02,200 --> 00:05:02,720
getting there.

103
00:05:02,720 --> 00:05:09,750
And this delta H of reaction is
going to be by definition

104
00:05:09,750 --> 00:05:18,250
four times our bond energy for
a carbon hydrogen bond.

105
00:05:18,250 --> 00:05:22,500
Now let's go to be elements that
are in their standards

106
00:05:22,500 --> 00:05:24,370
states at room temperature
and pressure.

107
00:05:24,370 --> 00:05:34,150
So let's go to carbon
as graphite.

108
00:05:34,150 --> 00:05:42,320
And let's go to two molecules of
hydrogen gas, so this will

109
00:05:42,320 --> 00:05:52,590
be step two and this
will be step three.

110
00:05:52,590 --> 00:05:56,420
And this will allow us to work
because now we're starting in

111
00:05:56,420 --> 00:05:57,830
standard states, so
we can just use

112
00:05:57,830 --> 00:06:00,420
regular heats of formation.

113
00:06:00,420 --> 00:06:01,510
And that's the key.

114
00:06:01,510 --> 00:06:08,140
So if we look at step one
delta H1 there as we've

115
00:06:08,140 --> 00:06:16,800
defined it, four times
our bond energy.

116
00:06:16,800 --> 00:06:24,180
Two, this is just negative heat
of formation of methane,

117
00:06:24,180 --> 00:06:33,390
which we can look up.

118
00:06:33,390 --> 00:06:43,690
And three, is similar.

119
00:06:43,690 --> 00:06:47,860
Essentially it's the heat of
formation of carbon in the gas

120
00:06:47,860 --> 00:06:52,330
phase and hydrogen atoms in the
gas phase, commonly called

121
00:06:52,330 --> 00:06:55,830
heats of atomization, but these
are also tabulated just

122
00:06:55,830 --> 00:06:57,820
like heats of formation
of ordinary compounds.

123
00:06:57,820 --> 00:06:59,870
In fact, in the appendix
to your book that has

124
00:06:59,870 --> 00:07:04,050
thermodynamic data, you can find
carbon gas phase atoms

125
00:07:04,050 --> 00:07:06,960
including heat of formation,
and same with individual

126
00:07:06,960 --> 00:07:08,800
hydrogen atom as opposed
to hydrogen

127
00:07:08,800 --> 00:07:10,390
molecules in the gas phase.

128
00:07:10,390 --> 00:07:12,380
So those data are available.

129
00:07:12,380 --> 00:07:25,450
So we can write delta Hc from
atomization, and two times

130
00:07:25,450 --> 00:07:31,800
delta H of H2.

131
00:07:31,800 --> 00:07:37,470
This is the way this is
tabulated and this is molar.

132
00:07:37,470 --> 00:07:39,460
And of course now we've
written a cycle.

133
00:07:39,460 --> 00:07:42,320
So we know that to get from here
to here is the same as to

134
00:07:42,320 --> 00:07:44,490
go through these two steps.

135
00:07:44,490 --> 00:07:48,050
In other words delta H1 is the
sum of delta H2 and delta H3.

136
00:08:01,300 --> 00:08:07,240
And so this says that our four
times the carbon hydrogen bond

137
00:08:07,240 --> 00:08:14,270
energy is just given by minus
the heat of formation of

138
00:08:14,270 --> 00:08:25,280
methane plus the heat of
atomization of carbon, plus

139
00:08:25,280 --> 00:08:29,080
the two times the heat
of atomization

140
00:08:29,080 --> 00:08:35,280
for hydrogen molecules.

141
00:08:35,280 --> 00:08:38,500
And if we look up the numbers
that are tabulated, what we

142
00:08:38,500 --> 00:08:50,090
discover is that our carbon
hydrogen bond energy is 416.2

143
00:08:50,090 --> 00:08:57,470
kilojoules per mole.

144
00:08:57,470 --> 00:09:01,310
Very useful to have numbers like
that stored in your head.

145
00:09:01,310 --> 00:09:05,030
To have some basic idea of
just ordinary chemical

146
00:09:05,030 --> 00:09:08,900
energetics in terms
of bond energies.

147
00:09:08,900 --> 00:09:14,265
Hydrogen bonds, you know roughly
20 kilojoules per

148
00:09:14,265 --> 00:09:15,650
mole, and so forth.

149
00:09:15,650 --> 00:09:19,570
Just having those kinds of
energetic enables you to think

150
00:09:19,570 --> 00:09:23,040
in a qualitative way about
what's likely to happen in an

151
00:09:23,040 --> 00:09:27,040
ordinary chemical or biochemical
situation.

152
00:09:27,040 --> 00:09:31,580
OK, so this is in a sense the
simplest case, because we've

153
00:09:31,580 --> 00:09:34,910
talked about the dissociation of
a molecule that consists of

154
00:09:34,910 --> 00:09:38,800
all identical bonds.

155
00:09:38,800 --> 00:09:41,710
But it's straightforward
to go from there to

156
00:09:41,710 --> 00:09:43,490
additional bond energies.

157
00:09:43,490 --> 00:09:48,380
So from this we've got a value
for a sort of typical carbon

158
00:09:48,380 --> 00:09:50,890
hydrogen bond, right.

159
00:09:50,890 --> 00:09:54,570
We can do the same thing now for
ethane, and that's got a

160
00:09:54,570 --> 00:09:58,640
single carbon carbon bond, as
well as a bunch of carbon

161
00:09:58,640 --> 00:10:01,900
hydrogen bonds, but now the we
know the carbon hydrogen bond

162
00:10:01,900 --> 00:10:05,370
energy, we can use that number
plus the relevant heats of

163
00:10:05,370 --> 00:10:08,480
formation to determine the
carbon carbon bond energy.

164
00:10:08,480 --> 00:10:10,900
And we can keep going and extend
this to essentially

165
00:10:10,900 --> 00:10:14,360
tabulate bond energies for a
very large number of different

166
00:10:14,360 --> 00:10:17,350
sorts of bonds.

167
00:10:17,350 --> 00:10:31,450
So just as an example, ethane,
so now we're going to have --

168
00:10:31,450 --> 00:10:34,920
this I'll write it all out just
some we can keep proper

169
00:10:34,920 --> 00:10:37,850
track of all the bonds that
we're going to be breaking.

170
00:10:37,850 --> 00:10:46,730
So C2H6 goes to two carbon
gas phase atoms, and

171
00:10:46,730 --> 00:10:54,080
six hydrogen atoms.

172
00:10:54,080 --> 00:11:04,020
So in this case, our, I can
write this again as one delta

173
00:11:04,020 --> 00:11:14,860
H1 is six times the carbon
hydrogen bond energy plus the

174
00:11:14,860 --> 00:11:20,320
carbon carbon bond energy that
we'd like to determine.

175
00:11:20,320 --> 00:11:23,760
And again we can go through
now a similar cycle.

176
00:11:23,760 --> 00:11:27,100
So again this now can be
equilibrated with carbon

177
00:11:27,100 --> 00:11:39,770
graphite plus three molecules of
hydrogen in the gas phase,

178
00:11:39,770 --> 00:11:40,950
just like before.

179
00:11:40,950 --> 00:11:45,230
And so from that we can see
that we'll end up with an

180
00:11:45,230 --> 00:11:51,740
equality between these, and
negative delta H naught

181
00:11:51,740 --> 00:12:05,140
formation for C2H6 or ethane,
plus two delta H of carbon

182
00:12:05,140 --> 00:12:09,940
atomization, plus three
delta H for

183
00:12:09,940 --> 00:12:17,920
atomization hydrogen molecule.

184
00:12:17,920 --> 00:12:20,880
So we've already seen we could
look up these numbers and

185
00:12:20,880 --> 00:12:25,170
this, and we've already
determined a carbon hydrogen

186
00:12:25,170 --> 00:12:26,120
bond energy.

187
00:12:26,120 --> 00:12:30,790
So again, if we find all the
relevant values, we can

188
00:12:30,790 --> 00:12:34,020
determine that our carbon carbon
bond energy is 342

189
00:12:34,020 --> 00:12:43,020
kilojoules.

190
00:12:43,020 --> 00:12:43,690
And so on.

191
00:12:43,690 --> 00:12:46,860
So we can keep going and again
build up a bigger and bigger

192
00:12:46,860 --> 00:12:50,980
inventory of bond energies just
to provide us with the

193
00:12:50,980 --> 00:12:53,140
kind of intuition that we'd
like to have to be able to

194
00:12:53,140 --> 00:12:57,240
think about ordinary molecular
energetics.

195
00:12:57,240 --> 00:13:00,740
Any questions about
bond energies?

196
00:13:00,740 --> 00:13:02,140
All right.

197
00:13:02,140 --> 00:13:05,250
Of course, if we know bond
energies, we also could make

198
00:13:05,250 --> 00:13:07,580
estimates of heats
of formation.

199
00:13:07,580 --> 00:13:09,650
So if we have some new compound,
we don't know its

200
00:13:09,650 --> 00:13:11,770
heat of formation, we
know its structure.

201
00:13:11,770 --> 00:13:13,570
We know what bonds
are involved.

202
00:13:13,570 --> 00:13:16,900
We could get an estimate for
what we might expect for its

203
00:13:16,900 --> 00:13:19,760
heat of formation if we know
those, and I think I'll just

204
00:13:19,760 --> 00:13:23,830
write this out on the board by
example, but not work through

205
00:13:23,830 --> 00:13:25,960
the numbers explicitly.

206
00:13:25,960 --> 00:13:31,190
You know, let's say we were
going to make, you know, n

207
00:13:31,190 --> 00:13:35,360
pentane C5H12.

208
00:13:44,670 --> 00:13:50,020
And of course again keeping
proper track of all the carbon

209
00:13:50,020 --> 00:13:51,650
carbon and carbon
hydrogen bonds.

210
00:13:51,650 --> 00:13:54,190
But now in principle we know
the carbon carbon bond

211
00:13:54,190 --> 00:13:56,980
energies and the carbon hydrogen
bond energies.

212
00:13:56,980 --> 00:13:59,330
So we should be able to figure
out the heat of formation of a

213
00:13:59,330 --> 00:14:03,900
compound like this, even if we
don't know it from a table.

214
00:14:03,900 --> 00:14:08,170
And it's again through a similar
sort of cycle so if we

215
00:14:08,170 --> 00:14:12,510
start with the atoms in the gas

216
00:14:12,510 --> 00:14:19,290
phase, and go to n pentane.

217
00:14:19,290 --> 00:14:25,810
So this is now the bond
energies which

218
00:14:25,810 --> 00:14:29,350
we basically know.

219
00:14:29,350 --> 00:14:40,810
And again make our cycle of
involving the elements in

220
00:14:40,810 --> 00:14:45,420
their stable form at standard
temperature and pressure.

221
00:14:45,420 --> 00:14:55,290
Then again, here's our
one, two, three.

222
00:14:55,290 --> 00:15:02,160
Here's our minus delta H of
atomization, and here's our

223
00:15:02,160 --> 00:15:11,940
heat of formation.

224
00:15:11,940 --> 00:15:14,080
And that's the point, is that
now we can use what we've

225
00:15:14,080 --> 00:15:19,300
already elaborated for the bond
energies and the known

226
00:15:19,300 --> 00:15:21,000
enthalpies of atomization,
and we could

227
00:15:21,000 --> 00:15:28,050
determine the heat of formation.

228
00:15:28,050 --> 00:15:33,760
If we do that, we wind up with
a value of minus 152.6

229
00:15:33,760 --> 00:15:40,580
kilojoules.

230
00:15:40,580 --> 00:15:41,340
If we measure it.

231
00:15:41,340 --> 00:15:51,870
If we look up in a table what
the actual value is, we

232
00:15:51,870 --> 00:15:59,530
discover it's minus
146.4 kilojoules.

233
00:15:59,530 --> 00:16:01,700
So it's a few percent off.

234
00:16:01,700 --> 00:16:02,510
Why is it off?

235
00:16:02,510 --> 00:16:03,130
Why isn't it right?

236
00:16:03,130 --> 00:16:11,180
STUDENT: [UNINTELLIGIBLE]

237
00:16:11,180 --> 00:16:12,080
PROFESSOR NELSON:
Yes, exactly.

238
00:16:12,080 --> 00:16:16,300
You know you can't use the C-H
bonds from methane for every

239
00:16:16,300 --> 00:16:20,990
C-H bond, or the C-C bond in
ethane for every carbon carbon

240
00:16:20,990 --> 00:16:21,960
single bond.

241
00:16:21,960 --> 00:16:26,810
There'll be variations, usually
of modest magnitude,

242
00:16:26,810 --> 00:16:28,350
in the values.

243
00:16:28,350 --> 00:16:31,910
So this isn't going to be an
exact calculation, but

244
00:16:31,910 --> 00:16:34,910
certainly this is close enough
for allowing us to think

245
00:16:34,910 --> 00:16:37,640
qualitatively and
semi-quantitatively about

246
00:16:37,640 --> 00:16:39,830
ordinary energetics.

247
00:16:39,830 --> 00:16:56,370
Another illustration of it is if
we look at neopentane -- so

248
00:16:56,370 --> 00:16:58,070
same chemical formula.

249
00:16:58,070 --> 00:17:02,060
Same number of carbon carbon
and carbon hydrogen bonds.

250
00:17:02,060 --> 00:17:04,530
So according to the way we've
done this calculation, we

251
00:17:04,530 --> 00:17:08,180
should get exactly the same
number, because all we're

252
00:17:08,180 --> 00:17:09,970
doing is adding up the total
number of bonds,

253
00:17:09,970 --> 00:17:11,870
and it's the same.

254
00:17:11,870 --> 00:17:16,790
But what we discover is that
for neopentane, delta H of

255
00:17:16,790 --> 00:17:28,080
formation, neopentane is
minus 166.1 kilojoules.

256
00:17:28,080 --> 00:17:29,550
So again it's different
in this case

257
00:17:29,550 --> 00:17:32,560
in the other direction.

258
00:17:32,560 --> 00:17:37,200
But certainly close enough
that allows us to think

259
00:17:37,200 --> 00:17:42,870
reasonably about what might
happen in ordinary situations.

260
00:17:42,870 --> 00:17:47,770
Any questions about
bond energies?

261
00:17:47,770 --> 00:17:55,700
OK, now we're going to go to a
new topic, and let me say, the

262
00:17:55,700 --> 00:17:58,680
topic we're going to start now,
the second law, is really

263
00:17:58,680 --> 00:18:02,120
in a sense, this is the start of
the whole rest of the term.

264
00:18:02,120 --> 00:18:06,180
So far, what we've covered
essentially is conservation of

265
00:18:06,180 --> 00:18:11,330
energy, how you think about
energetics and what

266
00:18:11,330 --> 00:18:12,320
contributes to them.

267
00:18:12,320 --> 00:18:14,800
That is heat and work.

268
00:18:14,800 --> 00:18:16,960
How to account for them
all properly.

269
00:18:16,960 --> 00:18:19,890
What happens under constant
volume or constant pressure

270
00:18:19,890 --> 00:18:24,280
conditions that led us to the
definition of enthalpy right

271
00:18:24,280 --> 00:18:27,360
and so forth.

272
00:18:27,360 --> 00:18:33,270
And once you get your arms
around these ideas, and it

273
00:18:33,270 --> 00:18:38,640
takes some work to do that, but
once you do, the actual

274
00:18:38,640 --> 00:18:42,110
execution of things can be
pretty straightforward, and

275
00:18:42,110 --> 00:18:44,440
some of this can seem like
just you know a lot of

276
00:18:44,440 --> 00:18:46,460
accounting.

277
00:18:46,460 --> 00:18:47,040
It's not.

278
00:18:47,040 --> 00:18:50,750
It takes some effort to become
accustomed to it and familiar

279
00:18:50,750 --> 00:18:53,070
with how to properly think about
heat and work and how

280
00:18:53,070 --> 00:18:55,380
they contribute to energy
and so forth.

281
00:18:55,380 --> 00:18:59,570
But given that amount of effort,
a lot of this can be

282
00:18:59,570 --> 00:19:02,490
reduced to fairly
straightforward

283
00:19:02,490 --> 00:19:04,430
calculational stuff.

284
00:19:04,430 --> 00:19:09,640
What we're about to start is a
little different from that in

285
00:19:09,640 --> 00:19:15,870
some sense, and really in some
ways more difficult because

286
00:19:15,870 --> 00:19:20,230
what we're going to try to
understand starting with this

287
00:19:20,230 --> 00:19:25,910
next set of topics is what
determines whether something

288
00:19:25,910 --> 00:19:29,020
happens spontaneously?

289
00:19:29,020 --> 00:19:32,650
We haven't really talked about
that in any of this.

290
00:19:32,650 --> 00:19:35,680
We've talked about whether
reactions are endothermic or

291
00:19:35,680 --> 00:19:38,190
exothermic.

292
00:19:38,190 --> 00:19:41,180
But as you're going to see that
doesn't determine what

293
00:19:41,180 --> 00:19:42,750
happens spontaneously.

294
00:19:42,750 --> 00:19:45,010
It certainly is one of the
factors, but by no

295
00:19:45,010 --> 00:19:47,180
means the only one.

296
00:19:47,180 --> 00:19:51,760
What determines what happens
just by itself?

297
00:19:51,760 --> 00:19:54,970
Or another way of saying that
is, if I have some sort of

298
00:19:54,970 --> 00:19:56,290
system, it could be an engine.

299
00:19:56,290 --> 00:19:57,830
It could be a chemical
reaction.

300
00:19:57,830 --> 00:20:01,560
It could be a biochemical system
or some part of it.

301
00:20:01,560 --> 00:20:07,660
What determines where the
equilibrium is and the

302
00:20:07,660 --> 00:20:11,320
direction that things would have
to go in order to reach

303
00:20:11,320 --> 00:20:15,280
or approach the equilibrium?

304
00:20:15,280 --> 00:20:19,990
What is the equilibrium
state of something?

305
00:20:19,990 --> 00:20:23,350
Actually, what we've discussed
so far really doesn't allow us

306
00:20:23,350 --> 00:20:27,630
to determine that, and there are
a few easy ways to sort of

307
00:20:27,630 --> 00:20:29,590
bring that out.

308
00:20:29,590 --> 00:20:35,130
One is you can imagine
constructing some kind of

309
00:20:35,130 --> 00:20:42,710
cyclic process that you know
it could remove heat like a

310
00:20:42,710 --> 00:20:49,453
refrigerator does from a cool
region and export the heat to

311
00:20:49,453 --> 00:20:51,910
a hotter region, like the room,
or outside a window if

312
00:20:51,910 --> 00:20:54,320
it's an air conditioner or
something like that.

313
00:20:54,320 --> 00:20:55,820
Just move the heat.

314
00:20:55,820 --> 00:20:57,770
That's it.

315
00:20:57,770 --> 00:21:01,210
Why not?

316
00:21:01,210 --> 00:21:05,000
I mean you could do that
and not necessarily

317
00:21:05,000 --> 00:21:08,030
violate the first law.

318
00:21:08,030 --> 00:21:11,060
Or what about, here's
a simpler case.

319
00:21:11,060 --> 00:21:16,690
What if I just have a chamber
with a divider, and I pump out

320
00:21:16,690 --> 00:21:22,090
half of it, and I put gas in
this half, so there's gas and

321
00:21:22,090 --> 00:21:29,770
there's vacuum, and then
I remove the divider.

322
00:21:29,770 --> 00:21:34,500
So I certainly expect that what
happens is the gas fills

323
00:21:34,500 --> 00:21:34,970
the volume.

324
00:21:34,970 --> 00:21:36,640
Why?

325
00:21:36,640 --> 00:21:40,230
The first law didn't tell me
that that needs to happen.

326
00:21:40,230 --> 00:21:43,500
Why doesn't it go back the
other way, anyway, even

327
00:21:43,500 --> 00:21:44,330
without the barrier?

328
00:21:44,330 --> 00:21:49,360
Why doesn't the gas just by
itself all wind up over here?

329
00:21:49,360 --> 00:21:52,845
Let's say it's a pretty dilute
gas, so even if it does all

330
00:21:52,845 --> 00:21:56,430
end up in this half, you know
the energy of any sort of

331
00:21:56,430 --> 00:21:59,970
unfavorable repulsions between
molecules is negligible.

332
00:21:59,970 --> 00:22:02,660
Maybe they even have
weak attractions?

333
00:22:02,660 --> 00:22:05,530
Why doesn't that happened?

334
00:22:05,530 --> 00:22:07,530
It's a good thing for us
that it doesn't happen.

335
00:22:07,530 --> 00:22:10,250
Why in this room doesn't the air
all just sort of collect

336
00:22:10,250 --> 00:22:11,820
over there somewhere?

337
00:22:11,820 --> 00:22:15,010
Or just the oxygen molecules
in the air and

338
00:22:15,010 --> 00:22:17,130
suffocate all of us.

339
00:22:17,130 --> 00:22:20,540
The first law doesn't
have anything to

340
00:22:20,540 --> 00:22:23,730
say about that actually.

341
00:22:23,730 --> 00:22:26,390
Whatever the reason it doesn't
happen, we're not going to

342
00:22:26,390 --> 00:22:30,200
find the answer to that
in the first law.

343
00:22:30,200 --> 00:22:34,330
So that's what the second law
of thermodynamics and the

344
00:22:34,330 --> 00:22:36,540
development of entropy
is all about.

345
00:22:36,540 --> 00:22:40,200
It's to help us understand
what is the direction of

346
00:22:40,200 --> 00:22:42,590
spontaneous change?

347
00:22:42,590 --> 00:22:46,650
What governs that, and what's
the equilibrium state that is

348
00:22:46,650 --> 00:22:51,280
reached when the spontaneous
change occurs?

349
00:22:51,280 --> 00:22:55,000
OK?

350
00:22:55,000 --> 00:22:59,590
So the second law is going to
give us basically a principle

351
00:22:59,590 --> 00:23:02,060
that'll tell us the direction
of spontaneous change.

352
00:23:02,060 --> 00:23:04,610
One way of thinking about that
is it's going to allow it to

353
00:23:04,610 --> 00:23:06,610
sort of determine the
direction of time.

354
00:23:06,610 --> 00:23:09,090
You know if we see initial or if
we see one state and we see

355
00:23:09,090 --> 00:23:12,370
another state, we'll be able or
know, time must have been

356
00:23:12,370 --> 00:23:15,070
going this way, right because
the spontaneous change would

357
00:23:15,070 --> 00:23:19,720
happen in this direction.

358
00:23:19,720 --> 00:23:30,470
So, I'm going to put up a couple
of just statements of

359
00:23:30,470 --> 00:23:34,110
the second law of
thermodynamics.

360
00:23:34,110 --> 00:23:38,160
I'll start with kind
of an easy one.

361
00:23:38,160 --> 00:23:56,400
So maybe I'll start
with that here.

362
00:23:56,400 --> 00:24:08,760
Here's a statement
by Clausius.

363
00:24:08,760 --> 00:24:12,390
The first law says that
the energy of

364
00:24:12,390 --> 00:24:16,750
the universe is constant.

365
00:24:16,750 --> 00:24:34,780
We're always conserving
in one way or another.

366
00:24:34,780 --> 00:24:57,320
And the second law is that the
entropy of the universe is

367
00:24:57,320 --> 00:24:58,600
increasing.

368
00:24:58,600 --> 00:25:03,350
Now we're going to define
entropy presently.

369
00:25:03,350 --> 00:25:06,340
But I'm writing this up just to
give you some foreshadowing

370
00:25:06,340 --> 00:25:10,350
of how we're going to try to
guide our thinking about

371
00:25:10,350 --> 00:25:13,310
spontaneous processes.

372
00:25:13,310 --> 00:25:17,200
This tells us about conservation
of energy.

373
00:25:17,200 --> 00:25:22,240
This tells us about which
direction things move in

374
00:25:22,240 --> 00:25:25,700
spontaneously, namely the
direction that leads to an

375
00:25:25,700 --> 00:25:33,390
increase in this soon to be
defined quantity entropy.

376
00:25:33,390 --> 00:25:38,010
It's going to turn out to be a
state function, and it'll help

377
00:25:38,010 --> 00:25:42,370
us understand the direction
of spontaneous change.

378
00:25:42,370 --> 00:25:46,300
You know, like the first law
the second law too was

379
00:25:46,300 --> 00:25:50,300
developed before there was
a very well defined

380
00:25:50,300 --> 00:25:53,620
understanding of the molecular
nature of matter.

381
00:25:53,620 --> 00:25:56,360
We're going to talk about the
second law and entropy in

382
00:25:56,360 --> 00:25:58,470
macroscopic terms.

383
00:25:58,470 --> 00:26:01,650
Later on in the semester we'll
also discuss them in

384
00:26:01,650 --> 00:26:03,300
microscopic terms.

385
00:26:03,300 --> 00:26:05,330
We'll do a little bit of what's
called statistical

386
00:26:05,330 --> 00:26:09,090
mechanics, of microscopic,
basically discussing the

387
00:26:09,090 --> 00:26:11,200
microscopic origins of
entropy in terms

388
00:26:11,200 --> 00:26:14,340
of disorder of molecules.

389
00:26:14,340 --> 00:26:18,420
But really, the thermodynamics
of entropy and the second law

390
00:26:18,420 --> 00:26:22,140
evolved because people were
trying to build things.

391
00:26:22,140 --> 00:26:24,350
It was the Industrial
Revolution. people were trying

392
00:26:24,350 --> 00:26:28,370
to build engines, steam engines,
and other kinds of

393
00:26:28,370 --> 00:26:31,890
devices, refrigerators
other things.

394
00:26:31,890 --> 00:26:35,680
And they couldn't understand --
first of all, why couldn't

395
00:26:35,680 --> 00:26:39,550
you make it perfectly
efficient?

396
00:26:39,550 --> 00:26:40,920
You know, you'd have
a steam engine.

397
00:26:40,920 --> 00:26:43,260
There'd be a source of heat.

398
00:26:43,260 --> 00:26:46,180
You could extract work.

399
00:26:46,180 --> 00:26:48,870
Never seemed like you
could get it all and

400
00:26:48,870 --> 00:26:52,280
turn it all into work.

401
00:26:52,280 --> 00:26:55,270
Why not?

402
00:26:55,270 --> 00:26:57,940
And if not, what were the
limitations on it?

403
00:26:57,940 --> 00:27:02,020
What was the best efficiency
you could achieve?

404
00:27:02,020 --> 00:27:06,170
So in a very practical way
people were motivated to think

405
00:27:06,170 --> 00:27:12,570
very hard about these
kinds of questions.

406
00:27:12,570 --> 00:27:17,880
So let's just look at some of
the things that brought out

407
00:27:17,880 --> 00:27:21,540
the need for this kind
of consideration.

408
00:27:21,540 --> 00:27:38,090
So let me start by drawing one
of the impossibilities.

409
00:27:38,090 --> 00:27:40,890
We could try to build
a heat engine.

410
00:27:40,890 --> 00:27:49,190
Where we've got some temperature
T1 which is hot,

411
00:27:49,190 --> 00:27:54,380
and some amount of heat, q1 goes
into our system, and our

412
00:27:54,380 --> 00:27:57,470
system runs as a cycle.

413
00:27:57,470 --> 00:28:00,410
It goes around and around,
because in any practical

414
00:28:00,410 --> 00:28:02,910
situation we're going to need
to keep going and repeating

415
00:28:02,910 --> 00:28:06,080
the process.

416
00:28:06,080 --> 00:28:09,400
Some amount of work comes out.

417
00:28:09,400 --> 00:28:14,670
We'll call it minus w, because
work is always defined as the

418
00:28:14,670 --> 00:28:18,760
work that's done by the
environment on the system.

419
00:28:18,760 --> 00:28:22,060
So if I'm drawing the arrow this
way, then I want to write

420
00:28:22,060 --> 00:28:27,740
it as minus w.

421
00:28:27,740 --> 00:28:31,510
Now this would be just swell.

422
00:28:31,510 --> 00:28:32,070
This is it.

423
00:28:32,070 --> 00:28:34,690
That's the whole heat engine.

424
00:28:34,690 --> 00:28:37,330
This is running in a cycle.

425
00:28:37,330 --> 00:28:41,610
So we know that, delta
u is zero.

426
00:28:41,610 --> 00:28:45,130
So that would mean that, you
know, the amount of work out

427
00:28:45,130 --> 00:28:51,110
would just equal the heat
in every time around.

428
00:28:51,110 --> 00:28:54,520
Never happens.

429
00:28:54,520 --> 00:28:57,510
Can't make it happen.

430
00:28:57,510 --> 00:29:02,310
The only way it works is
if instead there's

431
00:29:02,310 --> 00:29:12,250
an additional part.

432
00:29:12,250 --> 00:29:27,200
Somewhere heat is also lost
to a cold reservoir.

433
00:29:27,200 --> 00:29:30,390
In other words, you know
I burned some fuel.

434
00:29:30,390 --> 00:29:34,810
I consumed something to produce
my hot source, and I'm

435
00:29:34,810 --> 00:29:38,600
going to then try to turn it
into work, which I can, but

436
00:29:38,600 --> 00:29:41,700
only partly.

437
00:29:41,700 --> 00:29:45,890
There's going to be heat loss
somewhere to a colder region,

438
00:29:45,890 --> 00:29:48,650
and I can't avoid it.

439
00:29:48,650 --> 00:29:53,910
And it was discovered that
this was always the case.

440
00:29:53,910 --> 00:29:59,950
So this can be built where, just
to be clear on these. q1

441
00:29:59,950 --> 00:30:02,820
is a positive number, because
again that's heat going from

442
00:30:02,820 --> 00:30:04,570
the environment to the system.

443
00:30:04,570 --> 00:30:19,970
This is our system running
in a cycle.

444
00:30:19,970 --> 00:30:26,370
So q1 is positive, minus w is
positive, that is work is

445
00:30:26,370 --> 00:30:31,230
being done on the environment
by the engine.

446
00:30:31,230 --> 00:30:42,740
And minus q2 is positive.

447
00:30:42,740 --> 00:30:51,330
And T1 is greater than T2.

448
00:30:51,330 --> 00:30:55,630
That I can build.

449
00:30:55,630 --> 00:31:00,460
Here's another thing
we could try to do.

450
00:31:00,460 --> 00:31:01,550
It's sort of the opposite.

451
00:31:01,550 --> 00:31:04,840
We could try to produce a
refrigerator but not have to

452
00:31:04,840 --> 00:31:07,220
do any work.

453
00:31:07,220 --> 00:31:13,730
So let's go the other way, in
other words, let's go from T2

454
00:31:13,730 --> 00:31:20,220
which is cold we're going to
go in this direction now,

455
00:31:20,220 --> 00:31:26,050
which means q2 will be a
positive number and here's our

456
00:31:26,050 --> 00:31:29,600
system running in a cycle.

457
00:31:29,600 --> 00:31:34,000
And now here's minus q1 now is
going to be our positive

458
00:31:34,000 --> 00:31:37,590
number, and we're going to
remove heat from q2 and move

459
00:31:37,590 --> 00:31:43,660
it, or from T2 a cold region
and move it to some place

460
00:31:43,660 --> 00:31:46,110
that's hotter.

461
00:31:46,110 --> 00:31:49,960
Also a pretty nice idea.

462
00:31:49,960 --> 00:31:53,790
And also obviously impossible.

463
00:31:53,790 --> 00:31:59,770
It only works if I put work in
there to make it happen, then

464
00:31:59,770 --> 00:32:04,620
yes I can take heat out of a
cold body and move it up into

465
00:32:04,620 --> 00:32:11,970
a hotter reservoir
of some sort.

466
00:32:11,970 --> 00:32:21,560
So here's a refrigerator.

467
00:32:21,560 --> 00:32:28,450
Again T1 is greater than T2,
and in this case q2 is

468
00:32:28,450 --> 00:32:29,280
greater than zero.

469
00:32:29,280 --> 00:32:37,340
I'm removing heat, minus q1 is
greater than zero, that is

470
00:32:37,340 --> 00:32:44,460
heat is going up this way.

471
00:32:44,460 --> 00:32:45,900
Work is greater than zero.

472
00:32:45,900 --> 00:32:48,950
Has to be.

473
00:32:48,950 --> 00:32:55,310
Of course the thing is running
in a cycle. delta u is zero.

474
00:32:55,310 --> 00:33:09,390
So that means that work must
be minus q1 plus q2, right?

475
00:33:09,390 --> 00:33:13,870
And work is greater than zero,
so that's saying minus q1

476
00:33:13,870 --> 00:33:16,490
right that's a positive
number, must

477
00:33:16,490 --> 00:33:20,440
be bigger than q2.

478
00:33:20,440 --> 00:33:23,150
In other words, I am taking
some heat away

479
00:33:23,150 --> 00:33:25,120
from the cold region.

480
00:33:25,120 --> 00:33:27,780
The heat I'm dumping into the
hotter region is bigger than

481
00:33:27,780 --> 00:33:30,340
the amount that I taking away
here, because it's also got

482
00:33:30,340 --> 00:33:33,700
this amount.

483
00:33:33,700 --> 00:33:38,400
That's why, you know, if it's
a humid or warm summer

484
00:33:38,400 --> 00:33:41,190
afternoon and you think oh what
I a great idea, I've got

485
00:33:41,190 --> 00:33:42,770
this little fridge in my room.

486
00:33:42,770 --> 00:33:47,140
I'm going to open it up
and cool the room off.

487
00:33:47,140 --> 00:33:49,700
Turns out not to
work too well.

488
00:33:49,700 --> 00:33:50,920
Because of course what
the fridge is

489
00:33:50,920 --> 00:33:53,670
doing, it's cold inside.

490
00:33:53,670 --> 00:33:57,440
So it's a machine that's
removing heat from the inside

491
00:33:57,440 --> 00:33:58,960
and dumping it outside.

492
00:33:58,960 --> 00:34:01,630
There are coils in the back of
the fridge, and if you touch

493
00:34:01,630 --> 00:34:03,840
them they're a little
bit warm and so on.

494
00:34:03,840 --> 00:34:09,810
The heat is being lost
to the room.

495
00:34:09,810 --> 00:34:10,510
How much heat?

496
00:34:10,510 --> 00:34:14,950
Well, the work that goes
in is also added.

497
00:34:14,950 --> 00:34:17,170
So the amount of heat that
goes out into the room is

498
00:34:17,170 --> 00:34:19,010
bigger than the amount of
heat that you're taking

499
00:34:19,010 --> 00:34:22,040
away from the space.

500
00:34:22,040 --> 00:34:23,990
That's bad.

501
00:34:23,990 --> 00:34:26,530
So if you try opening the
refrigerator door to cool off

502
00:34:26,530 --> 00:34:28,750
your room at the same time as
you're dumping heat into your

503
00:34:28,750 --> 00:34:31,720
room, all you discover is
the net effect is to

504
00:34:31,720 --> 00:34:35,150
heat up your room.

505
00:34:35,150 --> 00:34:38,030
Because you know the amount
of heat that the thing is

506
00:34:38,030 --> 00:34:41,130
removing from somewhere on the
inside there and struggling to

507
00:34:41,130 --> 00:34:43,470
do that because you've left the
door to the fridge open,

508
00:34:43,470 --> 00:34:46,970
right, is not as big as the
amount out heat that's coming

509
00:34:46,970 --> 00:34:49,670
out in those coils
on the back.

510
00:34:49,670 --> 00:34:52,540
It's not as big because that
heat has not only the heat

511
00:34:52,540 --> 00:34:54,760
that you're removing from
the inside, but also

512
00:34:54,760 --> 00:34:57,300
this amount of work.

513
00:34:57,300 --> 00:34:58,970
It's all conserved because
delta u is zero.

514
00:34:58,970 --> 00:35:02,910
The thing is running
in a cycle.

515
00:35:02,910 --> 00:35:04,680
Try it sometime.

516
00:35:04,680 --> 00:35:06,940
You can verify this
experimentally in a very

517
00:35:06,940 --> 00:35:07,920
simple way.

518
00:35:07,920 --> 00:35:11,130
It's not a very effective way
to work, and it wastes a

519
00:35:11,130 --> 00:35:13,650
little bit of energy, but
could be worth it in the

520
00:35:13,650 --> 00:35:18,480
interest of knowledge
and discovery.

521
00:35:18,480 --> 00:35:23,080
Let me write an alternate
statement of the

522
00:35:23,080 --> 00:35:35,080
second law of Clausius.

523
00:35:35,080 --> 00:35:49,100
All spontaneous processes
are irreversible.

524
00:35:49,100 --> 00:35:54,550
When I open that panel in the
container, I've got gas on one

525
00:35:54,550 --> 00:35:58,650
side and vacuum in the other
and it expands in there, it

526
00:35:58,650 --> 00:36:03,500
happens spontaneously, and
it's irreversible.

527
00:36:03,500 --> 00:36:11,770
It's not just going
to go back.

528
00:36:11,770 --> 00:36:14,810
And now let me write a
mathematical statement of the

529
00:36:14,810 --> 00:36:28,370
second law.

530
00:36:28,370 --> 00:36:30,620
And we'll celebrate
it's importance

531
00:36:30,620 --> 00:36:38,490
by using this color.

532
00:36:38,490 --> 00:36:44,460
Going around in a cycle, if I
integrate the quantity dq

533
00:36:44,460 --> 00:36:50,690
reversible over T, I get zero.

534
00:36:50,690 --> 00:36:55,970
Remember this, this is
our special function.

535
00:36:55,970 --> 00:36:58,930
Let me just keep going
a little more though.

536
00:36:58,930 --> 00:37:02,210
Let me also write
another version.

537
00:37:02,210 --> 00:37:09,310
If I write dq for an
irreversible path over T,

538
00:37:09,310 --> 00:37:16,190
right, less than zero.

539
00:37:16,190 --> 00:37:22,380
It's not the same.

540
00:37:22,380 --> 00:37:28,300
This is a state function.

541
00:37:28,300 --> 00:37:29,380
This isn't.

542
00:37:29,380 --> 00:37:32,500
Remember of course that the heat
that's exchange between

543
00:37:32,500 --> 00:37:36,890
the system and the environment
depends on the path.

544
00:37:36,890 --> 00:37:42,280
If there is a reversible path,
and you see how much heat was

545
00:37:42,280 --> 00:37:46,410
exchange with the environment,
and you look at that divided

546
00:37:46,410 --> 00:37:50,390
by temperature integrate over
the whole thing, you discover

547
00:37:50,390 --> 00:37:56,940
that as long as the path is
reversible, it only depends on

548
00:37:56,940 --> 00:37:59,310
the states at the beginning
and the end of the path.

549
00:37:59,310 --> 00:38:01,780
In other words if you have
various ways you can go from

550
00:38:01,780 --> 00:38:06,030
state one to two that
are reversible,

551
00:38:06,030 --> 00:38:07,090
it's always the same.

552
00:38:07,090 --> 00:38:11,970
We saw that for just a
couple of examples, a

553
00:38:11,970 --> 00:38:13,430
couple lectures back.

554
00:38:13,430 --> 00:38:16,690
Remember, we looked at these
thermodynamic cycles and just

555
00:38:16,690 --> 00:38:18,320
said, well let's just
calculate those.

556
00:38:18,320 --> 00:38:22,700
And those were, those all
involved reversible processes.

557
00:38:22,700 --> 00:38:26,170
So, in effect, we looked at
different paths to go from one

558
00:38:26,170 --> 00:38:27,230
state to another.

559
00:38:27,230 --> 00:38:29,580
We had a cycle, and one path
went to here, and the other

560
00:38:29,580 --> 00:38:31,170
path went back.

561
00:38:31,170 --> 00:38:35,210
We discovered that, in fact,
this one zero around the cycle

562
00:38:35,210 --> 00:38:38,400
or the way we expressed it at
the time is the value of this

563
00:38:38,400 --> 00:38:42,120
was the same regardless of the
way we got from one state to

564
00:38:42,120 --> 00:38:44,740
the other, whether we took a
straightforward route or a

565
00:38:44,740 --> 00:39:09,800
more circuitous route, as long
as they were reversible.

566
00:39:09,800 --> 00:39:28,950
We're going to define dS as dq
reversible over T, and since

567
00:39:28,950 --> 00:39:35,260
we're dealing with a state
function delta S going from

568
00:39:35,260 --> 00:39:46,060
state one to two of dq
reversible over T is S2 minus

569
00:39:46,060 --> 00:39:52,630
S1 state function.

570
00:39:52,630 --> 00:40:03,650
And S as state function is the
entropy, and of course the us,

571
00:40:03,650 --> 00:40:19,880
it will always be special.

572
00:40:19,880 --> 00:40:27,480
All right, now, the second law,
you know it's difficult

573
00:40:27,480 --> 00:40:31,020
to understand and to get your
arms around, because you know,

574
00:40:31,020 --> 00:40:32,350
do I really calculate this?

575
00:40:32,350 --> 00:40:36,990
I actually have to find a
reversible path in order to do

576
00:40:36,990 --> 00:40:39,860
the calculation.

577
00:40:39,860 --> 00:40:43,460
Normally, you know, when you
calculate delta u and delta h

578
00:40:43,460 --> 00:40:48,190
and so forth, you have various
ways to calculate them that

579
00:40:48,190 --> 00:40:49,580
can be pretty straightforward.

580
00:40:49,580 --> 00:40:53,600
But here, you actually have to
determine the heat exchanged

581
00:40:53,600 --> 00:40:57,730
between the system and the
environment, and you know that

582
00:40:57,730 --> 00:41:02,840
does, in general, depend
on the path.

583
00:41:02,840 --> 00:41:07,390
But it turns out that this
quantity, you know, the

584
00:41:07,390 --> 00:41:13,970
differential of that heat over
the temperature, also depends

585
00:41:13,970 --> 00:41:18,410
on path unless it's
a reversible pass.

586
00:41:18,410 --> 00:41:21,370
Any reversible path will lead
to the same results.

587
00:41:21,370 --> 00:41:26,650
It doesn't depend on path
among reversible paths.

588
00:41:26,650 --> 00:41:30,200
What that means in practice is
if we say OK, start here and

589
00:41:30,200 --> 00:41:33,680
end here and calculate the
entropy, you actually have to

590
00:41:33,680 --> 00:41:36,510
sort of figure out a reversible
way of getting from

591
00:41:36,510 --> 00:41:41,900
here to here so that you can
do that calculation.

592
00:41:41,900 --> 00:41:44,520
So it's really very different
from ordinary functions that

593
00:41:44,520 --> 00:41:50,990
you've been dealing with.

594
00:41:50,990 --> 00:41:54,250
A lot of people, you know,
because the second law is

595
00:41:54,250 --> 00:41:59,010
difficult to understand, you
know you can easily go online

596
00:41:59,010 --> 00:42:01,900
and see thousands of violations
of the second law.

597
00:42:01,900 --> 00:42:06,110
It's still easy to look, to go
find claims of perpetual

598
00:42:06,110 --> 00:42:08,230
motion machines.

599
00:42:08,230 --> 00:42:10,140
Some of them cost
a lot of money.

600
00:42:10,140 --> 00:42:13,600
You can buy them, see
how they work.

601
00:42:13,600 --> 00:42:20,400
But and also, all sorts of
schemes for producing energy.

602
00:42:20,400 --> 00:42:22,650
Go online and see, right.

603
00:42:22,650 --> 00:42:25,000
You're just, they're just crazy
ideas about getting

604
00:42:25,000 --> 00:42:26,920
energy from nothing.

605
00:42:26,920 --> 00:42:29,500
Getting energy from the heat
that's just already

606
00:42:29,500 --> 00:42:31,650
present in the air.

607
00:42:31,650 --> 00:42:33,770
I mean there's heat in the air,
all this motion, it must

608
00:42:33,770 --> 00:42:34,400
have energy.

609
00:42:34,400 --> 00:42:40,330
We should be able to extract
it and use it.

610
00:42:40,330 --> 00:42:43,850
Turns out we can't do that.

611
00:42:43,850 --> 00:42:50,460
It has to look something
like this.

612
00:42:50,460 --> 00:42:52,530
OK.

613
00:42:52,530 --> 00:42:55,430
I want to look at some more
statements of the second law.

614
00:42:55,430 --> 00:43:00,340
To do that I just want to
indicate one definition which

615
00:43:00,340 --> 00:43:04,030
is just to be clear what
these things mean.

616
00:43:04,030 --> 00:43:08,530
These are what I've called
heat reservoirs

617
00:43:08,530 --> 00:43:10,800
or hot or cold bodies.

618
00:43:10,800 --> 00:43:14,020
Here's what I mean to
be more specific.

619
00:43:14,020 --> 00:43:20,400
A heat reservoir is basically
a very large thermal mass at

620
00:43:20,400 --> 00:43:21,430
the same temperature.

621
00:43:21,430 --> 00:43:25,080
And the real idea is that you
can bring heat out of it as

622
00:43:25,080 --> 00:43:30,410
much as you want and the
temperature won't change.

623
00:43:30,410 --> 00:43:33,350
It's an idealization. right If
you have something that's big

624
00:43:33,350 --> 00:43:36,120
enough, and it's at a constant
temperature, of course you can

625
00:43:36,120 --> 00:43:39,140
take heat away, but it's just
so enormous that you won't

626
00:43:39,140 --> 00:43:41,800
measurably change it's
temperature.

627
00:43:41,800 --> 00:43:47,740
In practice you might be able
or approach that limit.

628
00:43:47,740 --> 00:43:58,070
OK, now let's look at some more
definitions or statements

629
00:43:58,070 --> 00:44:19,990
of the second law.

630
00:44:19,990 --> 00:44:27,930
This is from Kelvin of Kelvin
temperature scale fame.

631
00:44:27,930 --> 00:44:35,860
It's impossible to convert heat
into work with a system

632
00:44:35,860 --> 00:44:37,110
that operates in a cycle.

633
00:44:37,110 --> 00:44:38,300
I'm going to write
this all out.

634
00:44:38,300 --> 00:44:39,650
I know you've got it
in your notes too,

635
00:44:39,650 --> 00:44:41,230
but it's super important.

636
00:44:41,230 --> 00:45:02,810
To convert heat into work with
a system that operates in a

637
00:45:02,810 --> 00:45:08,570
cycle, without at the same time
transferring some heat to

638
00:45:08,570 --> 00:45:31,430
a colder reservoir.

639
00:45:31,430 --> 00:45:34,590
OK, a couple of things
to notice.

640
00:45:34,590 --> 00:45:37,500
One is, you know, in some sense
the second law is kind

641
00:45:37,500 --> 00:45:39,710
of negative, right?

642
00:45:39,710 --> 00:45:44,670
Must not have been done
in the new age.

643
00:45:44,670 --> 00:45:49,060
It tells us what we can't do.

644
00:45:49,060 --> 00:45:52,610
And that really is in a sense
what it's all about.

645
00:45:52,610 --> 00:45:56,340
It's telling us what are our
limitations of what can be

646
00:45:56,340 --> 00:46:00,960
accomplished.

647
00:46:00,960 --> 00:46:09,480
Very important part of this
statement -- in a cycle.

648
00:46:09,480 --> 00:46:12,460
Of course any practical engine
has to keep going, so there's

649
00:46:12,460 --> 00:46:16,110
going to be a cycle in some
way or another, but it's

650
00:46:16,110 --> 00:46:19,990
important because, you know,
there are some -- if I'm not

651
00:46:19,990 --> 00:46:21,730
operating in a cycle,
I can convert heat

652
00:46:21,730 --> 00:46:24,470
into work just fine.

653
00:46:24,470 --> 00:46:34,190
You know, I could have a heat
source, got a candle, and I've

654
00:46:34,190 --> 00:46:38,410
got a piston, maybe I've
got a weight on it.

655
00:46:38,410 --> 00:46:45,000
I've got something
stopping it.

656
00:46:45,000 --> 00:46:48,970
And then I remove the stoppers
and let it go, and because of

657
00:46:48,970 --> 00:46:51,250
the heat, there's expansion.

658
00:46:51,250 --> 00:47:04,810
It pushes up, right, and it'll
be up higher somewhere.

659
00:47:04,810 --> 00:47:05,880
Worked!

660
00:47:05,880 --> 00:47:08,580
Heat turned into work.

661
00:47:08,580 --> 00:47:10,740
I don't have a cold
body somewhere.

662
00:47:10,740 --> 00:47:12,060
But I only did this once.

663
00:47:12,060 --> 00:47:14,690
There was just one stroke
of the piston.

664
00:47:14,690 --> 00:47:17,830
If I want to continue it and run
in a cycle, somehow I've

665
00:47:17,830 --> 00:47:31,550
got to have a place where
the heat goes.

666
00:47:31,550 --> 00:47:37,910
So this sort of diagram
describes effectively the way

667
00:47:37,910 --> 00:47:41,440
the Kelvin statement works.

668
00:47:41,440 --> 00:47:45,290
This works fine and like we
illustrated before, it doesn't

669
00:47:45,290 --> 00:47:50,000
work fine if I don't have
this part of it.

670
00:47:50,000 --> 00:47:53,740
I won't be able to just take all
the heat and convert it to

671
00:47:53,740 --> 00:47:58,170
work, like I, in principle,
could do, if I don't need to

672
00:47:58,170 --> 00:48:13,650
run it in a cycle.

673
00:48:13,650 --> 00:48:17,200
Here is yet another statement
by Clausius And we'll

674
00:48:17,200 --> 00:48:25,100
end with that one.

675
00:48:25,100 --> 00:48:27,950
Maybe I'll just read
this one, so we can

676
00:48:27,950 --> 00:48:29,630
not go over the time.

677
00:48:29,630 --> 00:48:32,960
So, it's impossible for any
system to operate in a cycle

678
00:48:32,960 --> 00:48:38,630
that takes heat from a colder
reservoir, transfers it to a

679
00:48:38,630 --> 00:48:42,690
hotter reservoir, without at the
same time converting some

680
00:48:42,690 --> 00:48:45,630
work into heat.

681
00:48:45,630 --> 00:48:47,700
In other words, it's a statement
kind of similar to

682
00:48:47,700 --> 00:48:51,720
the Kelvin statement, but
applying to the case of moving

683
00:48:51,720 --> 00:48:55,350
heat from a colder to
a hotter region.

684
00:48:55,350 --> 00:49:01,230
Can't do it, unless some work is
also converted to the heat

685
00:49:01,230 --> 00:49:14,110
that gets released into
the hot region.

686
00:49:14,110 --> 00:49:15,610
I think we'll stop there.

687
00:49:15,610 --> 00:49:21,560
Next time what we'll do is lay
out a very well-defined kind

688
00:49:21,560 --> 00:49:25,070
of engine called Carnot cycle
that allows us to very

689
00:49:25,070 --> 00:49:27,700
explicitly go through and say
OK, let's just work out the

690
00:49:27,700 --> 00:49:32,020
steps of isothermal and
adiabatic expansions and

691
00:49:32,020 --> 00:49:32,850
contractions.

692
00:49:32,850 --> 00:49:35,310
In other words, how does
the engine really work?

693
00:49:35,310 --> 00:49:39,000
And just calculate it going
around in a cycle and see

694
00:49:39,000 --> 00:49:41,290
exactly how all this
is born out.

695
00:49:41,290 --> 00:49:43,260
And we'll see that next time.