1
00:00:00,000 --> 00:00:00,410


2
00:00:00,410 --> 00:00:02,970
A couple of videos ago, we learned that if we started

3
00:00:02,970 --> 00:00:06,849
with solid water or ice at a reasonably low temperature--

4
00:00:06,849 --> 00:00:08,160
maybe this temperature right here is

5
00:00:08,160 --> 00:00:10,380
minus 10 degrees Celsius.

6
00:00:10,380 --> 00:00:12,670
And we can deal with Celsius when we're dealing with these

7
00:00:12,669 --> 00:00:14,609
phase changes, because we really just care about the

8
00:00:14,609 --> 00:00:16,929
difference in temperature, and not necessarily the absolute

9
00:00:16,929 --> 00:00:17,669
temperature.

10
00:00:17,670 --> 00:00:22,450
So one degree in Celsius is the same thing is one degree

11
00:00:22,449 --> 00:00:24,679
in Kelvin so the differences are the same whether you're

12
00:00:24,679 --> 00:00:26,300
dealing with Celsius or Kelvin.

13
00:00:26,300 --> 00:00:29,640
So we're starting with minus 10 degree Celsius

14
00:00:29,640 --> 00:00:32,770
ice or solid water.

15
00:00:32,770 --> 00:00:35,420
And we learned that as you heat it up, as you add heat

16
00:00:35,420 --> 00:00:38,170
energy to the water, the temperature goes up.

17
00:00:38,170 --> 00:00:40,940
The molecules, at least while they're in that ice lattice

18
00:00:40,939 --> 00:00:42,839
network, they just start vibrating.

19
00:00:42,840 --> 00:00:46,510
And their average kinetic energy goes up until we get to

20
00:00:46,509 --> 00:00:47,979
zero degrees.

21
00:00:47,979 --> 00:00:50,669
Which is the melting point of water.

22
00:00:50,670 --> 00:00:52,620
And at zero degrees, we already learned something

23
00:00:52,619 --> 00:00:53,909
interesting happens.

24
00:00:53,909 --> 00:00:56,989
The added heat in the system does not increase the

25
00:00:56,990 --> 00:00:59,440
temperature of the ice anymore.

26
00:00:59,439 --> 00:01:01,719
At least over that little period right here.

27
00:01:01,719 --> 00:01:05,019
What's happening is that heat energy is being used to kind

28
00:01:05,019 --> 00:01:06,620
of break the lattice structure.

29
00:01:06,620 --> 00:01:08,439
To add potential energy to the ice.

30
00:01:08,439 --> 00:01:10,079
Or essentially melt it.

31
00:01:10,079 --> 00:01:14,349
So for it here, right here, we're ice.

32
00:01:14,349 --> 00:01:17,009
Right at this point, we're zero degree ice.

33
00:01:17,010 --> 00:01:20,109
And then as we add more and more heat we get to zero

34
00:01:20,109 --> 00:01:21,269
degree water.

35
00:01:21,269 --> 00:01:24,589
So at zero degrees, you can either have water or ice.

36
00:01:24,590 --> 00:01:26,960
And if you have water, to turn it into ice, you have to take

37
00:01:26,959 --> 00:01:28,089
heat out of it.

38
00:01:28,090 --> 00:01:30,469
And if you have ice, and you want to turn it into water,

39
00:01:30,469 --> 00:01:31,829
you have to put heat into it.

40
00:01:31,829 --> 00:01:34,909
And then the heat is used again to warm up the

41
00:01:34,909 --> 00:01:36,489
water at some rate.

42
00:01:36,489 --> 00:01:40,309
And then at 100 degrees, which is the boiling point of water,

43
00:01:40,310 --> 00:01:44,480
right here, a similar phase change happens.

44
00:01:44,480 --> 00:01:47,200
Where the increased heat is not used to increase the

45
00:01:47,200 --> 00:01:51,150
temperature of the water, it's used to put potential energy

46
00:01:51,150 --> 00:01:52,150
into the system.

47
00:01:52,150 --> 00:01:55,900
So the water molecules are forced away from each other.

48
00:01:55,900 --> 00:01:58,260
The same way that if I'm forced away from the planet

49
00:01:58,260 --> 00:02:00,280
Earth, I have potential energy because I can

50
00:02:00,280 --> 00:02:01,769
fall back to the earth.

51
00:02:01,769 --> 00:02:03,819
Similarly, they have the potential energy of falling

52
00:02:03,819 --> 00:02:05,099
back to each other.

53
00:02:05,099 --> 00:02:07,969
But this energy, right here is the energy necessary to

54
00:02:07,969 --> 00:02:09,169
vaporize the water.

55
00:02:09,169 --> 00:02:13,800
Right here you have 100 degree water, 100 degree liquid.

56
00:02:13,800 --> 00:02:17,150
And here you have 100 degree vapor, water vapor.

57
00:02:17,150 --> 00:02:19,969
And then as you add more and more heat, once again it

58
00:02:19,969 --> 00:02:21,120
increases the temperature.

59
00:02:21,120 --> 00:02:24,560
But you, Sal, I already learned this a few videos ago,

60
00:02:24,560 --> 00:02:26,030
I have the intuition.

61
00:02:26,030 --> 00:02:27,710
But I want to deal with real numbers.

62
00:02:27,710 --> 00:02:30,310
I want to know exactly how much heat is required for

63
00:02:30,310 --> 00:02:32,090
these different things to happen.

64
00:02:32,090 --> 00:02:35,900
And for that, we can get these numbers.

65
00:02:35,900 --> 00:02:39,120
And these are specific to the different states of water.

66
00:02:39,120 --> 00:02:42,460
If you looked up any other element or molecule, you would

67
00:02:42,460 --> 00:02:45,099
have different values for these numbers we're going to

68
00:02:45,099 --> 00:02:46,509
be dealing with right now.

69
00:02:46,509 --> 00:02:49,399
But this first number right here is the heat of fusion.

70
00:02:49,400 --> 00:02:53,000
And this is the amount of heat that's required to fuse 100

71
00:02:53,000 --> 00:02:57,250
degree water into 100 degree ice.

72
00:02:57,250 --> 00:02:59,159
Or the amount of energy you have to take out of the water.

73
00:02:59,159 --> 00:03:02,129
So this distance right here, or along this

74
00:03:02,129 --> 00:03:06,139
axis, is 333 joules.

75
00:03:06,139 --> 00:03:08,319
If you're going in the the leftward direction, you have

76
00:03:08,319 --> 00:03:11,000
to take that much out of the system to turn into ice.

77
00:03:11,000 --> 00:03:12,849
If you're going in the rightward direction, you have

78
00:03:12,849 --> 00:03:14,599
to add that much to turn into water.

79
00:03:14,599 --> 00:03:15,909
So heat of fusion.

80
00:03:15,909 --> 00:03:17,900
It's called the heat of fusion because when you fuse

81
00:03:17,900 --> 00:03:19,349
something together you make it solid.

82
00:03:19,349 --> 00:03:21,989
So it could also be considered the heat of melting.

83
00:03:21,990 --> 00:03:24,280
Just two different words for the same, thing depending on

84
00:03:24,280 --> 00:03:25,219
what direction you going.

85
00:03:25,219 --> 00:03:28,500
The important thing is the number, 333.

86
00:03:28,500 --> 00:03:31,860
Similarly, you have the heat of vaporization.

87
00:03:31,860 --> 00:03:38,800
2257 joules per gram.

88
00:03:38,800 --> 00:03:42,420
That's this distance along this axis right here.

89
00:03:42,419 --> 00:03:47,039
So if you had one gram of 100 degree liquid water and you

90
00:03:47,039 --> 00:03:49,750
wanted to turn it into one gram of 100

91
00:03:49,750 --> 00:03:51,199
degree liquid vapor.

92
00:03:51,199 --> 00:03:54,619
And in all of this, we're assuming that nothing silly is

93
00:03:54,620 --> 00:03:55,770
happening to the pressure, that we're

94
00:03:55,770 --> 00:03:57,010
under constant pressure.

95
00:03:57,009 --> 00:04:01,829
You would have to put 2257 joules into the system.

96
00:04:01,830 --> 00:04:04,660
If you had 100 degree vapor and you wanted to condense it,

97
00:04:04,659 --> 00:04:08,210
you would have to take that much energy out of the system.

98
00:04:08,210 --> 00:04:11,080
OK, fine, you know how much energy is required for the

99
00:04:11,080 --> 00:04:11,810
phase changes.

100
00:04:11,810 --> 00:04:14,330
But what about these parts right here?

101
00:04:14,330 --> 00:04:21,250
How much energy is required to warm up a gram of ice by one

102
00:04:21,250 --> 00:04:23,029
degree Celsius or Kelvin?

103
00:04:23,029 --> 00:04:26,719
And for that we look at the specific heat.

104
00:04:26,720 --> 00:04:32,010
It takes 2 joules of energy to warm up 1

105
00:04:32,009 --> 00:04:34,879
gram 1 degree Kelvin.

106
00:04:34,879 --> 00:04:36,800
When water is in the solid state.

107
00:04:36,800 --> 00:04:39,460
When it's in the liquid state, it takes about double that.

108
00:04:39,459 --> 00:04:42,209
It takes about 4 joules per gram to

109
00:04:42,209 --> 00:04:44,079
raise it 1 degree Kelvin.

110
00:04:44,079 --> 00:04:45,659
And when you're in the vapor state, it's actually more

111
00:04:45,660 --> 00:04:49,020
similar to the solid state.

112
00:04:49,019 --> 00:04:52,919
So given what we know now, we can actually figure out how

113
00:04:52,920 --> 00:05:04,120
much energy it would take to go from minus 10 degree ice to

114
00:05:04,120 --> 00:05:07,600
110 degree vapor.

115
00:05:07,600 --> 00:05:09,379
Let's work this out.

116
00:05:09,379 --> 00:05:11,199
So the first thing we're going to be doing is, we're going to

117
00:05:11,199 --> 00:05:17,024
be going from minus 10 degree ice to zero degree ice.

118
00:05:17,024 --> 00:05:19,639


119
00:05:19,639 --> 00:05:21,110
So we're going to go 10 degrees.

120
00:05:21,110 --> 00:05:24,090
We have to figure out how much heat does it take to warm up

121
00:05:24,089 --> 00:05:25,849
ice by 10 degrees.

122
00:05:25,850 --> 00:05:29,360
So the heat is going to be equal to the change in

123
00:05:29,360 --> 00:05:30,470
temperature.

124
00:05:30,470 --> 00:05:35,110
So actually let me write the specific heat first. So 2.05

125
00:05:35,110 --> 00:05:37,160
joules per gram Kelvin.

126
00:05:37,160 --> 00:05:45,880


127
00:05:45,879 --> 00:05:49,000
Oh, and I should tell you, we can't different values for the

128
00:05:49,000 --> 00:05:51,399
amount of ice we're warming up to vapor, so let's say we're

129
00:05:51,399 --> 00:05:54,389
dealing with 200 grams.

130
00:05:54,389 --> 00:05:58,060
So it'll be the specific heat times the number of grams

131
00:05:58,060 --> 00:06:01,899
we're warming up of ice times the change in temperature that

132
00:06:01,899 --> 00:06:02,659
we're trying to get.

133
00:06:02,660 --> 00:06:06,610
So, times 10 degrees Kelvin.

134
00:06:06,610 --> 00:06:08,480
Le'ts just say it's a 10 degrees Kelvin change, it

135
00:06:08,480 --> 00:06:10,170
doesn't matter if we're using Kelvin or Celsius.

136
00:06:10,170 --> 00:06:12,750
I could have written a Celsius here.

137
00:06:12,750 --> 00:06:15,180
Let's put Celsius right there.

138
00:06:15,180 --> 00:06:16,750
So what is that equal to?

139
00:06:16,750 --> 00:06:19,069
Get the calculator.

140
00:06:19,069 --> 00:06:21,129
Clear it out.

141
00:06:21,129 --> 00:06:40,625
2.05 times 200 times times 10 is equal to 4,100 joules.

142
00:06:40,625 --> 00:06:42,689
Let me do this in a different color.

143
00:06:42,689 --> 00:06:46,810
This is 4,100 joules.

144
00:06:46,810 --> 00:06:47,769
Fair enough.

145
00:06:47,769 --> 00:06:50,299
Now, so what we've done is just this part right here.

146
00:06:50,300 --> 00:06:54,620
This distance right here is 4,100 joules.

147
00:06:54,620 --> 00:06:56,870
Now we have to turn that zero degree ice

148
00:06:56,870 --> 00:06:58,120
into zero degree water.

149
00:06:58,120 --> 00:07:07,560


150
00:07:07,560 --> 00:07:10,850
And for that we use the heat of fusion.

151
00:07:10,850 --> 00:07:12,900
We're adding that amount of heat.

152
00:07:12,899 --> 00:07:20,029
It's 333.5 joules per gram.

153
00:07:20,029 --> 00:07:27,529
So that's equal to 335.55 joules per gram times, we have

154
00:07:27,529 --> 00:07:30,879
200 grams of ice that we're trying to melt.

155
00:07:30,879 --> 00:07:32,699
So that is what?

156
00:07:32,699 --> 00:07:34,939
So let me get the calculator out.

157
00:07:34,939 --> 00:07:49,279
So I have 335.55 times 200 is equal to 67,110.

158
00:07:49,279 --> 00:07:52,149
Let me do it in that color so can sum them up at the end.

159
00:07:52,149 --> 00:07:58,639
67,110 joules to melt the water.

160
00:07:58,639 --> 00:07:59,860
Or take it from ice to water.

161
00:07:59,860 --> 00:08:02,310
Now, we have to go from, and this is the big one.

162
00:08:02,310 --> 00:08:09,480
We have to go from zero degree water to 100 degree water.

163
00:08:09,480 --> 00:08:11,000
Or liquid water.

164
00:08:11,000 --> 00:08:12,779
This is in the liquid state.

165
00:08:12,779 --> 00:08:22,209
So now we take the specific heat of water which was 4.178.

166
00:08:22,209 --> 00:08:24,159
For some reason I'm thinking it's 4.176

167
00:08:24,160 --> 00:08:24,960
but it doesn't matter.

168
00:08:24,959 --> 00:08:28,539
So it's 4.178.

169
00:08:28,540 --> 00:08:31,640
I might off a little bit on that number, but that digit is

170
00:08:31,639 --> 00:08:32,720
not that significant.

171
00:08:32,720 --> 00:08:38,298
Joules per gram Celsius times 200 grams

172
00:08:38,298 --> 00:08:42,928
times 100 degrees Celsius.

173
00:08:42,928 --> 00:08:45,449
And notice, the Celsius and the Celsius cancel out.

174
00:08:45,450 --> 00:08:47,009
The grams and the grams cancel out.

175
00:08:47,009 --> 00:08:49,519
So we are left with joules, which is what we want.

176
00:08:49,519 --> 00:08:52,139
We want to know how much heat or how much energy we're

177
00:08:52,139 --> 00:08:54,139
adding to the system.

178
00:08:54,139 --> 00:08:56,009
Let me get the calculator out.

179
00:08:56,009 --> 00:09:11,970
So this stage is going to be 4.178 times 200 times 100 is

180
00:09:11,970 --> 00:09:35,240
equal to 83,560 joules.

181
00:09:35,240 --> 00:09:36,230
Does that look about right?

182
00:09:36,230 --> 00:09:36,490
Let's see.

183
00:09:36,490 --> 00:09:41,649
4 times 200 is 800, 800 times 100; yeah, that's about right.

184
00:09:41,649 --> 00:09:45,149
Now, we're dealing with 100 degree water vapor, and we

185
00:09:45,149 --> 00:09:51,250
have to turn that 100 degree water vapor

186
00:09:51,250 --> 00:09:55,409
to 110 degree vapor.

187
00:09:55,409 --> 00:09:58,139
So we use the specific heat of vapor.

188
00:09:58,139 --> 00:10:06,980
1.89 joules per gram Kelvin.

189
00:10:06,980 --> 00:10:09,789
Multiplied by the amount of vapor we're dealing with, 200

190
00:10:09,789 --> 00:10:11,289
grams. That obviously doesn't change.

191
00:10:11,289 --> 00:10:14,899
We're not adding or taking away mass from the system.

192
00:10:14,899 --> 00:10:18,279
Times the temperature change, times 10.

193
00:10:18,279 --> 00:10:19,179
So what is that?

194
00:10:19,179 --> 00:10:22,750
Let me get the calculator out again.

195
00:10:22,750 --> 00:10:25,590
So we're dealing with a 10 degree change.

196
00:10:25,590 --> 00:10:43,269
10 degree Celsius times 200 times 1.89 is equal to 3,780.

197
00:10:43,269 --> 00:10:45,384
And I just realized, I made a horrible mistake.

198
00:10:45,384 --> 00:10:48,529


199
00:10:48,529 --> 00:10:51,089
It's not an irrevocable mistake, otherwise I would

200
00:10:51,090 --> 00:10:52,330
rerecord the video.

201
00:10:52,330 --> 00:10:54,530
But I just figured out the amount of energy to take it

202
00:10:54,529 --> 00:10:58,019
from zero degree water to 100 degree water, which is this

203
00:10:58,019 --> 00:11:00,720
energy right here.

204
00:11:00,720 --> 00:11:04,000
And now I just calculated how much energy to go from 100

205
00:11:04,000 --> 00:11:06,970
degree vapor to 110 degree vapor.

206
00:11:06,970 --> 00:11:09,470
Which is this right here, that distance right here.

207
00:11:09,470 --> 00:11:11,680
I forgot to figure out how much energy to turn that 100

208
00:11:11,679 --> 00:11:14,439
degree water into 100 degree vapor.

209
00:11:14,440 --> 00:11:16,000
So that's key.

210
00:11:16,000 --> 00:11:19,440
So I really should have done that up here before I

211
00:11:19,440 --> 00:11:20,360
calculated the vapor.

212
00:11:20,360 --> 00:11:21,720
But I'll do it down here.

213
00:11:21,720 --> 00:11:30,600
So to do 100 degree water to 100 degree vapor.

214
00:11:30,600 --> 00:11:33,580
That's this step right here, this is the phase change.

215
00:11:33,580 --> 00:11:38,710
I multiply the heat of vaporization, which is 2,257

216
00:11:38,710 --> 00:11:43,730
joules per gram times 200 grams. And

217
00:11:43,730 --> 00:11:57,865
this is equal to 451,400.

218
00:11:57,865 --> 00:11:59,970
I'll do it in that blue color.

219
00:11:59,970 --> 00:12:06,560
451,400 joules.

220
00:12:06,559 --> 00:12:14,849
So this piece right here is 451,000 for our sample of 200

221
00:12:14,850 --> 00:12:20,649
grams. This piece right here was 83,000 joules.

222
00:12:20,649 --> 00:12:25,579
This piece right here was 3,780 joules.

223
00:12:25,580 --> 00:12:28,470
So to know the total amount of energy, the total amount of

224
00:12:28,470 --> 00:12:31,580
heat that we had to put in the system to go from minus 10

225
00:12:31,580 --> 00:12:37,889
degree ice all the way to 110 degree vapor, we just add up

226
00:12:37,889 --> 00:12:41,169
all of the energies we had to do in all of these steps.

227
00:12:41,169 --> 00:12:41,799
Let's see.

228
00:12:41,799 --> 00:12:44,279
And I'll do them in order this time.

229
00:12:44,279 --> 00:12:53,079
So to go from minus 10 degree ice to zero degree ice.

230
00:12:53,080 --> 00:12:54,860
Of course we have 200 grams of it.

231
00:12:54,860 --> 00:12:58,940
It was 4,100.

232
00:12:58,940 --> 00:13:05,530
Plus the 67,000.

233
00:13:05,529 --> 00:13:06,850
I'm just doing this off the screen.

234
00:13:06,850 --> 00:13:12,710
So plus 67,110.

235
00:13:12,710 --> 00:13:15,780
Plus 83,000.

236
00:13:15,779 --> 00:13:19,449
That's to go from zero degree water to 100 degree water.

237
00:13:19,450 --> 00:13:24,210
Plus 83,560.

238
00:13:24,210 --> 00:13:27,360
So we're at 154,000 right now just to get

239
00:13:27,360 --> 00:13:29,129
to 100 degree water.

240
00:13:29,129 --> 00:13:31,950
And then we need to turn that 100 degree water into 100

241
00:13:31,950 --> 00:13:33,090
degree vapor.

242
00:13:33,090 --> 00:13:35,280
So you add the 451,000.

243
00:13:35,279 --> 00:13:41,329
So, plus 451,400 is equal to 606.

244
00:13:41,330 --> 00:13:44,840
And then finally, we're at 100 degree vapor, and we want to

245
00:13:44,840 --> 00:13:47,360
convert that to 110 degree vapor.

246
00:13:47,360 --> 00:13:50,029
So it's another 3,700 joules.

247
00:13:50,029 --> 00:14:00,429
So plus 3,780 is equal to 609,950 joules.

248
00:14:00,429 --> 00:14:03,839
So this whole thing when we're dealing with 200 grams, when

249
00:14:03,840 --> 00:14:07,399
you're going from minus 10 to 110.

250
00:14:07,399 --> 00:14:09,909
And remember, this is for 200 grams. It

251
00:14:09,909 --> 00:14:16,069
took us 609,950 joules.

252
00:14:16,070 --> 00:14:20,650
Or 609 kilojoules to do this.

253
00:14:20,649 --> 00:14:22,470
So that by itself is an interesting thing.

254
00:14:22,470 --> 00:14:24,340
You might think, wow, this is a huge number.

255
00:14:24,340 --> 00:14:26,830
But actually, it turns out joules isn't a lot of work.

256
00:14:26,830 --> 00:14:29,580
Kilojoules starts to become a little bit interesting.

257
00:14:29,580 --> 00:14:33,570
You might realize, 200 grams of ice, that's about half a

258
00:14:33,570 --> 00:14:34,410
pound of ice.

259
00:14:34,409 --> 00:14:37,649
So to take half a pound of ice and warm it up on your stove

260
00:14:37,649 --> 00:14:43,600
would take 609 kilojoules of heat to do that.

261
00:14:43,600 --> 00:14:45,889
So that's something that you probably could do on your

262
00:14:45,889 --> 00:14:48,009
stove at home.

263
00:14:48,009 --> 00:14:48,866