1 00:00:00,000 --> 00:00:02,400 The following content is provided under a Creative 2 00:00:02,400 --> 00:00:03,810 Commons license. 3 00:00:03,810 --> 00:00:06,840 Your support will help MIT OpenCourseWare continue to 4 00:00:06,840 --> 00:00:10,510 offer high-quality educational resources for free. 5 00:00:10,510 --> 00:00:13,390 To make a donation or view additional materials from 6 00:00:13,390 --> 00:00:16,190 hundreds of MIT courses, visit MIT OpenCourseWare at 7 00:00:16,190 --> 00:00:17,590 ocw.mit.edu. 8 00:00:17,590 --> 00:00:19,920 PROFESSOR: Thermodynamics, all right, let's start. 9 00:00:19,920 --> 00:00:31,270 Thermodynamics is the science of the flow of heat. 10 00:00:31,270 --> 00:00:37,680 So, thermo is heat, and dynamics is 11 00:00:37,680 --> 00:00:42,300 the motion of heat. 12 00:00:42,300 --> 00:00:46,730 Thermodynamics was developed largely beginning in the 13 00:00:46,730 --> 00:00:52,750 1800's, at the time of the Industrial Revolution. 14 00:00:52,750 --> 00:00:54,890 So, taming of steel. 15 00:00:54,890 --> 00:01:02,200 The beginning of generating power by burning fossil fuels. 16 00:01:02,200 --> 00:01:05,570 The beginning of the problems with CO2 and [NOISE OBSCURES] 17 00:01:05,570 --> 00:01:06,210 global warming. 18 00:01:06,210 --> 00:01:08,870 In fact, it's interesting to note that the first 19 00:01:08,870 --> 00:01:16,970 calculation on the impact of CO2 on climate was done in the 20 00:01:16,970 --> 00:01:21,170 late 1800's by Arrhenius. 21 00:01:21,170 --> 00:01:26,130 Beginning of a generation of power moving heat from fossil 22 00:01:26,130 --> 00:01:30,920 fuels to generating energy, locomotives, etcetera. 23 00:01:30,920 --> 00:01:34,360 So, he calculated what would happen to this burning of 24 00:01:34,360 --> 00:01:38,520 fossil fuels, and he decided in his calculation, he 25 00:01:38,520 --> 00:01:42,380 basically got the calculation right, by the way, but he came 26 00:01:42,380 --> 00:01:44,720 out that in 2,000 years from the time that he did the 27 00:01:44,720 --> 00:01:48,380 calculations, humans would be in trouble. 28 00:01:48,380 --> 00:01:51,090 Well, since his calculation, we've had an exponential 29 00:01:51,090 --> 00:01:54,150 growth in the amount of CO2, and if you go through the 30 00:01:54,150 --> 00:01:56,220 calculations of -- people have done these calculations 31 00:01:56,220 --> 00:02:00,190 throughout times since Arrhenius, the time that we're 32 00:02:00,190 --> 00:02:03,500 in trouble, 2,000 years and the calculation, has gone like 33 00:02:03,500 --> 00:02:08,250 this, and so now we're really in trouble. 34 00:02:08,250 --> 00:02:11,150 That's for a different lecture. 35 00:02:11,150 --> 00:02:15,590 So, anyway, thermodynamics dates from the same period as 36 00:02:15,590 --> 00:02:19,180 getting fossil fuels out of the ground. 37 00:02:19,180 --> 00:02:20,160 It's universal. 38 00:02:20,160 --> 00:02:24,310 It turns out everything around us moves energy around in one 39 00:02:24,310 --> 00:02:24,850 way or the other. 40 00:02:24,850 --> 00:02:28,090 If you're a biological system, you're burning calories, 41 00:02:28,090 --> 00:02:28,500 burning ATP. 42 00:02:28,500 --> 00:02:31,980 You're creating heat. 43 00:02:31,980 --> 00:02:34,040 If you're a warm-blooded animal. 44 00:02:34,040 --> 00:02:37,640 You need energy to move your arms around and move around -- 45 00:02:37,640 --> 00:02:41,590 mechanical systems, obviously, cars, boats, etcetera. 46 00:02:41,590 --> 00:02:44,900 And even in astrophysics, when you talk about stars, black 47 00:02:44,900 --> 00:02:46,600 holes, etcetera, you're moving energy around. 48 00:02:46,600 --> 00:02:50,830 You're moving heat around when you're changing matter through 49 00:02:50,830 --> 00:02:51,190 thermodynamics. 50 00:02:51,190 --> 00:02:54,610 And the cause of some thermodynamics have even been 51 00:02:54,610 --> 00:02:59,340 applied to economics, systems out of equilibrium, like big 52 00:02:59,340 --> 00:03:01,900 companies like Enron, you know, completely out of 53 00:03:01,900 --> 00:03:03,900 equilibrium, crash and burn. 54 00:03:03,900 --> 00:03:11,520 You can apply non-equilibrium thermodynamics to economics. 55 00:03:11,520 --> 00:03:13,430 It was developed before people knew 56 00:03:13,430 --> 00:03:15,630 about atoms and molecules. 57 00:03:15,630 --> 00:03:18,420 So it's a science that's based on macroscopic 58 00:03:18,420 --> 00:03:21,480 properties of matter. 59 00:03:21,480 --> 00:03:25,370 Since then, since we know about atoms and molecules now, 60 00:03:25,370 --> 00:03:28,990 we can rationalize the concepts of thermodynmamics 61 00:03:28,990 --> 00:03:33,840 using microscopic properties, and if you are going to take 62 00:03:33,840 --> 00:03:35,470 5.62, that's what you'd learn about. 63 00:03:35,470 --> 00:03:38,010 You'd learn about statistical mechanics, and how the 64 00:03:38,010 --> 00:03:41,840 atomistic concepts rationalize thermodynamics. 65 00:03:41,840 --> 00:03:45,970 It doesn't prove it, but it helps to getting more 66 00:03:45,970 --> 00:03:49,680 intuition about the consequences of 67 00:03:49,680 --> 00:03:53,570 thermodynamics. 68 00:03:53,570 --> 00:03:55,790 So it applies to macroscopic systems that are in 69 00:03:55,790 --> 00:03:59,340 equilibrium, and how to go from one equilibrium state to 70 00:03:59,340 --> 00:04:03,880 another equilibrium state, and it's entirely empirical in its 71 00:04:03,880 --> 00:04:05,730 foundation. 72 00:04:05,730 --> 00:04:08,270 People have done experiments through the ages, and they've 73 00:04:08,270 --> 00:04:11,310 accumulated the knowledge from these experiments, and they've 74 00:04:11,310 --> 00:04:16,210 synthesized these experiments into a few basic empirical 75 00:04:16,210 --> 00:04:19,610 rules, empirical laws, which are the laws of 76 00:04:19,610 --> 00:04:19,840 thermodynamics. 77 00:04:19,840 --> 00:04:25,415 And then they've taken these laws and added a structure of 78 00:04:25,415 --> 00:04:30,460 math upon it, to build this edifice, which is a very solid 79 00:04:30,460 --> 00:04:32,820 edifice of thermodynamics as a science 80 00:04:32,820 --> 00:04:36,810 of equilibrium systems. 81 00:04:36,810 --> 00:04:42,850 So these empirical observations then are 82 00:04:42,850 --> 00:04:46,410 summarized into four laws. 83 00:04:46,410 --> 00:04:51,380 So, these laws are, they're really depillars. 84 00:04:51,380 --> 00:04:55,950 They're not proven, but they're not wrong. 85 00:04:55,950 --> 00:04:59,340 They're very unlikely to be wrong. 86 00:04:59,340 --> 00:05:01,810 Let's just go through these laws, OK, very quickly. 87 00:05:01,810 --> 00:05:06,900 There's a zeroth law The zeroth law every one of these 88 00:05:06,900 --> 00:05:09,540 laws basically defines the quantity in thermodynamics and 89 00:05:09,540 --> 00:05:11,330 then defines the concept. 90 00:05:11,330 --> 00:05:13,770 The zeroth law defines temperature. 91 00:05:13,770 --> 00:05:19,000 That's a fairly common-sense idea, but it's important to 92 00:05:19,000 --> 00:05:23,090 define it, and I call that the common-sense law. 93 00:05:23,090 --> 00:05:30,150 So this is the common-sense law. 94 00:05:30,150 --> 00:05:37,800 The first law ends up defining energy, which we're going to 95 00:05:37,800 --> 00:05:44,680 call u, and the concept of energy conservation, energy 96 00:05:44,680 --> 00:05:48,880 can't be lost or gained. 97 00:05:48,880 --> 00:05:51,900 And I'm going to call this the you can break even law; you 98 00:05:51,900 --> 00:05:55,100 can break even law. 99 00:05:55,100 --> 00:06:00,000 You don't lose energy, you can't gain energy. 100 00:06:00,000 --> 00:06:02,090 You break even. 101 00:06:02,090 --> 00:06:09,585 The second law is going to define entropy, and is going 102 00:06:09,585 --> 00:06:11,820 to tell us about the direction of time, something that 103 00:06:11,820 --> 00:06:15,500 conceptually we, clearly, understand, but is going to 104 00:06:15,500 --> 00:06:20,190 put a mathematical foundation on which way does time go. 105 00:06:20,190 --> 00:06:23,180 Clearly, if I take a chalk like this one here, and I 106 00:06:23,180 --> 00:06:27,290 throw it on the ground, and it breaks in little pieces, if I 107 00:06:27,290 --> 00:06:30,110 run the movie backwards, that doesn't make sense, right? 108 00:06:30,110 --> 00:06:31,900 We have a concept of time going forward in 109 00:06:31,900 --> 00:06:33,370 a particular way. 110 00:06:33,370 --> 00:06:39,190 How does entropy play into that concept of time? 111 00:06:39,190 --> 00:06:48,750 And I'm going to call this the you can break even at zero 112 00:06:48,750 --> 00:06:49,510 degrees Kelvin law. 113 00:06:49,510 --> 00:06:53,560 You can only do it at zero degrees Kelvin. 114 00:06:53,560 --> 00:07:06,200 The third law is going to give a numerical value to the 115 00:07:06,200 --> 00:07:12,940 entropy, and the third law is going to be the depressing 116 00:07:12,940 --> 00:07:23,570 one, and it's going to say, you can't get to zero degrees. 117 00:07:23,570 --> 00:07:26,690 These laws are universally valid. 118 00:07:26,690 --> 00:07:29,820 They cannot be circumvented. 119 00:07:29,820 --> 00:07:33,620 Certainly people have tried to do that, and every year 120 00:07:33,620 --> 00:07:37,830 there's a newspaper story, Wall Street Journal, or New 121 00:07:37,830 --> 00:07:42,070 York Times about somebody that has invented the device that 122 00:07:42,070 --> 00:07:46,380 somehow goes around the second law and makes more energy than 123 00:07:46,380 --> 00:07:50,120 it creates, and this is going to be -- well, first of all, 124 00:07:50,120 --> 00:07:52,090 for the investors this is going to make them very, very 125 00:07:52,090 --> 00:07:57,040 rich, and for the rest of us, it's going to be wonderful. 126 00:07:57,040 --> 00:07:59,760 And they go through these arguments, and they find 127 00:07:59,760 --> 00:08:03,090 venture money to fund the company, and they get very 128 00:08:03,090 --> 00:08:06,530 famous people to endorse them, etcetera. 129 00:08:06,530 --> 00:08:10,770 But you guys know, because you have MIT degrees, and you've, 130 00:08:10,770 --> 00:08:14,080 later, and you've taken 5.60, that can't be the case, and 131 00:08:14,080 --> 00:08:16,876 you're not going to get fooled into investing money into 132 00:08:16,876 --> 00:08:18,470 these companies. 133 00:08:18,470 --> 00:08:22,980 But it's amazing, that every year you find somebody coming 134 00:08:22,980 --> 00:08:26,330 up with a way of going around the second law and somehow 135 00:08:26,330 --> 00:08:36,090 convincing people who are very smart that this will work. 136 00:08:36,090 --> 00:08:40,890 So, thermo is also a big tease, as you can see from my 137 00:08:40,890 --> 00:08:43,230 descriptions of these laws here. 138 00:08:43,230 --> 00:08:46,860 It makes you believe, initially, in the feasibility 139 00:08:46,860 --> 00:08:49,800 of perfect efficiency. 140 00:08:49,800 --> 00:08:54,190 The first law is very upbeat. 141 00:08:54,190 --> 00:08:58,490 It talks about the conservation of energy. 142 00:08:58,490 --> 00:09:01,860 Energy is conserved in all of its forms. 143 00:09:01,860 --> 00:09:04,740 You can take heat energy and convert it to work energy and 144 00:09:04,740 --> 00:09:08,880 vice versa, and it doesn't say anything about that you have 145 00:09:08,880 --> 00:09:11,860 to waste heat if you're going to transform heat into work. 146 00:09:11,860 --> 00:09:13,870 It just says it's energy. 147 00:09:13,870 --> 00:09:16,350 It's all the same thing, right? 148 00:09:16,350 --> 00:09:19,230 So, you could break even if you were very clever about it, 149 00:09:19,230 --> 00:09:22,400 and that's pretty neat. 150 00:09:22,400 --> 00:09:24,510 So, in a sense, it says, you know, if you wanted to build a 151 00:09:24,510 --> 00:09:29,550 boat that took energy out of the warmth of the air, to sail 152 00:09:29,550 --> 00:09:33,740 around the world, you can do that. 153 00:09:33,740 --> 00:09:38,530 And then the second law comes in and says well, that's not 154 00:09:38,530 --> 00:09:40,040 quite right. 155 00:09:40,040 --> 00:09:42,970 The second law says, yes, energy is pretty much the same 156 00:09:42,970 --> 00:09:46,040 in all this form, but if you want to convert one form of 157 00:09:46,040 --> 00:09:51,720 energy into another, if you want to convert work, heat 158 00:09:51,720 --> 00:09:55,020 into work, with 100% efficiency, you've got to go 159 00:09:55,020 --> 00:09:57,250 down to zero degrees Kelvin, to absolute zero if you want 160 00:09:57,250 --> 00:09:57,870 to do that. 161 00:09:57,870 --> 00:10:01,050 Otherwise you're going to waste some of that heat 162 00:10:01,050 --> 00:10:04,920 somewhere along the way, some of that energy. 163 00:10:04,920 --> 00:10:06,960 All right, so you can't get perfect efficiency, but at 164 00:10:06,960 --> 00:10:10,280 least if you were able to go to zero degrees Kelvin, then 165 00:10:10,280 --> 00:10:11,520 you'd be all set. 166 00:10:11,520 --> 00:10:14,200 You just got to find a good refrigerator on your boat, and 167 00:10:14,200 --> 00:10:16,250 then you can still go around the world. 168 00:10:16,250 --> 00:10:18,690 And then the third law comes in, and that's the 169 00:10:18,690 --> 00:10:19,810 depressing part here. 170 00:10:19,810 --> 00:10:21,710 It says, well, it's true. 171 00:10:21,710 --> 00:10:23,980 If you could get to zero degrees Kelvin, you'd get 172 00:10:23,980 --> 00:10:27,705 perfect efficiency, but you can't get to zero degrees 173 00:10:27,705 --> 00:10:31,180 Kelvin, you can't. 174 00:10:31,180 --> 00:10:34,180 Even if you have an infinite amount of resources, 175 00:10:34,180 --> 00:10:42,750 you can't get there. 176 00:10:42,750 --> 00:10:48,940 Any questions so far? 177 00:10:48,940 --> 00:10:52,720 So thermodynamics, based on these four laws now, requires 178 00:10:52,720 --> 00:10:56,420 an edifice, and it's a very mature science, and it 179 00:10:56,420 --> 00:10:58,600 requires that we define things carefully. 180 00:10:58,600 --> 00:11:01,120 So we're going to spend a little bit of time making sure 181 00:11:01,120 --> 00:11:06,410 we define our concepts and our words, and what you'll find 182 00:11:06,410 --> 00:11:13,680 that when you do problem sets, especially at the beginning, 183 00:11:13,680 --> 00:11:17,720 understanding the words and the conditions of the problem 184 00:11:17,720 --> 00:11:23,260 sets is most of the way into solving the problem. 185 00:11:23,260 --> 00:11:33,560 So we're going to talk about things like systems. 186 00:11:33,560 --> 00:11:36,110 The system, it's that part of the 187 00:11:36,110 --> 00:11:38,670 universe that we're studying. 188 00:11:38,670 --> 00:11:41,260 These are going to be fairly common-sense definitions, but 189 00:11:41,260 --> 00:11:44,390 they're important, and when you get to a problem set, 190 00:11:44,390 --> 00:11:50,440 really nailing down what the system is, not more, nor less, 191 00:11:50,440 --> 00:11:52,160 in terms of the amount of stuff, that's part of the 192 00:11:52,160 --> 00:11:55,940 system, it's going to be often very crucial. 193 00:11:55,940 --> 00:11:57,090 So you've got the system. 194 00:11:57,090 --> 00:11:59,010 For instance, it could be a person. 195 00:11:59,010 --> 00:11:59,850 I am the system. 196 00:11:59,850 --> 00:12:00,620 I could be a system. 197 00:12:00,620 --> 00:12:04,450 It could be a hot coffee in a thermos. 198 00:12:04,450 --> 00:12:07,620 So the coffee and the milk and whatever else you like in your 199 00:12:07,620 --> 00:12:08,920 coffee would be the system. 200 00:12:08,920 --> 00:12:12,140 It could be a glass of water with ice in it. 201 00:12:12,140 --> 00:12:13,520 That's a fine system. 202 00:12:13,520 --> 00:12:15,220 Volume of air in a part of a room. 203 00:12:15,220 --> 00:12:18,420 Take four liters on this corner of the room. 204 00:12:18,420 --> 00:12:21,570 That's my system. 205 00:12:21,570 --> 00:12:28,950 Then, after you define what your system is, whatever is 206 00:12:28,950 --> 00:12:32,190 left over of the universe is the surroundings. 207 00:12:32,190 --> 00:12:35,570 So, if I'm the system, then everything else is the 208 00:12:35,570 --> 00:12:35,860 surroundings. 209 00:12:35,860 --> 00:12:37,500 You are my surroundings. 210 00:12:37,500 --> 00:12:39,370 Saturn is my surroundings. 211 00:12:39,370 --> 00:12:41,340 As far as you can go in the universe, that's part of the 212 00:12:41,340 --> 00:12:43,300 surroundings. 213 00:12:43,300 --> 00:12:44,600 And then between the system and the 214 00:12:44,600 --> 00:12:47,120 surroundings is the boundary. 215 00:12:47,120 --> 00:12:56,990 And the boundary is a surface that's real, like the outsides 216 00:12:56,990 --> 00:13:01,740 of my skin, or the inner wall of the thermos that has the 217 00:13:01,740 --> 00:13:06,030 coffee in it, or it could be an imaginary boundary. 218 00:13:06,030 --> 00:13:09,340 For instance, I can imagine that there is a boundary that 219 00:13:09,340 --> 00:13:12,220 surrounds the four liters of air that's sitting in the 220 00:13:12,220 --> 00:13:12,700 corner there. 221 00:13:12,700 --> 00:13:15,790 It doesn't have to be a real container to contain it. 222 00:13:15,790 --> 00:13:21,420 It's just an imaginary boundary there. 223 00:13:21,420 --> 00:13:24,180 And where you place that boundary becomes important. 224 00:13:24,180 --> 00:13:28,210 So, for instance, for the thermos with the coffee in it, 225 00:13:28,210 --> 00:13:31,300 if you place the boundary in the inside wall of the glass 226 00:13:31,300 --> 00:13:33,600 or the outside wall of the glass and the inside of the 227 00:13:33,600 --> 00:13:35,560 thermos, that makes a difference; different heat 228 00:13:35,560 --> 00:13:36,740 capacity, etcetera. 229 00:13:36,740 --> 00:13:40,260 So this becomes where defining the system and the boundaries, 230 00:13:40,260 --> 00:13:42,260 and everything becomes important. 231 00:13:42,260 --> 00:13:43,970 You've got to place the boundary at exactly the right 232 00:13:43,970 --> 00:13:46,180 place, otherwise you've got a bit too much in your system or 233 00:13:46,180 --> 00:13:50,630 a bit too little. 234 00:13:50,630 --> 00:13:51,420 More definitions. 235 00:13:51,420 --> 00:13:59,170 The system can be an open system, or it can be a closed 236 00:13:59,170 --> 00:14:06,590 system, or it can be isolated. 237 00:14:06,590 --> 00:14:09,030 The definitions are also important here. 238 00:14:09,030 --> 00:14:16,200 An open system, as the name describes, allows mass and 239 00:14:16,200 --> 00:14:21,980 energy to freely flow through the boundary. 240 00:14:21,980 --> 00:14:37,690 Mass and energy flow through boundary. 241 00:14:37,690 --> 00:14:38,680 Mass and energy -- 242 00:14:38,680 --> 00:14:43,630 I'm an open system, right? 243 00:14:43,630 --> 00:14:45,910 Water vapor goes through my skin. 244 00:14:45,910 --> 00:14:53,210 I'm hot, compared to the air of the room, or cold if I'm 245 00:14:53,210 --> 00:14:54,780 somewhere that's warm. 246 00:14:54,780 --> 00:14:56,420 So energy can go back and forth. 247 00:14:56,420 --> 00:15:02,450 The thermos, with the lid on top, is not an open system. 248 00:15:02,450 --> 00:15:04,890 Hopefully, your coffee is going to stay warm or hot in 249 00:15:04,890 --> 00:15:05,850 the thermos. 250 00:15:05,850 --> 00:15:07,440 It's not going to get out. 251 00:15:07,440 --> 00:15:09,080 So the thermos is not an open system. 252 00:15:09,080 --> 00:15:13,320 In fact, the thermos is an isolated system. 253 00:15:13,320 --> 00:15:17,270 The isolated system is the opposite of the open system, 254 00:15:17,270 --> 00:15:22,060 no mass and no energy can flow through the boundary. 255 00:15:22,060 --> 00:15:26,700 The closed system allows energy to transfer through the 256 00:15:26,700 --> 00:15:28,320 boundary but not mass. 257 00:15:28,320 --> 00:15:32,080 So a closed system would be, for instance, a glass of ice 258 00:15:32,080 --> 00:15:35,220 water with an ice cube in it, with the lid on top. 259 00:15:35,220 --> 00:15:37,580 The glass is not very insulating. 260 00:15:37,580 --> 00:15:41,720 Energy can flow across the glass, but I put a lid on top, 261 00:15:41,720 --> 00:15:43,350 and so the water can't get out. 262 00:15:43,350 --> 00:15:45,060 And that's the closed system. 263 00:15:45,060 --> 00:15:50,230 Energy goes through the boundaries but nothing else. 264 00:15:50,230 --> 00:15:52,900 Important definitions, even though they may sound really 265 00:15:52,900 --> 00:15:55,980 kind of dumb, but they are really important, because when 266 00:15:55,980 --> 00:15:59,100 you get the problem, figuring out whether you have an open, 267 00:15:59,100 --> 00:16:01,460 closed, or isolated system, what are the surroundings? 268 00:16:01,460 --> 00:16:02,240 What's the boundary? 269 00:16:02,240 --> 00:16:04,360 What is the system? 270 00:16:04,360 --> 00:16:08,100 That's the first thing to make sure that is clear. 271 00:16:08,100 --> 00:16:10,710 If it's not clear, the problem is going to be 272 00:16:10,710 --> 00:16:14,200 impossible to solve. 273 00:16:14,200 --> 00:16:18,060 And that's also how people find ways to break the second 274 00:16:18,060 --> 00:16:21,520 law, because somehow they've messed up on what 275 00:16:21,520 --> 00:16:24,670 their system is. 276 00:16:24,670 --> 00:16:27,600 And they've included too much or too little in the system, 277 00:16:27,600 --> 00:16:30,640 and it looks to them that the second law is broken and 278 00:16:30,640 --> 00:16:35,710 they've created more energy than is being brought in. 279 00:16:35,710 --> 00:16:39,040 That's usually the case. 280 00:16:39,040 --> 00:16:42,650 Questions? 281 00:16:42,650 --> 00:16:44,880 Let's keep going. 282 00:16:44,880 --> 00:16:48,140 So, now that we've got a system, we've 283 00:16:48,140 --> 00:16:49,060 got to describe it. 284 00:16:49,060 --> 00:16:57,310 So, let's describe the system now. 285 00:16:57,310 --> 00:17:02,120 It turns out that when you're talking about macroscopic 286 00:17:02,120 --> 00:17:06,480 properties of matter, you don't need very many variables 287 00:17:06,480 --> 00:17:11,500 to describe the system completely thermodynamically. 288 00:17:11,500 --> 00:17:14,110 You just need a few macroscopic variables that are 289 00:17:14,110 --> 00:17:18,875 very familiar to you, like the pressure, the temperature, the 290 00:17:18,875 --> 00:17:22,970 volume, the number of moles of each component, the mass of 291 00:17:22,970 --> 00:17:25,760 the system. 292 00:17:25,760 --> 00:17:27,910 You've got a magnetic field, maybe even magnetic 293 00:17:27,910 --> 00:17:30,330 susceptibility, the electric field. 294 00:17:30,330 --> 00:17:32,750 We're not going to worry about these magnetic fields or 295 00:17:32,750 --> 00:17:34,620 electric fields in this class. 296 00:17:34,620 --> 00:17:37,590 So, pretty much we're going to focus on this set 297 00:17:37,590 --> 00:17:40,580 of variables here. 298 00:17:40,580 --> 00:17:42,670 You're going to have to know when you describe the system, 299 00:17:42,670 --> 00:17:48,020 if your system is homogeneous, like your coffee with milk in 300 00:17:48,020 --> 00:17:52,740 it, or heterogeneous, like water with an ice cube in it. 301 00:17:52,740 --> 00:17:55,760 So heterogeneous means that you've got different phases in 302 00:17:55,760 --> 00:17:56,640 your system. 303 00:17:56,640 --> 00:17:59,440 I'm the heterogeneous system, soft stuff, hard 304 00:17:59,440 --> 00:18:02,340 stuff, liquid stuff. 305 00:18:02,340 --> 00:18:04,730 Coffee is homogeneous, even though it's made up of many 306 00:18:04,730 --> 00:18:06,440 components. 307 00:18:06,440 --> 00:18:08,850 Many different kinds of molecules make up your coffee. 308 00:18:08,850 --> 00:18:11,190 There are the water molecules, the flavor molecules, the milk 309 00:18:11,190 --> 00:18:12,560 proteins, etcetera. 310 00:18:12,560 --> 00:18:13,930 But it's all mixed up together in a 311 00:18:13,930 --> 00:18:17,100 homogeneous, macroscopic fashion. 312 00:18:17,100 --> 00:18:20,640 If you drill down at the level of molecules you see that it's 313 00:18:20,640 --> 00:18:22,010 not homogeneous. 314 00:18:22,010 --> 00:18:25,590 But thermodynamics takes a bird's eye view. 315 00:18:25,590 --> 00:18:27,760 It looks pretty, beautiful. 316 00:18:27,760 --> 00:18:32,410 So, that's a homogeneous system, one phase. 317 00:18:32,410 --> 00:18:35,250 You have to know if your system is an equilibrium 318 00:18:35,250 --> 00:18:38,070 system or not. 319 00:18:38,070 --> 00:18:40,370 If it's an equilibrium system, then thermodynamics can 320 00:18:40,370 --> 00:18:41,750 describe it. 321 00:18:41,750 --> 00:18:44,810 If it's not, then you're going to have trouble describing it 322 00:18:44,810 --> 00:18:46,890 using thermodynamic properties. 323 00:18:46,890 --> 00:18:51,440 Thermodynamics talks about equilibrium systems and how to 324 00:18:51,440 --> 00:18:53,910 go from one state of equilibrium to another state 325 00:18:53,910 --> 00:18:55,810 of equilibrium. 326 00:18:55,810 --> 00:18:56,480 What does equilibrium mean? 327 00:18:56,480 --> 00:18:59,490 It means that the properties of the system, the properties 328 00:18:59,490 --> 00:19:04,140 that describe the system, don't change 329 00:19:04,140 --> 00:19:06,640 in time or in space. 330 00:19:06,640 --> 00:19:10,110 If I've got a gas in a container, the pressure of the 331 00:19:10,110 --> 00:19:12,510 gas has to be the same everywhere in the container, 332 00:19:12,510 --> 00:19:14,880 otherwise it's not equilibrium. 333 00:19:14,880 --> 00:19:17,930 If I place my container of gas on the table here, and I come 334 00:19:17,930 --> 00:19:21,020 back an hour later, the pressure needs to be the same 335 00:19:21,020 --> 00:19:22,680 when I come back. 336 00:19:22,680 --> 00:19:25,760 Otherwise it's not equilibrium. 337 00:19:25,760 --> 00:19:29,570 So it only talks about equilibrium systems. 338 00:19:29,570 --> 00:19:30,920 What else do you need to know? 339 00:19:30,920 --> 00:19:32,990 So, you need to know the variables. 340 00:19:32,990 --> 00:19:36,250 You need to know it's heterogeneous or homogeneous. 341 00:19:36,250 --> 00:19:39,260 You need to know if it's an equilibrium, and you also need 342 00:19:39,260 --> 00:19:47,820 to know how many components you have in your system. 343 00:19:47,820 --> 00:19:52,800 So, a glass of ice water with an ice cube in it, which is a 344 00:19:52,800 --> 00:19:54,470 heterogeneous system, has only one component, 345 00:19:54,470 --> 00:19:57,110 which is water, H2O. 346 00:19:57,110 --> 00:20:00,980 Two phases, but one component. 347 00:20:00,980 --> 00:20:04,860 Latte, which is a homogeneous system, has a very, very large 348 00:20:04,860 --> 00:20:07,370 number of components to it. 349 00:20:07,370 --> 00:20:09,020 All the components that make up the milk. 350 00:20:09,020 --> 00:20:12,550 All the components that make up the coffee, and all the 351 00:20:12,550 --> 00:20:15,770 impurities, etcetera. cadmium, heavy metals, arsenic, 352 00:20:15,770 --> 00:20:22,050 whatever is in your coffee. 353 00:20:22,050 --> 00:20:26,100 OK, any questions? 354 00:20:26,100 --> 00:20:30,480 All right, so we've described the system with these 355 00:20:30,480 --> 00:20:31,040 properties. 356 00:20:31,040 --> 00:20:33,040 Now these properties come in two flavors. 357 00:20:33,040 --> 00:20:37,650 You have extensive properties and intensive properties. 358 00:20:37,650 --> 00:20:43,230 The extensive properties are the ones that scale with the 359 00:20:43,230 --> 00:20:44,370 size of the system. 360 00:20:44,370 --> 00:20:46,890 If you double the system, they double in 361 00:20:46,890 --> 00:20:48,700 there numerical number. 362 00:20:48,700 --> 00:20:51,090 For instance, the volume. 363 00:20:51,090 --> 00:20:54,010 If you double the volume, the v doubles. 364 00:20:54,010 --> 00:20:55,400 I mean that's obvious. 365 00:20:55,400 --> 00:20:58,100 The mass, if you double the amount of stuff 366 00:20:58,100 --> 00:21:02,780 the mass will double. 367 00:21:02,780 --> 00:21:04,610 Intensive properties don't care about the 368 00:21:04,610 --> 00:21:06,860 scale of your system. 369 00:21:06,860 --> 00:21:10,730 If you double everything in the system, the temperature is 370 00:21:10,730 --> 00:21:12,540 not going to change, it's not going to double. 371 00:21:12,540 --> 00:21:14,050 The temperature stays the same. 372 00:21:14,050 --> 00:21:16,280 So the temperature is intensive, and you can make 373 00:21:16,280 --> 00:21:19,170 intensive properties out of the extensive properties by 374 00:21:19,170 --> 00:21:24,250 dividing by the number of moles in the system. 375 00:21:24,250 --> 00:21:27,920 So I can make a quantity that I'll call V bar, which is the 376 00:21:27,920 --> 00:21:32,370 molar volume, the volume of one mole of a component in my 377 00:21:32,370 --> 00:21:37,270 system, and that becomes an intensive quantity. 378 00:21:37,270 --> 00:21:41,650 A volume which is an intensive volume. 379 00:21:41,650 --> 00:21:51,460 The volumes per mole of that stuff. 380 00:21:51,460 --> 00:21:54,480 So, as I mentioned, thermodynamics is the science 381 00:21:54,480 --> 00:22:05,260 of equilibrium systems, and it also describes the evolution 382 00:22:05,260 --> 00:22:07,510 of one equilibrium to another equilibrium. 383 00:22:07,510 --> 00:22:09,770 How do you go from one to the other? 384 00:22:09,770 --> 00:22:13,850 And so the set of properties that describes the system -- 385 00:22:13,850 --> 00:22:16,550 the equilibrium doesn't change. 386 00:22:16,550 --> 00:22:20,250 So, these on-changing properties that describe the 387 00:22:20,250 --> 00:22:23,400 state of the equilibrium state of the system are 388 00:22:23,400 --> 00:22:24,410 called state variables. 389 00:22:24,410 --> 00:22:36,090 So the state variables describe the equilibrium's 390 00:22:36,090 --> 00:22:40,500 state, and they don't care about how this state got to 391 00:22:40,500 --> 00:22:41,800 where it is. 392 00:22:41,800 --> 00:22:44,760 They don't care about the history of the state. 393 00:22:44,760 --> 00:22:48,980 They just know that's if you have water at zero degrees 394 00:22:48,980 --> 00:22:53,490 Celsius with it ice in, that you can define it as a 395 00:22:53,490 --> 00:22:58,570 heterogeneous system with a certain density for the water 396 00:22:58,570 --> 00:23:01,350 or certain density for the ice, etcetera, etcetera. 397 00:23:01,350 --> 00:23:04,330 It doesn't care how you got there. 398 00:23:04,330 --> 00:23:06,960 We're going to find other properties that do care about 399 00:23:06,960 --> 00:23:09,730 the history of the system, like work, that you put in the 400 00:23:09,730 --> 00:23:11,450 system, or heat that you put in the system, 401 00:23:11,450 --> 00:23:13,330 or some other variables. 402 00:23:13,330 --> 00:23:18,180 But you can't use those to define the equilibrium state. 403 00:23:18,180 --> 00:23:19,830 You can only use the state variables, 404 00:23:19,830 --> 00:23:22,250 independent of history. 405 00:23:22,250 --> 00:23:24,980 And it turns out that for a one component system, one 406 00:23:24,980 --> 00:23:30,110 component meaning one kind of molecule in the system, all 407 00:23:30,110 --> 00:23:34,400 that you need to know to describe the system is the 408 00:23:34,400 --> 00:23:41,960 number of moles for a one component system, and to 409 00:23:41,960 --> 00:23:45,280 describe one phase in that system, one component, 410 00:23:45,280 --> 00:23:53,770 homogeneous system, you need n and two variables. 411 00:23:53,770 --> 00:23:58,810 For instance, the pressure and the temperature, or the volume 412 00:23:58,810 --> 00:24:00,450 and the pressure. 413 00:24:00,450 --> 00:24:03,700 If you have the number of moles and two intensive 414 00:24:03,700 --> 00:24:07,210 variables, then you know everything there is to know 415 00:24:07,210 --> 00:24:07,790 about the system. 416 00:24:07,790 --> 00:24:11,190 About the equilibrium state of that system. 417 00:24:11,190 --> 00:24:17,200 There are hundreds of quantities that you can 418 00:24:17,200 --> 00:24:19,590 calculate and measure that are interesting and important 419 00:24:19,590 --> 00:24:23,610 properties, and all you need is just a few variables to get 420 00:24:23,610 --> 00:24:26,020 everything out, and that's really the power of 421 00:24:26,020 --> 00:24:29,390 thermodynamics, is that it takes so little information to 422 00:24:29,390 --> 00:24:32,460 get so much information out. 423 00:24:32,460 --> 00:24:42,730 So little data to get a lot of predictive information out. 424 00:24:42,730 --> 00:24:51,200 As we're going on with our definitions, we can summarize 425 00:24:51,200 --> 00:24:56,360 a lot of these definitions into a notation, a chemical 426 00:24:56,360 --> 00:25:00,220 notation that that will be very important. 427 00:25:00,220 --> 00:25:04,440 So, for instance, if I'm talking about three moles of 428 00:25:04,440 --> 00:25:08,600 hydrogen, at one bar 100 degrees Celsius. 429 00:25:08,600 --> 00:25:12,190 I'm not going to write, given three moles of hydrogen at one 430 00:25:12,190 --> 00:25:14,210 bar and three degrees, blah, blah, blah. 431 00:25:14,210 --> 00:25:17,270 I'm going to write it in a compact notation. 432 00:25:17,270 --> 00:25:21,240 I'm going to write it like this: three moles of hydrogen 433 00:25:21,240 --> 00:25:28,090 which is a gas, one bar 100 degrees Celsius. 434 00:25:28,090 --> 00:25:30,210 This notation gives you everything you need to know 435 00:25:30,210 --> 00:25:31,590 about the system. 436 00:25:31,590 --> 00:25:33,320 It tells you the number of moles. 437 00:25:33,320 --> 00:25:34,320 It tells you the phase. 438 00:25:34,320 --> 00:25:37,810 It tells you what kind of molecule it is, and gives you 439 00:25:37,810 --> 00:25:41,090 two variables that are state variables. 440 00:25:41,090 --> 00:25:44,250 You could have the volume and the temperature. 441 00:25:44,250 --> 00:25:47,120 You could have the volume and the pressure. 442 00:25:47,120 --> 00:25:48,720 But this tells you everything. 443 00:25:48,720 --> 00:25:51,120 I don't need to write it down in words. 444 00:25:51,120 --> 00:25:55,270 And then if I want to tell you about a change of state, or 445 00:25:55,270 --> 00:25:57,360 let's first start with a mixture. 446 00:25:57,360 --> 00:26:02,400 Suppose that I give to a mixture like, this is a 447 00:26:02,400 --> 00:26:06,000 homogeneous system with two components, like five moles of 448 00:26:06,000 --> 00:26:13,870 H2O, which is a liquid, at one bar 25 degrees Celsius, plus 449 00:26:13,870 --> 00:26:23,030 five moles of CH3, CH2, OH, which is a liquid, and one bar 450 00:26:23,030 --> 00:26:26,460 at 25 degrees Celsius. 451 00:26:26,460 --> 00:26:30,340 This describes roughly something that is fairly 452 00:26:30,340 --> 00:26:36,460 commonplace, it's 100-proof vodka 1/2 water, 1/2 ethanol 453 00:26:36,460 --> 00:26:41,980 -- that describes that macroscopic system. 454 00:26:41,980 --> 00:26:43,960 You're missing all the impurities, all the little the 455 00:26:43,960 --> 00:26:47,870 flavor molecules that go into it, but basically, that's the 456 00:26:47,870 --> 00:26:50,790 homogeneous system we were describing, two component 457 00:26:50,790 --> 00:26:53,020 homogeneous systems. 458 00:26:53,020 --> 00:26:56,090 Then you can do all sorts of predictive 459 00:26:56,090 --> 00:26:59,910 stuff with that system. 460 00:26:59,910 --> 00:27:01,740 All right, that's the equilibrium system. 461 00:27:01,740 --> 00:27:04,560 Now we want to show a notation, how do we go from 462 00:27:04,560 --> 00:27:07,560 one equilibrium state like this describes to another 463 00:27:07,560 --> 00:27:16,360 equilibrium state? 464 00:27:16,360 --> 00:27:18,150 So, we take our two equilibrium states, and you 465 00:27:18,150 --> 00:27:24,450 just put an equal sign between them, and the equal sign means 466 00:27:24,450 --> 00:27:25,420 go from one to the other. 467 00:27:25,420 --> 00:27:31,470 So, if we took our three moles of hydrogen, which is a gas at 468 00:27:31,470 --> 00:27:38,150 five bar and 100 degrees Celsius, and, which is a nice 469 00:27:38,150 --> 00:27:40,190 equilibrium state here, and we say now we're going to change 470 00:27:40,190 --> 00:27:43,080 the equilibrium state to something new, we're going to 471 00:27:43,080 --> 00:27:48,430 do an expansion, let's say. 472 00:27:48,430 --> 00:27:50,265 We're going to drop the pressure, the volume 473 00:27:50,265 --> 00:27:51,440 is going to go up. 474 00:27:51,440 --> 00:27:53,670 I don't need to tell you the volume here, because you've 475 00:27:53,670 --> 00:27:56,500 got enough information to calculate the volume. 476 00:27:56,500 --> 00:28:01,770 The number of moles stays the same, a closed systems, gas 477 00:28:01,770 --> 00:28:03,500 doesn't come out. 478 00:28:03,500 --> 00:28:05,710 Stays a gas, but now the pressure is less, the 479 00:28:05,710 --> 00:28:06,510 temperature is less. 480 00:28:06,510 --> 00:28:10,680 I've done some sort of expansion on this. 481 00:28:10,680 --> 00:28:12,410 I've gone from 1 equilibrium state to another equilibrium 482 00:28:12,410 --> 00:28:15,360 state, and the equal sign means you go from this state 483 00:28:15,360 --> 00:28:16,090 to that state. 484 00:28:16,090 --> 00:28:17,420 It's not a chemical reaction. 485 00:28:17,420 --> 00:28:20,270 That's why we don't have an arrow here, because we could 486 00:28:20,270 --> 00:28:22,240 go back, this way too. 487 00:28:22,240 --> 00:28:23,510 We can go back and forth between these 488 00:28:23,510 --> 00:28:25,070 two equilibrium states. 489 00:28:25,070 --> 00:28:25,860 They're connected. 490 00:28:25,860 --> 00:28:27,210 This means they're connected. 491 00:28:27,210 --> 00:28:29,750 And when I put this, I have to tell you 492 00:28:29,750 --> 00:28:31,210 how they are connected. 493 00:28:31,210 --> 00:28:33,310 I have to tell you the path, if you're 494 00:28:33,310 --> 00:28:34,270 going to solve a problem. 495 00:28:34,270 --> 00:28:36,030 For instance, you want to know how much energy you're going 496 00:28:36,030 --> 00:28:39,260 to get out from doing this expansion. 497 00:28:39,260 --> 00:28:42,205 How much energy are you going to get out, and how far are 498 00:28:42,205 --> 00:28:44,610 you going to be able to drive a car with this expansion, 499 00:28:44,610 --> 00:28:46,540 let's say, so that's the problem. 500 00:28:46,540 --> 00:28:49,640 So, I need to tell you how you're doing the expansion, 501 00:28:49,640 --> 00:28:51,290 because that's going to tell you how much energy you're 502 00:28:51,290 --> 00:28:53,200 wasting during that expansion. 503 00:28:53,200 --> 00:28:56,420 It goes back to the second law. 504 00:28:56,420 --> 00:28:57,210 Nothing is efficient. 505 00:28:57,210 --> 00:28:59,220 You're always wasting energy into heat somewhere when you 506 00:28:59,220 --> 00:29:03,200 do a change that involves a mechanical change. 507 00:29:03,200 --> 00:29:07,250 All right, so I need to tell you the path, when I go from 508 00:29:07,250 --> 00:29:09,550 one state to the other. 509 00:29:09,550 --> 00:29:12,200 And the path is going to be the sequence, intermediate 510 00:29:12,200 --> 00:29:15,140 states going from the initial state the final state. 511 00:29:15,140 --> 00:29:22,670 So, for instance, if I draw a graph of pressure on one axis 512 00:29:22,670 --> 00:29:27,690 and temperature on the other axis, my initial state is at a 513 00:29:27,690 --> 00:29:34,950 temperature of 100 degrees Celsius and five bar. 514 00:29:34,950 --> 00:29:42,970 My final stage is 50 degrees Celsius and one bar. 515 00:29:42,970 --> 00:29:46,120 So, I could have two steps in my path. 516 00:29:46,120 --> 00:29:50,590 I could decide first of all to keep the pressure constant and 517 00:29:50,590 --> 00:29:53,780 lower the pressure. 518 00:29:53,780 --> 00:29:55,880 When I get to 50 degrees Celsius, I could choose to 519 00:29:55,880 --> 00:29:59,050 keep the temperature constant and lower the pressure. 520 00:29:59,050 --> 00:30:01,340 I'm sorry, my first step would be to keep the pressure 521 00:30:01,340 --> 00:30:04,340 constant and lower the temperature, then I lower the 522 00:30:04,340 --> 00:30:07,200 pressure, keeping the temperature constant. 523 00:30:07,200 --> 00:30:08,890 So there's my intermediate state there. 524 00:30:08,890 --> 00:30:12,700 This is one of many paths. 525 00:30:12,700 --> 00:30:15,660 There's an infinite number of paths you could take. 526 00:30:15,660 --> 00:30:19,490 You could take a continuous path, where you have an 527 00:30:19,490 --> 00:30:24,170 infinite number of equilibrium points in between the two, a 528 00:30:24,170 --> 00:30:27,840 smooth path, where you drop the pressure and the 529 00:30:27,840 --> 00:30:30,600 temperature simultaneously in little increments. 530 00:30:30,600 --> 00:30:36,000 All right, so when you do a problem, the path is going to 531 00:30:36,000 --> 00:30:38,470 turn out to be extremely important. 532 00:30:38,470 --> 00:30:40,830 How do you get from the initial state 533 00:30:40,830 --> 00:30:43,580 to the final state? 534 00:30:43,580 --> 00:30:44,770 Define the initial state. 535 00:30:44,770 --> 00:30:45,870 Define the final state. 536 00:30:45,870 --> 00:30:47,380 Define the path. 537 00:30:47,380 --> 00:30:50,990 Get all of these really clear, and you've basically solved 538 00:30:50,990 --> 00:30:51,420 the problem. 539 00:30:51,420 --> 00:30:55,900 You've got to spend the time to make sure that everything 540 00:30:55,900 --> 00:30:58,180 is well defined before you start trying to 541 00:30:58,180 --> 00:31:02,440 work out these problem. 542 00:31:02,440 --> 00:31:04,020 More about the path. 543 00:31:04,020 --> 00:31:08,500 There are a couple ways you could go through that path. 544 00:31:08,500 --> 00:31:10,830 If I look at this smooth path here. 545 00:31:10,830 --> 00:31:14,955 I could have that path be very slow and steady, so that at 546 00:31:14,955 --> 00:31:18,320 every point along the way, my gas is an equilibrium. 547 00:31:18,320 --> 00:31:21,730 So I've got, this piston here is compressed, and I slowly, 548 00:31:21,730 --> 00:31:25,150 slowly increase the volume, drop the temperature. 549 00:31:25,150 --> 00:31:29,910 Then I can go back, the gas is included at every 550 00:31:29,910 --> 00:31:33,220 point of the way. 551 00:31:33,220 --> 00:31:35,120 That's a reversible path. 552 00:31:35,120 --> 00:31:36,220 That can reverse the process. 553 00:31:36,220 --> 00:31:39,110 I expand it, and reverse it, no problem. 554 00:31:39,110 --> 00:31:49,740 So, I could have a reversible path, or I take my gas, and 555 00:31:49,740 --> 00:31:53,840 instead of slowly, slowly raising it, dropping the 556 00:31:53,840 --> 00:32:00,430 pressure, I go from five bar to one bar extremely fast. 557 00:32:00,430 --> 00:32:01,900 What happens to my gas inside? 558 00:32:01,900 --> 00:32:04,590 Well, my gas inside is going to be very unhappy. 559 00:32:04,590 --> 00:32:06,800 It's not going stay in equilibrium. 560 00:32:06,800 --> 00:32:08,940 Parts of the system are going to be at five bar. 561 00:32:08,940 --> 00:32:10,640 Parts of it at one bar. 562 00:32:10,640 --> 00:32:14,270 Parts of it may be even at zero bar, if I go really fast. 563 00:32:14,270 --> 00:32:15,910 I'm going to create a vacuum. 564 00:32:15,910 --> 00:32:21,780 So the system will not be described by a single state 565 00:32:21,780 --> 00:32:23,480 variable during the path. 566 00:32:23,480 --> 00:32:27,700 If I look at different points in my container during that 567 00:32:27,700 --> 00:32:31,250 path, I'm going to have to use a different value of pressure 568 00:32:31,250 --> 00:32:32,800 or different value of temperature at different 569 00:32:32,800 --> 00:32:35,080 points of the container. 570 00:32:35,080 --> 00:32:38,700 That's not an equilibrium state, and that process turns 571 00:32:38,700 --> 00:32:42,140 out then to be in irreversible process. 572 00:32:42,140 --> 00:32:43,410 Do it very quickly. 573 00:32:43,410 --> 00:32:46,440 Now to reverse it and get back to the initial point is going 574 00:32:46,440 --> 00:32:50,510 to require some input from outside, like heat or extra 575 00:32:50,510 --> 00:32:53,320 work or extra heat or something, because you've done 576 00:32:53,320 --> 00:32:54,850 an irreversible process. 577 00:32:54,850 --> 00:33:04,810 You've wasted a lot of energy in doing that process. 578 00:33:04,810 --> 00:33:09,720 I have to tell you whether the path is reversible or 579 00:33:09,720 --> 00:33:13,580 irreversible, and the irreversible path also defines 580 00:33:13,580 --> 00:33:15,100 the direction of time. 581 00:33:15,100 --> 00:33:19,000 You can only have an irreversible path go one way 582 00:33:19,000 --> 00:33:20,750 in time, not the other way. 583 00:33:20,750 --> 00:33:24,070 Chalk breaks irreversibly and you can't put it 584 00:33:24,070 --> 00:33:25,590 back together so easily. 585 00:33:25,590 --> 00:33:29,000 You've got to pretty much take that chalk, and make a slurry 586 00:33:29,000 --> 00:33:32,270 out of it, put water, and dry it back up, put in a mold, and 587 00:33:32,270 --> 00:33:34,570 then you can have the chalk again, but you can't just glue 588 00:33:34,570 --> 00:33:35,480 it back together. 589 00:33:35,480 --> 00:33:36,970 That would not be the same state as what 590 00:33:36,970 --> 00:33:40,990 you started out with. 591 00:33:40,990 --> 00:33:42,280 And then there are a bunch of words that 592 00:33:42,280 --> 00:33:43,820 describe these paths. 593 00:33:43,820 --> 00:33:47,750 Words like adiabatic, which we'll be very familiar with. 594 00:33:47,750 --> 00:33:50,290 Adiabatic means that there's no heat transferred between 595 00:33:50,290 --> 00:33:51,950 the system and the surrounding. 596 00:33:51,950 --> 00:33:54,520 The boundary is impervious to transfer of 597 00:33:54,520 --> 00:33:56,580 heat, like a thermos. 598 00:33:56,580 --> 00:33:59,800 Anything that happens inside of the thermos is an adiabatic 599 00:33:59,800 --> 00:34:03,220 change because the thermos has no connection in terms of 600 00:34:03,220 --> 00:34:04,560 energy to the outside world. 601 00:34:04,560 --> 00:34:05,940 There's no heat that can go through the 602 00:34:05,940 --> 00:34:07,530 walls of the thermos. 603 00:34:07,530 --> 00:34:10,760 Whereas, like isobaric means constant pressure. 604 00:34:10,760 --> 00:34:16,000 So, this path right here from this top red path is an 605 00:34:16,000 --> 00:34:18,380 isobaric process. 606 00:34:18,380 --> 00:34:21,685 Constant temperature means isothermal, so this part means 607 00:34:21,685 --> 00:34:23,250 an isothermal process. 608 00:34:23,250 --> 00:34:28,580 So then, going from the initial to final states with a 609 00:34:28,580 --> 00:34:32,160 red path, you start with an isobaric process and then you 610 00:34:32,160 --> 00:34:34,260 end with an isothermal process. 611 00:34:34,260 --> 00:34:36,570 And these are words that are very meaningful when you read 612 00:34:36,570 --> 00:34:42,650 the text of a problem or of a process. 613 00:34:42,650 --> 00:34:44,750 Any questions before we got to the zeroth law? 614 00:34:44,750 --> 00:34:49,230 We're pretty much done with our definitions here. 615 00:34:49,230 --> 00:34:49,690 Yes. 616 00:34:49,690 --> 00:34:53,040 STUDENT: Was adiabatic reversible? 617 00:34:53,040 --> 00:34:56,490 PROFESSOR: Adiabatic can be either reversible or not, and 618 00:34:56,490 --> 00:34:57,510 we're going to do that probably 619 00:34:57,510 --> 00:35:01,240 next time or two times. 620 00:35:01,240 --> 00:35:02,110 Any other questions? 621 00:35:02,110 --> 00:35:06,440 Yes. 622 00:35:06,440 --> 00:35:08,390 STUDENT: Is there a boundary between reversible and 623 00:35:08,390 --> 00:35:08,780 irreversible? 624 00:35:08,780 --> 00:35:12,520 PROFESSOR: A boundary between reversible and irreversible? 625 00:35:12,520 --> 00:35:14,930 Like something is almost reversible and almost 626 00:35:14,930 --> 00:35:15,040 irreversible. 627 00:35:15,040 --> 00:35:17,370 No, pretty much things are either reversible or 628 00:35:17,370 --> 00:35:19,490 irreversible. 629 00:35:19,490 --> 00:35:22,520 Now, in practice, it depends on how good 630 00:35:22,520 --> 00:35:28,950 your measurement is. 631 00:35:28,950 --> 00:35:35,400 And probably also in practice, nothing is truly reversible. 632 00:35:35,400 --> 00:35:43,650 So, it depends on your error bar in a sense. 633 00:35:43,650 --> 00:35:45,240 It depends on what what you define, exactly what you 634 00:35:45,240 --> 00:35:46,470 define in your system. 635 00:35:46,470 --> 00:35:50,230 It becomes a gray area, but it should be pretty clear if you 636 00:35:50,230 --> 00:35:57,720 can treat something is reversible are irreversible. 637 00:35:57,720 --> 00:36:03,970 Other questions, It's a good question. 638 00:36:03,970 --> 00:36:06,820 So the zeroth law we're going to go through the laws now. 639 00:36:06,820 --> 00:36:11,730 The zeroth law talks about defining temperature and it's 640 00:36:11,730 --> 00:36:12,440 the common-sense law. 641 00:36:12,440 --> 00:36:14,030 You all know how. 642 00:36:14,030 --> 00:36:16,640 When something hot, it's got a higher temperature than when 643 00:36:16,640 --> 00:36:18,320 something is cold. 644 00:36:18,320 --> 00:36:21,860 But it's important to define that, and define something 645 00:36:21,860 --> 00:36:23,830 that's a thermometer. 646 00:36:23,830 --> 00:36:26,820 So what do you know? 647 00:36:26,820 --> 00:36:28,180 What's the empirical information 648 00:36:28,180 --> 00:36:29,620 that everybody knows? 649 00:36:29,620 --> 00:36:34,132 Everybody knows that if you take something which is hot 650 00:36:34,132 --> 00:36:40,140 and something which is cold, and you bring them together, 651 00:36:40,140 --> 00:36:47,900 make them touch, that heat is going to flow from the hot to 652 00:36:47,900 --> 00:36:54,280 the cold, and make them touch, and heat 653 00:36:54,280 --> 00:36:56,310 flows from hot to cold. 654 00:36:56,310 --> 00:36:57,200 That's common sense. 655 00:36:57,200 --> 00:37:03,150 This is part of your DNA, And then their final product is an 656 00:37:03,150 --> 00:37:10,830 object, a b which ends up at a temperature or a warmness 657 00:37:10,830 --> 00:37:13,070 which is in between the hot and the cold. 658 00:37:13,070 --> 00:37:16,270 So, this turns out to be warm. 659 00:37:16,270 --> 00:37:19,280 You get your new equilibrium state, which is in between 660 00:37:19,280 --> 00:37:28,230 what this was, and what a and b were. 661 00:37:28,230 --> 00:37:34,530 Then how do you know that it's changed temperature, or that 662 00:37:34,530 --> 00:37:37,710 heat has flowed from a to b? 663 00:37:37,710 --> 00:37:41,070 Practically speaking, you need some sort of property that's 664 00:37:41,070 --> 00:37:43,030 changing as heat is flowing. 665 00:37:43,030 --> 00:37:50,420 For instance, if a were metallic, you could measure 666 00:37:50,420 --> 00:37:55,460 the connectivity of a or resistivity, and as heat flows 667 00:37:55,460 --> 00:38:01,870 out of a into b, the resistivity of a would change. 668 00:38:01,870 --> 00:38:04,520 Or you could have something that's color metric that 669 00:38:04,520 --> 00:38:09,710 changes color when it's colder, so you could see the 670 00:38:09,710 --> 00:38:13,840 heat flowing as a changes color or b changes color as 671 00:38:13,840 --> 00:38:15,130 heat flows into b. 672 00:38:15,130 --> 00:38:17,470 So, you need some sort of property, something you can 673 00:38:17,470 --> 00:38:21,130 see, something you can measure, that tells you that 674 00:38:21,130 --> 00:38:21,880 heat has flowed. 675 00:38:21,880 --> 00:38:25,315 Now, if you have three objects, if you have a, b, and 676 00:38:25,315 --> 00:38:35,960 c, and you bring them together, and a is the 677 00:38:35,960 --> 00:38:40,600 hottest, b is the medium one, and c is the coldest, so from 678 00:38:40,600 --> 00:38:43,150 hottest to coldest a, b, c, -- if you bring them together and 679 00:38:43,150 --> 00:38:53,300 make them touch, you know, intuitively, that heat will 680 00:38:53,300 --> 00:38:57,900 not flow like this. 681 00:38:57,900 --> 00:38:59,650 You know that's not going to happen. 682 00:38:59,650 --> 00:39:03,730 You know that what will happen is that heat will flow from a 683 00:39:03,730 --> 00:39:07,530 to b from b to c and from a to c. 684 00:39:07,530 --> 00:39:08,340 That's common-sense. 685 00:39:08,340 --> 00:39:11,090 You know that. 686 00:39:11,090 --> 00:39:13,170 And the other way in the circle will never happen. 687 00:39:13,170 --> 00:39:16,150 That would that would give rise to a perpetual motion 688 00:39:16,150 --> 00:39:18,030 machine, breaking of the second law. 689 00:39:18,030 --> 00:39:22,060 It can't happen. 690 00:39:22,060 --> 00:39:24,500 But that's an empirical observation, that heat flows 691 00:39:24,500 --> 00:39:27,100 in this direction. 692 00:39:27,100 --> 00:39:29,380 And that's the zeroth law thermodynamic. 693 00:39:29,380 --> 00:39:32,090 It's pretty simple. 694 00:39:32,090 --> 00:39:38,900 The zeroth law says that if a and b -- it doesn't exactly 695 00:39:38,900 --> 00:39:41,660 say that, but it implies this. 696 00:39:41,660 --> 00:39:45,230 It says that if a and b are in thermal equilibrium, if these 697 00:39:45,230 --> 00:39:48,060 two are in thermal equilibrium, meaning that 698 00:39:48,060 --> 00:39:50,890 there's no heat flows between them, so that's the definition 699 00:39:50,890 --> 00:39:53,210 of thermal equilibrium, that no heat flows between them, 700 00:39:53,210 --> 00:39:56,685 and these two are in thermal equilibrium, and these two are 701 00:39:56,685 --> 00:40:02,380 in thermal equilibrium, then a and c will be also be in 702 00:40:02,380 --> 00:40:04,910 thermal equilibrium. 703 00:40:04,910 --> 00:40:07,030 But if there's no heat flowing between these two, and no heat 704 00:40:07,030 --> 00:40:09,610 flowing between these two, then you can't have heat 705 00:40:09,610 --> 00:40:13,010 flowing between these two. 706 00:40:13,010 --> 00:40:15,920 So if I get rid of these arrows, there's no heat 707 00:40:15,920 --> 00:40:18,510 flowing because they're in thermal equilibrium, then I 708 00:40:18,510 --> 00:40:20,640 can't have an arrow here. 709 00:40:20,640 --> 00:40:22,505 That's what the zeroth law says. 710 00:40:22,505 --> 00:40:24,610 They're all the same temperature. 711 00:40:24,610 --> 00:40:25,260 That's what it says. 712 00:40:25,260 --> 00:40:28,530 If two object are in the same temperature, and two other 713 00:40:28,530 --> 00:40:30,610 object are in the same temperature, then all three 714 00:40:30,610 --> 00:40:34,610 must have the same temperature. 715 00:40:34,610 --> 00:40:37,680 It sounds pretty silly, but it's really important because 716 00:40:37,680 --> 00:40:44,020 it allows you to define a thermometer and temperature. 717 00:40:44,020 --> 00:40:48,790 Because now you can say, all right, well, now b can be my 718 00:40:48,790 --> 00:40:49,340 thermometer. 719 00:40:49,340 --> 00:40:54,290 I have two objects, I have an object which is in Madagascar 720 00:40:54,290 --> 00:40:59,140 and an object which is in Boston, and I want to know, 721 00:40:59,140 --> 00:41:01,920 are they the same temperature? 722 00:41:01,920 --> 00:41:05,040 So I come out with a third object, b, I go to Madagascar, 723 00:41:05,040 --> 00:41:06,570 and put b in contact with a. 724 00:41:06,570 --> 00:41:11,240 Then I insulate everything, you know, take it away and see 725 00:41:11,240 --> 00:41:12,640 if there's any heat flow. 726 00:41:12,640 --> 00:41:15,370 Let's say there's no heat flow. 727 00:41:15,370 --> 00:41:18,515 Then I insulate it, get back on the plane to Boston, and go 728 00:41:18,515 --> 00:41:20,010 back and touch b with c. 729 00:41:20,010 --> 00:41:22,680 If there's no heat flow between the b and c, then I 730 00:41:22,680 --> 00:41:27,280 can say all right, a and c were the same temperature. 731 00:41:27,280 --> 00:41:29,440 B is my thermometer that tells me that a and c are in the 732 00:41:29,440 --> 00:41:30,180 same temperature. 733 00:41:30,180 --> 00:41:33,165 And there's a certain property associated with heat flow with 734 00:41:33,165 --> 00:41:35,860 b, and it didn't change. 735 00:41:35,860 --> 00:41:37,490 And that property could be color. 736 00:41:37,490 --> 00:41:38,300 It could be resistivity. 737 00:41:38,300 --> 00:41:39,390 It could be a lot of different things. 738 00:41:39,390 --> 00:41:41,320 It could be volume. 739 00:41:41,320 --> 00:41:44,950 And the temperature then is associated with that property. 740 00:41:44,950 --> 00:41:47,380 And if it had changed, then the temperature between those 741 00:41:47,380 --> 00:41:50,830 two would have changed in a very particular way. 742 00:41:50,830 --> 00:41:57,700 So, zeroth law, then, allows you to define the concept of 743 00:41:57,700 --> 00:42:05,510 temperature and the measurement of temperature 744 00:42:05,510 --> 00:42:09,000 through a thermometer. 745 00:42:09,000 --> 00:42:12,010 Let's very briefly go through stuff that 746 00:42:12,010 --> 00:42:13,210 you've learned before. 747 00:42:13,210 --> 00:42:16,180 So, now you have this object which is going to tell you 748 00:42:16,180 --> 00:42:19,540 whether other things are in thermal equilibrium now. 749 00:42:19,540 --> 00:42:21,980 What do you need for that object? 750 00:42:21,980 --> 00:42:27,840 You need that object to be a substance, to be something. 751 00:42:27,840 --> 00:42:31,630 So, the active part of the thermometer could be water. 752 00:42:31,630 --> 00:42:35,900 It could be alcohol, mercury, it could be a piece of metal. 753 00:42:35,900 --> 00:42:39,210 You need a substance, and then that substance has to have a 754 00:42:39,210 --> 00:42:41,560 property that changes depending on the heat flow, 755 00:42:41,560 --> 00:42:44,820 i.e., depending on whether it's sensing that it's the 756 00:42:44,820 --> 00:42:46,270 same temperature or different temperature 757 00:42:46,270 --> 00:42:46,930 than something else. 758 00:42:46,930 --> 00:42:51,790 And that property could be the volume, like if you have a 759 00:42:51,790 --> 00:42:54,160 mercury thermometer, the volume of the mercury. 760 00:42:54,160 --> 00:42:55,090 It could be temperature. 761 00:42:55,090 --> 00:42:58,670 It could be resistivity, if you have a thermocouple. 762 00:42:58,670 --> 00:43:02,980 It could be the pressure. 763 00:43:02,980 --> 00:43:04,110 All right, so now you have an object. 764 00:43:04,110 --> 00:43:06,000 You've got a property that changes, 765 00:43:06,000 --> 00:43:07,180 depending on the heat flow. 766 00:43:07,180 --> 00:43:09,280 It's going to tell you about the temperature. 767 00:43:09,280 --> 00:43:11,220 Now you need to define the temperature scales. 768 00:43:11,220 --> 00:43:16,190 So, you need some reference points to be able to tell you, 769 00:43:16,190 --> 00:43:22,860 OK, this temperature is 550 degrees Smith, whatever. 770 00:43:22,860 --> 00:43:27,380 So, you assign values to very specific states of matter and 771 00:43:27,380 --> 00:43:29,610 call those the reference points for your temperature. 772 00:43:29,610 --> 00:43:32,840 For instance, freezing of water or boiling of water, the 773 00:43:32,840 --> 00:43:34,610 standard ones. 774 00:43:34,610 --> 00:43:36,150 And then an interpolation scheme. 775 00:43:36,150 --> 00:43:41,050 You need a functional form that connects the value at one 776 00:43:41,050 --> 00:43:45,240 state of matter, the freezing point of water, to another 777 00:43:45,240 --> 00:43:47,440 phase change, the boiling point of water. 778 00:43:47,440 --> 00:43:51,420 You can choose a linear interpolation or quadratic, 779 00:43:51,420 --> 00:43:54,610 but you've got to choose it. 780 00:43:54,610 --> 00:43:56,140 And it turns out not to be so easy. 781 00:43:56,140 --> 00:43:58,630 And if you go back into the 1800's when thermodynamics was 782 00:43:58,630 --> 00:44:02,680 starting, there were a zillion different temperatures scales. 783 00:44:02,680 --> 00:44:06,620 Everybody had their own favorite temperature scales. 784 00:44:06,620 --> 00:44:08,550 The one that we're most familiar with is the 785 00:44:08,550 --> 00:44:11,190 centigrade or Celsius scale where mercury was the 786 00:44:11,190 --> 00:44:13,970 substance, and the volume of mercury is the property. 787 00:44:13,970 --> 00:44:16,510 The reference points are water, freezing or boiling, 788 00:44:16,510 --> 00:44:19,180 and the interpolation is linear, and then that morphed 789 00:44:19,180 --> 00:44:21,940 into the Kelvin scale, as we're going to see later. 790 00:44:21,940 --> 00:44:24,070 The Fahrenheit scale is an interesting scale. 791 00:44:24,070 --> 00:44:26,130 It turns out the U.S. and Jamaica are the only two 792 00:44:26,130 --> 00:44:28,670 places on Earth now that use the Fahrenheit scale. 793 00:44:28,670 --> 00:44:33,800 Mr. Fahrenheit, Daniel Gabriel Fahrenheit was a German 794 00:44:33,800 --> 00:44:37,890 instrument maker. 795 00:44:37,890 --> 00:44:41,600 The way he came up with his scale was actually he borrowed 796 00:44:41,600 --> 00:44:43,810 the Romer scale, which came beforehand. 797 00:44:43,810 --> 00:44:47,990 The Romer scale was, Romer was a Dane, and he defined 798 00:44:47,990 --> 00:44:53,900 freezing of water at 7.5 degrees Roemer, and 22.5 799 00:44:53,900 --> 00:44:56,480 degrees Romer as blood-warm. 800 00:44:56,480 --> 00:45:00,180 That was his definition. 801 00:45:00,180 --> 00:45:03,510 Two substances, blood and water. 802 00:45:03,510 --> 00:45:06,160 Two reference points, freezing and blood-warm, you know, the 803 00:45:06,160 --> 00:45:07,190 human body. 804 00:45:07,190 --> 00:45:09,760 A linear interpolation between the two, and then some numbers 805 00:45:09,760 --> 00:45:12,660 associated with them, 7-1/2 and 22-1/2. 806 00:45:12,660 --> 00:45:15,960 Why does he choose 7-1/2 as the freezing point of water? 807 00:45:15,960 --> 00:45:19,290 Because he thought that would be big enough that in Denmark, 808 00:45:19,290 --> 00:45:22,560 the temperature wouldn't go below zero. 809 00:45:22,560 --> 00:45:24,140 That's how he picked 7-1/2. 810 00:45:24,140 --> 00:45:25,900 Why not? 811 00:45:25,900 --> 00:45:28,480 He didn't want to use negative numbers to measure temperature 812 00:45:28,480 --> 00:45:31,130 in Denmark outside. 813 00:45:31,130 --> 00:45:32,740 Well, Fahrenheit came along and thought, well, you know, 814 00:45:32,740 --> 00:45:36,340 7-1/2, that's kind of silly; 22-1/2 that's, kind of silly. 815 00:45:36,340 --> 00:45:40,160 So let's multiply everything by four. 816 00:45:40,160 --> 00:45:46,390 I think it becomes 30 degrees for the freezing of water and 817 00:45:46,390 --> 00:45:49,860 22.5 x 4, which I don't know what it is, 100 or something 818 00:45:49,860 --> 00:45:55,480 -- no, it's 90 I think. 819 00:45:55,480 --> 00:45:58,040 And then for some reason, that nobody understands, he decided 820 00:45:58,040 --> 00:46:04,200 to multiply again by 16/15, and that's how we get 32 for 821 00:46:04,200 --> 00:46:08,340 freezing of water and 96 in his words for the temperature 822 00:46:08,340 --> 00:46:10,190 in the mouth or underneath the armpit of a 823 00:46:10,190 --> 00:46:12,390 living man in good health. 824 00:46:12,390 --> 00:46:14,170 What a great temperature scale. 825 00:46:14,170 --> 00:46:16,630 It turns out that 96 wasn't quite right. 826 00:46:16,630 --> 00:46:21,110 Then he interpolated and found out water boils at 212. 827 00:46:21,110 --> 00:46:23,920 But, you know, his experiment wasn't so great, and, you 828 00:46:23,920 --> 00:46:26,790 know, maybe had a fever when he did the reference point 829 00:46:26,790 --> 00:46:28,720 with 96, whatever. 830 00:46:28,720 --> 00:46:31,290 It turns out that it's not 96 to be in good health, it's 831 00:46:31,290 --> 00:46:34,120 98.6 -- whatever. 832 00:46:34,120 --> 00:46:37,760 That's how we got to the Fahrenheit scale. 833 00:46:37,760 --> 00:46:40,090 All right, next time we're going to talk about a much 834 00:46:40,090 --> 00:46:43,330 better scale, which is the ideal gas thermometer and how 835 00:46:43,330 --> 00:46:45,380 we get to the Kelvin scale.