1 00:00:00,030 --> 00:00:02,535 The following content is provided under a creative 2 00:00:02,535 --> 00:00:03,810 commons license. 3 00:00:03,810 --> 00:00:06,850 Your support will help MIT OpenCourseWare continue to 4 00:00:06,850 --> 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 --> 00:00:17,150 hundreds of MIT courses, visit MIT OpenCourseWare at 7 00:00:17,150 --> 00:00:21,490 ocw.mit.edu 8 00:00:21,490 --> 00:00:26,390 PROFESSOR NELSON: So, over the last few lectures we've worked 9 00:00:26,390 --> 00:00:30,650 and struggled so formulate the second and third laws of 10 00:00:30,650 --> 00:00:33,150 thermodynamics in addition to the first. 11 00:00:33,150 --> 00:00:36,900 Last time we reach the third law which is telling us that 12 00:00:36,900 --> 00:00:40,450 we can't quite get to zero degrees Kelvin, but that as 13 00:00:40,450 --> 00:00:44,020 the temperature approaches zero degrees Kelvin, the 14 00:00:44,020 --> 00:00:48,950 absolute entropy of a pure substance in perfect 15 00:00:48,950 --> 00:00:51,270 crystalline form is zero. 16 00:00:51,270 --> 00:00:53,900 And what that corresponds to, if you recall, is the idea 17 00:00:53,900 --> 00:00:57,700 that in a perfect crystal at zero degrees Kelvin then you 18 00:00:57,700 --> 00:01:00,060 have no disorder at all. 19 00:01:00,060 --> 00:01:02,000 You have a perfectly ordered system. 20 00:01:02,000 --> 00:01:05,230 And in that case, the entropy is absolutely zero. 21 00:01:05,230 --> 00:01:09,410 And the bigger lesson from that is that entropy, unlike 22 00:01:09,410 --> 00:01:14,260 energy u or enthalpy H, we could define an absolutely 23 00:01:14,260 --> 00:01:15,490 number for it. 24 00:01:15,490 --> 00:01:18,430 The zero of it wasn't arbitrary. 25 00:01:18,430 --> 00:01:21,020 Unlike the case for energy like you've seen in lots and 26 00:01:21,020 --> 00:01:24,150 lots of disciplines, where you can arbitrarily set the zero 27 00:01:24,150 --> 00:01:26,260 in a way that makes it convenient for you. 28 00:01:26,260 --> 00:01:28,390 Entropy really is not like that. 29 00:01:28,390 --> 00:01:32,540 There is an absolute zero of entropy, and that's really 30 00:01:32,540 --> 00:01:33,910 what we learn. 31 00:01:33,910 --> 00:01:39,350 So now, now that we've got all three of the major laws of 32 00:01:39,350 --> 00:01:43,770 thermodynamics, what I want to start in on is a discussion of 33 00:01:43,770 --> 00:01:45,420 what happens spontaneously. 34 00:01:45,420 --> 00:01:49,590 We've seen that in just one specialized case so far, but 35 00:01:49,590 --> 00:01:53,580 we should in a more general way be able to tell when is a 36 00:01:53,580 --> 00:01:58,440 system at equilibrium, where there's no net change taking 37 00:01:58,440 --> 00:02:04,910 place, and when is it still undergoing spontaneous change 38 00:02:04,910 --> 00:02:07,860 towards some other state, presumably toward an 39 00:02:07,860 --> 00:02:09,180 equilibrium state. 40 00:02:09,180 --> 00:02:11,320 How do we tell? 41 00:02:11,320 --> 00:02:15,310 So that's the topic that I'd like to address today. 42 00:02:15,310 --> 00:02:40,350 So, that's the big question, right? 43 00:02:40,350 --> 00:02:52,580 So let's say that we've got our stuff in some state. 44 00:02:52,580 --> 00:02:59,130 A, whatever it is. 45 00:02:59,130 --> 00:03:00,830 And there's some other possible state, 46 00:03:00,830 --> 00:03:03,050 B, whatever it is. 47 00:03:03,050 --> 00:03:05,920 And maybe if it some well-defined 48 00:03:05,920 --> 00:03:09,470 temperature and pressure. 49 00:03:09,470 --> 00:03:13,360 What do we do to tell whether that change will happen 50 00:03:13,360 --> 00:03:14,890 spontaneously? 51 00:03:14,890 --> 00:03:22,070 Do we calculate, you know, delta S, delta u, delta H? 52 00:03:22,070 --> 00:03:26,830 What tells us whether or not the change happens? 53 00:03:26,830 --> 00:03:29,770 Certainly in principle we know how to calculate this and 54 00:03:29,770 --> 00:03:33,570 other stuff for a change in state of this sort, for lots 55 00:03:33,570 --> 00:03:35,710 of changes of state. 56 00:03:35,710 --> 00:03:39,920 But calculating it alone doesn't necessarily tell us 57 00:03:39,920 --> 00:03:44,490 whether or not it will just happened of its own accord. 58 00:03:44,490 --> 00:03:46,860 And that's the issue that we'd like to be able to address. 59 00:03:46,860 --> 00:03:51,330 Now, we have addressed this in some cases. 60 00:03:51,330 --> 00:03:59,310 So, for example, we know that if we take, you know, gas A 61 00:03:59,310 --> 00:04:05,980 and gas B with a barrier between them, and we remove 62 00:04:05,980 --> 00:04:15,360 the barrier, they're going to mix. 63 00:04:15,360 --> 00:04:20,690 And we saw that and went through it somewhat carefully 64 00:04:20,690 --> 00:04:31,350 and saw that if the system is isolated, for that case we do 65 00:04:31,350 --> 00:04:35,170 have a criterion that tells us whether change happens 66 00:04:35,170 --> 00:04:35,730 spontaneously. 67 00:04:35,730 --> 00:04:54,520 Namely, it's delta S is greater than zero. 68 00:04:54,520 --> 00:04:56,790 That tells us whether the change is spontaneous. 69 00:04:56,790 --> 00:05:00,280 And we saw that in fact in this case delta S of mixing, 70 00:05:00,280 --> 00:05:03,520 we calculated it, saw that it is positive. 71 00:05:03,520 --> 00:05:06,230 So, clearly, if we remove this barrier mixing takes place, 72 00:05:06,230 --> 00:05:08,040 and obviously you know that that happens from lots of 73 00:05:08,040 --> 00:05:10,350 experience. 74 00:05:10,350 --> 00:05:14,370 In general, the second law gave us the Clausius 75 00:05:14,370 --> 00:05:17,800 inequality for spontaneous change. 76 00:05:17,800 --> 00:05:35,730 Namely dS is greater than dq over T. I suppose we could 77 00:05:35,730 --> 00:05:40,490 specify the surroundings temperature. 78 00:05:40,490 --> 00:05:45,940 We saw that in general dS is greater than or equal to dq 79 00:05:45,940 --> 00:05:50,660 over T. if it's a reversible process then the equality 80 00:05:50,660 --> 00:05:54,410 holds, but if it's irreversible, which means it 81 00:05:54,410 --> 00:06:29,300 happens spontaneously, then dS is greater than this. 82 00:06:29,300 --> 00:06:34,990 Just to illustrate the kind of issues that we're up against 83 00:06:34,990 --> 00:06:39,990 here, let me just consider a few different chemical 84 00:06:39,990 --> 00:06:45,590 reactions, all of which happen spontaneously. 85 00:06:45,590 --> 00:06:49,140 So, I just want to write a few examples down with a few 86 00:06:49,140 --> 00:06:55,540 values for delta u or delta H or delta S, and see whether we 87 00:06:55,540 --> 00:06:58,220 can get any clues from what we see. 88 00:06:58,220 --> 00:07:11,670 So here are some spontaneous chemical changes. 89 00:07:11,670 --> 00:07:13,550 Here's one. 90 00:07:13,550 --> 00:07:21,910 If we take hydrogen peroxide in the liquid state, it can 91 00:07:21,910 --> 00:07:29,890 break down to form water and oxygen. 92 00:07:29,890 --> 00:07:32,660 If we look at the thermodynamic quantities, the 93 00:07:32,660 --> 00:07:36,670 enthalpy and the entropy of the reaction, what we find is 94 00:07:36,670 --> 00:07:44,100 delta H is minus 209 kiloJoules and delta S is plus 95 00:07:44,100 --> 00:07:52,260 132 joules per Kelvin. 96 00:07:52,260 --> 00:07:57,250 So it seems like there's a favorable change in entropy 97 00:07:57,250 --> 00:07:57,980 going this way. 98 00:07:57,980 --> 00:08:00,140 That is, you've got lower energy on the right and also 99 00:08:00,140 --> 00:08:02,070 higher entropy. 100 00:08:02,070 --> 00:08:05,870 Higher entropy basically because you're forming 101 00:08:05,870 --> 00:08:08,660 molecules of gas where there weren't any before, and 102 00:08:08,660 --> 00:08:11,530 there's more disorder in the gas phase than in the liquid. 103 00:08:11,530 --> 00:08:12,980 That is, the gas phase molecules have 104 00:08:12,980 --> 00:08:15,270 more freedom to roam. 105 00:08:15,270 --> 00:08:17,540 Okay, that's one example. 106 00:08:17,540 --> 00:08:19,200 Here's another. 107 00:08:19,200 --> 00:08:27,655 Let's just take hydrogen and nitrogen in the gas phase and 108 00:08:27,655 --> 00:08:32,390 form ammonia. 109 00:08:32,390 --> 00:08:38,860 Well, here we get, we find that delta H is negative 92 110 00:08:38,860 --> 00:08:40,610 kiloJoules. 111 00:08:40,610 --> 00:08:47,910 Delta S is negative 198 joules per Kelvin. 112 00:08:47,910 --> 00:08:51,280 This one also happens spontaneously. 113 00:08:51,280 --> 00:08:54,820 One thing that makes it pretty clear is that certainly delta 114 00:08:54,820 --> 00:08:58,200 S or the sign of it alone is not 115 00:08:58,200 --> 00:09:01,580 dictating the outcome here. 116 00:09:01,580 --> 00:09:06,750 All right, here's a third example. 117 00:09:06,750 --> 00:09:15,660 Let's take salt, solid, and dissolve it in a bunch of 118 00:09:15,660 --> 00:09:18,530 liquid water. 119 00:09:18,530 --> 00:09:22,050 Hopefully you've got experience saying that this 120 00:09:22,050 --> 00:09:31,910 happens, of course it does. 121 00:09:31,910 --> 00:09:34,800 If we measure the thermodynamics, we discover 122 00:09:34,800 --> 00:09:39,560 that delta H is 4 kiloJoules, plus 4 kiloJoules. 123 00:09:39,560 --> 00:09:47,530 Delta S is 45 joules per Kelvin. 124 00:09:47,530 --> 00:09:51,460 So now we have a different sign for delta H and it still 125 00:09:51,460 --> 00:09:55,650 happens spontaneously. 126 00:09:55,650 --> 00:10:00,280 So clearly, we've got signs and magnitudes of delta H and 127 00:10:00,280 --> 00:10:03,490 delta S, and if we wanted to put delta u there, similar 128 00:10:03,490 --> 00:10:05,500 things would happen. 129 00:10:05,500 --> 00:10:07,310 They're all over the map. 130 00:10:07,310 --> 00:10:12,620 And yet, these things are all spontaneous processes. 131 00:10:12,620 --> 00:10:15,420 And I didn't specify the conditions, but if we were to 132 00:10:15,420 --> 00:10:19,210 do this under ordinary chemical conditions of some, 133 00:10:19,210 --> 00:10:23,480 you'd say room temperature and pressure, right, they all 134 00:10:23,480 --> 00:10:25,800 happen spontaneously. 135 00:10:25,800 --> 00:10:30,850 OK, clearly we'd be much better off if we had some 136 00:10:30,850 --> 00:10:36,320 systematic quantitative way to tell whether something would 137 00:10:36,320 --> 00:10:39,280 happen spontaneously. 138 00:10:39,280 --> 00:10:44,550 In other words, we need criteria for equilibrium under 139 00:10:44,550 --> 00:10:47,590 more general conditions than the ones that we've dealt with 140 00:10:47,590 --> 00:10:49,890 so far, than the one set of conditions that we've dealt 141 00:10:49,890 --> 00:10:52,420 with so far, which is isolated system. 142 00:10:52,420 --> 00:10:56,780 Most chemical changes, most physical changes don't happen 143 00:10:56,780 --> 00:11:02,020 in isolated systems. 144 00:11:02,020 --> 00:11:26,840 So let's start by writing down our definition of equilibrium. 145 00:11:26,840 --> 00:11:28,560 It's very simple. 146 00:11:28,560 --> 00:11:34,160 The equilibrium state is the one, and it's just one, in 147 00:11:34,160 --> 00:11:38,400 which there are no spontaneous changes that can take place to 148 00:11:38,400 --> 00:11:40,700 any other state. 149 00:11:40,700 --> 00:11:43,340 Now that's under whatever constraints there are. 150 00:11:43,340 --> 00:11:44,360 There's a box around it. 151 00:11:44,360 --> 00:11:45,560 The temperature or the pressure are 152 00:11:45,560 --> 00:11:47,730 fixed, what have you. 153 00:11:47,730 --> 00:12:08,150 But the point is, no spontaneous changes can occur 154 00:12:08,150 --> 00:12:11,930 to any other state. 155 00:12:11,930 --> 00:12:17,680 So for example, when we remove the barrier and the gases mix, 156 00:12:17,680 --> 00:12:18,890 you know it's over. 157 00:12:18,890 --> 00:12:21,780 Once the gases are mixed, there's not going to be any 158 00:12:21,780 --> 00:12:27,340 further net change in the system. 159 00:12:27,340 --> 00:12:31,130 It's at equilibrium, under the new condition, that is with 160 00:12:31,130 --> 00:12:34,430 the barrier removed. 161 00:12:34,430 --> 00:12:39,830 OK, so now let's try to formulate how to describe the 162 00:12:39,830 --> 00:12:43,590 equilibrium state and what dictates spontaneity. 163 00:12:43,590 --> 00:12:45,710 So what we're going to do is consider the 164 00:12:45,710 --> 00:12:48,320 first and second laws. 165 00:12:48,320 --> 00:12:56,890 So our first law, du is dq plus dw. 166 00:13:01,770 --> 00:13:13,180 And our second law, dS is greater than dq over the 167 00:13:13,180 --> 00:13:25,010 temperature of surroundings for a change that happens 168 00:13:25,010 --> 00:13:29,370 spontaneously. 169 00:13:29,370 --> 00:13:33,430 And now, I want to combine these two, which I 170 00:13:33,430 --> 00:13:34,640 of course can do. 171 00:13:34,640 --> 00:13:40,280 I can substitute dq from this expression in here. 172 00:13:40,280 --> 00:13:43,600 I also want to assume for our present purposes that there's 173 00:13:43,600 --> 00:13:46,810 only pressure volume work going on, which is to say I 174 00:13:46,810 --> 00:13:50,380 want to put p dV in here minus p dV for dw. 175 00:14:01,790 --> 00:14:11,810 So for combining for p V work, what we see then is du has to 176 00:14:11,810 --> 00:14:20,670 be less than T surroundings dS minus p external dV. 177 00:14:27,140 --> 00:14:36,740 Or we can rewrite this as du plus external pressure dV 178 00:14:36,740 --> 00:14:43,580 minus T surroundings dS is less than zero. 179 00:14:43,580 --> 00:14:48,970 Now this is fundamentally important, and as you know 180 00:14:48,970 --> 00:14:54,700 that means that it warrants the exalted distinction of 181 00:14:54,700 --> 00:14:56,250 being put up in colored chalk. 182 00:14:56,250 --> 00:14:59,030 And, in fact, since we're going to reuse this again and 183 00:14:59,030 --> 00:15:02,460 again during today's lecture, I'm going to put it over here 184 00:15:02,460 --> 00:15:08,170 and leave it sacrosanct for our further use. du plus p 185 00:15:08,170 --> 00:15:14,380 external dV minus T surroundings dS 186 00:15:14,380 --> 00:15:19,300 is less than zero. 187 00:15:19,300 --> 00:15:29,890 This Is our condition for spontaneous change. 188 00:15:29,890 --> 00:15:35,350 Now this is a really quite useful expression. 189 00:15:35,350 --> 00:15:38,820 For one thing what we have here are all functions of 190 00:15:38,820 --> 00:15:47,330 state and parameters that we can control like temperature 191 00:15:47,330 --> 00:16:09,910 and pressure. 192 00:16:09,910 --> 00:16:11,940 So that's a big help. 193 00:16:11,940 --> 00:16:17,510 And equilibrium happens when there isn't any possible 194 00:16:17,510 --> 00:16:22,480 change of state that would satisfy this. 195 00:16:22,480 --> 00:16:37,690 In other words, you've got your system in some state. 196 00:16:37,690 --> 00:16:41,680 You know it's in some state A, there are some 197 00:16:41,680 --> 00:16:46,200 other states around. 198 00:16:46,200 --> 00:16:51,590 Here is what we calculate to tell whether it happens 199 00:16:51,590 --> 00:16:53,640 spontaneously. 200 00:16:53,640 --> 00:16:58,020 So we now have a real usable criterion to help guide our 201 00:16:58,020 --> 00:17:00,710 understanding of whether things happen by themselves of 202 00:17:00,710 --> 00:17:05,180 their own accord or not. 203 00:17:05,180 --> 00:17:09,890 Now, this is still a little bit cumbersome, in part 204 00:17:09,890 --> 00:17:14,850 because of the variables involved, including S. That 205 00:17:14,850 --> 00:17:19,170 is, most processes that we're concerned with, they'll happen 206 00:17:19,170 --> 00:17:22,550 with something held constant like pressure or temperature 207 00:17:22,550 --> 00:17:24,330 or maybe volume. 208 00:17:24,330 --> 00:17:28,310 So this isn't the most useful form that we can have, but 209 00:17:28,310 --> 00:17:33,350 what we'll see shortly is that from this, we can then derive 210 00:17:33,350 --> 00:17:37,800 further criteria for essentially any set of 211 00:17:37,800 --> 00:17:40,870 variables or any set of external constraints, like 212 00:17:40,870 --> 00:17:42,980 constant temperature or pressure or volume and so 213 00:17:42,980 --> 00:17:46,330 forth that we might set. 214 00:17:46,330 --> 00:17:58,520 And so that's what I now want to do. 215 00:17:58,520 --> 00:18:02,810 So I just want to use that again and again, starting from 216 00:18:02,810 --> 00:18:07,560 that, for various different sorts of conditions and derive 217 00:18:07,560 --> 00:18:29,500 the criterion for equilibrium in each set of conditions. 218 00:18:29,500 --> 00:18:34,760 So first, let's start with the one that we already know, and 219 00:18:34,760 --> 00:18:43,490 make sure that it still works, starting from here, mainly our 220 00:18:43,490 --> 00:18:45,640 isolated system. 221 00:18:45,640 --> 00:18:47,060 So remember what that means? 222 00:18:47,060 --> 00:18:50,750 It means no heat, no work. 223 00:18:50,750 --> 00:18:52,720 Delta V is zero. 224 00:18:52,720 --> 00:18:57,000 Delta u is zero. 225 00:18:57,000 --> 00:19:05,580 So looking at this, du is zero. dV is zero. 226 00:19:05,580 --> 00:19:12,050 So all that's left is negative T dS is less than zero. 227 00:19:12,050 --> 00:19:18,020 In other words, T surrounding dS has to be greater than 228 00:19:18,020 --> 00:19:18,880 zero, and of course 229 00:19:18,880 --> 00:19:20,670 temperature is always positive. 230 00:19:20,670 --> 00:19:32,180 So dS for u and V fixed is greater than zero. 231 00:19:32,180 --> 00:19:34,750 All right, so that's sounds right. 232 00:19:34,750 --> 00:19:37,310 That's what we saw before. 233 00:19:37,310 --> 00:19:40,060 When we have an isolated system, the criterion that 234 00:19:40,060 --> 00:19:43,020 determines whether something happens spontaneously is the 235 00:19:43,020 --> 00:19:49,130 entropy has to increase. 236 00:19:49,130 --> 00:20:04,910 Now, what this means too is if we imagine a bunch of 237 00:20:04,910 --> 00:20:08,810 different states, and this is the entropy of them, so this 238 00:20:08,810 --> 00:20:11,300 could be any sort of variable but the point is there are a 239 00:20:11,300 --> 00:20:25,210 bunch of possible states around, whichever one has the 240 00:20:25,210 --> 00:20:33,620 maximum entropy, that's the equilibrium state. 241 00:20:33,620 --> 00:20:37,260 In other words, you know we've got the two gases on either 242 00:20:37,260 --> 00:20:38,660 side of that partition. 243 00:20:38,660 --> 00:20:41,690 We remove the partition, and they mix. 244 00:20:41,690 --> 00:20:45,050 Well, the equilibrium state is the one with the gases 245 00:20:45,050 --> 00:20:46,130 completely mixed. 246 00:20:46,130 --> 00:20:49,580 Of course there are lots of states that would have maybe 247 00:20:49,580 --> 00:20:54,270 local pockets of one substance in excess and another 248 00:20:54,270 --> 00:20:56,200 substance in excess somewhere else. 249 00:20:56,200 --> 00:21:00,140 In other words, there would be lots of states nearby to the 250 00:21:00,140 --> 00:21:01,200 equilibrium state. 251 00:21:01,200 --> 00:21:03,550 That is, the chain, they could they could be approached with 252 00:21:03,550 --> 00:21:06,850 very little change from the equilibrium state. 253 00:21:06,850 --> 00:21:09,220 They aren't the equilibrium state. 254 00:21:09,220 --> 00:21:12,580 The entropy in all of those states will be lower than the 255 00:21:12,580 --> 00:21:18,330 entropy of the fully mixed state. 256 00:21:18,330 --> 00:21:22,010 So the point is, once you're at equilibrium none of the 257 00:21:22,010 --> 00:21:25,700 other states, they're accessible, the system could 258 00:21:25,700 --> 00:21:30,330 rearrange itself to form them, but there is no accessible 259 00:21:30,330 --> 00:21:39,630 state that has higher entropy than the equilibrium state. 260 00:21:39,630 --> 00:21:52,690 OK, that's our familiar isolated system. 261 00:21:52,690 --> 00:21:58,260 Now let's try moving to unfamiliar territory and 262 00:21:58,260 --> 00:22:08,060 extending what we know. 263 00:22:08,060 --> 00:22:19,750 So, let's try constant entropy and volume. 264 00:22:19,750 --> 00:22:23,810 And the motivation for choosing a pair like that is 265 00:22:23,810 --> 00:22:26,710 easy to see, if we look at our condition for spontaneous 266 00:22:26,710 --> 00:22:28,510 change or general condition. 267 00:22:28,510 --> 00:22:31,780 Well, entropy and volume constant means dV and dS are 268 00:22:31,780 --> 00:22:32,930 equal to zero. 269 00:22:32,930 --> 00:22:33,760 What does that say? 270 00:22:33,760 --> 00:22:35,770 It means du is less than zero. 271 00:22:35,770 --> 00:22:39,420 That's our condition. 272 00:22:39,420 --> 00:22:46,102 So we immediately get du at constant S and V 273 00:22:46,102 --> 00:22:51,700 is less than zero. 274 00:22:51,700 --> 00:23:01,050 That's our condition for spontaneous change. 275 00:23:01,050 --> 00:23:05,100 In other words, if we don't have to worry about entropy or 276 00:23:05,100 --> 00:23:09,960 volume equilibrium is achieved when energy is at a minimum. 277 00:23:09,960 --> 00:23:13,060 Now this is what you learn in elementary physics and in 278 00:23:13,060 --> 00:23:14,130 mechanics, right. 279 00:23:14,130 --> 00:23:16,450 You're not worried about entropy. 280 00:23:16,450 --> 00:23:22,170 So, you know, if you've got a hill or valley and there's a 281 00:23:22,170 --> 00:23:28,360 cart on wheels, it's going to go down to the bottom. 282 00:23:28,360 --> 00:23:31,400 The spontaneous change lowers the potential 283 00:23:31,400 --> 00:23:36,720 energy in that case. 284 00:23:36,720 --> 00:23:50,720 So this is a simple condition that's very familiar. 285 00:23:50,720 --> 00:23:54,470 Now, the reason this condition always holds in ordinary 286 00:23:54,470 --> 00:23:58,120 mechanics is because you're never, in that case, concerned 287 00:23:58,120 --> 00:24:02,230 with a huge statistical population of particles where 288 00:24:02,230 --> 00:24:06,810 the disorder among them is an issue. 289 00:24:06,810 --> 00:24:09,820 We're not worrying then about the fact that, well like in 290 00:24:09,820 --> 00:24:16,050 the case of gas molecules mixing, the macroscopic state 291 00:24:16,050 --> 00:24:19,290 of the whole thing, all those molecules, how many different 292 00:24:19,290 --> 00:24:21,750 microscopic configurations are there? 293 00:24:21,750 --> 00:24:24,500 Remember, I mentioned then we'll go further later on into 294 00:24:24,500 --> 00:24:27,170 this, that entropy can be related to 295 00:24:27,170 --> 00:24:28,490 the extent of disorder. 296 00:24:28,490 --> 00:24:32,010 That is, how many different possible configurations of all 297 00:24:32,010 --> 00:24:35,830 those molecules there would be for a particular state. 298 00:24:35,830 --> 00:24:40,320 The reason the entropy of the mixed gases is the highest is 299 00:24:40,320 --> 00:24:43,770 because that has the most possible configurations. 300 00:24:43,770 --> 00:24:48,190 If you start segregating the gases, there are fewer 301 00:24:48,190 --> 00:24:51,410 possible configurations that the whole system can be in 302 00:24:51,410 --> 00:24:54,740 because you're forcing a particular set of 303 00:24:54,740 --> 00:24:58,220 circumstances. 304 00:24:58,220 --> 00:25:01,390 When you don't have to worry about criteria like that, 305 00:25:01,390 --> 00:25:05,860 ordinary, mechanical energy rules supreme, and that's 306 00:25:05,860 --> 00:25:10,860 dictating where equilibrium lies. 307 00:25:10,860 --> 00:25:14,230 But of course, most chemical and biological systems aren't 308 00:25:14,230 --> 00:25:18,460 that simple precisely because you have to worry about many 309 00:25:18,460 --> 00:25:22,590 particles and their statistics and the way they might order 310 00:25:22,590 --> 00:25:25,340 or disorder. 311 00:25:25,340 --> 00:25:31,700 So, and of course, you know, keeping entropy as a fixed 312 00:25:31,700 --> 00:25:35,740 variable for a system like that is extremely cumbersome. 313 00:25:35,740 --> 00:25:38,180 As soon as you allow anything to mix, like you might if you 314 00:25:38,180 --> 00:25:41,040 want to do any chemistry, entropy changes. 315 00:25:41,040 --> 00:25:46,730 If you change the temperature entropy changes and so on. 316 00:25:46,730 --> 00:25:47,850 So let's go on. 317 00:25:47,850 --> 00:26:01,590 Let's consider a few other examples. 318 00:26:01,590 --> 00:26:07,910 Let's hang on for a little while longer to a set of 319 00:26:07,910 --> 00:26:11,810 conditions where we will maintain constant entropy, 320 00:26:11,810 --> 00:26:24,380 namely constant entropy and pressure. 321 00:26:24,380 --> 00:26:33,250 So, the dS term is zero, but the other two are not. 322 00:26:33,250 --> 00:26:46,830 So, du plus p dV is less than zero. 323 00:26:46,830 --> 00:26:56,210 I can write this as d(u + pV) less than zero. 324 00:26:56,210 --> 00:26:58,600 Normally I couldn't do that because this term would have p 325 00:26:58,600 --> 00:27:04,320 dV plus V dp, but we've specified the pressure is 326 00:27:04,320 --> 00:27:09,180 constant, so the dp part is zero. 327 00:27:09,180 --> 00:27:12,470 And this is a quantity that you know, right? 328 00:27:12,470 --> 00:27:15,320 What's u plus pV? 329 00:27:15,320 --> 00:27:18,060 STUDENT: dH. 330 00:27:18,060 --> 00:27:28,200 PROFESSOR NELSON: dH less than zero, criterion for 331 00:27:28,200 --> 00:27:34,400 spontaneous change. 332 00:27:34,400 --> 00:27:44,560 In the case where S and p are held constant. 333 00:27:44,560 --> 00:27:51,730 Now, once again, like I illustrated for entropy, and I 334 00:27:51,730 --> 00:27:58,090 could have done the same for energy here, you know, if we 335 00:27:58,090 --> 00:28:02,310 again look at a bunch of different states, and look at 336 00:28:02,310 --> 00:28:07,520 their enthalpy, well, like before, they'll be invariably 337 00:28:07,520 --> 00:28:21,230 lots of possible states. 338 00:28:21,230 --> 00:28:24,800 And now, what is this saying, the equilibrium state is the 339 00:28:24,800 --> 00:28:28,690 one with the lowest possible enthalpy. 340 00:28:28,690 --> 00:28:32,110 In the case here, that I just illustrated with the little 341 00:28:32,110 --> 00:28:34,760 cart going down the valley, would be exactly the same with 342 00:28:34,760 --> 00:28:37,180 regular energy, the equilibrium state is one of 343 00:28:37,180 --> 00:28:39,590 lowest energy, right. 344 00:28:39,590 --> 00:28:41,770 And of course there are lots of nearby states. 345 00:28:41,770 --> 00:28:45,830 The cart could be a little ways up the hill, and in this 346 00:28:45,830 --> 00:28:48,900 case, it's enthalpy, but again, there would be lots of 347 00:28:48,900 --> 00:28:51,030 accessible states. 348 00:28:51,030 --> 00:28:54,450 But if the system is in equilibrium, none of those 349 00:28:54,450 --> 00:28:58,930 states has lower enthalpy. 350 00:28:58,930 --> 00:29:00,870 It's already in the lowest enthalpy state. 351 00:29:00,870 --> 00:29:06,840 That is the equilibrium state. 352 00:29:06,840 --> 00:29:15,190 OK, well, now, let's get to the big ones. 353 00:29:15,190 --> 00:29:18,630 That is, in real life, the variables that you'd normally 354 00:29:18,630 --> 00:29:23,280 control aren't some combination of entropy and 355 00:29:23,280 --> 00:29:27,220 these variables, but really their temperature, volume and 356 00:29:27,220 --> 00:29:30,660 pressure, any couple of those, might be what you'd really 357 00:29:30,660 --> 00:29:34,770 have under experimental control. 358 00:29:34,770 --> 00:30:04,250 So now let's go to them. 359 00:30:04,250 --> 00:30:22,540 Let's control T and V. So, all right, so now 360 00:30:22,540 --> 00:30:24,510 we're getting serious. 361 00:30:24,510 --> 00:30:29,660 All right, well, there's our equilibrium criterion. 362 00:30:29,660 --> 00:30:31,700 We're still going back to it. 363 00:30:31,700 --> 00:30:32,860 It still holds. 364 00:30:32,860 --> 00:30:37,720 So we've now got the dV part equal to zero. 365 00:30:37,720 --> 00:30:48,010 So what this says is that du minus T dS is less than zero, 366 00:30:48,010 --> 00:30:54,460 and we can combine those to say d(u - TS) 367 00:30:54,460 --> 00:30:55,640 is less than zero. 368 00:30:55,640 --> 00:30:58,720 And again, just like before, we can do that although this 369 00:30:58,720 --> 00:31:04,600 normally would say this has T dS and also minus S dT. 370 00:31:04,600 --> 00:31:05,650 T is fixed. 371 00:31:05,650 --> 00:31:08,480 So that part is zero. 372 00:31:08,480 --> 00:31:11,890 So this is really the equivalent of this. 373 00:31:11,890 --> 00:31:17,420 So when we did this here, we conveniently found that that 374 00:31:17,420 --> 00:31:22,080 quantity u plus pV is something we know and love, 375 00:31:22,080 --> 00:31:23,085 and we're familiar with it. 376 00:31:23,085 --> 00:31:25,900 It's our enthalpy H. So we could write that criterion as 377 00:31:25,900 --> 00:31:28,740 dH less than zero. 378 00:31:28,740 --> 00:31:35,680 So here, let's combine these to define a new quantity. 379 00:31:35,680 --> 00:31:38,650 It obviously has importance because what it's going to say 380 00:31:38,650 --> 00:31:42,830 is that that's the quantity that defines equilibrium, that 381 00:31:42,830 --> 00:31:47,320 tells us about equilibrium, under the very important 382 00:31:47,320 --> 00:31:50,810 practical constraints of having fixed 383 00:31:50,810 --> 00:31:52,400 temperature and volume. 384 00:31:52,400 --> 00:31:55,470 Realistically, the more likely constraints 385 00:31:55,470 --> 00:31:57,930 than either of those. 386 00:31:57,930 --> 00:32:08,550 So let's -- we'll go to a brand new color, define 387 00:32:08,550 --> 00:32:13,550 A as u minus TS. 388 00:32:13,550 --> 00:32:26,460 it's called the Helmholtz free energy. 389 00:32:26,460 --> 00:32:30,610 OK, and then our criterion for equilibrium under these 390 00:32:30,610 --> 00:32:39,685 conditions is dA, V and T equal to the temperature of 391 00:32:39,685 --> 00:32:47,760 the surroundings, is less than zero. 392 00:32:47,760 --> 00:32:56,910 OK, and once again, you know if we wanted to look at a 393 00:32:56,910 --> 00:33:09,900 bunch of states that could be accessed, well, we would find 394 00:33:09,900 --> 00:33:13,480 lots of states near by, in character to 395 00:33:13,480 --> 00:33:15,260 the equilibrium state. 396 00:33:15,260 --> 00:33:18,810 The one that is at equilibrium, there is only one 397 00:33:18,810 --> 00:33:21,450 macroscopic state at equilibrium. 398 00:33:21,450 --> 00:33:31,950 It has the lowest A. 399 00:33:31,950 --> 00:33:35,800 In some sense, that's one reason to associate this as a 400 00:33:35,800 --> 00:33:41,270 kind of energy, just like mechanical energy u or 401 00:33:41,270 --> 00:33:47,320 enthalpy H, it's the minimum free energy state that is the 402 00:33:47,320 --> 00:34:02,320 equilibrium state under the relevant conditions. 403 00:34:02,320 --> 00:34:06,440 Now, let's take the step to the biggest set of 404 00:34:06,440 --> 00:34:08,280 conditions of all. 405 00:34:08,280 --> 00:34:11,220 What is it when you run a chemical reaction under 406 00:34:11,220 --> 00:34:18,160 ordinary circumstances, what's constant? 407 00:34:18,160 --> 00:34:18,720 STUDENT: [UNINTELLIGIBLE] 408 00:34:18,720 --> 00:34:20,500 PROFESSOR NELSON: A little louder. 409 00:34:20,500 --> 00:34:21,140 STUDENT: Pressure and temperature. 410 00:34:21,140 --> 00:34:21,820 PROFESSOR NELSON: Pressure and temperature, right. 411 00:34:21,820 --> 00:34:23,930 You're running, you're shaking a beaker up here at room 412 00:34:23,930 --> 00:34:27,820 temperature. 413 00:34:27,820 --> 00:34:49,950 So let's look at that set of conditions. 414 00:34:49,950 --> 00:34:51,580 All right, there it is. 415 00:34:51,580 --> 00:34:54,560 This is the condition for really the lion's share of 416 00:34:54,560 --> 00:34:58,360 chemistry, biology, and other kinds of changes we'll be 417 00:34:58,360 --> 00:35:00,370 concerned with. 418 00:35:00,370 --> 00:35:07,730 So, there's our condition for equilibrium. 419 00:35:07,730 --> 00:35:11,550 We don't get to set any of them to zero, right? 420 00:35:11,550 --> 00:35:21,640 So, okay and we can handle that. du plus p dV minus T dS 421 00:35:21,640 --> 00:35:28,080 is less than zero, but we do get to simplify in writing 422 00:35:28,080 --> 00:35:36,110 this as d(u + pV - TS) is less than zero, and just like we've 423 00:35:36,110 --> 00:35:41,840 seen before, yes, this has p dV and V dp, but the dp is 424 00:35:41,840 --> 00:35:43,750 zero because we're at constant pressure. 425 00:35:43,750 --> 00:35:49,160 This has minus T dS minus S dT, but the dT part is zero 426 00:35:49,160 --> 00:35:52,380 because we're at constant temperature. 427 00:35:52,380 --> 00:35:55,360 So the result is we can combine all of these as a 428 00:35:55,360 --> 00:35:59,240 single differential, and just like we've seen before, what 429 00:35:59,240 --> 00:36:04,490 that suggests is that we define another new quantity 430 00:36:04,490 --> 00:36:07,430 given by this expression. 431 00:36:07,430 --> 00:36:13,100 And that is the last one we're going to describe. 432 00:36:13,100 --> 00:36:21,010 And that is G, u plus pV minus TS. 433 00:36:28,280 --> 00:36:34,220 The Gibbs free energy. 434 00:36:34,220 --> 00:36:38,020 Notice, we could also write, let's rewrite that. 435 00:36:38,020 --> 00:36:47,270 G is u plus the pV minus TS, but u plus pV is H. So we also 436 00:36:47,270 --> 00:36:54,050 can write this as H minus TS and u minus TS is what we just 437 00:36:54,050 --> 00:36:57,200 defined a minute ago as A. So we can also write 438 00:36:57,200 --> 00:37:01,710 this as A plus pV. 439 00:37:05,090 --> 00:37:08,800 And the main thing of crucial importance is what, by 440 00:37:08,800 --> 00:37:11,540 defining this in the way we have, what that's saying is 441 00:37:11,540 --> 00:37:37,320 that dG at constant p and T is less than zero. 442 00:37:37,320 --> 00:37:49,390 There's our condition for equilibrium at constant 443 00:37:49,390 --> 00:37:56,480 temperature and pressure. 444 00:37:56,480 --> 00:37:58,830 Boy, is that going to be important for the whole rest 445 00:37:58,830 --> 00:38:02,990 of the course. 446 00:38:02,990 --> 00:38:14,400 So, and of course, I hardly need to emphasize further, but 447 00:38:14,400 --> 00:38:19,790 we could do the exact same consideration that we have for 448 00:38:19,790 --> 00:38:28,020 H and A, there's G. There's our equilibrium state. 449 00:38:28,020 --> 00:38:34,640 It's the state that has the lowest Gibbs free energy. 450 00:38:34,640 --> 00:38:37,050 All these things though are incredibly 451 00:38:37,050 --> 00:38:40,780 practical, useful criteria. 452 00:38:40,780 --> 00:38:47,670 This is only defined in terms of state functions. 453 00:38:47,670 --> 00:38:51,070 And just like we saw before for the case of entropy in an 454 00:38:51,070 --> 00:38:56,900 isolated system, now we have something we can calculate. 455 00:38:56,900 --> 00:39:01,340 It's a state function, so we're at constant temperature 456 00:39:01,340 --> 00:39:04,770 and pressure, and now we want to consider some chemical 457 00:39:04,770 --> 00:39:08,500 change or a phase transition or you name it. 458 00:39:08,500 --> 00:39:10,740 Does it happen of its own accord? 459 00:39:10,740 --> 00:39:14,630 Well now we know what needs to be calculated in order to 460 00:39:14,630 --> 00:39:17,550 determine that. 461 00:39:17,550 --> 00:39:23,410 So this one is so uniquely pervasive, let's just really 462 00:39:23,410 --> 00:39:28,060 explicitly write it all out. 463 00:39:28,060 --> 00:39:39,550 For constant pressure and temperature delta G is less 464 00:39:39,550 --> 00:39:50,960 than zero, means A going to B is, all right, let's consider 465 00:39:50,960 --> 00:40:02,450 some process state A and state B. If delta G is less than 466 00:40:02,450 --> 00:40:09,130 zero, it happens spontaneously. 467 00:40:09,130 --> 00:40:29,480 If delta G equals zero, then we're already in equilibrium. 468 00:40:29,480 --> 00:40:37,430 And if delta G is greater than zero, then it goes 469 00:40:37,430 --> 00:40:49,000 spontaneously in the other direction. 470 00:40:49,000 --> 00:40:54,370 Any questions about any of this? 471 00:40:54,370 --> 00:40:58,860 Let me just give a couple of examples. 472 00:40:58,860 --> 00:41:01,520 If we go back to any of those chemical reactions that I 473 00:41:01,520 --> 00:41:07,180 wrote on the board before, right, well certainly we can 474 00:41:07,180 --> 00:41:11,850 calculate what delta G would be for each one of them. 475 00:41:11,850 --> 00:41:15,120 Because we know how to calculate all the parts of it. 476 00:41:15,120 --> 00:41:18,010 It's state functions, it's composed of state functions 477 00:41:18,010 --> 00:41:20,270 that we know how to calculate. 478 00:41:20,270 --> 00:41:23,570 So we could tell. 479 00:41:23,570 --> 00:41:28,200 When delta G is zero, you know, it doesn't mean that 480 00:41:28,200 --> 00:41:32,310 you've got all of one side, all reactants and zero 481 00:41:32,310 --> 00:41:36,290 products or all products and zero reactants. 482 00:41:36,290 --> 00:41:38,130 There is some mixture of them. 483 00:41:38,130 --> 00:41:44,440 What this will tell us is what mixture. 484 00:41:44,440 --> 00:41:46,900 You know the stuff is in there in equilibrium, you know the 485 00:41:46,900 --> 00:41:50,430 hydrogen and nitrogen that will form ammonia. 486 00:41:50,430 --> 00:41:53,840 And in the end, when it's at equilibrium, and you look and 487 00:41:53,840 --> 00:41:55,740 you'd make a measurement, right, you could do 488 00:41:55,740 --> 00:41:56,560 spectroscopy. 489 00:41:56,560 --> 00:42:00,180 You could easily see how much of each thing is there. 490 00:42:00,180 --> 00:42:05,570 It doesn't go all the way to absolutely 100 percent 491 00:42:05,570 --> 00:42:09,260 ammonia, zero hydrogen zero nitrogen if they were mixed 492 00:42:09,260 --> 00:42:10,660 together with the right ratios. 493 00:42:10,660 --> 00:42:11,720 Doesn't happen. 494 00:42:11,720 --> 00:42:14,280 There would be some of the reactants 495 00:42:14,280 --> 00:42:17,790 and some of the products. 496 00:42:17,790 --> 00:42:20,840 In the biochemical reactions that are taking place in your 497 00:42:20,840 --> 00:42:26,680 body, there is equilibrium between a whole myriad of 498 00:42:26,680 --> 00:42:29,510 reactants and products, and thank heavens that gets 499 00:42:29,510 --> 00:42:33,700 maintained. 500 00:42:33,700 --> 00:42:36,750 So that's what this will guide us through, and of course 501 00:42:36,750 --> 00:42:42,170 that's incredibly, incredibly important. 502 00:42:42,170 --> 00:42:45,880 Here's another thing that's worth thinking about. 503 00:42:45,880 --> 00:42:54,430 There's a balance here between ordinary energy or enthalpy 504 00:42:54,430 --> 00:42:58,120 and entropy. 505 00:42:58,120 --> 00:43:02,130 Energy means, you know, chemical reactions happen, and 506 00:43:02,130 --> 00:43:06,330 you end up with something that might be exothermic, that is, 507 00:43:06,330 --> 00:43:09,940 the products are more stable then the reactants. 508 00:43:09,940 --> 00:43:14,070 You burn methane, and it combines with oxygen to form 509 00:43:14,070 --> 00:43:19,070 water, to form CO2. 510 00:43:19,070 --> 00:43:21,910 And if you work out the energetics as we've gone with 511 00:43:21,910 --> 00:43:26,580 thermochemistry, you discover there's a huge negative delta 512 00:43:26,580 --> 00:43:30,320 H. In other words, the bonds are much stronger. 513 00:43:30,320 --> 00:43:34,450 CO2 is really a stable molecule. 514 00:43:34,450 --> 00:43:37,280 Methane, there are certainly some solid bonds there, but 515 00:43:37,280 --> 00:43:43,690 breaking those to form CO2 and water, well it's worth it, 516 00:43:43,690 --> 00:43:45,440 right, energetically. 517 00:43:45,440 --> 00:43:54,280 Still, the actual equilibrium depends on entropy also, not 518 00:43:54,280 --> 00:43:55,330 only on the energy. 519 00:43:55,330 --> 00:43:57,910 And that's why, when I put up those three different 520 00:43:57,910 --> 00:44:02,860 reactions, and we saw the signs could vary. 521 00:44:02,860 --> 00:44:05,370 It's because there's a balance between the two. 522 00:44:05,370 --> 00:44:09,650 Energy may be favoring reaction in one direction, 523 00:44:09,650 --> 00:44:13,480 toward let's say products that have lower energy. 524 00:44:13,480 --> 00:44:17,080 But at the same time, entropy is going to be favoring 525 00:44:17,080 --> 00:44:22,020 whichever side has higher entropy, has more disorder, 526 00:44:22,020 --> 00:44:26,810 and there's a balance that's achieved. 527 00:44:26,810 --> 00:44:30,510 And that's why all those reactions, first of all, in 528 00:44:30,510 --> 00:44:34,400 some sense what I put up was kind of a trivial statement in 529 00:44:34,400 --> 00:44:39,630 actual fact saying they all happen spontaneously, because 530 00:44:39,630 --> 00:44:43,630 I didn't specify what we were starting with exactly, what 531 00:44:43,630 --> 00:44:45,410 concentrations we were starting with. 532 00:44:45,410 --> 00:44:47,890 Even something quite unfavorable might happen at 533 00:44:47,890 --> 00:44:49,540 least a little bit spontaneously. 534 00:44:49,540 --> 00:44:51,150 You'll have equilibrium. 535 00:44:51,150 --> 00:44:53,980 In those cases, though, you'd have quite a reasonable 536 00:44:53,980 --> 00:44:56,550 equilibrium, spontaneously, that is there would be a lot 537 00:44:56,550 --> 00:45:00,060 of reaction that went if you simply started under practical 538 00:45:00,060 --> 00:45:03,390 conditions and let it go. 539 00:45:03,390 --> 00:45:06,820 Even though the signs of the enthalpy changed, and the 540 00:45:06,820 --> 00:45:10,430 signs of the entropy changed because it's a combination of 541 00:45:10,430 --> 00:45:11,990 the two that matters. 542 00:45:11,990 --> 00:45:14,840 Here's a really simple example. 543 00:45:14,840 --> 00:45:19,440 Mixing of oil and water. 544 00:45:19,440 --> 00:45:22,230 You know from experience if you've ever mixed them to make 545 00:45:22,230 --> 00:45:25,740 salad dressing, they don't mix too well. 546 00:45:25,740 --> 00:45:28,850 And you may know that if you heat them up, 547 00:45:28,850 --> 00:45:33,930 they mix much better. 548 00:45:33,930 --> 00:45:35,550 Why? 549 00:45:35,550 --> 00:45:39,550 You know, we've done a bunch of thermochemistry, and we've 550 00:45:39,550 --> 00:45:44,050 kind of seen that the energy of mixing, your energetics 551 00:45:44,050 --> 00:45:48,890 don't change too much as a function of temperature. 552 00:45:48,890 --> 00:45:49,820 What's changing? 553 00:45:49,820 --> 00:45:56,250 Why does it mix better when you warm it up? 554 00:45:56,250 --> 00:46:00,150 But, you know, looking at our definition of Gibbs free 555 00:46:00,150 --> 00:46:09,070 energy, here it is, right, or here. 556 00:46:09,070 --> 00:46:13,500 Let me just say, actually if you calculated delta S for the 557 00:46:13,500 --> 00:46:17,450 mixing as a function of temperature, it doesn't change 558 00:46:17,450 --> 00:46:18,500 all that much. 559 00:46:18,500 --> 00:46:21,180 You know, the amount of disorder upon mixing is not 560 00:46:21,180 --> 00:46:22,860 really sensitive to temperature. 561 00:46:22,860 --> 00:46:27,320 What does change though? 562 00:46:27,320 --> 00:46:33,500 T, and the entropy is weighted by the temperature, so the 563 00:46:33,500 --> 00:46:38,850 entropy matters more and more the hotter it gets. 564 00:46:38,850 --> 00:46:40,480 And that's consistent with other things 565 00:46:40,480 --> 00:46:41,650 that we've seen, right? 566 00:46:41,650 --> 00:46:44,400 Remember the whole thing about the perfect crystal at zero 567 00:46:44,400 --> 00:46:48,490 degrees Kelvin has zero entropy. 568 00:46:48,490 --> 00:46:49,610 It's completely ordered. 569 00:46:49,610 --> 00:46:51,150 Entropy doesn't matter anymore. 570 00:46:51,150 --> 00:46:55,580 It'll go to the lowest energy state. 571 00:46:55,580 --> 00:47:03,660 Raise the temperature, and now entropy plays a bigger role. 572 00:47:03,660 --> 00:47:07,990 So the point is, this balance between energy that you could 573 00:47:07,990 --> 00:47:12,190 think of as say bond energies in chemical reactions, and 574 00:47:12,190 --> 00:47:15,420 entropy that you can think of in terms of disorder, how many 575 00:47:15,420 --> 00:47:18,700 different possible combinations or configurations 576 00:47:18,700 --> 00:47:21,290 of something wrong, will dictate where 577 00:47:21,290 --> 00:47:22,830 the equilibrium lies. 578 00:47:22,830 --> 00:47:26,630 And knowing now how to calculate these free energies 579 00:47:26,630 --> 00:47:29,580 especially the Helmholtz and the Gibbs free energies, 580 00:47:29,580 --> 00:47:32,760 that's what's going to guide us in really calculating 581 00:47:32,760 --> 00:47:37,750 quantitatively, OK, where will equilibrium lie. 582 00:47:37,750 --> 00:47:42,490 And before long, we'll start in on discussing chemical 583 00:47:42,490 --> 00:47:46,810 equilibrium, does deriving where they lie phase 584 00:47:46,810 --> 00:47:47,490 equilibrium? 585 00:47:47,490 --> 00:47:50,570 Does stuff change phase to go from liquid to solid and so 586 00:47:50,570 --> 00:47:51,620 forth, right? 587 00:47:51,620 --> 00:47:54,960 And where does that happen, at what temperature and pressure 588 00:47:54,960 --> 00:47:56,530 and so forth. 589 00:47:56,530 --> 00:48:01,590 And it's always going to come down to calculating the 590 00:48:01,590 --> 00:48:05,900 appropriate free energy, and how it changes in the process. 591 00:48:05,900 --> 00:48:09,230 So this is going to be a guide for us for essentially all 592 00:48:09,230 --> 00:48:11,760 that we're going to do in the rest of the term.