WEBVTT 00:00:00.000 --> 00:00:02.420 align:middle line:84% The following content is provided under a Creative 00:00:02.420 --> 00:00:03.600 align:middle line:90% Commons license. 00:00:03.600 --> 00:00:06.050 align:middle line:84% Your support will help MIT OpenCourseWare 00:00:06.050 --> 00:00:09.650 align:middle line:84% continue to offer high quality educational resources for free. 00:00:09.650 --> 00:00:12.620 align:middle line:84% To make a donation or to view additional materials 00:00:12.620 --> 00:00:16.070 align:middle line:84% from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:16.070 --> 00:00:17.270 align:middle line:90% at ocw.mit.edu. 00:00:17.270 --> 00:00:20.555 align:middle line:90% 00:00:20.555 --> 00:00:23.300 align:middle line:84% GANG CHEN: I have a set of handouts. 00:00:23.300 --> 00:00:26.720 align:middle line:84% If you don't get a copy, it's all on the web. 00:00:26.720 --> 00:00:34.730 align:middle line:84% And if I do this well, every time you should get a handout. 00:00:34.730 --> 00:00:38.840 align:middle line:84% And my objective is for you to focus 00:00:38.840 --> 00:00:45.180 align:middle line:84% on listening and discussion, not to take notes. 00:00:45.180 --> 00:00:50.240 align:middle line:84% So it's a [? similar ?] handout, or you go-- 00:00:50.240 --> 00:00:50.815 align:middle line:90% it's online. 00:00:50.815 --> 00:00:55.750 align:middle line:90% 00:00:55.750 --> 00:01:02.440 align:middle line:84% It's an experimental course, the first time I'm offering it. 00:01:02.440 --> 00:01:11.690 align:middle line:84% So it has a special, say, 997 number, 6 units. 00:01:11.690 --> 00:01:16.090 align:middle line:84% If you look at the handout, if you print it out yesterday, 00:01:16.090 --> 00:01:21.130 align:middle line:84% I changed something and one of the changes is very important. 00:01:21.130 --> 00:01:26.230 align:middle line:84% This course will be pass fail basis. 00:01:26.230 --> 00:01:30.070 align:middle line:84% And what does it mean is if you are 00:01:30.070 --> 00:01:35.800 align:middle line:84% undergraduate student, for example, in course 2, 00:01:35.800 --> 00:01:41.740 align:middle line:84% pass fail could count for unrestricted elective. 00:01:41.740 --> 00:01:47.500 align:middle line:84% But it does not count for restricted elective. 00:01:47.500 --> 00:01:53.170 align:middle line:84% And if you are course 2a, it does not count 00:01:53.170 --> 00:01:58.090 align:middle line:90% for your concentration. 00:01:58.090 --> 00:02:01.690 align:middle line:84% And if you are a graduate student, 00:02:01.690 --> 00:02:05.710 align:middle line:84% this is another entry level course. 00:02:05.710 --> 00:02:08.229 align:middle line:90% It's not an entry level course. 00:02:08.229 --> 00:02:11.980 align:middle line:84% So those are just for your clarification. 00:02:11.980 --> 00:02:19.720 align:middle line:84% And if you look at the handout, the syllabus, what we will have 00:02:19.720 --> 00:02:22.720 align:middle line:90% is once a week at this time. 00:02:22.720 --> 00:02:27.880 align:middle line:90% And also, I have office hour. 00:02:27.880 --> 00:02:31.150 align:middle line:90% And I have volunteer TA. 00:02:31.150 --> 00:02:32.860 align:middle line:90% Daniel is here. 00:02:32.860 --> 00:02:36.460 align:middle line:84% You can contact him if you have questions. 00:02:36.460 --> 00:02:41.470 align:middle line:84% If necessary, we'll ask Daniel also set up an office hour. 00:02:41.470 --> 00:02:44.660 align:middle line:90% And what else? 00:02:44.660 --> 00:02:48.360 align:middle line:90% I don't have a copy in my hand. 00:02:48.360 --> 00:02:48.860 align:middle line:90% Thank you. 00:02:48.860 --> 00:02:56.800 align:middle line:84% In terms of the requirement homework, 00:02:56.800 --> 00:03:03.560 align:middle line:84% the homework is every week I will assign one reading. 00:03:03.560 --> 00:03:07.520 align:middle line:84% And you will turn in your report, one page 00:03:07.520 --> 00:03:10.820 align:middle line:90% summary of the reading. 00:03:10.820 --> 00:03:14.870 align:middle line:84% You can summarize what you understand, 00:03:14.870 --> 00:03:17.090 align:middle line:90% what you do not understand. 00:03:17.090 --> 00:03:20.570 align:middle line:90% And that's the-- 00:03:20.570 --> 00:03:24.370 align:middle line:84% I do not see will give an extra number of homeworks. 00:03:24.370 --> 00:03:27.200 align:middle line:84% So it's a reading based homework. 00:03:27.200 --> 00:03:31.730 align:middle line:84% And at the end of the semester, you 00:03:31.730 --> 00:03:35.870 align:middle line:84% will write a final report, project report. 00:03:35.870 --> 00:03:39.800 align:middle line:84% And the detail of the report will answer 00:03:39.800 --> 00:03:42.085 align:middle line:90% in the middle of the semester. 00:03:42.085 --> 00:03:44.840 align:middle line:90% 00:03:44.840 --> 00:03:46.050 align:middle line:90% Any questions? 00:03:46.050 --> 00:03:49.320 align:middle line:90% 00:03:49.320 --> 00:03:52.800 align:middle line:90% OK if not, I will start. 00:03:52.800 --> 00:03:58.830 align:middle line:84% Like I said already, everything is online. 00:03:58.830 --> 00:04:03.070 align:middle line:84% And you can jot down whatever notes you want. 00:04:03.070 --> 00:04:07.480 align:middle line:84% But my purpose is not to have you write too much 00:04:07.480 --> 00:04:09.690 align:middle line:90% and focus on this. 00:04:09.690 --> 00:04:12.960 align:middle line:84% I do not have a textbook on this. 00:04:12.960 --> 00:04:14.560 align:middle line:90% So let me start. 00:04:14.560 --> 00:04:17.040 align:middle line:84% So this course, if you look at the title, 00:04:17.040 --> 00:04:22.590 align:middle line:84% is a direct solar thermal to electric energy conversion 00:04:22.590 --> 00:04:23.730 align:middle line:90% technologies. 00:04:23.730 --> 00:04:27.810 align:middle line:84% There are few points I want to emphasize. 00:04:27.810 --> 00:04:31.980 align:middle line:90% One is a heat-based course. 00:04:31.980 --> 00:04:37.380 align:middle line:84% Solar thermal, this is all focused on the thermal aspect. 00:04:37.380 --> 00:04:40.500 align:middle line:84% The solar energy is, in this course, 00:04:40.500 --> 00:04:43.380 align:middle line:90% is a big, giant heat source. 00:04:43.380 --> 00:04:47.910 align:middle line:84% And the other aspect important in this course 00:04:47.910 --> 00:04:51.220 align:middle line:90% is the direct energy conversion. 00:04:51.220 --> 00:04:54.730 align:middle line:84% So the focus is on how to convert 00:04:54.730 --> 00:04:57.880 align:middle line:84% the heat into electricity directly 00:04:57.880 --> 00:05:00.340 align:middle line:90% without the moving parts. 00:05:00.340 --> 00:05:07.330 align:middle line:84% And when I say the technology, you realize that we move on. 00:05:07.330 --> 00:05:11.980 align:middle line:84% Those technologies, some already existing. 00:05:11.980 --> 00:05:16.330 align:middle line:84% But clearly is not widely spread used. 00:05:16.330 --> 00:05:19.270 align:middle line:90% It's not widely used. 00:05:19.270 --> 00:05:23.230 align:middle line:84% So they are still under development. 00:05:23.230 --> 00:05:27.550 align:middle line:84% And whether they will work out or not down 00:05:27.550 --> 00:05:30.880 align:middle line:90% the road is not completely sure. 00:05:30.880 --> 00:05:33.070 align:middle line:90% But that's your opportunity. 00:05:33.070 --> 00:05:37.210 align:middle line:84% You're here to do research and future development. 00:05:37.210 --> 00:05:43.420 align:middle line:84% And maybe you will push some of this technology to real world. 00:05:43.420 --> 00:05:48.490 align:middle line:84% So I will start with this slide to make 00:05:48.490 --> 00:05:54.100 align:middle line:84% a case that it's important that we think about the heat. 00:05:54.100 --> 00:05:57.880 align:middle line:84% You can start either from the input side, 00:05:57.880 --> 00:06:01.750 align:middle line:84% look at how we are using all the energy. 00:06:01.750 --> 00:06:06.250 align:middle line:84% Fossil fuel or even nuclear, the energy source 00:06:06.250 --> 00:06:09.640 align:middle line:84% from the energy source to convert this energy 00:06:09.640 --> 00:06:13.160 align:middle line:84% into electricity, into mechanical energy. 00:06:13.160 --> 00:06:20.770 align:middle line:84% You can see more than 90% is [? VIP. ?] Mostly is 00:06:20.770 --> 00:06:23.440 align:middle line:84% thermal mechanical means to convert 00:06:23.440 --> 00:06:31.570 align:middle line:84% the energy into mechanical energy or electrical energy. 00:06:31.570 --> 00:06:37.130 align:middle line:84% And the other aspect is look at the end 00:06:37.130 --> 00:06:41.080 align:middle line:90% use, how much energy is lost. 00:06:41.080 --> 00:06:45.520 align:middle line:84% And you can only see the numbers here. 00:06:45.520 --> 00:06:50.050 align:middle line:84% You'll find out that more than 60, about 60% to 70% 00:06:50.050 --> 00:06:53.490 align:middle line:90% of the energy are wasted. 00:06:53.490 --> 00:06:57.540 align:middle line:84% So what are we are looking into is 00:06:57.540 --> 00:07:01.380 align:middle line:84% whether we can develop alternative ways 00:07:01.380 --> 00:07:07.980 align:middle line:84% to either use the input energy or convert some of the waste 00:07:07.980 --> 00:07:10.551 align:middle line:90% energy into electricity. 00:07:10.551 --> 00:07:13.580 align:middle line:90% 00:07:13.580 --> 00:07:14.080 align:middle line:90% Yes. 00:07:14.080 --> 00:07:16.960 align:middle line:90% 00:07:16.960 --> 00:07:22.610 align:middle line:84% STUDENT: Are there 10% missing or [INAUDIBLE] 00:07:22.610 --> 00:07:26.125 align:middle line:84% GANG CHEN: 10% missing, you have to look at some of this in here. 00:07:26.125 --> 00:07:35.640 align:middle line:90% 00:07:35.640 --> 00:07:37.230 align:middle line:84% We're talking about heat sources. 00:07:37.230 --> 00:07:39.210 align:middle line:90% Just a few examples. 00:07:39.210 --> 00:07:44.760 align:middle line:84% If you look at the automobile, the driving efficiency 00:07:44.760 --> 00:07:48.820 align:middle line:84% as a measurement is less than 20%. 00:07:48.820 --> 00:07:53.700 align:middle line:84% And if you want to remember, it's easy to say about one third 00:07:53.700 --> 00:07:59.220 align:middle line:84% of the energy goes through the tailpipe exhaust. 00:07:59.220 --> 00:08:04.320 align:middle line:84% The other third roughly goes to the radiator. 00:08:04.320 --> 00:08:07.650 align:middle line:90% Those are completed with-- 00:08:07.650 --> 00:08:12.210 align:middle line:84% so can we recover some of this energy? 00:08:12.210 --> 00:08:16.950 align:middle line:84% And in fact, this is challenging because it's a model. 00:08:16.950 --> 00:08:21.210 align:middle line:84% You have to feed into the compact systems. 00:08:21.210 --> 00:08:27.520 align:middle line:84% And in those cases, it turns out people look at various options 00:08:27.520 --> 00:08:31.860 align:middle line:84% by say the mechanical way of converting 00:08:31.860 --> 00:08:35.770 align:middle line:84% those energy into electricity is not very feasible. 00:08:35.770 --> 00:08:38.730 align:middle line:84% So there are a lot of companies looking into thermoelectric, 00:08:38.730 --> 00:08:41.600 align:middle line:90% for example. 00:08:41.600 --> 00:08:49.820 align:middle line:84% And now you look at another way that we use energy is buildings. 00:08:49.820 --> 00:08:52.020 align:middle line:90% And give me an example. 00:08:52.020 --> 00:08:57.110 align:middle line:84% In New England in the winter, home furnace, boilers, 00:08:57.110 --> 00:08:59.240 align:middle line:90% most of the time they are off. 00:08:59.240 --> 00:09:01.490 align:middle line:90% Very often, they are on. 00:09:01.490 --> 00:09:04.970 align:middle line:84% And there's a combustion process. 00:09:04.970 --> 00:09:08.630 align:middle line:84% And [INAUDIBLE] what we're using for-- 00:09:08.630 --> 00:09:12.240 align:middle line:90% hot shower, heat up the room. 00:09:12.240 --> 00:09:15.200 align:middle line:90% That's a low quality source. 00:09:15.200 --> 00:09:16.790 align:middle line:84% Once you switch to this temperature, 00:09:16.790 --> 00:09:19.850 align:middle line:84% you have high temperature combustion. 00:09:19.850 --> 00:09:24.590 align:middle line:84% You quench to low temperature just take a shower. 00:09:24.590 --> 00:09:28.970 align:middle line:84% And you are generating a lot of entropy. 00:09:28.970 --> 00:09:34.370 align:middle line:84% And in some regions, there are big coal fired power plant 00:09:34.370 --> 00:09:37.130 align:middle line:90% or oil fired power plant. 00:09:37.130 --> 00:09:40.250 align:middle line:84% In this case, the people take the steam 00:09:40.250 --> 00:09:43.910 align:middle line:84% and supply the heat to the community. 00:09:43.910 --> 00:09:48.680 align:middle line:84% That's electricity, heat cogeneration, cogen plant. 00:09:48.680 --> 00:09:52.040 align:middle line:90% But we don't do this at home. 00:09:52.040 --> 00:09:55.310 align:middle line:90% The technology is not there yet. 00:09:55.310 --> 00:09:57.150 align:middle line:84% People are still-- people are pushing. 00:09:57.150 --> 00:10:02.160 align:middle line:84% And in fact, there is a, say, [? Honda, ?] is fighting, 00:10:02.160 --> 00:10:06.630 align:middle line:84% for example, developing home stand-alone internal combustion 00:10:06.630 --> 00:10:09.360 align:middle line:90% based system. 00:10:09.360 --> 00:10:12.980 align:middle line:84% But it's still not taking advantage. 00:10:12.980 --> 00:10:15.530 align:middle line:84% During the combustion, during the heat 00:10:15.530 --> 00:10:18.530 align:middle line:84% of the hot water process, we are really 00:10:18.530 --> 00:10:20.430 align:middle line:90% generating a lot of entropy. 00:10:20.430 --> 00:10:24.020 align:middle line:90% We are wasting useful energy. 00:10:24.020 --> 00:10:30.600 align:middle line:84% Can we develop technologies that can do home cogeneration? 00:10:30.600 --> 00:10:34.700 align:middle line:90% 00:10:34.700 --> 00:10:38.810 align:middle line:84% Industrial process, that's about another third 00:10:38.810 --> 00:10:41.780 align:middle line:90% of the energy that's used. 00:10:41.780 --> 00:10:46.070 align:middle line:84% And their heat sources are different temperature, 00:10:46.070 --> 00:10:48.230 align:middle line:90% where wide temperature range. 00:10:48.230 --> 00:10:52.010 align:middle line:84% Once I visited the aluminum smelting plant. 00:10:52.010 --> 00:10:58.790 align:middle line:84% So that's just converting aluminum oxide into aluminum. 00:10:58.790 --> 00:11:02.750 align:middle line:84% And the process is a high temperature electrochemical 00:11:02.750 --> 00:11:03.890 align:middle line:90% process. 00:11:03.890 --> 00:11:08.420 align:middle line:84% So you heat up aluminum oxide to molten state. 00:11:08.420 --> 00:11:11.300 align:middle line:84% And then you use a electrochemical way 00:11:11.300 --> 00:11:14.600 align:middle line:90% to extract the aluminum. 00:11:14.600 --> 00:11:17.330 align:middle line:84% And those plants are typically built just 00:11:17.330 --> 00:11:21.350 align:middle line:84% beside power plants, the electrical power plants. 00:11:21.350 --> 00:11:22.770 align:middle line:90% They travel the highways. 00:11:22.770 --> 00:11:25.795 align:middle line:84% There's a 500 megawatt electrical input. 00:11:25.795 --> 00:11:28.550 align:middle line:90% 00:11:28.550 --> 00:11:32.190 align:middle line:84% That's a huge power generation, power requirement. 00:11:32.190 --> 00:11:36.450 align:middle line:84% Just give you an example, how much is a 500 megawatt? 00:11:36.450 --> 00:11:41.850 align:middle line:84% A typical power plant is about a one gigawatt. 00:11:41.850 --> 00:11:45.690 align:middle line:84% And the world solar installation, 00:11:45.690 --> 00:11:52.000 align:middle line:84% solar photovoltaic installation, it's about six gigawatts. 00:11:52.000 --> 00:11:57.070 align:middle line:84% So one power plant, one aluminum smelting plant, 00:11:57.070 --> 00:11:59.410 align:middle line:90% takes 500 megawatt. 00:11:59.410 --> 00:12:02.530 align:middle line:84% And, of course, there is a part of this aluminum 00:12:02.530 --> 00:12:06.700 align:middle line:84% oxide to aluminum energy stored as chemical energy. 00:12:06.700 --> 00:12:14.040 align:middle line:84% But the half of this is dumped into our environment as heat. 00:12:14.040 --> 00:12:19.740 align:middle line:84% And right now there's no technology to really recoup this 00:12:19.740 --> 00:12:22.920 align:middle line:90% into anything useful. 00:12:22.920 --> 00:12:33.010 align:middle line:84% So now, you think about this is a waste heat, renewables. 00:12:33.010 --> 00:12:35.920 align:middle line:84% When we think about the photovoltaic solar, 00:12:35.920 --> 00:12:38.620 align:middle line:84% we often think about photovoltaic. 00:12:38.620 --> 00:12:44.670 align:middle line:84% But fundamentally, solar is a high temperature heat source. 00:12:44.670 --> 00:12:47.220 align:middle line:84% Anyone knows the equivalent temperature 00:12:47.220 --> 00:12:50.730 align:middle line:84% of the solar radiation coming to Earth? 00:12:50.730 --> 00:12:52.110 align:middle line:90% STUDENT: 20,000. 00:12:52.110 --> 00:12:52.950 align:middle line:90% GANG CHEN: Close. 00:12:52.950 --> 00:12:56.285 align:middle line:90% STUDENT: 7, 5, 7,000 kelvin. 00:12:56.285 --> 00:13:02.820 align:middle line:90% GANG CHEN: 6,000 kelvin, 5,800. 00:13:02.820 --> 00:13:03.990 align:middle line:90% And geothermal. 00:13:03.990 --> 00:13:05.050 align:middle line:90% Those are renewable. 00:13:05.050 --> 00:13:07.500 align:middle line:90% Those are heat sources. 00:13:07.500 --> 00:13:13.390 align:middle line:90% So how we can use as a heat? 00:13:13.390 --> 00:13:16.320 align:middle line:84% And in fact, if you look at how people, what people 00:13:16.320 --> 00:13:21.840 align:middle line:84% are doing now, the solar utilization, 00:13:21.840 --> 00:13:25.950 align:middle line:84% the biggest installation is in solar water, 00:13:25.950 --> 00:13:29.460 align:middle line:84% not in [INAUDIBLE], just hot water. 00:13:29.460 --> 00:13:33.240 align:middle line:90% And I came from China. 00:13:33.240 --> 00:13:35.350 align:middle line:84% When I grew up, there was no hot water. 00:13:35.350 --> 00:13:36.850 align:middle line:90% [INAUDIBLE] didn't sell them. 00:13:36.850 --> 00:13:38.010 align:middle line:90% I take a shower. 00:13:38.010 --> 00:13:40.290 align:middle line:90% No water in the winter. 00:13:40.290 --> 00:13:46.050 align:middle line:84% And nowadays when I go back home, we have solar hot water. 00:13:46.050 --> 00:13:50.700 align:middle line:84% And it was a really fundamental life changing technology, 00:13:50.700 --> 00:13:52.290 align:middle line:90% very cheap. 00:13:52.290 --> 00:13:54.480 align:middle line:90% But it's actually high-tech. 00:13:54.480 --> 00:14:00.540 align:middle line:84% So here I'm showing the solar hot water system 00:14:00.540 --> 00:14:03.120 align:middle line:90% that's widely used in China. 00:14:03.120 --> 00:14:06.480 align:middle line:84% And give us a order of magnitude, 00:14:06.480 --> 00:14:12.030 align:middle line:84% it's about 100,000,000 square meter installation. 00:14:12.030 --> 00:14:14.100 align:middle line:90% 100,000,000 square meter. 00:14:14.100 --> 00:14:16.500 align:middle line:84% And if you take 100,000,000 square meter, 00:14:16.500 --> 00:14:18.790 align:middle line:90% you take a solar energy. 00:14:18.790 --> 00:14:22.710 align:middle line:84% One square meter is about one kilowatt. 00:14:22.710 --> 00:14:28.220 align:middle line:84% And thermal efficiency, they collect the heat around 60%. 00:14:28.220 --> 00:14:30.540 align:middle line:90% So you multiply this together. 00:14:30.540 --> 00:14:31.470 align:middle line:90% How much you get? 00:14:31.470 --> 00:14:39.920 align:middle line:84% You get about 60 gigawatt solar energy being used. 00:14:39.920 --> 00:14:47.330 align:middle line:84% And I said as a high-tech, this is a [INAUDIBLE] tube-- 00:14:47.330 --> 00:14:48.980 align:middle line:90% vacuum tube. 00:14:48.980 --> 00:14:52.190 align:middle line:84% And so there is an inner layer, outer layer. 00:14:52.190 --> 00:14:54.830 align:middle line:90% And in between is a vacuum tube. 00:14:54.830 --> 00:15:00.650 align:middle line:84% And in the inner layer tube, there's a coating. 00:15:00.650 --> 00:15:04.460 align:middle line:84% This coating will absorb the solar radiation, 00:15:04.460 --> 00:15:08.120 align:middle line:84% but the minimize the thermal radiation. 00:15:08.120 --> 00:15:11.120 align:middle line:90% And it's done very cheaply. 00:15:11.120 --> 00:15:17.240 align:middle line:84% In a typical tube like this high, it's only-- 00:15:17.240 --> 00:15:21.500 align:middle line:84% I waste of the ones that are factory, $1.5 a tube, 00:15:21.500 --> 00:15:25.050 align:middle line:90% [INAUDIBLE], all manufactured. 00:15:25.050 --> 00:15:28.260 align:middle line:84% So because of the really the low cost, 00:15:28.260 --> 00:15:32.270 align:middle line:84% it's widely used in developing countries. 00:15:32.270 --> 00:15:36.090 align:middle line:84% And of course, you can talk about the electrical generation. 00:15:36.090 --> 00:15:39.230 align:middle line:90% 00:15:39.230 --> 00:15:43.340 align:middle line:84% This is their installation in US Kramer Junction, where 00:15:43.340 --> 00:15:50.270 align:middle line:84% the heat from the sun is a focus through those parabolic troughs. 00:15:50.270 --> 00:15:51.650 align:middle line:90% Heat up the fluids. 00:15:51.650 --> 00:15:56.620 align:middle line:84% And these fluids are used to drive steam turbines. 00:15:56.620 --> 00:16:01.060 align:middle line:84% And there are also the power system 00:16:01.060 --> 00:16:04.280 align:middle line:90% that people are developing. 00:16:04.280 --> 00:16:09.280 align:middle line:84% Some are used in Spain, and I think also Algeria, 00:16:09.280 --> 00:16:14.440 align:middle line:84% where the mirrors focus and heat up the power here. 00:16:14.440 --> 00:16:16.750 align:middle line:84% And this goes to a higher temperature. 00:16:16.750 --> 00:16:21.860 align:middle line:84% And the conversion is we have mechanical systems. 00:16:21.860 --> 00:16:25.970 align:middle line:84% And the question, [INAUDIBLE] here in this course will not-- 00:16:25.970 --> 00:16:29.150 align:middle line:84% as I said, we're not looking into mechanical energy 00:16:29.150 --> 00:16:30.020 align:middle line:90% conversion. 00:16:30.020 --> 00:16:33.520 align:middle line:90% We're looking into alternatives. 00:16:33.520 --> 00:16:36.070 align:middle line:90% And I just want-- 00:16:36.070 --> 00:16:40.210 align:middle line:84% so some of those alternatives that we're going to discuss, 00:16:40.210 --> 00:16:43.210 align:middle line:90% one is a thermoelectric. 00:16:43.210 --> 00:16:48.040 align:middle line:90% In fact, Daniel, does that work? 00:16:48.040 --> 00:16:49.780 align:middle line:90% If you can turn it on. 00:16:49.780 --> 00:16:54.130 align:middle line:84% So you will see that this is a conversion 00:16:54.130 --> 00:16:57.130 align:middle line:84% that, as long as there's a temperature difference, 00:16:57.130 --> 00:16:59.120 align:middle line:90% you can generate electricity. 00:16:59.120 --> 00:17:00.820 align:middle line:90% It's by solid. 00:17:00.820 --> 00:17:05.829 align:middle line:84% If you have used thermocouples, those are essentially 00:17:05.829 --> 00:17:08.720 align:middle line:90% thermocouples putting together. 00:17:08.720 --> 00:17:10.780 align:middle line:84% Thermocouple, of course, we just want 00:17:10.780 --> 00:17:13.359 align:middle line:84% to generate an electrical signal. 00:17:13.359 --> 00:17:19.210 align:middle line:84% But in this case, you can also, if you make the efficient, 00:17:19.210 --> 00:17:24.030 align:middle line:84% you convert heat into electricity. 00:17:24.030 --> 00:17:32.520 align:middle line:84% The second-- here, the working fluids is electron. 00:17:32.520 --> 00:17:37.300 align:middle line:84% And in this demo, what we have is just a copper. 00:17:37.300 --> 00:17:38.250 align:middle line:90% Here is a heat source. 00:17:38.250 --> 00:17:41.070 align:middle line:84% Copper coming out heat to this side. 00:17:41.070 --> 00:17:42.690 align:middle line:90% The top side is hot. 00:17:42.690 --> 00:17:46.180 align:middle line:84% And there is this thermoelectric device, very thin. 00:17:46.180 --> 00:17:49.350 align:middle line:84% It's about two millimeter, three millimeter sandwiched 00:17:49.350 --> 00:17:54.900 align:middle line:84% between this copper and the heatsink, aluminum block. 00:17:54.900 --> 00:17:56.560 align:middle line:90% And hopefully I don't see it. 00:17:56.560 --> 00:18:00.030 align:middle line:84% But once the temperature difference, there a difference, 00:18:00.030 --> 00:18:06.210 align:middle line:84% you'll start to see the LEDs lighting up. 00:18:06.210 --> 00:18:10.740 align:middle line:84% So that's direct, no moving parts, using electronics 00:18:10.740 --> 00:18:13.020 align:middle line:90% as working fluids. 00:18:13.020 --> 00:18:16.840 align:middle line:84% And the second example is thermionic energy conversion. 00:18:16.840 --> 00:18:19.880 align:middle line:90% 00:18:19.880 --> 00:18:22.730 align:middle line:84% How many of you know that in our department 00:18:22.730 --> 00:18:25.740 align:middle line:84% there is a microfluidic catabolism plant? 00:18:25.740 --> 00:18:28.270 align:middle line:90% 00:18:28.270 --> 00:18:29.230 align:middle line:90% Fabulous. 00:18:29.230 --> 00:18:33.940 align:middle line:84% That's on the second building 3, second floor. 00:18:33.940 --> 00:18:38.080 align:middle line:84% [INAUDIBLE] was a professor in the mechanical engineering 00:18:38.080 --> 00:18:41.470 align:middle line:90% department, 1950s. 00:18:41.470 --> 00:18:46.420 align:middle line:84% And he developed this thermionic engine. 00:18:46.420 --> 00:18:50.055 align:middle line:90% So you can see it lighting up. 00:18:50.055 --> 00:18:53.440 align:middle line:84% And of course, you have to maintain this temperature 00:18:53.440 --> 00:18:53.990 align:middle line:90% difference. 00:18:53.990 --> 00:18:56.800 align:middle line:84% So if we burn it for a long time, the other side, 00:18:56.800 --> 00:18:59.690 align:middle line:90% the cooling is not there. 00:18:59.690 --> 00:19:02.330 align:middle line:84% The temperature difference will be becomes small. 00:19:02.330 --> 00:19:06.110 align:middle line:84% Your power, I saw it before, it actually fluctuated before. 00:19:06.110 --> 00:19:09.080 align:middle line:84% But this is also another important aspect. 00:19:09.080 --> 00:19:10.190 align:middle line:90% It's a thermal system. 00:19:10.190 --> 00:19:13.900 align:middle line:84% So you have to put the heat in, take the heat out. 00:19:13.900 --> 00:19:19.570 align:middle line:84% And the converter is small, but your thermal [? auxiliary ?] 00:19:19.570 --> 00:19:20.980 align:middle line:90% system may be very big. 00:19:20.980 --> 00:19:22.935 align:middle line:84% So you have to do a good engineering design. 00:19:22.935 --> 00:19:25.500 align:middle line:90% 00:19:25.500 --> 00:19:30.470 align:middle line:84% I was mentioning thermionic energy emission and energy 00:19:30.470 --> 00:19:31.550 align:middle line:90% conversion. 00:19:31.550 --> 00:19:35.780 align:middle line:84% And Professor [INAUDIBLE] started his PhD 00:19:35.780 --> 00:19:38.390 align:middle line:90% on thermionic engines. 00:19:38.390 --> 00:19:43.010 align:middle line:84% And it's been off thermo electron. 00:19:43.010 --> 00:19:47.090 align:middle line:84% If you drive 128, you probably see that [? component. ?] 00:19:47.090 --> 00:19:51.290 align:middle line:84% Thermo electron is called thermo feature. 00:19:51.290 --> 00:19:59.060 align:middle line:84% And the original purpose was to develop the thermionic engines. 00:19:59.060 --> 00:20:04.940 align:middle line:84% In fact, if you go to read it, it's 1956 or 58, I forgot. 00:20:04.940 --> 00:20:12.040 align:middle line:84% In the 1950s and 1960s, the efficiency was about 18% from 00:20:12.040 --> 00:20:12.780 align:middle line:90% heat [INAUDIBLE]. 00:20:12.780 --> 00:20:14.330 align:middle line:84% But it's a very high temperature. 00:20:14.330 --> 00:20:16.490 align:middle line:84% So there are a lot of technological difficulties 00:20:16.490 --> 00:20:19.370 align:middle line:84% and at the end they didn't pursue 00:20:19.370 --> 00:20:22.950 align:middle line:90% in terms of commercialization. 00:20:22.950 --> 00:20:27.000 align:middle line:84% Of course, photovoltaic, normally we 00:20:27.000 --> 00:20:30.060 align:middle line:84% don't think of it as a heat engine. 00:20:30.060 --> 00:20:32.670 align:middle line:90% But it is a heat engine. 00:20:32.670 --> 00:20:37.690 align:middle line:84% It's limited by the second law of thermodynamics. 00:20:37.690 --> 00:20:41.110 align:middle line:84% And in fact, any time we can get close to the second law, 00:20:41.110 --> 00:20:44.210 align:middle line:90% you'd be really happy. 00:20:44.210 --> 00:20:48.530 align:middle line:84% But see, this is, of course, using the photon from the sun. 00:20:48.530 --> 00:20:53.030 align:middle line:84% And there's another way is using the photon from a [INAUDIBLE] 00:20:53.030 --> 00:20:54.380 align:middle line:90% or a resource. 00:20:54.380 --> 00:20:56.330 align:middle line:90% You have a home furnace. 00:20:56.330 --> 00:20:59.340 align:middle line:84% And you can use the photon from there to put a photovoltaic. 00:20:59.340 --> 00:21:01.370 align:middle line:84% That's called a thermophotovoltaic. 00:21:01.370 --> 00:21:05.270 align:middle line:84% So those are all ways some of the direct energy 00:21:05.270 --> 00:21:10.250 align:middle line:84% conversion, no moving parts here is using the charge as a fluid. 00:21:10.250 --> 00:21:14.930 align:middle line:84% And we'll be talking some of those technologies 00:21:14.930 --> 00:21:17.060 align:middle line:90% and the basic principles. 00:21:17.060 --> 00:21:19.160 align:middle line:84% And of course, when we think about the solar, 00:21:19.160 --> 00:21:23.060 align:middle line:84% the advantage compare potential advantage-- 00:21:23.060 --> 00:21:25.640 align:middle line:84% doesn't say it's demonstrated fully yet-- 00:21:25.640 --> 00:21:28.820 align:middle line:84% is that in the case of photovoltaic, 00:21:28.820 --> 00:21:33.230 align:middle line:84% only the energy above the bandgap of semiconductor useful. 00:21:33.230 --> 00:21:35.270 align:middle line:84% But when you think about solar thermal, 00:21:35.270 --> 00:21:39.590 align:middle line:84% you can think about the full spectrum of the solar energy. 00:21:39.590 --> 00:21:48.050 align:middle line:84% So this year we started actually department energy center 00:21:48.050 --> 00:21:51.950 align:middle line:84% looking into how we can advance this technology. 00:21:51.950 --> 00:21:55.580 align:middle line:84% What is solar thermal photovoltaic? 00:21:55.580 --> 00:22:01.010 align:middle line:84% So here, the idea is I take the solar energy, absorb it. 00:22:01.010 --> 00:22:04.400 align:middle line:84% This is not directly onto photovoltaic cell. 00:22:04.400 --> 00:22:09.920 align:middle line:84% But they absorb it to heat up this and re-emit the photon. 00:22:09.920 --> 00:22:11.190 align:middle line:90% Why do you do that? 00:22:11.190 --> 00:22:12.920 align:middle line:84% Because when you re-emit the photon, 00:22:12.920 --> 00:22:15.150 align:middle line:84% if you can do better control, you 00:22:15.150 --> 00:22:17.940 align:middle line:84% can emit photons right at the bandgap 00:22:17.940 --> 00:22:20.100 align:middle line:90% of the photovoltaic cell. 00:22:20.100 --> 00:22:23.160 align:middle line:84% And theory says you can potentially 00:22:23.160 --> 00:22:27.450 align:middle line:84% get a really high efficiency with a single junction 00:22:27.450 --> 00:22:31.390 align:middle line:90% cell, but no demonstration. 00:22:31.390 --> 00:22:36.070 align:middle line:84% So that's one of the direction we're looking in this center. 00:22:36.070 --> 00:22:40.480 align:middle line:84% And the other direction is looking into thermoelectric, 00:22:40.480 --> 00:22:42.550 align:middle line:90% just like what we have here. 00:22:42.550 --> 00:22:46.600 align:middle line:84% The temperature difference, instead of the burner here, 00:22:46.600 --> 00:22:50.140 align:middle line:84% using this anytime you have temperature difference. 00:22:50.140 --> 00:22:54.880 align:middle line:84% And again, the k is how we can make this efficient, 00:22:54.880 --> 00:22:57.760 align:middle line:90% how we can make that low cost. 00:22:57.760 --> 00:23:02.950 align:middle line:84% So when you think about energy, the cost is the main concern. 00:23:02.950 --> 00:23:06.440 align:middle line:84% The photovoltaic cost right now is just too high. 00:23:06.440 --> 00:23:12.190 align:middle line:84% So most people are reluctant to put on their rooftop. 00:23:12.190 --> 00:23:19.160 align:middle line:84% So that's the motivations for this course. 00:23:19.160 --> 00:23:22.990 align:middle line:84% And to really understand those technology, 00:23:22.990 --> 00:23:26.380 align:middle line:84% we'll have to dive into, for some of us-- 00:23:26.380 --> 00:23:32.830 align:middle line:84% [INAUDIBLE] For some of us, this may be unfamiliar, 00:23:32.830 --> 00:23:36.400 align:middle line:84% territory, particularly, I think for mechanical engineers, 00:23:36.400 --> 00:23:44.050 align:middle line:84% because most of the time, we are familiar with heat engines 00:23:44.050 --> 00:23:47.620 align:middle line:90% using steam, using molecules. 00:23:47.620 --> 00:23:51.370 align:middle line:84% And here we're talking about heat engine 00:23:51.370 --> 00:23:54.970 align:middle line:90% using electrons and solid. 00:23:54.970 --> 00:24:00.430 align:middle line:84% So we'll have to cover some of the basic background 00:24:00.430 --> 00:24:04.060 align:middle line:84% knowledge in this area and understand the technology, 00:24:04.060 --> 00:24:08.590 align:middle line:84% understand the limitations, and I 00:24:08.590 --> 00:24:10.830 align:middle line:84% want to bring you to the forefront of research. 00:24:10.830 --> 00:24:12.760 align:middle line:90% What are people doing? 00:24:12.760 --> 00:24:16.390 align:middle line:84% Maybe you have new ideas in doing new things. 00:24:16.390 --> 00:24:20.110 align:middle line:84% Now, just make another comment, this is very different. 00:24:20.110 --> 00:24:25.200 align:middle line:84% You can say the dying down process is slow. 00:24:25.200 --> 00:24:29.220 align:middle line:84% Thermal has a potential to do storage. 00:24:29.220 --> 00:24:33.150 align:middle line:84% With a thermal mass, you can store the energy. 00:24:33.150 --> 00:24:35.700 align:middle line:84% A photovoltaic will take if there's no light emitted, 00:24:35.700 --> 00:24:37.710 align:middle line:90% don't have any power in it. 00:24:37.710 --> 00:24:42.320 align:middle line:84% So that's one potential advantage of thinking thermal. 00:24:42.320 --> 00:24:45.390 align:middle line:90% 00:24:45.390 --> 00:24:49.380 align:middle line:84% OK, so now I'm going to move into really-- 00:24:49.380 --> 00:24:51.840 align:middle line:84% the first what I want to use here 00:24:51.840 --> 00:24:59.580 align:middle line:84% is to review some thermodynamics and the heat transfer. 00:24:59.580 --> 00:25:04.260 align:middle line:84% And if you have taken thermodynamics, 00:25:04.260 --> 00:25:06.840 align:middle line:84% you will know some of the material. 00:25:06.840 --> 00:25:11.100 align:middle line:84% If you are from other department like physics, 00:25:11.100 --> 00:25:13.860 align:middle line:90% you also know some material. 00:25:13.860 --> 00:25:17.130 align:middle line:84% Most groups have some material, maybe enough material. 00:25:17.130 --> 00:25:20.160 align:middle line:84% But my advice is just to take it. 00:25:20.160 --> 00:25:22.650 align:middle line:84% This is, I would say this is my starting point 00:25:22.650 --> 00:25:25.820 align:middle line:90% for future discussions. 00:25:25.820 --> 00:25:29.685 align:middle line:84% So when we think about the first law, 00:25:29.685 --> 00:25:31.560 align:middle line:84% with thermodynamics we think about two laws-- 00:25:31.560 --> 00:25:34.430 align:middle line:84% First law of thermodynamics, second law of thermodynamics. 00:25:34.430 --> 00:25:41.240 align:middle line:84% We take a system and we define by defining the boundaries. 00:25:41.240 --> 00:25:45.030 align:middle line:84% So the boundary define our system. 00:25:45.030 --> 00:25:48.140 align:middle line:84% And across the boundary we have heat flow. 00:25:48.140 --> 00:25:49.820 align:middle line:90% We have work flow. 00:25:49.820 --> 00:25:57.050 align:middle line:84% And typical convention is that they say heat goes in. 00:25:57.050 --> 00:25:58.520 align:middle line:90% We take the positive. 00:25:58.520 --> 00:25:59.810 align:middle line:90% And work goes out. 00:25:59.810 --> 00:26:01.520 align:middle line:90% We take as a positive. 00:26:01.520 --> 00:26:03.330 align:middle line:90% That's just due to convention. 00:26:03.330 --> 00:26:06.320 align:middle line:84% If you get a negative sign, it means your heat goes out 00:26:06.320 --> 00:26:08.510 align:middle line:90% or work goes in. 00:26:08.510 --> 00:26:11.040 align:middle line:84% And then we have closed system means 00:26:11.040 --> 00:26:14.270 align:middle line:84% that there is no mass flow across the system boundary, 00:26:14.270 --> 00:26:18.980 align:middle line:84% or open system when there is a mass flow across system. 00:26:18.980 --> 00:26:22.580 align:middle line:84% In the simplest form of thermodynamics, 00:26:22.580 --> 00:26:27.770 align:middle line:84% the first law is just the energy balance. 00:26:27.770 --> 00:26:30.140 align:middle line:84% On the left hand side, I have the energy 00:26:30.140 --> 00:26:34.250 align:middle line:84% of the system, the energy change. 00:26:34.250 --> 00:26:37.460 align:middle line:84% And on the right hand side is the heat transfer 00:26:37.460 --> 00:26:40.820 align:middle line:84% into the system minus the work output. 00:26:40.820 --> 00:26:45.050 align:middle line:90% Simple energy balance. 00:26:45.050 --> 00:26:46.970 align:middle line:84% You can write it in the differential form 00:26:46.970 --> 00:26:49.250 align:middle line:84% or you can write into [INAUDIBLE] form. 00:26:49.250 --> 00:26:50.540 align:middle line:90% And then you do heat transfer. 00:26:50.540 --> 00:26:54.850 align:middle line:84% You actually use the [INAUDIBLE] form most often. 00:26:54.850 --> 00:26:58.420 align:middle line:84% See, some of you may still remember 00:26:58.420 --> 00:27:03.010 align:middle line:84% what's important is to recognize on the left hand 00:27:03.010 --> 00:27:08.170 align:middle line:84% side is a state property that does not depend on the process. 00:27:08.170 --> 00:27:11.660 align:middle line:84% On the right hand side is a process dependent. 00:27:11.660 --> 00:27:13.910 align:middle line:90% So it's actually very amazing. 00:27:13.910 --> 00:27:16.960 align:middle line:84% You take two process dependent quantity. 00:27:16.960 --> 00:27:18.280 align:middle line:90% You take a difference. 00:27:18.280 --> 00:27:22.280 align:middle line:84% You get a quantity that's independent of the process. 00:27:22.280 --> 00:27:23.450 align:middle line:90% Looks very simple. 00:27:23.450 --> 00:27:27.000 align:middle line:84% But this is a truly important aspect. 00:27:27.000 --> 00:27:29.870 align:middle line:90% 00:27:29.870 --> 00:27:32.600 align:middle line:84% And the energy of the system, including 00:27:32.600 --> 00:27:38.480 align:middle line:84% kinetic energy, potential energy, and internal energy. 00:27:38.480 --> 00:27:43.445 align:middle line:84% Or if you have other forms of energy, like elastic, magnetic, 00:27:43.445 --> 00:27:43.945 align:middle line:90% or those. 00:27:43.945 --> 00:27:46.780 align:middle line:90% 00:27:46.780 --> 00:27:51.100 align:middle line:84% And consider your relation that we're using 00:27:51.100 --> 00:27:53.650 align:middle line:90% is specific heat, for example. 00:27:53.650 --> 00:28:01.810 align:middle line:84% And here the specific heat is the temperature derivative 00:28:01.810 --> 00:28:03.850 align:middle line:90% of the internal energy. 00:28:03.850 --> 00:28:06.310 align:middle line:84% Here, the internal energy, I use a small [INAUDIBLE]. 00:28:06.310 --> 00:28:09.010 align:middle line:84% It could be either per unit mass based 00:28:09.010 --> 00:28:11.595 align:middle line:90% or per unit of volume based. 00:28:11.595 --> 00:28:14.840 align:middle line:90% 00:28:14.840 --> 00:28:18.540 align:middle line:90% So, that's the first law. 00:28:18.540 --> 00:28:21.090 align:middle line:90% Second law. 00:28:21.090 --> 00:28:26.310 align:middle line:84% Second law we're written into our equation. 00:28:26.310 --> 00:28:29.100 align:middle line:90% But it's not an equation. 00:28:29.100 --> 00:28:32.160 align:middle line:90% It's an inequality. 00:28:32.160 --> 00:28:35.930 align:middle line:84% And what we have here is the entropy change. 00:28:35.930 --> 00:28:41.010 align:middle line:84% Again, this is a state property, entropy, equals 00:28:41.010 --> 00:28:45.900 align:middle line:84% the entropy transferred across the system boundary 00:28:45.900 --> 00:28:50.370 align:middle line:84% and pass entropy generation in the system. 00:28:50.370 --> 00:28:54.570 align:middle line:84% On the right hand side it's process dependent. 00:28:54.570 --> 00:28:57.840 align:middle line:84% And on the left hand side is state properties 00:28:57.840 --> 00:29:02.080 align:middle line:90% that's independent processes. 00:29:02.080 --> 00:29:07.600 align:middle line:84% Now, I think about the heat engines. 00:29:07.600 --> 00:29:11.560 align:middle line:84% The heat engine, which when we think about engine, 00:29:11.560 --> 00:29:13.690 align:middle line:90% we think about cyclic motion. 00:29:13.690 --> 00:29:15.730 align:middle line:90% You don't want to design engine. 00:29:15.730 --> 00:29:18.880 align:middle line:84% You only go one direction, doesn't come back. 00:29:18.880 --> 00:29:25.810 align:middle line:84% And so when we think about cyclic motion 00:29:25.810 --> 00:29:28.190 align:middle line:84% during a cycle, any state property, 00:29:28.190 --> 00:29:31.090 align:middle line:84% go back to the original, the independent process. 00:29:31.090 --> 00:29:33.910 align:middle line:84% Once it goes back, the charge is 0. 00:29:33.910 --> 00:29:37.160 align:middle line:84% So here, we just wrote the entropy and energy, 00:29:37.160 --> 00:29:39.580 align:middle line:90% and other state properties. 00:29:39.580 --> 00:29:43.990 align:middle line:84% So if the entropy change is 0, now 00:29:43.990 --> 00:29:48.640 align:middle line:84% what's the maximum efficiency you can get? 00:29:48.640 --> 00:29:54.160 align:middle line:84% And maximum happens when there's no entropy generation. 00:29:54.160 --> 00:29:57.310 align:middle line:84% So if there is no entropy generation. [? SG ?] is 0. 00:29:57.310 --> 00:29:59.660 align:middle line:90% And I look at this is my system. 00:29:59.660 --> 00:30:01.450 align:middle line:90% The heat is positive. 00:30:01.450 --> 00:30:03.100 align:middle line:90% Heat output is negative. 00:30:03.100 --> 00:30:09.230 align:middle line:84% So I have my second law written into left hand side is 0. 00:30:09.230 --> 00:30:10.910 align:middle line:90% Entropy generation is 0. 00:30:10.910 --> 00:30:13.820 align:middle line:84% This entropy transfer across system boundary. 00:30:13.820 --> 00:30:19.840 align:middle line:84% And this gives me a relation between the heat in and heat out 00:30:19.840 --> 00:30:22.240 align:middle line:84% and temperature of the two reservoirs. 00:30:22.240 --> 00:30:26.560 align:middle line:84% And if I use this relation, I go to calculate 00:30:26.560 --> 00:30:30.760 align:middle line:84% what's in this case, what's the efficiency of this heat engine. 00:30:30.760 --> 00:30:32.440 align:middle line:84% You can see the efficiency, of course, 00:30:32.440 --> 00:30:36.310 align:middle line:84% we define as the work we get versus the price you 00:30:36.310 --> 00:30:39.740 align:middle line:90% pay as the heat in. 00:30:39.740 --> 00:30:43.170 align:middle line:90% The efficiency here is the work. 00:30:43.170 --> 00:30:45.250 align:middle line:84% Now, the work first all tells you 00:30:45.250 --> 00:30:48.040 align:middle line:84% the work equals heat in minus heat out 00:30:48.040 --> 00:30:53.260 align:middle line:84% because the internal energy during a cycle change is 0. 00:30:53.260 --> 00:30:56.290 align:middle line:84% So you can see you've got a [? power ?] efficiency. 00:30:56.290 --> 00:30:59.800 align:middle line:84% That's the maximum you can get for any heat engine 00:30:59.800 --> 00:31:04.495 align:middle line:84% operating between two constant temperature [INAUDIBLE]. 00:31:04.495 --> 00:31:08.140 align:middle line:90% 00:31:08.140 --> 00:31:14.550 align:middle line:84% People sometimes look down into heat engine. 00:31:14.550 --> 00:31:19.500 align:middle line:84% It's a heat engine, meaning it's thermal dynamic. 00:31:19.500 --> 00:31:23.500 align:middle line:84% It's not-- you can't convert all the heat into electricity. 00:31:23.500 --> 00:31:26.530 align:middle line:84% That's correct, unless you have 0 Kelvin. 00:31:26.530 --> 00:31:31.290 align:middle line:84% But the important thing is that you put in the lumber 00:31:31.290 --> 00:31:33.930 align:middle line:90% and you see where we are. 00:31:33.930 --> 00:31:36.960 align:middle line:84% The heat engine is very [? respectful ?] if you have 00:31:36.960 --> 00:31:41.060 align:middle line:84% even just a 200 degrees temperature heat source 00:31:41.060 --> 00:31:43.890 align:middle line:84% and if you can get [INAUDIBLE] efficiency-- 00:31:43.890 --> 00:31:46.620 align:middle line:90% 40%. 00:31:46.620 --> 00:31:50.603 align:middle line:90% If you take the sun, 95%. 00:31:50.603 --> 00:31:53.200 align:middle line:90% 00:31:53.200 --> 00:32:00.040 align:middle line:84% And then more than thermal power plant is about 40%. 00:32:00.040 --> 00:32:04.270 align:middle line:84% I said automobile internal combustion engines. 00:32:04.270 --> 00:32:06.550 align:middle line:84% The driving efficiency is less than 20% 00:32:06.550 --> 00:32:11.840 align:middle line:84% and the AC engine efficiency is probably around 25%. 00:32:11.840 --> 00:32:15.710 align:middle line:84% So heat engine, if you can achieve 00:32:15.710 --> 00:32:22.520 align:middle line:84% the theoretical efficiency, you're doing really well. 00:32:22.520 --> 00:32:24.740 align:middle line:84% The problem is there are a lot of losses 00:32:24.740 --> 00:32:28.400 align:middle line:84% that limits us to get to practical [INAUDIBLE], 00:32:28.400 --> 00:32:32.690 align:middle line:84% practically get too close to the economy efficiency. 00:32:32.690 --> 00:32:39.470 align:middle line:84% So that's what you learn in 2005 thermodynamics. 00:32:39.470 --> 00:32:43.200 align:middle line:84% Now I want to go to a little bit microscopic picture. 00:32:43.200 --> 00:32:46.640 align:middle line:84% Because what's an entropy, for example? 00:32:46.640 --> 00:32:52.520 align:middle line:84% And so let's look at an isolated system. 00:32:52.520 --> 00:32:56.600 align:middle line:84% An isolated means there is no heat transfer 00:32:56.600 --> 00:33:01.850 align:middle line:84% across system boundary, no work transfer, no mass transfer. 00:33:01.850 --> 00:33:03.710 align:middle line:90% It's isolated. 00:33:03.710 --> 00:33:09.170 align:middle line:84% And I'm going to look at, imagine I have the magic eye, 00:33:09.170 --> 00:33:12.230 align:middle line:84% can look at the individual molecules, the electrons 00:33:12.230 --> 00:33:14.120 align:middle line:90% in the system. 00:33:14.120 --> 00:33:21.320 align:middle line:84% And there are many different possible configurations. 00:33:21.320 --> 00:33:24.170 align:middle line:84% A molecule, so the molecules in the system 00:33:24.170 --> 00:33:28.040 align:middle line:84% could be at different states, different position. 00:33:28.040 --> 00:33:31.820 align:middle line:84% And each atom could have many different possible energy 00:33:31.820 --> 00:33:32.410 align:middle line:90% states. 00:33:32.410 --> 00:33:35.550 align:middle line:90% This is from quantum mechanics. 00:33:35.550 --> 00:33:40.350 align:middle line:84% So every possible configuration possibility-- 00:33:40.350 --> 00:33:45.690 align:middle line:84% you can go back and take a two color, two different color beads 00:33:45.690 --> 00:33:46.770 align:middle line:90% and mix them up. 00:33:46.770 --> 00:33:51.360 align:middle line:84% That's your experiment on this micro picture. 00:33:51.360 --> 00:33:57.870 align:middle line:84% And every possible configuration is a micro state. 00:33:57.870 --> 00:34:01.170 align:middle line:84% And let's suppose we know how to count 00:34:01.170 --> 00:34:05.070 align:middle line:84% what's the total number of those possible configurations. 00:34:05.070 --> 00:34:11.080 align:middle line:84% So the total number, that's omega microscopic state. 00:34:11.080 --> 00:34:15.060 align:middle line:90% Those are very big numbers. 00:34:15.060 --> 00:34:18.600 align:middle line:84% Now, what are the basic principle 00:34:18.600 --> 00:34:22.920 align:middle line:84% of this microscopic picture says every state 00:34:22.920 --> 00:34:28.980 align:middle line:84% that is equally possible, equal rights, no discrimination. 00:34:28.980 --> 00:34:34.290 align:middle line:84% And so this is the equal probability principle. 00:34:34.290 --> 00:34:38.730 align:middle line:84% Every micro state is equally possible. 00:34:38.730 --> 00:34:41.350 align:middle line:90% And it's based on this. 00:34:41.350 --> 00:34:45.080 align:middle line:84% All the statistical description of 00:34:45.080 --> 00:34:49.830 align:middle line:84% the statistical thermodynamics is based on, starting from here. 00:34:49.830 --> 00:34:55.260 align:middle line:84% And what Boltzmann did is to relate 00:34:55.260 --> 00:35:00.720 align:middle line:84% this number of total microstates to interpol. 00:35:00.720 --> 00:35:03.510 align:middle line:84% This is actually in Boltzmann tombstone. 00:35:03.510 --> 00:35:06.270 align:middle line:90% It goes to Vienna. 00:35:06.270 --> 00:35:11.670 align:middle line:84% And this kB is the Boltzmann constant, 1.3. 00:35:11.670 --> 00:35:13.200 align:middle line:90% I don't remember any-- 00:35:13.200 --> 00:35:16.380 align:middle line:84% people in physics, they use atomic units. 00:35:16.380 --> 00:35:20.280 align:middle line:84% I always remember things in the SI unit. 00:35:20.280 --> 00:35:23.850 align:middle line:84% So that's a difficult large exponent, 00:35:23.850 --> 00:35:28.130 align:middle line:90% 10 to the minus third [? jar. ?] 00:35:28.130 --> 00:35:30.210 align:middle line:84% That's good to keep some numbers in mind. 00:35:30.210 --> 00:35:36.220 align:middle line:84% So that's the, like I said, a starting point 00:35:36.220 --> 00:35:39.400 align:middle line:90% for the microscopic description. 00:35:39.400 --> 00:35:44.770 align:middle line:84% And here, we'll consider an isolated system. 00:35:44.770 --> 00:35:50.170 align:middle line:84% And now if you think about a not isolated system, 00:35:50.170 --> 00:35:53.020 align:middle line:84% a system that can thermally [INAUDIBLE] 00:35:53.020 --> 00:35:56.200 align:middle line:84% exchange energy with the environment. 00:35:56.200 --> 00:35:59.860 align:middle line:84% And because of that, each micro state 00:35:59.860 --> 00:36:03.650 align:middle line:84% is no longer have equal right in terms of observation. 00:36:03.650 --> 00:36:08.110 align:middle line:84% The probability of this system, if you can observe this system 00:36:08.110 --> 00:36:13.480 align:middle line:84% in certain specific micro state that has certain energy, e. 00:36:13.480 --> 00:36:18.890 align:middle line:84% And in this case, this is no longer equal probability. 00:36:18.890 --> 00:36:21.590 align:middle line:84% And we're not going to derivation. 00:36:21.590 --> 00:36:24.830 align:middle line:84% But you can go from here, equal probability, 00:36:24.830 --> 00:36:26.960 align:middle line:84% to construct an isolated system that 00:36:26.960 --> 00:36:30.090 align:middle line:84% made up your system and the environment. 00:36:30.090 --> 00:36:33.170 align:middle line:84% And with all that derivation at the end. 00:36:33.170 --> 00:36:38.240 align:middle line:84% We get the probability of the system actually inserting 00:36:38.240 --> 00:36:39.240 align:middle line:90% one micro state. 00:36:39.240 --> 00:36:44.540 align:middle line:84% This is the one micro state that has an energy, e. 00:36:44.540 --> 00:36:46.550 align:middle line:84% It's depending on the temperature 00:36:46.550 --> 00:36:52.420 align:middle line:84% of the system and the energy here, [? exposure. ?] 00:36:52.420 --> 00:36:56.200 align:middle line:84% So you can see higher energy, less probable. 00:36:56.200 --> 00:37:00.490 align:middle line:84% And if you do chemical combustion or a lot of Arrhenius 00:37:00.490 --> 00:37:05.200 align:middle line:84% law you probably learned in high school, that's the exponent. 00:37:05.200 --> 00:37:09.520 align:middle line:84% That's coming from here, [? personal ?] statistics. 00:37:09.520 --> 00:37:12.180 align:middle line:90% 00:37:12.180 --> 00:37:15.120 align:middle line:90% And so here is a closed system. 00:37:15.120 --> 00:37:19.050 align:middle line:84% What if there is a mass flow, particle flow across system 00:37:19.050 --> 00:37:21.360 align:middle line:90% boundary? 00:37:21.360 --> 00:37:27.160 align:middle line:84% And in that case, this is similar. 00:37:27.160 --> 00:37:32.730 align:middle line:84% But there is an extra chemical potential 00:37:32.730 --> 00:37:36.060 align:middle line:90% uphill in the exponent. 00:37:36.060 --> 00:37:41.400 align:middle line:84% And this is a constant temperature, but open system. 00:37:41.400 --> 00:37:44.950 align:middle line:84% And mu here is a [? chemical ?] potential. 00:37:44.950 --> 00:37:48.350 align:middle line:84% What is [? chemical ?] potential? 00:37:48.350 --> 00:37:49.500 align:middle line:90% Think about temperature. 00:37:49.500 --> 00:37:54.410 align:middle line:84% Temperature is a driving force for heat flow. 00:37:54.410 --> 00:37:58.040 align:middle line:84% [? Chemical ?] potential is the driving force 00:37:58.040 --> 00:38:02.780 align:middle line:90% for mass diffusion, mass flow. 00:38:02.780 --> 00:38:08.300 align:middle line:84% Pressure is the driving force for mechanical motion. 00:38:08.300 --> 00:38:11.750 align:middle line:84% Those are all thermodynamic, intrinsic thermodynamic 00:38:11.750 --> 00:38:13.490 align:middle line:90% quantities-- 00:38:13.490 --> 00:38:17.360 align:middle line:84% pressure, chemical potential, temperature. 00:38:17.360 --> 00:38:19.910 align:middle line:84% The other way to think about the chemical potential 00:38:19.910 --> 00:38:23.570 align:middle line:84% is it's the average energy needed 00:38:23.570 --> 00:38:27.080 align:middle line:84% to add a particle into a system or take a particle out 00:38:27.080 --> 00:38:27.690 align:middle line:90% of the system. 00:38:27.690 --> 00:38:30.630 align:middle line:90% 00:38:30.630 --> 00:38:33.330 align:middle line:84% So first chemical potential is the energy look at. 00:38:33.330 --> 00:38:35.640 align:middle line:90% This is the equivalent here. 00:38:35.640 --> 00:38:41.070 align:middle line:84% And second is driving force for the mass transfer. 00:38:41.070 --> 00:38:47.070 align:middle line:84% So if you do, say chemistry, you do mass diffusion 00:38:47.070 --> 00:38:49.260 align:middle line:84% or you do batteries, this is a quantity 00:38:49.260 --> 00:38:53.680 align:middle line:84% you will be dealing with all the time. 00:38:53.680 --> 00:38:56.650 align:middle line:90% So this is a microscopic. 00:38:56.650 --> 00:39:02.780 align:middle line:84% And now I'm going to apply what I just 00:39:02.780 --> 00:39:07.220 align:middle line:84% wrote down in the previous slide to molecules. 00:39:07.220 --> 00:39:10.910 align:middle line:90% I have lots of molecules. 00:39:10.910 --> 00:39:15.290 align:middle line:84% And I have an equilibrium, temperature t. 00:39:15.290 --> 00:39:17.120 align:middle line:90% I think the one molecule. 00:39:17.120 --> 00:39:20.810 align:middle line:84% It has a kinetic energy, a single, simple kinetic energy 00:39:20.810 --> 00:39:23.030 align:middle line:90% of the molecule. 00:39:23.030 --> 00:39:27.440 align:middle line:90% So it's 1/2 mv squared. 00:39:27.440 --> 00:39:30.530 align:middle line:84% [INAUDIBLE], molecule is the velocity 00:39:30.530 --> 00:39:34.280 align:middle line:84% is the three components, the vx square, vy square, vz square. 00:39:34.280 --> 00:39:37.180 align:middle line:90% So that's what I have here. 00:39:37.180 --> 00:39:38.480 align:middle line:90% And this is the energy. 00:39:38.480 --> 00:39:41.530 align:middle line:84% Remember, in the previous slide we 00:39:41.530 --> 00:39:43.990 align:middle line:84% say this is now a constant temperature 00:39:43.990 --> 00:39:47.050 align:middle line:84% molecule in thermal equilibrium at constant temperature. 00:39:47.050 --> 00:39:51.640 align:middle line:84% So that's the statistical system I'm using. 00:39:51.640 --> 00:39:56.170 align:middle line:84% And this is the energy that's a kinetic energy. 00:39:56.170 --> 00:40:00.520 align:middle line:84% And here is a probability, probability 00:40:00.520 --> 00:40:03.100 align:middle line:90% I have a normalization factor. 00:40:03.100 --> 00:40:09.330 align:middle line:84% So I put in the probability of this molecule 00:40:09.330 --> 00:40:11.470 align:middle line:90% having the velocity vx, vy, vz. 00:40:11.470 --> 00:40:14.150 align:middle line:90% 00:40:14.150 --> 00:40:18.720 align:middle line:84% And the next step I want to determine a, determine that pre 00:40:18.720 --> 00:40:21.110 align:middle line:90% vector, a. 00:40:21.110 --> 00:40:21.890 align:middle line:90% What I do? 00:40:21.890 --> 00:40:24.590 align:middle line:84% The probability-- so the molecule probability 00:40:24.590 --> 00:40:28.310 align:middle line:84% is the velocity is from minus infinity to positive infinity. 00:40:28.310 --> 00:40:32.060 align:middle line:90% I include every possible chance. 00:40:32.060 --> 00:40:39.610 align:middle line:84% So if I equal the error possible chance, 00:40:39.610 --> 00:40:44.230 align:middle line:84% that's my normal, the way I find out this factor a. 00:40:44.230 --> 00:40:49.600 align:middle line:84% That's all, say, velocity from negative infinity 00:40:49.600 --> 00:40:51.370 align:middle line:90% to positive infinite. 00:40:51.370 --> 00:40:53.770 align:middle line:90% And this should sum up to 1. 00:40:53.770 --> 00:40:57.640 align:middle line:84% They've got to have the velocity in between these. 00:40:57.640 --> 00:41:02.000 align:middle line:84% And if you do this integration, you find your factor, a. 00:41:02.000 --> 00:41:06.200 align:middle line:90% 00:41:06.200 --> 00:41:12.490 align:middle line:84% And this is the famous Maxwell distribution for molecules. 00:41:12.490 --> 00:41:15.115 align:middle line:90% STUDENT: It should be a minus. 00:41:15.115 --> 00:41:15.990 align:middle line:90% GANG CHEN: Thank you. 00:41:15.990 --> 00:41:16.680 align:middle line:90% Yes. 00:41:16.680 --> 00:41:17.550 align:middle line:90% STUDENT: [INAUDIBLE] 00:41:17.550 --> 00:41:18.717 align:middle line:90% GANG CHEN: There is a minus. 00:41:18.717 --> 00:41:20.700 align:middle line:90% There's this minus sign here. 00:41:20.700 --> 00:41:22.930 align:middle line:90% Thank you. 00:41:22.930 --> 00:41:26.050 align:middle line:90% And see the other one. 00:41:26.050 --> 00:41:26.900 align:middle line:90% Yes. 00:41:26.900 --> 00:41:31.540 align:middle line:84% Please add [? another ?] [? 7. ?] And here it's the same 00:41:31.540 --> 00:41:32.040 align:middle line:90% problem. 00:41:32.040 --> 00:41:35.050 align:middle line:90% I just copied. 00:41:35.050 --> 00:41:39.270 align:middle line:84% So now if it's a probability, once you have a probability, 00:41:39.270 --> 00:41:42.540 align:middle line:84% you can calculate your observation. 00:41:42.540 --> 00:41:46.560 align:middle line:84% What's the average once you have probability? 00:41:46.560 --> 00:41:49.920 align:middle line:84% So I want to find the average energy, 00:41:49.920 --> 00:41:53.640 align:middle line:84% kinetic translational energy motion, kinetic energy 00:41:53.640 --> 00:41:55.110 align:middle line:90% of this molecule. 00:41:55.110 --> 00:42:01.650 align:middle line:84% So here is the energy weighed by this probability 00:42:01.650 --> 00:42:06.660 align:middle line:90% over all possible velocities. 00:42:06.660 --> 00:42:09.900 align:middle line:90% And again, it's an integration. 00:42:09.900 --> 00:42:13.230 align:middle line:84% You can do yourself if you look at a table. 00:42:13.230 --> 00:42:18.350 align:middle line:84% And you find out is a very simple result e equals two 00:42:18.350 --> 00:42:24.780 align:middle line:90% thirds, 3/2 kbt [INAUDIBLE]. 00:42:24.780 --> 00:42:28.320 align:middle line:90% It's 3/2 kbt, actually. 00:42:28.320 --> 00:42:32.460 align:middle line:84% It's a very good language to remember, kbt. 00:42:32.460 --> 00:42:34.590 align:middle line:90% But also it's a fundamental. 00:42:34.590 --> 00:42:36.990 align:middle line:84% There is a fundamental principle, equal partition 00:42:36.990 --> 00:42:42.540 align:middle line:84% principle, which says if your microscopic energy is 00:42:42.540 --> 00:42:45.270 align:middle line:84% quadratic-- so if you look at this, 00:42:45.270 --> 00:42:50.790 align:middle line:84% kinetic energy is quadratic in velocity and v squared. 00:42:50.790 --> 00:42:54.990 align:middle line:84% So if energy is quadratic, each of these quadratic terms 00:42:54.990 --> 00:42:58.770 align:middle line:84% contribute to average energy half kbt. 00:42:58.770 --> 00:43:00.780 align:middle line:84% So if you look at this molecule there, 00:43:00.780 --> 00:43:03.390 align:middle line:84% because it has three quadratic terms, 00:43:03.390 --> 00:43:10.140 align:middle line:84% so each contribute one part kbt in total [INAUDIBLE]. 00:43:10.140 --> 00:43:15.940 align:middle line:84% So this is the equal partition principle. 00:43:15.940 --> 00:43:19.530 align:middle line:84% And now I would like you to get an idea of what is kbt. 00:43:19.530 --> 00:43:23.890 align:middle line:84% This is really something that if you 00:43:23.890 --> 00:43:27.970 align:middle line:84% want to have microscopic mind, you should remember. 00:43:27.970 --> 00:43:31.235 align:middle line:90% How large is it? 00:43:31.235 --> 00:43:35.555 align:middle line:84% kbt, 1.3 times [INAUDIBLE] times third, 300 degrees Kelvin. 00:43:35.555 --> 00:43:38.420 align:middle line:90% 00:43:38.420 --> 00:43:41.450 align:middle line:84% I think I forgot to correct this again. 00:43:41.450 --> 00:43:43.670 align:middle line:90% This should be 4, not 5-- 00:43:43.670 --> 00:43:47.690 align:middle line:90% 4.14. 00:43:47.690 --> 00:43:48.890 align:middle line:90% 4.14. 00:43:48.890 --> 00:43:53.910 align:middle line:84% And if you take a 4.14 divided by 4, that's a big number. 00:43:53.910 --> 00:43:55.820 align:middle line:90% Too hard to remember. 00:43:55.820 --> 00:44:00.410 align:middle line:84% And people-- again, different field people use different ways, 00:44:00.410 --> 00:44:02.210 align:middle line:90% different measures. 00:44:02.210 --> 00:44:11.150 align:middle line:84% And one often used the unit is electron volt as an energy unit. 00:44:11.150 --> 00:44:12.920 align:middle line:90% What is the electron volt? 00:44:12.920 --> 00:44:14.620 align:middle line:90% You have a charge. 00:44:14.620 --> 00:44:20.330 align:middle line:84% You apply an electric field, one volt, say under one volt. 00:44:20.330 --> 00:44:23.450 align:middle line:84% That's a potential how much energy it has. 00:44:23.450 --> 00:44:28.730 align:middle line:84% So one electron volt is 1.6, 10 to the minus 19 [? JR. ?] 00:44:28.730 --> 00:44:33.530 align:middle line:84% So I translate this into a room temperature one kbt 00:44:33.530 --> 00:44:36.080 align:middle line:90% 26 literally electron volts. 00:44:36.080 --> 00:44:41.930 align:middle line:90% 00:44:41.930 --> 00:44:46.760 align:middle line:84% Now, think about if this is the average energy 00:44:46.760 --> 00:44:50.870 align:middle line:84% of the molecule, what's how fast they are moving? 00:44:50.870 --> 00:44:53.060 align:middle line:84% So the molecule moving in this room. 00:44:53.060 --> 00:44:58.280 align:middle line:84% You can go to estimate, because this energy equals 1/2 mv 00:44:58.280 --> 00:44:59.090 align:middle line:90% squared. 00:44:59.090 --> 00:45:04.400 align:middle line:84% So you can go to estimate the velocity of the molecule, one 00:45:04.400 --> 00:45:05.330 align:middle line:90% half cancel. 00:45:05.330 --> 00:45:06.470 align:middle line:90% You do the math. 00:45:06.470 --> 00:45:10.140 align:middle line:90% I took the oxygen as an example. 00:45:10.140 --> 00:45:15.090 align:middle line:84% And all the number of oxygen atomic number is 8. 00:45:15.090 --> 00:45:17.180 align:middle line:90% So it's 16 neutron proton. 00:45:17.180 --> 00:45:22.490 align:middle line:84% And each of the proton mass is 1.677 plus 27. 00:45:22.490 --> 00:45:27.260 align:middle line:84% So number is about 200 meter per second. 00:45:27.260 --> 00:45:32.270 align:middle line:84% Depends on whether it's a light molecule, heavy molecules. 00:45:32.270 --> 00:45:37.550 align:middle line:84% So those are the microscopic molecular picture. 00:45:37.550 --> 00:45:40.710 align:middle line:90% That's about molecules. 00:45:40.710 --> 00:45:44.360 align:middle line:90% 00:45:44.360 --> 00:45:46.230 align:middle line:90% Let's think about the electrons. 00:45:46.230 --> 00:45:51.320 align:middle line:84% Molecules, what we see, we did not do anything quantum side. 00:45:51.320 --> 00:45:56.300 align:middle line:84% The Maxwell distribution is a classical statistical 00:45:56.300 --> 00:45:58.680 align:middle line:90% thermodynamics. 00:45:58.680 --> 00:46:03.010 align:middle line:84% Now, when I do electrons, the quantum mechanics 00:46:03.010 --> 00:46:04.750 align:middle line:90% sometimes is very important. 00:46:04.750 --> 00:46:08.350 align:middle line:90% So it's the more common picture. 00:46:08.350 --> 00:46:11.410 align:middle line:84% From quantum mechanics, we learn-- 00:46:11.410 --> 00:46:14.410 align:middle line:84% you have a physics before, basic idea. 00:46:14.410 --> 00:46:17.950 align:middle line:84% I'm sure you all heard about energy levels of quantum 00:46:17.950 --> 00:46:21.070 align:middle line:90% mechanics. 00:46:21.070 --> 00:46:27.820 align:middle line:84% And some of you may still remember, 00:46:27.820 --> 00:46:31.450 align:middle line:84% if you have quantum mechanical state, 00:46:31.450 --> 00:46:35.530 align:middle line:90% you can only have one electron-- 00:46:35.530 --> 00:46:37.400 align:middle line:90% Pauli exclusion principle. 00:46:37.400 --> 00:46:45.080 align:middle line:90% 00:46:45.080 --> 00:46:48.710 align:middle line:84% And the quantum mechanics, actually here 00:46:48.710 --> 00:46:52.250 align:middle line:84% I have listed the quantum Einstein 00:46:52.250 --> 00:46:55.050 align:middle line:90% relation that gives the energy. 00:46:55.050 --> 00:46:56.770 align:middle line:84% This actually started from photons. 00:46:56.770 --> 00:47:00.830 align:middle line:84% So next slide I have more energy related to frequency 00:47:00.830 --> 00:47:03.590 align:middle line:84% of the photon and the momentum relates 00:47:03.590 --> 00:47:05.090 align:middle line:90% to wavelengths of the photon. 00:47:05.090 --> 00:47:10.040 align:middle line:84% So that's the so-called the Planck Einstein relation. 00:47:10.040 --> 00:47:13.340 align:middle line:84% And again, this is another number. 00:47:13.340 --> 00:47:15.230 align:middle line:84% If you think about the quantum, you always 00:47:15.230 --> 00:47:20.930 align:middle line:84% see h Planck constant at 6.6 10 to the minus 34 00:47:20.930 --> 00:47:22.846 align:middle line:90% [? jar ?] [INAUDIBLE]. 00:47:22.846 --> 00:47:26.570 align:middle line:90% 00:47:26.570 --> 00:47:32.630 align:middle line:84% Now I'm going to look at one quantum mechanical state. 00:47:32.630 --> 00:47:35.960 align:middle line:84% And this quantum mechanical state 00:47:35.960 --> 00:47:39.380 align:middle line:84% can have maximum of one electron. 00:47:39.380 --> 00:47:40.850 align:middle line:90% It can have 0 electron. 00:47:40.850 --> 00:47:43.460 align:middle line:90% You have one electron. 00:47:43.460 --> 00:47:45.330 align:middle line:84% And this quantum state has an energy, 00:47:45.330 --> 00:47:50.180 align:middle line:84% e, quantum mechanically allowable energy. 00:47:50.180 --> 00:47:54.140 align:middle line:84% When the electron is there, this state has energy, e. 00:47:54.140 --> 00:47:58.160 align:middle line:84% When it's empty, the electron, the actual energy of the system 00:47:58.160 --> 00:47:58.680 align:middle line:90% is 0. 00:47:58.680 --> 00:48:03.806 align:middle line:84% But I only have two possibilities. 00:48:03.806 --> 00:48:06.380 align:middle line:90% 00:48:06.380 --> 00:48:08.760 align:middle line:84% So I have-- there's two possibilities. 00:48:08.760 --> 00:48:10.190 align:middle line:90% I sum this up. 00:48:10.190 --> 00:48:15.080 align:middle line:84% I want to find this a, the difference between the molecule 00:48:15.080 --> 00:48:16.460 align:middle line:90% I did before. 00:48:16.460 --> 00:48:20.720 align:middle line:84% And here, for molecule velocity I say, OK, from minus infinity 00:48:20.720 --> 00:48:24.020 align:middle line:84% to plus infinity, I include everything. 00:48:24.020 --> 00:48:25.970 align:middle line:84% But for the electron here, I only 00:48:25.970 --> 00:48:29.890 align:middle line:90% have 0 electron or 1 electron. 00:48:29.890 --> 00:48:34.630 align:middle line:84% So I sum this up to what I will find a. 00:48:34.630 --> 00:48:39.120 align:middle line:84% I'm not going to detail the math. 00:48:39.120 --> 00:48:42.450 align:middle line:84% So from the previous relation, I found a. 00:48:42.450 --> 00:48:44.760 align:middle line:90% And now I give you an average. 00:48:44.760 --> 00:48:47.820 align:middle line:84% Again, I can give you the average energy. 00:48:47.820 --> 00:48:52.410 align:middle line:84% Because if I do observation, it's 0 or e. 00:48:52.410 --> 00:48:54.270 align:middle line:84% And if I do a lot of observation, 00:48:54.270 --> 00:48:57.720 align:middle line:84% it's a equilibrium temperature t, 00:48:57.720 --> 00:49:01.320 align:middle line:84% what's the average time, average energy, 00:49:01.320 --> 00:49:04.470 align:middle line:90% or average number of electrons? 00:49:04.470 --> 00:49:07.440 align:middle line:84% Each individual observation could be 0 or 1. 00:49:07.440 --> 00:49:11.730 align:middle line:84% But there is an average possibility. 00:49:11.730 --> 00:49:15.390 align:middle line:84% So if I look at the average, again, 00:49:15.390 --> 00:49:17.940 align:middle line:90% say this is an n could be 0, 1. 00:49:17.940 --> 00:49:22.300 align:middle line:84% And they sum of two Fermi-Dirac distribution. 00:49:22.300 --> 00:49:27.250 align:middle line:90% 00:49:27.250 --> 00:49:28.330 align:middle line:90% You look at that. 00:49:28.330 --> 00:49:31.160 align:middle line:84% What's the range of this [? F, ?] the average? 00:49:31.160 --> 00:49:36.560 align:middle line:90% 00:49:36.560 --> 00:49:39.441 align:middle line:90% STUDENT: [INAUDIBLE] 00:49:39.441 --> 00:49:40.670 align:middle line:90% 0 to 1. 00:49:40.670 --> 00:49:43.040 align:middle line:90% That's so they can't be above 1. 00:49:43.040 --> 00:49:45.290 align:middle line:90% Its maximum is the 1. 00:49:45.290 --> 00:49:46.650 align:middle line:90% Minimum 0. 00:49:46.650 --> 00:49:48.710 align:middle line:90% So it's between 0 and 1. 00:49:48.710 --> 00:49:53.180 align:middle line:84% And then you plot this depend on the temperature. 00:49:53.180 --> 00:49:58.760 align:middle line:84% And it depends on whether the energy of this level 00:49:58.760 --> 00:50:04.530 align:middle line:84% is above the chemical potential or below the chemical potential. 00:50:04.530 --> 00:50:08.270 align:middle line:84% The chemical potential is they say, 00:50:08.270 --> 00:50:12.330 align:middle line:84% we said before, now you can think of this as a one quantum 00:50:12.330 --> 00:50:15.570 align:middle line:84% state that the open state system, the electron can come in 00:50:15.570 --> 00:50:16.950 align:middle line:90% and goes out. 00:50:16.950 --> 00:50:20.310 align:middle line:84% The chemical potential is what's the average energy 00:50:20.310 --> 00:50:24.210 align:middle line:84% you need to take the electron in or the electron out-- 00:50:24.210 --> 00:50:27.210 align:middle line:84% take the electron out for put electron in. 00:50:27.210 --> 00:50:30.440 align:middle line:84% So depends on whether it's above or below. 00:50:30.440 --> 00:50:33.180 align:middle line:84% You can say it's close to 1 or close to 0. 00:50:33.180 --> 00:50:37.890 align:middle line:84% Very narrowly distributed near the chemical potential. 00:50:37.890 --> 00:50:41.280 align:middle line:84% And in fact, if your [INAUDIBLE] is 0, 00:50:41.280 --> 00:50:43.860 align:middle line:90% this will be a sharp position. 00:50:43.860 --> 00:50:47.310 align:middle line:84% At the chemical potential above is 1, here below. 00:50:47.310 --> 00:50:51.450 align:middle line:90% Let's say above 0 and below 1. 00:50:51.450 --> 00:50:55.020 align:middle line:84% And the chemical potential at 0 temperature, 00:50:55.020 --> 00:50:58.680 align:middle line:84% there is a special name people give often 00:50:58.680 --> 00:51:01.020 align:middle line:90% called that Fermi level. 00:51:01.020 --> 00:51:04.000 align:middle line:84% But in a lot of different fields, 00:51:04.000 --> 00:51:08.260 align:middle line:84% sometimes people just call Fermi level for energy transfer. 00:51:08.260 --> 00:51:10.130 align:middle line:90% It's terminology convention. 00:51:10.130 --> 00:51:14.450 align:middle line:90% 00:51:14.450 --> 00:51:16.910 align:middle line:90% So that's for electron. 00:51:16.910 --> 00:51:20.120 align:middle line:90% Now we're going to lecture two. 00:51:20.120 --> 00:51:21.920 align:middle line:90% We talk about molecule. 00:51:21.920 --> 00:51:23.690 align:middle line:90% We'll talk about electron. 00:51:23.690 --> 00:51:26.030 align:middle line:84% Next I'm going to talk about electromagnetic wave, 00:51:26.030 --> 00:51:27.830 align:middle line:90% the photons. 00:51:27.830 --> 00:51:37.400 align:middle line:84% I mentioned before, the Planck Einstein relationship is really 00:51:37.400 --> 00:51:38.630 align:middle line:90% looking into photon. 00:51:38.630 --> 00:51:42.440 align:middle line:84% And later on was generalized for any material wave. 00:51:42.440 --> 00:51:49.850 align:middle line:84% And so what we have is if there is electromagnetic wave 00:51:49.850 --> 00:51:53.480 align:middle line:84% at a certain frequency, mu, what Planck 00:51:53.480 --> 00:51:58.670 align:middle line:84% found is that the energy of that mu, the quantum 00:51:58.670 --> 00:51:59.960 align:middle line:90% mechanical state-- 00:51:59.960 --> 00:52:02.120 align:middle line:84% at the time there was no quantum mechanics. 00:52:02.120 --> 00:52:06.520 align:middle line:84% So electromagnetic mode, of specific mode, 00:52:06.520 --> 00:52:10.010 align:middle line:90% the energy has to be quantized. 00:52:10.010 --> 00:52:15.320 align:middle line:84% And basically energy quanta is [? hmu. ?] 00:52:15.320 --> 00:52:18.530 align:middle line:84% And this other quantum [INAUDIBLE] 00:52:18.530 --> 00:52:24.380 align:middle line:84% was called a [? photon. ?] And when Einstein came in, 00:52:24.380 --> 00:52:29.750 align:middle line:84% he's saying that the quanta not only just have the wave, 00:52:29.750 --> 00:52:32.270 align:middle line:90% but also has a momentum. 00:52:32.270 --> 00:52:36.470 align:middle line:84% So this is where the wave particle duality came from. 00:52:36.470 --> 00:52:40.670 align:middle line:84% So the momentum of the quanta is related 00:52:40.670 --> 00:52:47.630 align:middle line:84% to the wavelength of the wave, and again, the edge. 00:52:47.630 --> 00:52:53.450 align:middle line:84% And so each quantum state, the energy 00:52:53.450 --> 00:52:57.140 align:middle line:84% can only be multiple of the edge mu. 00:52:57.140 --> 00:52:59.270 align:middle line:84% Normally when we think about the continuum 00:52:59.270 --> 00:53:01.530 align:middle line:90% mechanics can be any value. 00:53:01.530 --> 00:53:07.350 align:middle line:84% But the important difference is that the energy 00:53:07.350 --> 00:53:09.610 align:middle line:90% could be only multiple. 00:53:09.610 --> 00:53:12.510 align:middle line:90% So n is now integer. 00:53:12.510 --> 00:53:14.800 align:middle line:90% And it has a one half. 00:53:14.800 --> 00:53:16.680 align:middle line:84% That's also called this one half. 00:53:16.680 --> 00:53:17.920 align:middle line:90% Normal is not important. 00:53:17.920 --> 00:53:19.680 align:middle line:90% It's called 0 point energy. 00:53:19.680 --> 00:53:24.000 align:middle line:84% And it's really-- if you still recall from quantum mechanics, 00:53:24.000 --> 00:53:26.970 align:middle line:84% that's the so-called the Heisenberg Uncertainty 00:53:26.970 --> 00:53:28.240 align:middle line:90% Principle requirement. 00:53:28.240 --> 00:53:32.070 align:middle line:90% So this is 0 point energy. 00:53:32.070 --> 00:53:33.180 align:middle line:90% Normally it's not. 00:53:33.180 --> 00:53:34.870 align:middle line:90% So I'm not going to give much. 00:53:34.870 --> 00:53:37.550 align:middle line:90% 00:53:37.550 --> 00:53:39.650 align:middle line:90% So that's a photon. 00:53:39.650 --> 00:53:45.060 align:middle line:84% Now I'm going to-- it turns out the photon, 00:53:45.060 --> 00:53:47.840 align:middle line:84% you can think of this as the electromagnetic wave. 00:53:47.840 --> 00:53:49.950 align:middle line:84% Now I'm going to talk about different waves. 00:53:49.950 --> 00:53:53.850 align:middle line:84% That's the lattice wave, the atomic vibration. 00:53:53.850 --> 00:53:55.940 align:middle line:84% The [INAUDIBLE] vibration now, you 00:53:55.940 --> 00:53:59.180 align:middle line:84% can think about starting with classical mechanics. 00:53:59.180 --> 00:54:02.720 align:middle line:84% If you have a mass spring system, 00:54:02.720 --> 00:54:06.800 align:middle line:84% the fundamental natural frequency 00:54:06.800 --> 00:54:08.570 align:middle line:90% is square root of k over m. 00:54:08.570 --> 00:54:11.570 align:middle line:90% 00:54:11.570 --> 00:54:14.240 align:middle line:84% And, of course, in classical mechanics, 00:54:14.240 --> 00:54:16.670 align:middle line:84% we see the energy is related to the amplitude 00:54:16.670 --> 00:54:19.880 align:middle line:90% of the wave, the velocity. 00:54:19.880 --> 00:54:23.990 align:middle line:84% And once you go to quantum, it turns out this way, 00:54:23.990 --> 00:54:27.290 align:middle line:84% the energy cannot be any value, same as the electromagnetic 00:54:27.290 --> 00:54:28.520 align:middle line:90% wave. 00:54:28.520 --> 00:54:32.460 align:middle line:84% And the energy can only be multiples-- 00:54:32.460 --> 00:54:38.040 align:middle line:84% same, you can say multiples of [? SU. ?] 00:54:38.040 --> 00:54:41.430 align:middle line:84% And now there was an analogy made 00:54:41.430 --> 00:54:45.570 align:middle line:90% for this compound of vibration. 00:54:45.570 --> 00:54:49.990 align:middle line:90% That analogy is [INAUDIBLE]. 00:54:49.990 --> 00:54:54.720 align:middle line:84% Electromagnetic wave, the basic energy quanta is the photon. 00:54:54.720 --> 00:54:57.960 align:middle line:84% That is atomic vibration or the energy 00:54:57.960 --> 00:55:02.620 align:middle line:90% based energy quanta is photon. 00:55:02.620 --> 00:55:06.610 align:middle line:84% OK, so what's the statistic they obeyed? 00:55:06.610 --> 00:55:09.770 align:middle line:84% At a certain quantum state, if you think about electrons, 00:55:09.770 --> 00:55:13.780 align:middle line:90% could be 0 and 1. 00:55:13.780 --> 00:55:15.520 align:middle line:90% Maximum is 1. 00:55:15.520 --> 00:55:19.540 align:middle line:84% And here, at the mole, at this frequency, 00:55:19.540 --> 00:55:23.130 align:middle line:90% it could be 0, 1, to infinite. 00:55:23.130 --> 00:55:24.420 align:middle line:90% So that's a difference. 00:55:24.420 --> 00:55:27.000 align:middle line:90% Electron, 0, 1. 00:55:27.000 --> 00:55:31.230 align:middle line:84% And here, it could be any number of integer numbers. 00:55:31.230 --> 00:55:35.670 align:middle line:84% So I need to find the distribution average 00:55:35.670 --> 00:55:41.240 align:middle line:84% number of photon or [INAUDIBLE] if I have a equilibrium system. 00:55:41.240 --> 00:55:47.540 align:middle line:90% 00:55:47.540 --> 00:55:49.880 align:middle line:90% Do the same thing. 00:55:49.880 --> 00:55:52.010 align:middle line:90% I have the probability. 00:55:52.010 --> 00:55:57.950 align:middle line:84% And now, if I have n photon or [INAUDIBLE] 00:55:57.950 --> 00:56:02.630 align:middle line:84% in this microstate, the quantum mechanical state that 00:56:02.630 --> 00:56:07.350 align:middle line:84% has this specific frequency, that's the probability. 00:56:07.350 --> 00:56:11.000 align:middle line:84% I sum this up from a equals 0 to infinite. 00:56:11.000 --> 00:56:13.160 align:middle line:90% That still should give me 1. 00:56:13.160 --> 00:56:16.340 align:middle line:84% You have either 0 or 1, or infinite number, 00:56:16.340 --> 00:56:18.650 align:middle line:84% or the in between, somewhere in between. 00:56:18.650 --> 00:56:20.630 align:middle line:90% So sum up, I have one. 00:56:20.630 --> 00:56:21.470 align:middle line:90% I will determine a. 00:56:21.470 --> 00:56:26.570 align:middle line:84% And this a, from this a, I go to find the average again. 00:56:26.570 --> 00:56:31.580 align:middle line:84% Once I find the probability, I find the average number same way 00:56:31.580 --> 00:56:33.560 align:middle line:90% as I did for electron. 00:56:33.560 --> 00:56:42.530 align:middle line:84% And this average number now is the Bose-Einstein distribution. 00:56:42.530 --> 00:56:44.840 align:middle line:84% And this Bose-Einstein distribution, 00:56:44.840 --> 00:56:48.140 align:middle line:84% if you compare it with the previous Fermi-Dirac 00:56:48.140 --> 00:56:50.930 align:middle line:84% distribution, the only thing changed 00:56:50.930 --> 00:56:55.580 align:middle line:84% is a plus sign now goes to minus sign. 00:56:55.580 --> 00:56:58.520 align:middle line:84% And because of that, it's no longer between 0 to 1. 00:56:58.520 --> 00:57:02.680 align:middle line:90% It's between 0 to infinite. 00:57:02.680 --> 00:57:07.900 align:middle line:84% And in fact, for photon and photon, 00:57:07.900 --> 00:57:10.310 align:middle line:84% because the number is not conserved. 00:57:10.310 --> 00:57:12.970 align:middle line:84% It's not like the electron is conserved [INAUDIBLE]. 00:57:12.970 --> 00:57:16.000 align:middle line:84% So chemical potential concept is not [INAUDIBLE]-- 00:57:16.000 --> 00:57:17.080 align:middle line:90% is not a good one. 00:57:17.080 --> 00:57:18.710 align:middle line:90% So that's a 0. 00:57:18.710 --> 00:57:20.320 align:middle line:90% We take it to 0. 00:57:20.320 --> 00:57:25.615 align:middle line:84% And this is the distribution for the Bose-Einstein distribution. 00:57:25.615 --> 00:57:31.000 align:middle line:84% STUDENT: What's the reason for setting mu at 0? 00:57:31.000 --> 00:57:34.330 align:middle line:84% GANG CHEN: It's not a conserved quantity. 00:57:34.330 --> 00:57:37.990 align:middle line:84% It's, say, when we talk of mass transfer particle, that's 00:57:37.990 --> 00:57:39.790 align:middle line:90% a fixed number. 00:57:39.790 --> 00:57:41.920 align:middle line:84% Total number either going out or going in. 00:57:41.920 --> 00:57:43.960 align:middle line:90% But that's a conserved number. 00:57:43.960 --> 00:57:46.910 align:middle line:90% Here is another number. 00:57:46.910 --> 00:57:49.040 align:middle line:84% But there are actually-- see, later 00:57:49.040 --> 00:57:52.790 align:middle line:84% on when we talk about the solar cell, you'll find out 00:57:52.790 --> 00:57:56.040 align:middle line:84% there is a quasi Fermi level getting into here. 00:57:56.040 --> 00:58:00.270 align:middle line:84% So it's actually a very deep similarity. 00:58:00.270 --> 00:58:01.870 align:middle line:84% So this is just a simple argument. 00:58:01.870 --> 00:58:10.640 align:middle line:90% 00:58:10.640 --> 00:58:16.580 align:middle line:84% That's about-- now, in this time frame, like I said, 00:58:16.580 --> 00:58:19.760 align:middle line:84% you're probably familiar with the classical thermodynamic. 00:58:19.760 --> 00:58:22.810 align:middle line:84% You're now familiar with statistical side. 00:58:22.810 --> 00:58:24.170 align:middle line:90% Like you just take it. 00:58:24.170 --> 00:58:26.720 align:middle line:84% This is all the result we'll be using 00:58:26.720 --> 00:58:28.780 align:middle line:90% when they get into [INAUDIBLE]. 00:58:28.780 --> 00:58:31.910 align:middle line:84% Then microscopically we have [INAUDIBLE] distribution. 00:58:31.910 --> 00:58:34.830 align:middle line:84% We have Fermi-Dirac distribution for electron. 00:58:34.830 --> 00:58:38.180 align:middle line:84% We have Bose-Einstein distribution for phonon photon. 00:58:38.180 --> 00:58:40.430 align:middle line:90% That's what you need to know. 00:58:40.430 --> 00:58:48.200 align:middle line:84% And what we need, I'm going to summarize next. 00:58:48.200 --> 00:58:50.090 align:middle line:90% This is the heat transfer. 00:58:50.090 --> 00:58:52.430 align:middle line:90% Before it was thermodynamics. 00:58:52.430 --> 00:58:59.250 align:middle line:84% Now, heat transfer, again, you take the 2005, 2006. 00:58:59.250 --> 00:59:01.040 align:middle line:90% This is a very-- 00:59:01.040 --> 00:59:04.880 align:middle line:90% should be very familiar. 00:59:04.880 --> 00:59:08.610 align:middle line:84% We have three modes of heat transfer-- conduction, 00:59:08.610 --> 00:59:10.860 align:middle line:90% convection, and radiation. 00:59:10.860 --> 00:59:16.950 align:middle line:84% And describing the conduction is a Fourier law of diffusion. 00:59:16.950 --> 00:59:22.560 align:middle line:84% So the heat transfer rate, here for the rate in watts, 00:59:22.560 --> 00:59:24.730 align:middle line:84% it's proportional to the area, proportional 00:59:24.730 --> 00:59:26.790 align:middle line:90% to temperature gradient. 00:59:26.790 --> 00:59:31.020 align:middle line:84% A proportionality constant is the thermal conductivity. 00:59:31.020 --> 00:59:33.630 align:middle line:90% And that's a material property. 00:59:33.630 --> 00:59:37.830 align:middle line:84% Normally, we think of it as a material property. 00:59:37.830 --> 00:59:42.120 align:middle line:84% And the negative sign actually take care of the second law, 00:59:42.120 --> 00:59:45.300 align:middle line:84% says temperature, heat will flow from high temperature 00:59:45.300 --> 00:59:48.370 align:middle line:90% to low temperature. 00:59:48.370 --> 00:59:52.990 align:middle line:84% And you can do that. from watt you can do flux. 00:59:52.990 --> 00:59:55.240 align:middle line:90% That's a per unit area based. 00:59:55.240 --> 00:59:58.330 align:middle line:90% So just normalize the area. 00:59:58.330 --> 01:00:02.320 align:middle line:84% Or you generalize it to 3 dimension 01:00:02.320 --> 01:00:05.820 align:middle line:84% rather than writing into one dimension. 01:00:05.820 --> 01:00:09.030 align:middle line:90% So that's [INAUDIBLE]. 01:00:09.030 --> 01:00:17.120 align:middle line:84% And convection is we have fluid flow in the surrounding 01:00:17.120 --> 01:00:21.290 align:middle line:90% of a heated or cold surface. 01:00:21.290 --> 01:00:26.360 align:middle line:84% The heat transfer between the surface and the fluid 01:00:26.360 --> 01:00:29.420 align:middle line:84% is proportional to the temperature difference 01:00:29.420 --> 01:00:31.280 align:middle line:90% of the wall and the fluid. 01:00:31.280 --> 01:00:33.230 align:middle line:84% This fluids are actually transition. 01:00:33.230 --> 01:00:34.760 align:middle line:84% The temperature goes from the wall 01:00:34.760 --> 01:00:41.150 align:middle line:84% to gradually to the center of the fluid or ambient. 01:00:41.150 --> 01:00:45.290 align:middle line:84% And the proportionality constant here 01:00:45.290 --> 01:00:50.960 align:middle line:84% is h, the heat transfer coefficient. 01:00:50.960 --> 01:00:56.030 align:middle line:90% But h is a flow dependent. 01:00:56.030 --> 01:00:58.680 align:middle line:90% It's not a mature property. 01:00:58.680 --> 01:01:02.870 align:middle line:84% It depends on how fast the fluid flow 01:01:02.870 --> 01:01:05.750 align:middle line:90% and depends on the geometry. 01:01:05.750 --> 01:01:11.540 align:middle line:84% So this is a big topic in 2005, 2006. 01:01:11.540 --> 01:01:15.500 align:middle line:84% And we know there is a natural convection, forced convection, 01:01:15.500 --> 01:01:21.290 align:middle line:84% just in terms of the terminology there. 01:01:21.290 --> 01:01:25.670 align:middle line:84% So those are conduction and convection. 01:01:25.670 --> 01:01:28.970 align:middle line:84% And, of course, the thermal of heat transfer 01:01:28.970 --> 01:01:33.780 align:middle line:90% is radiation, thermal radiation. 01:01:33.780 --> 01:01:41.150 align:middle line:84% Thermal radiation for blackbody one single surface 01:01:41.150 --> 01:01:43.880 align:middle line:90% or black object. 01:01:43.880 --> 01:01:49.460 align:middle line:84% The emission is given by the Stefan-Boltzmann law 01:01:49.460 --> 01:01:53.570 align:middle line:84% as the proportional to temperature force power. 01:01:53.570 --> 01:01:57.220 align:middle line:84% The proportionality constant is Stefan-Boltzmann constant. 01:01:57.220 --> 01:02:02.030 align:middle line:90% So this is a for black object. 01:02:02.030 --> 01:02:04.260 align:middle line:90% A real object is not black. 01:02:04.260 --> 01:02:07.490 align:middle line:84% So we use a emissivity to characterize it. 01:02:07.490 --> 01:02:11.850 align:middle line:84% And we'll discuss some more down the road. 01:02:11.850 --> 01:02:16.650 align:middle line:84% Now, if I have two objects, exchange heat, in this case, 01:02:16.650 --> 01:02:18.230 align:middle line:90% it could be vacuum. 01:02:18.230 --> 01:02:20.990 align:middle line:84% That's the difference of radiation 01:02:20.990 --> 01:02:24.470 align:middle line:84% compared to conduction and convection, which 01:02:24.470 --> 01:02:25.560 align:middle line:90% requires a media. 01:02:25.560 --> 01:02:29.680 align:middle line:84% And here, the heat transfer is by electromagnetic waves. 01:02:29.680 --> 01:02:36.020 align:middle line:84% So I wrote a simple form of relating the heat transfer 01:02:36.020 --> 01:02:38.840 align:middle line:84% is the [INAUDIBLE] to the fourth power. 01:02:38.840 --> 01:02:41.630 align:middle line:84% And remember here, you have to use a Kelvin, not 01:02:41.630 --> 01:02:43.070 align:middle line:90% degree Celsius. 01:02:43.070 --> 01:02:45.530 align:middle line:84% Look at the units and so on in Kelvin. 01:02:45.530 --> 01:02:50.250 align:middle line:84% And if the object is not black, we use the emissivity. 01:02:50.250 --> 01:02:52.730 align:middle line:84% And here is the factor between two surfaces, 01:02:52.730 --> 01:02:55.010 align:middle line:84% because the two surfaces may be different. 01:02:55.010 --> 01:02:59.100 align:middle line:84% Like I said, we'll discuss more down the road. 01:02:59.100 --> 01:03:02.670 align:middle line:84% So those are three modes of heat [? conduction. ?] 01:03:02.670 --> 01:03:08.470 align:middle line:84% And in this course, we'll talk more on conduction 01:03:08.470 --> 01:03:11.710 align:middle line:84% and we'll talk more on radiation. 01:03:11.710 --> 01:03:13.090 align:middle line:90% You have learned a lot. 01:03:13.090 --> 01:03:14.960 align:middle line:84% Some of you learned a lot of convection. 01:03:14.960 --> 01:03:19.510 align:middle line:90% So that's probably fear. 01:03:19.510 --> 01:03:23.530 align:middle line:84% Now, let's think a little bit more on conduction. 01:03:23.530 --> 01:03:26.740 align:middle line:84% If I have a one dimensional multi generation inside, 01:03:26.740 --> 01:03:30.280 align:middle line:84% I can say heat flow is constant and secure is constant. 01:03:30.280 --> 01:03:32.090 align:middle line:90% You go back to the Fourier law. 01:03:32.090 --> 01:03:33.110 align:middle line:90% You integrate it. 01:03:33.110 --> 01:03:35.650 align:middle line:84% You find out that the heat transfer between the two 01:03:35.650 --> 01:03:40.420 align:middle line:84% points from this to the other side at steady state 01:03:40.420 --> 01:03:45.250 align:middle line:84% is proportional to thermal conductivity area inversely 01:03:45.250 --> 01:03:47.080 align:middle line:90% proportional to the length. 01:03:47.080 --> 01:03:50.470 align:middle line:84% So if you want to do thermal isolation, what do you do? 01:03:50.470 --> 01:03:52.720 align:middle line:90% You use a long object. 01:03:52.720 --> 01:03:55.870 align:middle line:90% You use a small cross section. 01:03:55.870 --> 01:03:58.100 align:middle line:90% That's the thermal isolation. 01:03:58.100 --> 01:04:02.320 align:middle line:84% A lot of times when you design a thermal system, 01:04:02.320 --> 01:04:07.030 align:middle line:84% not only heat getting in, you also want to isolate it. 01:04:07.030 --> 01:04:14.890 align:middle line:84% And we can combine all this right into thermal resistance. 01:04:14.890 --> 01:04:16.570 align:middle line:90% That's just a definition. 01:04:16.570 --> 01:04:20.230 align:middle line:84% Because this way, it looks very similar to electrical circuit 01:04:20.230 --> 01:04:25.450 align:middle line:84% where your driving voltage is now the temperature difference 01:04:25.450 --> 01:04:30.680 align:middle line:84% and your current is the heat current and your resistance. 01:04:30.680 --> 01:04:35.890 align:middle line:84% So you can use the same way as you do circuit analysis if you 01:04:35.890 --> 01:04:37.690 align:middle line:90% know the thermal resistance. 01:04:37.690 --> 01:04:40.660 align:middle line:84% This is for different geometries, different. 01:04:40.660 --> 01:04:45.940 align:middle line:84% And even for convection, you can express, 01:04:45.940 --> 01:04:48.200 align:middle line:90% you go to do thermal resistance. 01:04:48.200 --> 01:04:52.270 align:middle line:84% So you can build some resistor network 01:04:52.270 --> 01:04:56.540 align:middle line:90% to do some simple heat transfer. 01:04:56.540 --> 01:05:02.310 align:middle line:84% And another thing that's important to keep in mind 01:05:02.310 --> 01:05:03.690 align:middle line:90% is the order of magnitude. 01:05:03.690 --> 01:05:05.250 align:middle line:90% What are the good conductors? 01:05:05.250 --> 01:05:06.990 align:middle line:90% What are good insulators? 01:05:06.990 --> 01:05:11.200 align:middle line:84% And the best conductor turns out is diamond. 01:05:11.200 --> 01:05:11.700 align:middle line:90% Why? 01:05:11.700 --> 01:05:13.930 align:middle line:84% That's because the bumping, the spring. 01:05:13.930 --> 01:05:18.210 align:middle line:84% So in this case is the wave, atomic wave 01:05:18.210 --> 01:05:20.750 align:middle line:90% that carries the heat. 01:05:20.750 --> 01:05:24.320 align:middle line:84% So if the bonding between the atoms is strong, 01:05:24.320 --> 01:05:27.200 align:middle line:90% the spring constant is large. 01:05:27.200 --> 01:05:28.760 align:middle line:90% The velocity is large. 01:05:28.760 --> 01:05:31.790 align:middle line:84% So that's why diamond is a good conductor. 01:05:31.790 --> 01:05:34.790 align:middle line:90% And metals are not that good. 01:05:34.790 --> 01:05:36.770 align:middle line:90% Metals are by electrons. 01:05:36.770 --> 01:05:41.840 align:middle line:84% And insulators, you can see the wood, amorphous material, pores, 01:05:41.840 --> 01:05:44.450 align:middle line:84% those are poor thermal conductors 01:05:44.450 --> 01:05:47.420 align:middle line:84% because the atomic arrangement is random. 01:05:47.420 --> 01:05:50.840 align:middle line:84% And that randomness makes the wave harder 01:05:50.840 --> 01:05:54.390 align:middle line:90% to propagate in the material. 01:05:54.390 --> 01:06:00.390 align:middle line:90% So this is, again, macroscopic. 01:06:00.390 --> 01:06:05.940 align:middle line:84% Now I'm going to also give you the other view, microscopic 01:06:05.940 --> 01:06:13.730 align:middle line:84% of heat transfer, and the kinetic picture. 01:06:13.730 --> 01:06:18.120 align:middle line:84% So what happens, how heat really is conducting? 01:06:18.120 --> 01:06:21.180 align:middle line:90% Let's think about the molecules. 01:06:21.180 --> 01:06:27.210 align:middle line:84% And the molecules, let's say we have a box. 01:06:27.210 --> 01:06:28.320 align:middle line:90% And one side is hot. 01:06:28.320 --> 01:06:29.500 align:middle line:90% The other side is cold. 01:06:29.500 --> 01:06:31.420 align:middle line:90% Let's forget about convection. 01:06:31.420 --> 01:06:34.410 align:middle line:84% How quick it goes from one [INAUDIBLE] side, 01:06:34.410 --> 01:06:38.480 align:middle line:84% we add the molecule to the cosine. 01:06:38.480 --> 01:06:41.840 align:middle line:84% It's really on the hot side, the air molecule 01:06:41.840 --> 01:06:44.570 align:middle line:90% collided with the wall. 01:06:44.570 --> 01:06:46.100 align:middle line:90% And on the wall is hot. 01:06:46.100 --> 01:06:49.220 align:middle line:90% It means the velocity is faster. 01:06:49.220 --> 01:06:53.090 align:middle line:84% So this molecule will get a faster velocity 01:06:53.090 --> 01:06:56.300 align:middle line:84% due to that energy exchange between the wall and the air 01:06:56.300 --> 01:06:58.460 align:middle line:90% molecules. 01:06:58.460 --> 01:07:01.910 align:middle line:84% Now, this hot air molecule will collide with the [INAUDIBLE] 01:07:01.910 --> 01:07:02.690 align:middle line:90% molecule. 01:07:02.690 --> 01:07:05.930 align:middle line:84% Of course, we have a chance to go randomly. 01:07:05.930 --> 01:07:08.750 align:middle line:84% Every molecule is moving a few 100 meters per second, 01:07:08.750 --> 01:07:09.810 align:middle line:90% as we talked before. 01:07:09.810 --> 01:07:15.050 align:middle line:84% And they collide with the cooler one. 01:07:15.050 --> 01:07:18.590 align:middle line:84% And they pump some of that excess energy to the next 01:07:18.590 --> 01:07:21.350 align:middle line:84% [? level. ?] The next [? level ?] will go back 01:07:21.350 --> 01:07:23.120 align:middle line:90% and forth. 01:07:23.120 --> 01:07:26.180 align:middle line:84% Again, they do this, cascade energy from the hot 01:07:26.180 --> 01:07:27.980 align:middle line:90% to the cold side. 01:07:27.980 --> 01:07:31.220 align:middle line:90% It's a diffusion process. 01:07:31.220 --> 01:07:37.670 align:middle line:84% And typically, there is a the distance of this collision. 01:07:37.670 --> 01:07:40.250 align:middle line:90% You can go to estimate it. 01:07:40.250 --> 01:07:43.400 align:middle line:84% And just turns out that this distance 01:07:43.400 --> 01:07:45.860 align:middle line:84% between the average of multiple collision 01:07:45.860 --> 01:07:48.470 align:middle line:90% is about 100 nanometer. 01:07:48.470 --> 01:07:51.770 align:middle line:84% In this room, the air molecule distance between collision 01:07:51.770 --> 01:07:54.370 align:middle line:90% is about 100 nanometer. 01:07:54.370 --> 01:08:02.530 align:middle line:84% And so now I give you a few more definition. 01:08:02.530 --> 01:08:07.270 align:middle line:84% The energy per particle, let's take energy per particle as e. 01:08:07.270 --> 01:08:12.970 align:middle line:84% And the average velocity is v. And time between collision 01:08:12.970 --> 01:08:14.410 align:middle line:90% is tau. 01:08:14.410 --> 01:08:18.170 align:middle line:84% And distance between collision is gamma. 01:08:18.170 --> 01:08:19.490 align:middle line:90% That's the mean free path. 01:08:19.490 --> 01:08:22.359 align:middle line:84% So time is the average time between collision 01:08:22.359 --> 01:08:24.100 align:middle line:90% is the relaxation time. 01:08:24.100 --> 01:08:30.430 align:middle line:84% And this distance and the time is related by the velocity. 01:08:30.430 --> 01:08:34.510 align:middle line:90% So what is a heat transfer? 01:08:34.510 --> 01:08:40.600 align:middle line:84% When I think about heat going through this imaginary surface 01:08:40.600 --> 01:08:43.840 align:middle line:90% here, how I calculate it? 01:08:43.840 --> 01:08:45.010 align:middle line:90% I can't. 01:08:45.010 --> 01:08:47.500 align:middle line:90% I do [INAUDIBLE]. 01:08:47.500 --> 01:08:52.510 align:middle line:84% I will say, OK, only those molecules within one 01:08:52.510 --> 01:08:54.040 align:middle line:90% mean free path. 01:08:54.040 --> 01:08:59.140 align:middle line:84% vx is a velocity component in the x direction, 01:08:59.140 --> 01:09:00.560 align:middle line:90% times the collision time. 01:09:00.560 --> 01:09:05.380 align:middle line:84% So only those molecules can go zip through the interface 01:09:05.380 --> 01:09:08.620 align:middle line:84% without collision, because tau is the average time 01:09:08.620 --> 01:09:11.520 align:middle line:90% between collision. 01:09:11.520 --> 01:09:15.450 align:middle line:84% So this part of the molecule is harder to go from this side 01:09:15.450 --> 01:09:16.920 align:middle line:90% to the other side. 01:09:16.920 --> 01:09:20.160 align:middle line:84% And on this side, the molecule is cooler again, 01:09:20.160 --> 01:09:22.260 align:middle line:84% in the vx times tau [? average, ?] 01:09:22.260 --> 01:09:25.890 align:middle line:84% they go from this side to the other side. 01:09:25.890 --> 01:09:28.870 align:middle line:90% And I take the difference. 01:09:28.870 --> 01:09:30.899 align:middle line:90% I count all the molecules. 01:09:30.899 --> 01:09:31.899 align:middle line:90% I take the difference. 01:09:31.899 --> 01:09:33.840 align:middle line:90% That's my reflux. 01:09:33.840 --> 01:09:37.710 align:middle line:90% So let me write down the math. 01:09:37.710 --> 01:09:39.240 align:middle line:90% That's what I do. 01:09:39.240 --> 01:09:43.140 align:middle line:84% I say on the left hand side, this 01:09:43.140 --> 01:09:45.479 align:middle line:84% is a per unit volume of how many. 01:09:45.479 --> 01:09:51.420 align:middle line:84% N is the particle number density, the second bullet 01:09:51.420 --> 01:09:52.529 align:middle line:90% there. 01:09:52.529 --> 01:09:56.460 align:middle line:84% Each particle, how much energy it has? 01:09:56.460 --> 01:09:59.970 align:middle line:84% And this is the velocity in the x direction. 01:09:59.970 --> 01:10:05.770 align:middle line:84% So I say only in this range, from x to vx minus tau. 01:10:05.770 --> 01:10:07.590 align:middle line:84% In this range, you can go through. 01:10:07.590 --> 01:10:11.710 align:middle line:84% On the other side is x plus vx tau. 01:10:11.710 --> 01:10:13.360 align:middle line:90% You can do more detail. 01:10:13.360 --> 01:10:16.690 align:middle line:84% I hear this is a very simple argument. 01:10:16.690 --> 01:10:20.650 align:middle line:84% So that gives me a [INAUDIBLE] for heat plotting. 01:10:20.650 --> 01:10:26.435 align:middle line:84% Go check a unit is a watt per meter squared, [INAUDIBLE] plus. 01:10:26.435 --> 01:10:28.810 align:middle line:84% In the next lecture we'll just do a [INAUDIBLE] expansion 01:10:28.810 --> 01:10:34.360 align:middle line:84% of these two terms and write it into a differential form, 01:10:34.360 --> 01:10:36.320 align:middle line:84% because this is about 100 nanometers. 01:10:36.320 --> 01:10:41.050 align:middle line:84% If I do meters or centimeters or millimeters, 01:10:41.050 --> 01:10:43.930 align:middle line:84% that's essentially continuum, a very small delta. 01:10:43.930 --> 01:10:46.600 align:middle line:90% So I do the derivative. 01:10:46.600 --> 01:10:49.040 align:middle line:90% And I do a Taylor expansion. 01:10:49.040 --> 01:10:53.800 align:middle line:84% This one half is because there's only half of this go this way, 01:10:53.800 --> 01:10:54.710 align:middle line:90% half goes that way. 01:10:54.710 --> 01:10:57.290 align:middle line:84% So that's where the [INAUDIBLE] came from. 01:10:57.290 --> 01:11:00.940 align:middle line:84% And after I do the Taylor expansion, 01:11:00.940 --> 01:11:04.870 align:middle line:90% I have e and v and vx. 01:11:04.870 --> 01:11:06.850 align:middle line:90% vx is random velocity. 01:11:06.850 --> 01:11:10.760 align:middle line:84% I pull out this independent of distance. 01:11:10.760 --> 01:11:12.010 align:middle line:90% It could be dependent on this. 01:11:12.010 --> 01:11:15.010 align:middle line:84% I'm just making an assumption, approximation. 01:11:15.010 --> 01:11:16.420 align:middle line:90% In there are different distance. 01:11:16.420 --> 01:11:18.250 align:middle line:90% This vx square. 01:11:18.250 --> 01:11:20.140 align:middle line:90% vx square is random. 01:11:20.140 --> 01:11:24.120 align:middle line:84% So it's one third of the average velocity, one third 01:11:24.120 --> 01:11:24.970 align:middle line:90% of v squared. 01:11:24.970 --> 01:11:29.270 align:middle line:84% So that's my one third v square replacing this vx square. 01:11:29.270 --> 01:11:30.560 align:middle line:90% Tau is here. 01:11:30.560 --> 01:11:35.240 align:middle line:84% And the n times e is a per unit volume 01:11:35.240 --> 01:11:38.610 align:middle line:84% how much energy, internal energy the molecule has. 01:11:38.610 --> 01:11:43.760 align:middle line:90% So I have this n times e is u. 01:11:43.760 --> 01:11:46.120 align:middle line:84% And I take a general do, dg, dbdx. 01:11:46.120 --> 01:11:49.320 align:middle line:90% 01:11:49.320 --> 01:11:50.970 align:middle line:90% OK, what you get? 01:11:50.970 --> 01:11:54.750 align:middle line:90% You got [INAUDIBLE]. 01:11:54.750 --> 01:11:58.500 align:middle line:84% Because here is one third v squared, tau [INAUDIBLE]. 01:11:58.500 --> 01:12:00.790 align:middle line:84% And that's the thermal conductivity. 01:12:00.790 --> 01:12:03.810 align:middle line:84% And this is the temperature gradient. 01:12:03.810 --> 01:12:04.740 align:middle line:90% You can do that. 01:12:04.740 --> 01:12:08.640 align:middle line:84% You can go back and do your Fick's law and Newton's shear 01:12:08.640 --> 01:12:09.370 align:middle line:90% stress law. 01:12:09.370 --> 01:12:15.110 align:middle line:84% In fact, all the diffusion law you learn in three steps. 01:12:15.110 --> 01:12:18.110 align:middle line:90% 01:12:18.110 --> 01:12:19.280 align:middle line:90% But yes. 01:12:19.280 --> 01:12:21.320 align:middle line:84% STUDENT: You said we could move the velocity out 01:12:21.320 --> 01:12:23.570 align:middle line:84% of the derivative because of its constant. 01:12:23.570 --> 01:12:26.170 align:middle line:84% But isn't the velocity related to the temperature? 01:12:26.170 --> 01:12:28.340 align:middle line:90% GANG CHEN: Yeah, good question. 01:12:28.340 --> 01:12:32.900 align:middle line:84% This is later on when discuss the thermoelectric effect. 01:12:32.900 --> 01:12:35.810 align:middle line:90% I'll come back to this. 01:12:35.810 --> 01:12:37.700 align:middle line:84% Here I'm talking about a molecule. 01:12:37.700 --> 01:12:41.615 align:middle line:84% And I just wanted to show you the [? Fourier ?] law. 01:12:41.615 --> 01:12:43.520 align:middle line:84% And they're clearly approximation. 01:12:43.520 --> 01:12:48.410 align:middle line:84% And what are you talking is more like a coupled mass and heat 01:12:48.410 --> 01:12:49.520 align:middle line:90% transfer. 01:12:49.520 --> 01:12:53.030 align:middle line:84% And, in fact, if you learn once the heat transfer, 01:12:53.030 --> 01:12:54.895 align:middle line:84% you know mass and heat transfer couples. 01:12:54.895 --> 01:12:59.210 align:middle line:90% 01:12:59.210 --> 01:13:06.650 align:middle line:84% So the thermal conductivity is one third specific heat velocity 01:13:06.650 --> 01:13:09.020 align:middle line:90% and mean free path. 01:13:09.020 --> 01:13:13.220 align:middle line:84% And the specific heat is per unit volume. 01:13:13.220 --> 01:13:16.700 align:middle line:84% If I do capital sales per unit volume based, 01:13:16.700 --> 01:13:19.910 align:middle line:84% and typically we do per unit mass based since this 01:13:19.910 --> 01:13:24.550 align:middle line:84% is a density price per unit mass basis. 01:13:24.550 --> 01:13:30.360 align:middle line:84% So this is the a very useful relation to keep in mind. 01:13:30.360 --> 01:13:33.460 align:middle line:84% Simple thermal conductivity depends 01:13:33.460 --> 01:13:38.080 align:middle line:84% on how many energy is stored by the molecule, how fast they 01:13:38.080 --> 01:13:41.740 align:middle line:84% travel, and how far they travel between quality. 01:13:41.740 --> 01:13:43.540 align:middle line:84% So if you want a high thermal conductivity, 01:13:43.540 --> 01:13:46.840 align:middle line:84% you want the power of [INAUDIBLE]. 01:13:46.840 --> 01:13:50.480 align:middle line:84% Low thermal conductivity, you reduce that. 01:13:50.480 --> 01:13:53.800 align:middle line:90% 01:13:53.800 --> 01:14:00.430 align:middle line:84% And for most solid, they say is about 10 to the sixth power. 01:14:00.430 --> 01:14:03.490 align:middle line:84% It doesn't vary by a factor of 5. 01:14:03.490 --> 01:14:07.630 align:middle line:84% So when I do on my back of envelope order of magnitude 01:14:07.630 --> 01:14:10.130 align:middle line:84% estimation, I say is 10 to the sixth. 01:14:10.130 --> 01:14:12.490 align:middle line:90% You go to check. 01:14:12.490 --> 01:14:18.130 align:middle line:84% And velocity in solid is just you can roughly think the speed 01:14:18.130 --> 01:14:23.230 align:middle line:84% of sound, few 100 or few 1,000 meters per second. 01:14:23.230 --> 01:14:26.720 align:middle line:90% The mean free path is short-- 01:14:26.720 --> 01:14:30.020 align:middle line:90% nanometers, 100 nanometers. 01:14:30.020 --> 01:14:34.430 align:middle line:90% So that's the range order. 01:14:34.430 --> 01:14:38.690 align:middle line:84% So this is I think most of you, probably 01:14:38.690 --> 01:14:40.700 align:middle line:90% in 2005, you haven't seen it. 01:14:40.700 --> 01:14:42.180 align:middle line:90% It's very simple. 01:14:42.180 --> 01:14:49.220 align:middle line:84% But the picture is really the diffusion picture or similar. 01:14:49.220 --> 01:14:52.190 align:middle line:90% Let me give you-- 01:14:52.190 --> 01:14:55.340 align:middle line:90% I haven't finished radiation. 01:14:55.340 --> 01:14:56.330 align:middle line:90% So I come back to-- 01:14:56.330 --> 01:14:58.170 align:middle line:84% I said that Stefan-Boltzmann law. 01:14:58.170 --> 01:15:03.770 align:middle line:84% And what I want to show you next is 01:15:03.770 --> 01:15:06.350 align:middle line:84% how I can derive Stefan-Boltzmann law 01:15:06.350 --> 01:15:08.750 align:middle line:90% from the statistics. 01:15:08.750 --> 01:15:11.420 align:middle line:90% I just showed. 01:15:11.420 --> 01:15:17.480 align:middle line:90% So I'm considering enclosure. 01:15:17.480 --> 01:15:21.500 align:middle line:84% Let me imagine the enclosure is perfectly reflecting. 01:15:21.500 --> 01:15:22.340 align:middle line:90% There are photons. 01:15:22.340 --> 01:15:24.410 align:middle line:84% And the walls is the temperature, t. 01:15:24.410 --> 01:15:26.010 align:middle line:90% So it's a equilibrium system. 01:15:26.010 --> 01:15:29.480 align:middle line:84% I want to see how many the electromagnetic waves 01:15:29.480 --> 01:15:35.040 align:middle line:84% inside this box, how much energy they have, 01:15:35.040 --> 01:15:36.840 align:middle line:84% a constant temperature-- equilibrium, 01:15:36.840 --> 01:15:38.230 align:middle line:90% thermal equilibrium. 01:15:38.230 --> 01:15:45.000 align:middle line:84% So let's go back to a little bit of the basic relations 01:15:45.000 --> 01:15:47.300 align:middle line:90% of thermal electromagnetic wave. 01:15:47.300 --> 01:15:51.270 align:middle line:84% We know the speed of light is proportional to its speed 01:15:51.270 --> 01:15:55.470 align:middle line:84% of light as a wavelength times frequency. 01:15:55.470 --> 01:15:58.740 align:middle line:90% That's a high school learn. 01:15:58.740 --> 01:16:04.470 align:middle line:84% And definition, I say angular velocity is 2 pi mu. 01:16:04.470 --> 01:16:08.430 align:middle line:84% We vector magnitude is 2 pi over lambda. 01:16:08.430 --> 01:16:09.900 align:middle line:90% What is the wave vector? 01:16:09.900 --> 01:16:13.320 align:middle line:84% The wave propagates in certain direction. 01:16:13.320 --> 01:16:19.080 align:middle line:84% And so because the direction is a vector. 01:16:19.080 --> 01:16:21.840 align:middle line:84% 2 pi lambda, lambda is a wavelength. 01:16:21.840 --> 01:16:23.250 align:middle line:90% It's a scalar. 01:16:23.250 --> 01:16:26.020 align:middle line:90% And the rationale is the vector. 01:16:26.020 --> 01:16:32.970 align:middle line:84% So it's a kx, ky, kz if you do Cartesian coordinate. 01:16:32.970 --> 01:16:38.130 align:middle line:84% And so I can write it C equals mu times lambda. 01:16:38.130 --> 01:16:41.280 align:middle line:84% In terms of frequency and vector, 01:16:41.280 --> 01:16:44.520 align:middle line:90% it's c times omega equals to ct. 01:16:44.520 --> 01:16:48.000 align:middle line:84% So this relation between the vector, magnitude, 01:16:48.000 --> 01:16:50.430 align:middle line:84% and the frequency is called dispersion. 01:16:50.430 --> 01:16:51.870 align:middle line:90% And in the speed-- 01:16:51.870 --> 01:16:54.660 align:middle line:84% in the case of light, it's a linear. 01:16:54.660 --> 01:17:00.060 align:middle line:84% C is 310 to the eighth meter per second. 01:17:00.060 --> 01:17:02.280 align:middle line:84% And, of course, because the vector, 01:17:02.280 --> 01:17:04.600 align:middle line:84% so it's a square root of the components. 01:17:04.600 --> 01:17:07.160 align:middle line:90% 01:17:07.160 --> 01:17:09.980 align:middle line:90% So that's the dispersion. 01:17:09.980 --> 01:17:12.440 align:middle line:90% And now I want to count. 01:17:12.440 --> 01:17:18.470 align:middle line:84% My question is, how much energy photon has inside this box? 01:17:18.470 --> 01:17:23.330 align:middle line:84% I'm going to count how many modes you have. 01:17:23.330 --> 01:17:26.990 align:middle line:84% Remember each mode, the Bose-Einstein distribution 01:17:26.990 --> 01:17:34.430 align:middle line:84% already tells me for each mode how many photons. 01:17:34.430 --> 01:17:37.510 align:middle line:90% So how many modes? 01:17:37.510 --> 01:17:39.030 align:middle line:84% So that's basically I'm counting. 01:17:39.030 --> 01:17:42.510 align:middle line:90% 01:17:42.510 --> 01:17:44.670 align:middle line:84% Because I'm a perfect [INAUDIBLE], 01:17:44.670 --> 01:17:48.330 align:middle line:84% you can see the mode has to be standing wave here, 01:17:48.330 --> 01:17:51.300 align:middle line:90% either this way or this way. 01:17:51.300 --> 01:17:53.820 align:middle line:90% That boundary is 0. 01:17:53.820 --> 01:17:55.740 align:middle line:90% STUDENT: Why is it 0? 01:17:55.740 --> 01:17:57.540 align:middle line:90% Why should it be 0? 01:17:57.540 --> 01:17:59.910 align:middle line:84% GANG CHEN: Otherwise it doesn't get a steady state. 01:17:59.910 --> 01:18:03.720 align:middle line:90% It keeps propagating. 01:18:03.720 --> 01:18:07.350 align:middle line:84% So this is my wavelength component 01:18:07.350 --> 01:18:12.090 align:middle line:84% in the x direction. kx is a corresponding wavelength 01:18:12.090 --> 01:18:13.740 align:middle line:90% in x direction. 01:18:13.740 --> 01:18:18.000 align:middle line:90% And the lx is the length here. 01:18:18.000 --> 01:18:21.030 align:middle line:84% So if I just say, this must satisfy the rule, 01:18:21.030 --> 01:18:23.490 align:middle line:90% then I have to have integer. 01:18:23.490 --> 01:18:26.790 align:middle line:90% Those are the possibilities. 01:18:26.790 --> 01:18:31.800 align:middle line:84% And that translated in the possibility of my k. 01:18:31.800 --> 01:18:35.190 align:middle line:90% kx just is 2 pi over lambda x. 01:18:35.190 --> 01:18:39.960 align:middle line:90% So this is n tau pi 2lx. 01:18:39.960 --> 01:18:47.160 align:middle line:84% OK, so each combination of x and y and z, each set 01:18:47.160 --> 01:18:50.490 align:middle line:90% gives me one mode. 01:18:50.490 --> 01:18:54.330 align:middle line:84% And I want to find out how much energy, I just 01:18:54.330 --> 01:18:56.430 align:middle line:90% sum up all those modes. 01:18:56.430 --> 01:19:00.400 align:middle line:90% So I sum that up. 01:19:00.400 --> 01:19:02.230 align:middle line:84% And remember, when I do molecules, 01:19:02.230 --> 01:19:06.370 align:middle line:84% I do velocity from minus infinity to plus infinity. 01:19:06.370 --> 01:19:10.270 align:middle line:84% And here when I do this, I do discreet summation 01:19:10.270 --> 01:19:12.370 align:middle line:90% of nx, and ny, and nz. 01:19:12.370 --> 01:19:16.840 align:middle line:90% So I do this summation. 01:19:16.840 --> 01:19:20.290 align:middle line:90% This is an x, y, and z. 01:19:20.290 --> 01:19:25.300 align:middle line:84% Each mode has this is the number of photons in this area set. 01:19:25.300 --> 01:19:30.030 align:middle line:84% And this is the energy of a photon is [INAUDIBLE]. 01:19:30.030 --> 01:19:32.550 align:middle line:84% I got the factor of 2 because the electromagnetic wave 01:19:32.550 --> 01:19:33.960 align:middle line:90% is a transverse wave. 01:19:33.960 --> 01:19:39.420 align:middle line:84% And it has a two component, two polarizations, so that factor 01:19:39.420 --> 01:19:42.400 align:middle line:90% of 2 [INAUDIBLE]. 01:19:42.400 --> 01:19:47.530 align:middle line:84% OK, if you don't look at this, that's where my starting point. 01:19:47.530 --> 01:19:50.740 align:middle line:84% And what I want to do is, rather than do the summation, 01:19:50.740 --> 01:19:54.460 align:middle line:84% I'm going to translate it into integration. 01:19:54.460 --> 01:19:56.950 align:middle line:90% Summation is over n. 01:19:56.950 --> 01:20:02.650 align:middle line:84% So if you look at this interval between n and k, it's 2 pi 2lx, 01:20:02.650 --> 01:20:08.260 align:middle line:84% so when I have a dkx, I divide by 2 pi 2lx. 01:20:08.260 --> 01:20:11.470 align:middle line:84% That's n if this is large number. 01:20:11.470 --> 01:20:15.510 align:middle line:84% If small, you have a lot of problem. 01:20:15.510 --> 01:20:22.680 align:middle line:84% So I translate this summation, nx, into this dkx integration. 01:20:22.680 --> 01:20:26.350 align:middle line:90% I do same for ky, kz. 01:20:26.350 --> 01:20:27.515 align:middle line:90% This is-- I'm just copying. 01:20:27.515 --> 01:20:30.810 align:middle line:90% 01:20:30.810 --> 01:20:35.910 align:middle line:84% I go the extra step here just for the later purpose. 01:20:35.910 --> 01:20:38.980 align:middle line:84% Because my function is a is even function. 01:20:38.980 --> 01:20:42.840 align:middle line:84% So I extend to minus infinity to plus infinity. 01:20:42.840 --> 01:20:44.460 align:middle line:84% The difference is the factor of 2. 01:20:44.460 --> 01:20:47.940 align:middle line:84% So I don't have this 2 here anymore, because the factor of 2 01:20:47.940 --> 01:20:51.030 align:middle line:90% is gone. 01:20:51.030 --> 01:20:53.640 align:middle line:84% That's just for my later purpose. 01:20:53.640 --> 01:20:56.790 align:middle line:84% The end result, this is just an equivalent. 01:20:56.790 --> 01:20:59.610 align:middle line:84% And what it means is I can, rather than standing wave, 01:20:59.610 --> 01:21:01.740 align:middle line:84% I can say do two counter-propagating. 01:21:01.740 --> 01:21:03.730 align:middle line:90% One goes left, one goes right. 01:21:03.730 --> 01:21:07.470 align:middle line:84% That's when you do the maximal velocity is minus 01:21:07.470 --> 01:21:08.670 align:middle line:90% infinity, plus infinity. 01:21:08.670 --> 01:21:11.580 align:middle line:90% So that's equivalent. 01:21:11.580 --> 01:21:16.130 align:middle line:84% OK, I think I will probably have to stop here. 01:21:16.130 --> 01:21:19.500 align:middle line:84% There are two more slides you can look at, but I'll discuss. 01:21:19.500 --> 01:21:23.490 align:middle line:84% What's coming is the blackbody radiation 01:21:23.490 --> 01:21:25.860 align:middle line:84% in each wavelength, how much energy 01:21:25.860 --> 01:21:28.375 align:middle line:90% varies with simple [INAUDIBLE]. 01:21:28.375 --> 01:21:30.990 align:middle line:90% 01:21:30.990 --> 01:21:32.540 align:middle line:90% OK.