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 --> 00:00:16.520 align:middle line:84% from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:16.520 --> 00:00:19.910 align:middle line:90% at ocw.mit.edu. 00:00:19.910 --> 00:00:23.390 align:middle line:84% GANG CHEN: So if I give a very quick summary of what we're 00:00:23.390 --> 00:00:29.810 align:middle line:84% talking in the first lecture, we reviewed first and second law. 00:00:29.810 --> 00:00:32.720 align:middle line:84% And of course, I assume that you all 00:00:32.720 --> 00:00:35.180 align:middle line:90% have seen in various courses. 00:00:35.180 --> 00:00:39.530 align:middle line:84% And this is the maximum thermodynamic efficiency 00:00:39.530 --> 00:00:45.300 align:middle line:84% of any heat engine operating in addition to the reservoirs. 00:00:45.300 --> 00:00:50.450 align:middle line:90% One is cold, the other is hot. 00:00:50.450 --> 00:00:53.150 align:middle line:90% So that's the key point. 00:00:53.150 --> 00:00:58.040 align:middle line:84% And then for many of you, probably first time is, 00:00:58.040 --> 00:01:01.080 align:middle line:84% I introduced if you go to the statistical side, 00:01:01.080 --> 00:01:05.940 align:middle line:84% the microscopic picture, the one quantum mechanical state, 00:01:05.940 --> 00:01:12.660 align:middle line:84% you count how many particles, either electrons or molecules 00:01:12.660 --> 00:01:17.190 align:middle line:84% or photons or lattice vibration photons. 00:01:17.190 --> 00:01:21.990 align:middle line:84% And for electrons is given by Fermi-Dirac distribution, 00:01:21.990 --> 00:01:25.990 align:middle line:84% and where this mu is the chemical potential. 00:01:25.990 --> 00:01:30.660 align:middle line:84% That's the energy you need to take a particle in or out 00:01:30.660 --> 00:01:32.040 align:middle line:90% of the system. 00:01:32.040 --> 00:01:36.690 align:middle line:84% And e is the energy of that quantum state 00:01:36.690 --> 00:01:39.640 align:middle line:90% and t is the temperature. 00:01:39.640 --> 00:01:44.890 align:middle line:84% And then say that's for electrons where the Pauli 00:01:44.890 --> 00:01:48.520 align:middle line:84% exclusion principle will state the maximum possibility 00:01:48.520 --> 00:01:51.910 align:middle line:84% of having an electron in accordance with this one. 00:01:51.910 --> 00:01:56.140 align:middle line:84% So this number is between 0 and 1. 00:01:56.140 --> 00:02:05.470 align:middle line:84% And then I introduced also the other type of particles, those-- 00:02:05.470 --> 00:02:11.170 align:middle line:84% the photon electromagnetic wave or lattice 00:02:11.170 --> 00:02:14.920 align:middle line:84% vibration we call [? photon ?] or even molecules. 00:02:14.920 --> 00:02:18.310 align:middle line:84% This is the Poisson [INAUDIBLE] distribution 00:02:18.310 --> 00:02:21.010 align:middle line:84% where, again, this is the energy and mu 00:02:21.010 --> 00:02:22.420 align:middle line:90% is the chemical potential. 00:02:22.420 --> 00:02:26.890 align:middle line:84% But here we're not limited by the Pauli exclusion. 00:02:26.890 --> 00:02:32.200 align:middle line:84% So in one quantum state, this number can be larger than one. 00:02:32.200 --> 00:02:35.830 align:middle line:84% And if you take out this minus 1 plus one, 00:02:35.830 --> 00:02:42.580 align:middle line:84% you go to the classical regime where we call the distribution 00:02:42.580 --> 00:02:46.910 align:middle line:84% f, doesn't have that one, the exponential distribution, 00:02:46.910 --> 00:02:48.910 align:middle line:84% that's the board's mass statistics, 00:02:48.910 --> 00:02:50.350 align:middle line:90% horizontal distribution. 00:02:50.350 --> 00:02:53.020 align:middle line:84% This is the one you see in [INAUDIBLE] nor 00:02:53.020 --> 00:02:55.390 align:middle line:90% in chemical reaction. 00:02:55.390 --> 00:02:59.140 align:middle line:84% So that's a review of thermodynamics. 00:02:59.140 --> 00:03:03.370 align:middle line:84% And then I went on to heat transfer 00:03:03.370 --> 00:03:06.970 align:middle line:84% where we have three modes of heat transfer. 00:03:06.970 --> 00:03:09.020 align:middle line:84% The first mode is the heat conduction. 00:03:09.020 --> 00:03:11.680 align:middle line:84% The [INAUDIBLE] tells us the heat flux 00:03:11.680 --> 00:03:16.030 align:middle line:84% is proportional to the thermal conductivity and the temperature 00:03:16.030 --> 00:03:17.410 align:middle line:90% gradient. 00:03:17.410 --> 00:03:20.350 align:middle line:84% But I went one step further to show you 00:03:20.350 --> 00:03:23.800 align:middle line:84% in a very simple kinetic picture, 00:03:23.800 --> 00:03:27.220 align:middle line:84% just count the number of molecules going from left 00:03:27.220 --> 00:03:28.960 align:middle line:90% to right and right to left. 00:03:28.960 --> 00:03:32.870 align:middle line:84% Then we have a simple expression for thermal conductivity. 00:03:32.870 --> 00:03:37.810 align:middle line:84% That's 1/3 c is the specific heat, v is the velocity, 00:03:37.810 --> 00:03:40.440 align:middle line:90% and gamma is the mean free path. 00:03:40.440 --> 00:03:42.800 align:middle line:84% That's how a lot of the molecules travel. 00:03:42.800 --> 00:03:46.320 align:middle line:84% So this is the heat conduction mode. 00:03:46.320 --> 00:03:50.630 align:middle line:84% And then we have the Newton's law of cooling for convection 00:03:50.630 --> 00:03:54.930 align:middle line:84% or the e-transfer's proportional transfer coefficient area 00:03:54.930 --> 00:03:56.360 align:middle line:90% and counter difference. 00:03:56.360 --> 00:03:59.390 align:middle line:84% And the difference is this heat transfer coefficient 00:03:59.390 --> 00:04:03.570 align:middle line:84% is no longer property of the material. 00:04:03.570 --> 00:04:06.380 align:middle line:84% Thermal conductivity is a material property. 00:04:06.380 --> 00:04:09.440 align:middle line:84% And h depends on the flow configuration, 00:04:09.440 --> 00:04:11.660 align:middle line:84% natural convection, forced convection, 00:04:11.660 --> 00:04:13.700 align:middle line:90% what kind of geometry? 00:04:13.700 --> 00:04:16.640 align:middle line:84% And then the third mode of heat transfer 00:04:16.640 --> 00:04:18.589 align:middle line:90% was the thermal radiation. 00:04:18.589 --> 00:04:21.170 align:middle line:84% And I gave the [INAUDIBLE] model, 00:04:21.170 --> 00:04:27.920 align:middle line:84% that's the maximum emission of an object in half in the-- 00:04:27.920 --> 00:04:30.230 align:middle line:84% So this is called the Stefan-Boltzmann law. 00:04:30.230 --> 00:04:33.470 align:middle line:84% It's proportional to [INAUDIBLE] fourth power. 00:04:33.470 --> 00:04:37.020 align:middle line:84% A real object, the emission is less than that. 00:04:37.020 --> 00:04:40.990 align:middle line:84% So we normalize the real object emission by this number, 00:04:40.990 --> 00:04:43.090 align:middle line:84% we get the so-called the emissivity. 00:04:43.090 --> 00:04:47.260 align:middle line:84% So it's a number between 0 and 1. 00:04:47.260 --> 00:04:52.160 align:middle line:84% So I moved on at the end of the last lecture, 00:04:52.160 --> 00:04:56.185 align:middle line:84% I was trying to show you the thermal radiation can 00:04:56.185 --> 00:04:56.685 align:middle line:90% be derived. 00:04:56.685 --> 00:05:00.250 align:middle line:90% 00:05:00.250 --> 00:05:04.810 align:middle line:84% There are continual, and they give you a derivation 00:05:04.810 --> 00:05:07.270 align:middle line:90% of the Planck's law again. 00:05:07.270 --> 00:05:11.570 align:middle line:84% Now we move from continuum to a microscopic picture. 00:05:11.570 --> 00:05:15.040 align:middle line:84% And once we go to microscopic, I use the same strategy, 00:05:15.040 --> 00:05:20.080 align:middle line:84% I'm going to do the counting, the number of modes, 00:05:20.080 --> 00:05:22.510 align:middle line:84% quantum mechanical state, because I already 00:05:22.510 --> 00:05:26.500 align:middle line:84% know from statistics each quantum mechanical state, how 00:05:26.500 --> 00:05:27.220 align:middle line:90% many photon. 00:05:27.220 --> 00:05:30.410 align:middle line:84% That's the Poisson [INAUDIBLE] distribution, 00:05:30.410 --> 00:05:32.750 align:middle line:90% that's the previous slide here. 00:05:32.750 --> 00:05:38.540 align:middle line:84% So I know each mode, this is a number at this temperature. 00:05:38.540 --> 00:05:41.930 align:middle line:84% That's the number of photons in the mode. 00:05:41.930 --> 00:05:49.060 align:middle line:84% And also I commented before for photon, photon equals 0. 00:05:49.060 --> 00:05:50.990 align:middle line:90% So we'll use that. 00:05:50.990 --> 00:05:58.000 align:middle line:84% And the task is really just count the number of modes. 00:05:58.000 --> 00:06:06.070 align:middle line:84% So I will take a cubit, and I assume that the [INAUDIBLE] 00:06:06.070 --> 00:06:08.910 align:middle line:90% is perfectly reflected. 00:06:08.910 --> 00:06:11.310 align:middle line:90% And this is a [INAUDIBLE] t. 00:06:11.310 --> 00:06:13.560 align:middle line:84% And now I want to see how much is 00:06:13.560 --> 00:06:18.630 align:middle line:84% radiation energy is contained inside this cube 00:06:18.630 --> 00:06:20.820 align:middle line:90% by counting the modes. 00:06:20.820 --> 00:06:24.480 align:middle line:84% I want to show you this because we will actually 00:06:24.480 --> 00:06:26.700 align:middle line:84% use a lot of those common techniques 00:06:26.700 --> 00:06:29.900 align:middle line:84% towards electrons, towards the photons. 00:06:29.900 --> 00:06:34.590 align:middle line:84% So it's a general way of doing the counting. 00:06:34.590 --> 00:06:38.870 align:middle line:84% And of course, we have the electromagnetic wave. 00:06:38.870 --> 00:06:41.910 align:middle line:84% So here are our basic relationships. 00:06:41.910 --> 00:06:46.020 align:middle line:84% And, you know, the wavelength times frequency 00:06:46.020 --> 00:06:48.090 align:middle line:90% equals the speed of light. 00:06:48.090 --> 00:06:51.130 align:middle line:84% So I write it rather than wavelengths, 00:06:51.130 --> 00:06:52.560 align:middle line:84% I write it in terms of wave vector 00:06:52.560 --> 00:06:56.040 align:middle line:84% is the numerous wavelengths and the angular frequency, 00:06:56.040 --> 00:07:00.990 align:middle line:84% so [INAUDIBLE] to near relation between the amplitude 00:07:00.990 --> 00:07:05.220 align:middle line:90% and the c of the wave vector. 00:07:05.220 --> 00:07:08.400 align:middle line:84% Wave vector is vector, so it's a kx, ky, 00:07:08.400 --> 00:07:11.470 align:middle line:90% kz in Cartesian coordinate. 00:07:11.470 --> 00:07:15.070 align:middle line:84% And that's what we call the dispersion relation. 00:07:15.070 --> 00:07:20.470 align:middle line:84% The relation between wave vector and frequency is dispersion. 00:07:20.470 --> 00:07:25.840 align:middle line:84% So now I want to see how many moles in this cavity. 00:07:25.840 --> 00:07:29.260 align:middle line:84% And then my simple picture is this 00:07:29.260 --> 00:07:32.560 align:middle line:84% is the length in the x direction. 00:07:32.560 --> 00:07:36.860 align:middle line:84% and because a perfect wall, so it's reflecting and it's a wave. 00:07:36.860 --> 00:07:40.300 align:middle line:84% So the only way that this wave can exist 00:07:40.300 --> 00:07:44.140 align:middle line:84% is having 0 amplitude at the end-- 00:07:44.140 --> 00:07:45.980 align:middle line:90% on the surface of the wall. 00:07:45.980 --> 00:07:48.190 align:middle line:84% So this is-- if you have a string 00:07:48.190 --> 00:07:51.370 align:middle line:84% and you want to do the, go to think about that, 00:07:51.370 --> 00:07:56.200 align:middle line:84% you play violin and you have the nodes at the two ends 00:07:56.200 --> 00:08:00.020 align:middle line:84% and the vibrational modes at the two ends, 0. 00:08:00.020 --> 00:08:02.030 align:middle line:90% So we have different modes. 00:08:02.030 --> 00:08:05.230 align:middle line:84% The first mode is a half and the second mode 00:08:05.230 --> 00:08:08.110 align:middle line:90% is including the [INAUDIBLE]. 00:08:08.110 --> 00:08:12.550 align:middle line:84% And I can use this as my constraint 00:08:12.550 --> 00:08:17.260 align:middle line:84% in the x direction, that's the length and a half modes 00:08:17.260 --> 00:08:21.790 align:middle line:84% or twice or in [INAUDIBLE] and half mode, half wavelengths. 00:08:21.790 --> 00:08:27.640 align:middle line:84% So with that I go to, because if we factor in the x direction 00:08:27.640 --> 00:08:33.610 align:middle line:84% is just 2 pi over lambda, so I can write this in terms of n 00:08:33.610 --> 00:08:38.260 align:middle line:84% and L of x, the length of the box. 00:08:38.260 --> 00:08:44.290 align:middle line:84% And if I write that kx, I can same way write ky and kz, 00:08:44.290 --> 00:08:50.290 align:middle line:84% so I have a lot more numbers for this kx, ky, kz. 00:08:50.290 --> 00:08:55.870 align:middle line:84% And then each set of kx, ky, kz, if you think about the wave, 00:08:55.870 --> 00:08:58.120 align:middle line:90% give me a distinct wave. 00:08:58.120 --> 00:09:03.240 align:middle line:84% And that's one mode, except that the electromagnetic wave 00:09:03.240 --> 00:09:07.020 align:middle line:84% you learned before, it's a transverse wave. 00:09:07.020 --> 00:09:10.230 align:middle line:84% The sound wave is a longitudinal wave, right. 00:09:10.230 --> 00:09:15.510 align:middle line:84% When I speak here, I'm pressing the air 00:09:15.510 --> 00:09:18.570 align:middle line:84% and the direction of propagation of the wave 00:09:18.570 --> 00:09:22.140 align:middle line:84% is in the same direction as the air doing 00:09:22.140 --> 00:09:23.620 align:middle line:90% expansion and contraction. 00:09:23.620 --> 00:09:25.620 align:middle line:90% So that's a longitudinal wave. 00:09:25.620 --> 00:09:28.020 align:middle line:84% The transverse wave, electromagnetic wave 00:09:28.020 --> 00:09:32.020 align:middle line:84% from the sun, that's direction to the Earth, the k vector. 00:09:32.020 --> 00:09:35.460 align:middle line:84% But the electric field, the magnetic field 00:09:35.460 --> 00:09:38.320 align:middle line:84% is perpendicular to the direction of propagation. 00:09:38.320 --> 00:09:42.150 align:middle line:84% And I have two, so I put a two here. 00:09:42.150 --> 00:09:46.170 align:middle line:84% And then I sum up all the modes, so n number, 00:09:46.170 --> 00:09:51.960 align:middle line:84% each set of n number, nx, ny, and z is one mole. 00:09:51.960 --> 00:09:58.120 align:middle line:84% So I count how many moles there are inside this cavity. 00:09:58.120 --> 00:10:01.750 align:middle line:84% So I just sum up all possible combinations of 00:10:01.750 --> 00:10:04.960 align:middle line:84% and each combination of one mode. 00:10:04.960 --> 00:10:10.690 align:middle line:84% Each mode has a polarization, vibration direction. 00:10:10.690 --> 00:10:14.180 align:middle line:84% And then each mode, the photon has an energy, 00:10:14.180 --> 00:10:16.850 align:middle line:84% each and every photon has an energy, that's what we got. 00:10:16.850 --> 00:10:18.170 align:middle line:90% Yes? 00:10:18.170 --> 00:10:19.340 align:middle line:90% AUDIENCE: I have a question. 00:10:19.340 --> 00:10:21.220 align:middle line:84% How does the factor two relate to the fact 00:10:21.220 --> 00:10:24.940 align:middle line:84% that the electric field is transverse to the wave vector? 00:10:24.940 --> 00:10:29.290 align:middle line:84% GANG CHEN: So when I have a set of x and y and z, 00:10:29.290 --> 00:10:34.960 align:middle line:84% so in one case, the electric field is this direction. 00:10:34.960 --> 00:10:36.970 align:middle line:84% In the next case is this direction, 00:10:36.970 --> 00:10:38.740 align:middle line:84% or other is a combination of the two. 00:10:38.740 --> 00:10:41.680 align:middle line:90% So it's not a fundamental mode. 00:10:41.680 --> 00:10:46.570 align:middle line:84% So you have a factor of 2 is because in this one set of nx, 00:10:46.570 --> 00:10:51.400 align:middle line:84% and ny and z, you can have two possible e directions, 00:10:51.400 --> 00:10:54.790 align:middle line:90% electric field direction. 00:10:54.790 --> 00:10:58.090 align:middle line:90% So I do my summation here. 00:10:58.090 --> 00:11:02.820 align:middle line:84% And the only thing, this is the trick I will use many times. 00:11:02.820 --> 00:11:06.900 align:middle line:84% I do my summation because I don't know how to do it easily, 00:11:06.900 --> 00:11:12.810 align:middle line:84% analytically, so I'm converting that summation into integration. 00:11:12.810 --> 00:11:16.320 align:middle line:84% So if I think about n at this [INAUDIBLE] 00:11:16.320 --> 00:11:21.300 align:middle line:84% and the wave vector is great, but if this separation 00:11:21.300 --> 00:11:23.760 align:middle line:84% between the energy is small enough, 00:11:23.760 --> 00:11:27.450 align:middle line:84% so I can say in this distance dkx, 00:11:27.450 --> 00:11:30.360 align:middle line:84% and this is the unit of this discrete, 00:11:30.360 --> 00:11:34.200 align:middle line:84% so that's the equivalent that a continuous number of n 00:11:34.200 --> 00:11:37.530 align:middle line:90% rather than discrete number n. 00:11:37.530 --> 00:11:40.620 align:middle line:84% So this is the equivalent of summation 00:11:40.620 --> 00:11:44.250 align:middle line:84% into integration as long as this function doesn't change 00:11:44.250 --> 00:11:48.390 align:middle line:90% a lot between the [INAUDIBLE]. 00:11:48.390 --> 00:11:54.900 align:middle line:84% And I do that for y and for z, so this step 00:11:54.900 --> 00:11:57.210 align:middle line:90% is just for my future. 00:11:57.210 --> 00:12:02.770 align:middle line:84% What this step means, rather than doing this effect of two 00:12:02.770 --> 00:12:09.220 align:middle line:84% hear from 0 to infinite, which is the standing wave, 00:12:09.220 --> 00:12:15.340 align:middle line:84% OK, n is an integer, positive integer is a standing wave, 00:12:15.340 --> 00:12:19.240 align:middle line:84% I'm going to do from negative infinity to positive infinite 00:12:19.240 --> 00:12:23.860 align:middle line:84% because this is a unit function, And this way, 00:12:23.860 --> 00:12:28.340 align:middle line:84% I'm really rather than what I miss is this factor of two, 00:12:28.340 --> 00:12:30.050 align:middle line:84% I don't have a factor of two anymore. 00:12:30.050 --> 00:12:34.450 align:middle line:84% And physically what I'm saying is the standing wave summation 00:12:34.450 --> 00:12:37.570 align:middle line:84% is the same as two propagating wave, [INAUDIBLE] 00:12:37.570 --> 00:12:38.710 align:middle line:90% propagating wave. 00:12:38.710 --> 00:12:40.720 align:middle line:84% When kx is negative, it means going 00:12:40.720 --> 00:12:43.750 align:middle line:84% negative direction, positive, going positive direction. 00:12:43.750 --> 00:12:48.130 align:middle line:84% So this is mathematically equivalent. 00:12:48.130 --> 00:12:52.030 align:middle line:84% And later on, a lot of this minus 00:12:52.030 --> 00:12:55.680 align:middle line:84% infinity to positive infinite summation of the standing wave 00:12:55.680 --> 00:12:57.130 align:middle line:90% summation. 00:12:57.130 --> 00:13:02.280 align:middle line:90% So it's a more mathematics. 00:13:02.280 --> 00:13:06.390 align:middle line:84% I can walk you through, but there's no physics here. 00:13:06.390 --> 00:13:10.560 align:middle line:90% It's a book doing the latter. 00:13:10.560 --> 00:13:12.960 align:middle line:84% Are you ready to hear the dkx, dky, 00:13:12.960 --> 00:13:16.050 align:middle line:84% so I wrote it into Cartesian coordinate. 00:13:16.050 --> 00:13:19.060 align:middle line:84% Now it's not x, y, z, but kx, ky, kz, 00:13:19.060 --> 00:13:20.820 align:middle line:90% it's the Cartesian coordinate. 00:13:20.820 --> 00:13:23.910 align:middle line:84% And three dimensional integration, the rest 00:13:23.910 --> 00:13:28.470 align:middle line:84% is just the numerator here I had before. 00:13:28.470 --> 00:13:34.530 align:middle line:84% Those numerator are lx, ly, lz, so 8 pi cubic. 00:13:34.530 --> 00:13:37.800 align:middle line:84% So that's just a copying what I had before. 00:13:37.800 --> 00:13:41.220 align:middle line:84% And x when we got f is [INAUDIBLE] copying. 00:13:41.220 --> 00:13:46.860 align:middle line:84% So I'm doing all the copying now to simplify again, 00:13:46.860 --> 00:13:50.500 align:middle line:84% simplify [INAUDIBLE] the integration, 00:13:50.500 --> 00:13:53.310 align:middle line:84% you can say I have a conflict, the conflict 00:13:53.310 --> 00:13:57.540 align:middle line:84% is y is integrating over k, but my function is 00:13:57.540 --> 00:14:02.830 align:middle line:84% a function of omega, so I have to transfer either y into omega 00:14:02.830 --> 00:14:05.400 align:middle line:90% into k or k into omega. 00:14:05.400 --> 00:14:10.020 align:middle line:84% And I would like to transfer k into omega in this case, 00:14:10.020 --> 00:14:12.850 align:middle line:84% it's your choice actually, when you do it. 00:14:12.850 --> 00:14:16.360 align:middle line:84% So I transfer that k into omega, and I 00:14:16.360 --> 00:14:21.940 align:middle line:84% want to do spherical coordinate because that's easier. 00:14:21.940 --> 00:14:26.080 align:middle line:84% OK, so dk, dx, dk, dx, dk [INAUDIBLE] 00:14:26.080 --> 00:14:30.460 align:middle line:84% is 4 pi k squared dk is spherical coordinate. 00:14:30.460 --> 00:14:36.680 align:middle line:84% And now you go to look at the kx squared, 00:14:36.680 --> 00:14:40.340 align:middle line:84% I hope I read them down in the previous slides. 00:14:40.340 --> 00:14:45.980 align:middle line:84% OK, kx squared equals omega squared divided by c squared. 00:14:45.980 --> 00:14:51.150 align:middle line:84% So this is how I change k into omega. 00:14:51.150 --> 00:14:53.370 align:middle line:84% That's where the dispersion relation, 00:14:53.370 --> 00:14:58.990 align:middle line:84% the relation between omega and the k is very important. 00:14:58.990 --> 00:15:05.680 align:middle line:84% So k into omega, that's just omega equals k. 00:15:05.680 --> 00:15:12.440 align:middle line:84% So dk is d omega, d over c And now I combine everything. 00:15:12.440 --> 00:15:17.840 align:middle line:84% I do per unit volume, how much energy we have. 00:15:17.840 --> 00:15:23.630 align:middle line:84% And I write all this other factors into the integration 00:15:23.630 --> 00:15:27.440 align:middle line:90% and this is what I have here. 00:15:27.440 --> 00:15:30.130 align:middle line:90% Everything is a mess. 00:15:30.130 --> 00:15:34.570 align:middle line:84% And then this t, I call it density of states. 00:15:34.570 --> 00:15:36.760 align:middle line:84% What it means is how many quantum 00:15:36.760 --> 00:15:40.930 align:middle line:84% mechanical states or electromagnetic modes 00:15:40.930 --> 00:15:42.580 align:middle line:90% we have between-- 00:15:42.580 --> 00:15:45.700 align:middle line:90% around omega. 00:15:45.700 --> 00:15:52.890 align:middle line:84% And so this is the default count, energy, one photon, 00:15:52.890 --> 00:15:56.040 align:middle line:84% one state, how many photons we have. 00:15:56.040 --> 00:16:02.790 align:middle line:84% And in this state, in this region, how many states we have. 00:16:02.790 --> 00:16:08.340 align:middle line:84% So this is also the energy density. 00:16:08.340 --> 00:16:10.350 align:middle line:90% Did I write everything together? 00:16:10.350 --> 00:16:14.100 align:middle line:84% It's just an energy density in the frequency. 00:16:14.100 --> 00:16:16.660 align:middle line:90% 00:16:16.660 --> 00:16:22.030 align:middle line:84% OK, so this is the energy density, as I wrote down. 00:16:22.030 --> 00:16:27.190 align:middle line:84% And if I want to write out the density of states, f, 00:16:27.190 --> 00:16:28.935 align:middle line:84% and the actual [INAUDIBLE] combined. 00:16:28.935 --> 00:16:31.630 align:middle line:90% 00:16:31.630 --> 00:16:36.070 align:middle line:84% That's Planck's law, Planck's blackbody radiation. 00:16:36.070 --> 00:16:41.940 align:middle line:84% The energy density per unit volume, and these 00:16:41.940 --> 00:16:45.465 align:middle line:84% were actually the start of quantum mechanics. 00:16:45.465 --> 00:16:50.270 align:middle line:84% Planck was trying to explain the blackbody radiation. 00:16:50.270 --> 00:16:53.360 align:middle line:90% And if this is not called-- 00:16:53.360 --> 00:16:56.540 align:middle line:84% because the energy state, in fact, most time we 00:16:56.540 --> 00:16:58.070 align:middle line:84% don't talk about energy state, we 00:16:58.070 --> 00:17:01.220 align:middle line:84% talk about radiation leaving a surface, 00:17:01.220 --> 00:17:06.410 align:middle line:84% not just how many energy in per unit volume. 00:17:06.410 --> 00:17:12.079 align:middle line:84% And in that case, the definition is the intensity, energy flux 00:17:12.079 --> 00:17:13.670 align:middle line:90% per unit, solid angle. 00:17:13.670 --> 00:17:15.349 align:middle line:90% What is a solid angle? 00:17:15.349 --> 00:17:19.430 align:middle line:84% A solid angle is if you have a two dimension, 00:17:19.430 --> 00:17:22.220 align:middle line:90% you know, a polar angle, x, y. 00:17:22.220 --> 00:17:26.750 align:middle line:84% From x, y, you want to use a circle polar coordinate, 00:17:26.750 --> 00:17:31.580 align:middle line:84% you have polar angle and in three dimension, 00:17:31.580 --> 00:17:35.020 align:middle line:84% that angle is a space, angle in space. 00:17:35.020 --> 00:17:38.690 align:middle line:84% That's a solid angle, per unit area normalized 00:17:38.690 --> 00:17:41.240 align:middle line:90% to the distance r squared. 00:17:41.240 --> 00:17:47.130 align:middle line:84% So a sphere, the area is a 4 pi r squared. 00:17:47.130 --> 00:17:53.100 align:middle line:84% The solid angle then is 4 pi, because r squared [INAUDIBLE]. 00:17:53.100 --> 00:17:57.305 align:middle line:90% In 2D, what's the phi? 00:17:57.305 --> 00:17:58.630 align:middle line:90% 2 pi. 00:17:58.630 --> 00:18:02.020 align:middle line:90% 2 pi versus phase for 4 pi. 00:18:02.020 --> 00:18:03.880 align:middle line:90% That's the solid angle. 00:18:03.880 --> 00:18:08.280 align:middle line:84% So that's because that's the terminology we use often, 00:18:08.280 --> 00:18:13.540 align:middle line:84% so this intensity is just now, I know the energy density 00:18:13.540 --> 00:18:16.690 align:middle line:84% per unit volume, this energy is propagating 00:18:16.690 --> 00:18:22.450 align:middle line:84% at the speed of light, So is the energy density times c, 00:18:22.450 --> 00:18:25.630 align:middle line:84% and it's going radiation, thermal radiation 00:18:25.630 --> 00:18:27.580 align:middle line:90% is going in all directions. 00:18:27.580 --> 00:18:31.210 align:middle line:84% So per unit, solid angle is a 4 pi. 00:18:31.210 --> 00:18:35.140 align:middle line:84% So this way, I write the speed of light times energy 00:18:35.140 --> 00:18:36.650 align:middle line:90% density divided by 4 pi. 00:18:36.650 --> 00:18:37.900 align:middle line:90% That's the intensity. 00:18:37.900 --> 00:18:41.860 align:middle line:84% And this is just so you go continue substitution, 00:18:41.860 --> 00:18:45.070 align:middle line:84% you get the intensity, and sometimes 00:18:45.070 --> 00:18:48.250 align:middle line:84% we do per unit wavelength interval 00:18:48.250 --> 00:18:51.010 align:middle line:84% rather than per unit frequency interval. 00:18:51.010 --> 00:18:54.160 align:middle line:84% So rather than doing d omega integration, 00:18:54.160 --> 00:18:57.620 align:middle line:84% you do d lambda integration, and because lambda 00:18:57.620 --> 00:19:00.890 align:middle line:84% is times omega equals 2 pi c, so you 00:19:00.890 --> 00:19:04.930 align:middle line:90% convert the omega into lambda. 00:19:04.930 --> 00:19:10.900 align:middle line:84% Again, this is when you actually take a radiation course, 00:19:10.900 --> 00:19:15.580 align:middle line:84% this will be the Planck's law as written [INAUDIBLE]. 00:19:15.580 --> 00:19:19.090 align:middle line:90% And what are they? 00:19:19.090 --> 00:19:22.060 align:middle line:84% So that's a per unit solid angle. 00:19:22.060 --> 00:19:26.550 align:middle line:84% And when I do the total radiation per unit area, 00:19:26.550 --> 00:19:31.930 align:middle line:84% so this is the area, [? dense ?] area, so that's 00:19:31.930 --> 00:19:34.610 align:middle line:84% the total radiation is a pi times i, 00:19:34.610 --> 00:19:37.300 align:middle line:84% that's the mathematical, we're not getting into it. 00:19:37.300 --> 00:19:39.490 align:middle line:84% With that, what I want to show you 00:19:39.490 --> 00:19:42.430 align:middle line:84% is from here, if you do your integration, 00:19:42.430 --> 00:19:45.800 align:middle line:90% you get Stefan-Boltzmann. 00:19:45.800 --> 00:19:46.490 align:middle line:90% OK. 00:19:46.490 --> 00:19:50.270 align:middle line:84% Stefan-Boltzmann law, if you take a 2 double 5, 00:19:50.270 --> 00:19:54.750 align:middle line:84% is where we get-- we start on thermal radiation. 00:19:54.750 --> 00:20:00.300 align:middle line:84% And what I gave you is a way of going from basic concept 00:20:00.300 --> 00:20:05.100 align:middle line:84% to go to the Stefan-Boltzmann, but say, 00:20:05.100 --> 00:20:08.300 align:middle line:84% what's important is for you to look 00:20:08.300 --> 00:20:11.190 align:middle line:84% at the curve of blackbody radiation. 00:20:11.190 --> 00:20:14.750 align:middle line:84% This is very much relevant to the way 00:20:14.750 --> 00:20:18.230 align:middle line:84% we want to do solar cells or solar thermal, 00:20:18.230 --> 00:20:25.730 align:middle line:84% because the sun's radiation is about 50-- 00:20:25.730 --> 00:20:33.180 align:middle line:84% here I wrote 56 as hundred, but it's really around 5,800 Kelvin, 00:20:33.180 --> 00:20:35.030 align:middle line:90% that's the solar radiation. 00:20:35.030 --> 00:20:39.120 align:middle line:84% It's like a blackbody, the spectrum 00:20:39.120 --> 00:20:41.880 align:middle line:90% is very similar to this curve. 00:20:41.880 --> 00:20:45.270 align:middle line:84% OK, outside the atmosphere, to go to measure the solar 00:20:45.270 --> 00:20:52.860 align:middle line:84% radiation, it's close to 5,800 kelvins curve. 00:20:52.860 --> 00:20:59.640 align:middle line:84% And at 300, I didn't plot, 300 Kelvin, this peak 00:20:59.640 --> 00:21:01.410 align:middle line:90% will be around 10. 00:21:01.410 --> 00:21:04.620 align:middle line:84% So here you can see the peak start decreasing 00:21:04.620 --> 00:21:09.630 align:middle line:84% and that relation is the wave's displacement mode. 00:21:09.630 --> 00:21:14.820 align:middle line:84% Wavelength times temperature is about, back of the envelope, 00:21:14.820 --> 00:21:15.720 align:middle line:90% three solid. 00:21:15.720 --> 00:21:17.730 align:middle line:84% If you don't remember that detail, 00:21:17.730 --> 00:21:19.800 align:middle line:84% whether it's 289 [INAUDIBLE] and in fact, 00:21:19.800 --> 00:21:25.490 align:middle line:84% every time I go back to check, I remember about 3,000. 00:21:25.490 --> 00:21:31.100 align:middle line:84% OK, so 3,000 micron, and that's why our eyes are sensitive 00:21:31.100 --> 00:21:35.420 align:middle line:84% to the 0.5 micron, in the solar system. 00:21:35.420 --> 00:21:39.710 align:middle line:84% And the solar radiation, you put about 6,000, 00:21:39.710 --> 00:21:45.020 align:middle line:84% 3,000 divided by 6,000, our eyes are the evolution choose us 00:21:45.020 --> 00:21:49.130 align:middle line:84% to be more sensitive to the peak of solar radiation. 00:21:49.130 --> 00:21:52.970 align:middle line:84% And during night, there is no sun. 00:21:52.970 --> 00:21:56.360 align:middle line:84% Everybody is emitting, you're emitting, I'm emitting, 00:21:56.360 --> 00:21:58.220 align:middle line:90% we're emitting 10 microns. 00:21:58.220 --> 00:22:00.980 align:middle line:84% 300 kelvin [INAUDIBLE] 10 microns. 00:22:00.980 --> 00:22:07.580 align:middle line:84% Of course, if you take a detector, you can look at it. 00:22:07.580 --> 00:22:12.410 align:middle line:84% So you are like that, the infrared radiation measurement. 00:22:12.410 --> 00:22:16.550 align:middle line:84% But if you look at just a common-- 00:22:16.550 --> 00:22:21.380 align:middle line:84% a solar cell, silicon solar cell, 00:22:21.380 --> 00:22:26.330 align:middle line:84% the wavelengths that you can take, the shortest wavelengths 00:22:26.330 --> 00:22:28.880 align:middle line:90% is about 1.12 micron. 00:22:28.880 --> 00:22:34.500 align:middle line:90% So 1.3 is about 1.112. 00:22:34.500 --> 00:22:36.280 align:middle line:84% So that's-- this is the 1 micron. 00:22:36.280 --> 00:22:37.480 align:middle line:90% This is the 1.12. 00:22:37.480 --> 00:22:46.120 align:middle line:84% So only radiation in this range can be utilized in solar cells. 00:22:46.120 --> 00:22:50.990 align:middle line:84% You have a lot that's wasted if you do [INAUDIBLE] or yourself, 00:22:50.990 --> 00:22:56.560 align:middle line:84% this rest of the wave length's energy cannot be used 00:22:56.560 --> 00:22:58.300 align:middle line:90% to generate the electron holes. 00:22:58.300 --> 00:23:00.880 align:middle line:90% We'll talk about that later. 00:23:00.880 --> 00:23:07.240 align:middle line:84% So that's a completely what I was 00:23:07.240 --> 00:23:10.510 align:middle line:84% talking in the review, basically heat 00:23:10.510 --> 00:23:13.990 align:middle line:90% transfer and thermodynamics. 00:23:13.990 --> 00:23:20.170 align:middle line:84% What I'm going to move on is giving you 00:23:20.170 --> 00:23:23.620 align:middle line:84% a brief introduction of thermoelectric energy 00:23:23.620 --> 00:23:26.440 align:middle line:90% conversion. 00:23:26.440 --> 00:23:31.420 align:middle line:84% In the last lecture, you have seen a basic demonstration 00:23:31.420 --> 00:23:34.540 align:middle line:90% of thermoelectric generation. 00:23:34.540 --> 00:23:40.210 align:middle line:84% And in fact, this is the module that used to generate the power. 00:23:40.210 --> 00:23:42.610 align:middle line:90% Pass around. 00:23:42.610 --> 00:23:44.530 align:middle line:90% Take a look. 00:23:44.530 --> 00:23:49.970 align:middle line:84% And basically here we are using direct energy conversion, 00:23:49.970 --> 00:23:53.570 align:middle line:84% we're using electrons or holes in semiconductor. 00:23:53.570 --> 00:23:57.040 align:middle line:84% We have names for positive electrons and holes. 00:23:57.040 --> 00:24:03.520 align:middle line:84% And we're using this as a working fluid to carry it around 00:24:03.520 --> 00:24:05.590 align:middle line:90% from one place to another. 00:24:05.590 --> 00:24:10.510 align:middle line:84% So let's look at the phenomena, basic thermoelectric phenomena. 00:24:10.510 --> 00:24:15.190 align:middle line:84% And then we will see do a simple analysis of that device 00:24:15.190 --> 00:24:18.220 align:middle line:84% and pass it around and then look at the current 00:24:18.220 --> 00:24:19.970 align:middle line:90% and the potential application. 00:24:19.970 --> 00:24:24.070 align:middle line:90% 00:24:24.070 --> 00:24:27.220 align:middle line:84% First system I like the effect is not new. 00:24:27.220 --> 00:24:31.870 align:middle line:84% And in fact, this were about the same time people started 00:24:31.870 --> 00:24:34.930 align:middle line:90% to investigate the electricity. 00:24:34.930 --> 00:24:44.290 align:middle line:84% And Seebeck discovered that in 1821, 00:24:44.290 --> 00:24:48.220 align:middle line:84% that when they put the two metals actually at the junction, 00:24:48.220 --> 00:24:52.210 align:middle line:84% and the one side is hot, the other side is cold, 00:24:52.210 --> 00:24:54.370 align:middle line:90% we measure the voltage. 00:24:54.370 --> 00:24:58.270 align:middle line:84% Seebeck, now we call it Seebeck effect. 00:24:58.270 --> 00:25:02.720 align:middle line:84% And Seebeck himself, actually, you go to read the history, 00:25:02.720 --> 00:25:04.810 align:middle line:90% he didn't know what's going on. 00:25:04.810 --> 00:25:08.320 align:middle line:84% He thought that was a magnetic effect, because at the time 00:25:08.320 --> 00:25:12.940 align:middle line:84% there are a lot of interest in say, magnetic Faraday 00:25:12.940 --> 00:25:14.290 align:middle line:90% or the experiment. 00:25:14.290 --> 00:25:20.160 align:middle line:84% So he saw thought that was a magnetic effect. 00:25:20.160 --> 00:25:27.630 align:middle line:84% And about 10 years later, Peltier 00:25:27.630 --> 00:25:31.230 align:middle line:84% discovered another effect, that's the same two, 00:25:31.230 --> 00:25:35.010 align:middle line:84% say kind of junction, two metals, 00:25:35.010 --> 00:25:39.390 align:middle line:90% was pass the current through it. 00:25:39.390 --> 00:25:44.040 align:middle line:84% Actually, one side cools down, the other side heats up. 00:25:44.040 --> 00:25:47.640 align:middle line:90% He could make ice at the time. 00:25:47.640 --> 00:25:52.380 align:middle line:84% In fact, the Seebeck, if we choose this material 00:25:52.380 --> 00:25:56.640 align:middle line:84% to make a device, even at that time, a power generation device, 00:25:56.640 --> 00:26:02.570 align:middle line:84% you will get about a 2% to 3% efficiency using this material. 00:26:02.570 --> 00:26:06.830 align:middle line:84% Somebody do the power generator, so at the same time, 00:26:06.830 --> 00:26:10.310 align:middle line:84% people were starting to develop electric motors. 00:26:10.310 --> 00:26:13.400 align:middle line:84% You can see the history was really interesting. 00:26:13.400 --> 00:26:15.770 align:middle line:90% This one actually worked out. 00:26:15.770 --> 00:26:17.900 align:middle line:84% First, there will be a lot of study, 00:26:17.900 --> 00:26:19.970 align:middle line:90% and it will be different, right. 00:26:19.970 --> 00:26:24.830 align:middle line:84% Let's say, this effect is reversible. 00:26:24.830 --> 00:26:29.730 align:middle line:84% You just pass the current first, one is one direction. 00:26:29.730 --> 00:26:32.120 align:middle line:84% It will be cooling, and the other direction you 00:26:32.120 --> 00:26:32.850 align:middle line:90% will be heating. 00:26:32.850 --> 00:26:37.150 align:middle line:90% 00:26:37.150 --> 00:26:42.310 align:middle line:84% And so both those were experimental discoveries, 00:26:42.310 --> 00:26:47.160 align:middle line:84% comes in, gives us the theoretical prediction. 00:26:47.160 --> 00:26:50.190 align:middle line:84% And Thomson prediction is that based 00:26:50.190 --> 00:26:53.640 align:middle line:84% on the experimental discovery and understanding 00:26:53.640 --> 00:26:58.380 align:middle line:84% of the effects, he predicted that when you have a material, 00:26:58.380 --> 00:27:01.360 align:middle line:84% one side is cold and the other side of the hot. 00:27:01.360 --> 00:27:04.080 align:middle line:84% So a material under temperature difference and you 00:27:04.080 --> 00:27:08.610 align:middle line:84% pass current through it, there will be heating or cooling 00:27:08.610 --> 00:27:11.340 align:middle line:90% along the material. 00:27:11.340 --> 00:27:13.590 align:middle line:90% So this is not char heating. 00:27:13.590 --> 00:27:15.510 align:middle line:90% Char heating is always heating. 00:27:15.510 --> 00:27:17.340 align:middle line:90% This is a reversible. 00:27:17.340 --> 00:27:19.200 align:middle line:84% It will be either heating or cooling, 00:27:19.200 --> 00:27:22.850 align:middle line:84% depending on the direction of the current. 00:27:22.850 --> 00:27:27.560 align:middle line:84% as of Thomson's, Thomson is also Law of Kelvin, 00:27:27.560 --> 00:27:31.050 align:middle line:84% and you'll probably see a lot of Kelvin work, 00:27:31.050 --> 00:27:34.970 align:middle line:84% Kelvin relation for this, Kelvin relation for that. 00:27:34.970 --> 00:27:41.370 align:middle line:84% It pops in more than 500 papers, very productive 00:27:41.370 --> 00:27:42.430 align:middle line:90% in this lifetime. 00:27:42.430 --> 00:27:49.130 align:middle line:84% So now let's get a very intuitive picture. 00:27:49.130 --> 00:27:52.100 align:middle line:84% We have to go to, for those understanding, 00:27:52.100 --> 00:27:54.830 align:middle line:84% we have to go to microscopic again 00:27:54.830 --> 00:27:57.900 align:middle line:84% and we now have to look at electrons. 00:27:57.900 --> 00:28:02.900 align:middle line:84% Let's look at the electrons and I'm going first 00:28:02.900 --> 00:28:04.850 align:middle line:84% to just look at the isothermal, there 00:28:04.850 --> 00:28:08.990 align:middle line:84% is no temperature difference in the material. 00:28:08.990 --> 00:28:12.860 align:middle line:84% Isothermal conductor, a lot of electrons inside, 00:28:12.860 --> 00:28:16.130 align:middle line:84% and that's why you have to feel the current will flow. 00:28:16.130 --> 00:28:17.210 align:middle line:90% We all know that. 00:28:17.210 --> 00:28:21.260 align:middle line:90% So I have a current flow. 00:28:21.260 --> 00:28:26.470 align:middle line:84% Now again, I'm doing number crunching of this number. 00:28:26.470 --> 00:28:27.800 align:middle line:90% What's the current density? 00:28:27.800 --> 00:28:32.690 align:middle line:84% Current density is amp per meter squared 00:28:32.690 --> 00:28:37.430 align:middle line:90% is the charge per electron. 00:28:37.430 --> 00:28:40.850 align:middle line:84% Hence, the per unit volume or how many 00:28:40.850 --> 00:28:44.840 align:middle line:84% electrons I have times the velocity of those 00:28:44.840 --> 00:28:46.150 align:middle line:90% electrons moving. 00:28:46.150 --> 00:28:48.810 align:middle line:90% 00:28:48.810 --> 00:28:50.350 align:middle line:90% It's a very intuitive. 00:28:50.350 --> 00:28:53.520 align:middle line:84% So you go to look at the unit, you'll 00:28:53.520 --> 00:28:57.710 align:middle line:90% be adding per meter squared. 00:28:57.710 --> 00:29:01.560 align:middle line:90% And the velocity is related. 00:29:01.560 --> 00:29:03.110 align:middle line:84% I'll give you the relation more later 00:29:03.110 --> 00:29:07.070 align:middle line:90% on through a electrical field. 00:29:07.070 --> 00:29:11.630 align:middle line:84% And this, the coefficient proportionality, coefficient 00:29:11.630 --> 00:29:16.790 align:middle line:84% is called the mobility mu, relating 00:29:16.790 --> 00:29:21.680 align:middle line:84% the velocity of the electron to the electric field. 00:29:21.680 --> 00:29:27.150 align:middle line:84% Again, this I'll give more detail derivation. 00:29:27.150 --> 00:29:30.190 align:middle line:84% And of course that will be the ohm's law, 00:29:30.190 --> 00:29:33.420 align:middle line:84% the current is proportional to the electric field 00:29:33.420 --> 00:29:41.280 align:middle line:84% and the proportionality constant is the electric conductivity. 00:29:41.280 --> 00:29:44.170 align:middle line:84% And sometimes we don't talk about conductivity, 00:29:44.170 --> 00:29:49.380 align:middle line:84% we talk about resistivity, just 1 over the conductivity. 00:29:49.380 --> 00:29:55.740 align:middle line:84% So this is the ohm's law, and all the definitions, 00:29:55.740 --> 00:29:59.820 align:middle line:90% their units are given here. 00:29:59.820 --> 00:30:02.620 align:middle line:84% So this is when we talk about the electrical flow, 00:30:02.620 --> 00:30:05.670 align:middle line:90% we care about current. 00:30:05.670 --> 00:30:10.380 align:middle line:84% But each charge also carry heat with it. 00:30:10.380 --> 00:30:13.470 align:middle line:84% I can do the same thing for heat, 00:30:13.470 --> 00:30:19.200 align:middle line:84% So rather than the charge, electron charge, 00:30:19.200 --> 00:30:24.540 align:middle line:84% I'm going to say the heat carried by each carrier. 00:30:24.540 --> 00:30:27.990 align:middle line:84% I don't define how much or how I write that heat yet. 00:30:27.990 --> 00:30:32.130 align:middle line:84% I'm just saying per carrier, heel 00:30:32.130 --> 00:30:35.130 align:middle line:84% is the heat carried by each charge. 00:30:35.130 --> 00:30:39.570 align:middle line:84% Again number, density, velocity, they're moving. 00:30:39.570 --> 00:30:45.650 align:middle line:84% And of course I can replace the n by j the electric current. 00:30:45.650 --> 00:30:51.860 align:middle line:84% So now the heat current is proportional to electric current 00:30:51.860 --> 00:30:56.660 align:middle line:84% and the proportionality constant is the property of efficient. 00:30:56.660 --> 00:31:03.720 align:middle line:84% So associated with the current flow, there is a heat flow. 00:31:03.720 --> 00:31:06.230 align:middle line:90% 00:31:06.230 --> 00:31:09.230 align:middle line:84% So Peltier coefficient can be defined 00:31:09.230 --> 00:31:11.450 align:middle line:90% for each individual material. 00:31:11.450 --> 00:31:13.910 align:middle line:84% You don't have to have a junction. 00:31:13.910 --> 00:31:19.070 align:middle line:84% The junction is only when you do experiment, how you observe it. 00:31:19.070 --> 00:31:22.760 align:middle line:90% OK, so this is the-- 00:31:22.760 --> 00:31:25.760 align:middle line:84% when I want to observe the Peltier effect, 00:31:25.760 --> 00:31:28.430 align:middle line:84% the best way is to put a junction there. 00:31:28.430 --> 00:31:32.570 align:middle line:84% I have two different materials, and when 00:31:32.570 --> 00:31:35.570 align:middle line:84% I pass a current through, then you 00:31:35.570 --> 00:31:38.000 align:middle line:84% can say the current has to be-- electric, 00:31:38.000 --> 00:31:39.950 align:middle line:90% current has to be continuous. 00:31:39.950 --> 00:31:41.300 align:middle line:90% That's a [INAUDIBLE]. 00:31:41.300 --> 00:31:44.240 align:middle line:84% You have [INAUDIBLE] in and of course out. 00:31:44.240 --> 00:31:48.850 align:middle line:84% So that's the continuity, current continuity. 00:31:48.850 --> 00:31:53.490 align:middle line:84% But the heat carried by the electrons in 1 or 2 00:31:53.490 --> 00:31:57.790 align:middle line:84% of the different from the other, so if I do my first low energy 00:31:57.790 --> 00:32:03.200 align:middle line:84% balance, I find out if I have more heat flow out, then 00:32:03.200 --> 00:32:06.470 align:middle line:84% come see it, I have the supply with me. 00:32:06.470 --> 00:32:09.080 align:middle line:84% So what does this mean, supply the heat. 00:32:09.080 --> 00:32:11.330 align:middle line:90% The lattice cools down. 00:32:11.330 --> 00:32:15.170 align:middle line:84% The atoms cool down, because I'm talking about electron, 00:32:15.170 --> 00:32:17.930 align:middle line:84% The atom can supply the heat to the electron 00:32:17.930 --> 00:32:19.760 align:middle line:90% cool down the junction. 00:32:19.760 --> 00:32:25.010 align:middle line:84% So this cool down, and on the other side, 00:32:25.010 --> 00:32:30.590 align:middle line:84% you have to reject that heat, energy values. 00:32:30.590 --> 00:32:32.630 align:middle line:84% So this is the Peltier phenomenon, 00:32:32.630 --> 00:32:35.060 align:middle line:90% you observe experimentally. 00:32:35.060 --> 00:32:38.720 align:middle line:84% And you can say, if I reverse current, 00:32:38.720 --> 00:32:42.490 align:middle line:90% this phenomenon is reverse. 00:32:42.490 --> 00:32:46.790 align:middle line:90% So this is the Peltier effect. 00:32:46.790 --> 00:32:49.820 align:middle line:90% It's reversible. 00:32:49.820 --> 00:32:53.660 align:middle line:90% Now look at the Seebeck effect. 00:32:53.660 --> 00:32:54.690 align:middle line:90% There's a seat here. 00:32:54.690 --> 00:32:57.200 align:middle line:90% 00:32:57.200 --> 00:32:58.160 align:middle line:90% OK. 00:32:58.160 --> 00:33:05.780 align:middle line:84% Seebeck effect, Seebeck effect is the voltage generation 00:33:05.780 --> 00:33:09.150 align:middle line:90% under a temperature difference. 00:33:09.150 --> 00:33:11.370 align:middle line:90% And you think about-- 00:33:11.370 --> 00:33:15.880 align:middle line:84% we have charge in the conductor, and then 00:33:15.880 --> 00:33:22.510 align:middle line:84% when one side is the hot, the electrons are near the hot side, 00:33:22.510 --> 00:33:27.640 align:middle line:84% have more energy they move more violently. 00:33:27.640 --> 00:33:31.810 align:middle line:84% So they will diffuse to the cosine. 00:33:31.810 --> 00:33:35.470 align:middle line:84% So you have at the end after diffusion, 00:33:35.470 --> 00:33:37.420 align:middle line:90% you have more electrons here. 00:33:37.420 --> 00:33:41.830 align:middle line:84% When you have more electrons, the electron imbalance 00:33:41.830 --> 00:33:48.310 align:middle line:84% will happen, you have electrical field building, 00:33:48.310 --> 00:33:51.850 align:middle line:84% The internal electric field will resist the diffusion. 00:33:51.850 --> 00:33:54.580 align:middle line:84% So at the end you have a steady state 00:33:54.580 --> 00:33:57.910 align:middle line:84% for the diffusion current balance, 00:33:57.910 --> 00:34:02.140 align:middle line:84% the electric field will drive the current back. 00:34:02.140 --> 00:34:06.915 align:middle line:84% So this balance will give you the Seebeck voltage. 00:34:06.915 --> 00:34:10.489 align:middle line:90% 00:34:10.489 --> 00:34:14.010 align:middle line:90% That's the process here. 00:34:14.010 --> 00:34:17.150 align:middle line:90% 00:34:17.150 --> 00:34:17.650 align:middle line:90% OK. 00:34:17.650 --> 00:34:23.469 align:middle line:84% The Seebeck voltage is defined, I put the [INAUDIBLE] sign. 00:34:23.469 --> 00:34:25.449 align:middle line:84% This is when you do an experiment, 00:34:25.449 --> 00:34:28.630 align:middle line:84% you want the one side is hot, the other side is cold. 00:34:28.630 --> 00:34:33.699 align:middle line:84% You put a probe, normally you say, OK, the definition, I 00:34:33.699 --> 00:34:35.949 align:middle line:84% put a hot probe on the high temperature 00:34:35.949 --> 00:34:39.219 align:middle line:84% side, positive voltage on the high temperature 00:34:39.219 --> 00:34:41.380 align:middle line:84% side, negative voltage on low temperature side. 00:34:41.380 --> 00:34:44.980 align:middle line:84% And if you do that, here is written very clearly, 00:34:44.980 --> 00:34:47.560 align:middle line:84% you should have put a negative sign in front, 00:34:47.560 --> 00:34:49.420 align:middle line:90% that's the definition. 00:34:49.420 --> 00:34:53.330 align:middle line:84% I remember the first time I measured a sample. 00:34:53.330 --> 00:34:56.030 align:middle line:84% I just got a wrong sign, I didn't know why. 00:34:56.030 --> 00:35:00.670 align:middle line:84% Everybody measured differently, because people normally just say 00:35:00.670 --> 00:35:03.430 align:middle line:84% Seebeck voltage is the voltage divided by delta t, 00:35:03.430 --> 00:35:04.930 align:middle line:84% but then when you do experiment, you 00:35:04.930 --> 00:35:06.490 align:middle line:90% have to see which side it falls. 00:35:06.490 --> 00:35:11.030 align:middle line:90% 00:35:11.030 --> 00:35:13.040 align:middle line:90% Thomson effect. 00:35:13.040 --> 00:35:17.240 align:middle line:84% Thomson effect is when you have a temperature difference 00:35:17.240 --> 00:35:25.820 align:middle line:84% and you flow a current through and if you look at every point, 00:35:25.820 --> 00:35:28.400 align:middle line:90% there is a Peltier coefficient. 00:35:28.400 --> 00:35:31.190 align:middle line:84% The Peltier coefficient can depend on temperature. 00:35:31.190 --> 00:35:35.960 align:middle line:84% So that means when current flow in, the energy carried in 00:35:35.960 --> 00:35:39.920 align:middle line:84% could be different from the energy carried out. 00:35:39.920 --> 00:35:45.470 align:middle line:84% So the heat carried out could be different from current in. 00:35:45.470 --> 00:35:48.890 align:middle line:84% And then that difference must be made up, cooling in 00:35:48.890 --> 00:35:52.550 align:middle line:90% by either cool or rejected. 00:35:52.550 --> 00:35:56.030 align:middle line:84% So that's the Thomson effect and Thomson 00:35:56.030 --> 00:36:01.280 align:middle line:84% to efficient is defined the low amount of heat absorbed 00:36:01.280 --> 00:36:05.480 align:middle line:84% or rejected versus the gradient divided by temperature 00:36:05.480 --> 00:36:08.680 align:middle line:90% gradient normalized to current. 00:36:08.680 --> 00:36:12.050 align:middle line:90% [INAUDIBLE] comes into it. 00:36:12.050 --> 00:36:18.700 align:middle line:84% OK, so we have this phenomenological explanation. 00:36:18.700 --> 00:36:22.630 align:middle line:84% And now I want to do more detail. 00:36:22.630 --> 00:36:28.100 align:middle line:84% I want to put this in more-- into more mathematics into it. 00:36:28.100 --> 00:36:32.050 align:middle line:84% I forgot to mention here, Kelvin, of course, 00:36:32.050 --> 00:36:36.190 align:middle line:84% the concept of Kelvin realized, based on his understanding, 00:36:36.190 --> 00:36:39.250 align:middle line:84% those three effects are interrelated, 00:36:39.250 --> 00:36:42.220 align:middle line:84% and he actually gives the relation between the Peltier 00:36:42.220 --> 00:36:44.880 align:middle line:84% coefficient and Seebeck temperature, 00:36:44.880 --> 00:36:48.550 align:middle line:84% and constant coefficient is a Seebeck derivative 00:36:48.550 --> 00:36:50.160 align:middle line:90% with respect to temperature. 00:36:50.160 --> 00:36:53.800 align:middle line:90% 00:36:53.800 --> 00:36:54.300 align:middle line:90% OK. 00:36:54.300 --> 00:36:56.530 align:middle line:84% Those are [INAUDIBLE] dependent properties. 00:36:56.530 --> 00:37:00.930 align:middle line:90% Like I said, let's go the-- 00:37:00.930 --> 00:37:03.690 align:middle line:90% 00:37:03.690 --> 00:37:08.550 align:middle line:84% so let's go listen to the device, and we want to say, 00:37:08.550 --> 00:37:13.500 align:middle line:84% based on this, what are the material properties I want? 00:37:13.500 --> 00:37:15.870 align:middle line:90% So I show this device. 00:37:15.870 --> 00:37:19.770 align:middle line:84% And again, you can buy the commercially, 00:37:19.770 --> 00:37:22.110 align:middle line:84% particularly some of you may be interested 00:37:22.110 --> 00:37:26.790 align:middle line:84% in various competitions, MIT has a different competitions, 00:37:26.790 --> 00:37:29.980 align:middle line:84% and if you want to build this device, it's not expensive. 00:37:29.980 --> 00:37:36.030 align:middle line:84% This is a $10 to $20 commercially. you Can buy one. 00:37:36.030 --> 00:37:41.640 align:middle line:84% And the again, the basic concept, now 00:37:41.640 --> 00:37:49.110 align:middle line:84% even cheaper device, you see a lot of legs, they are electric. 00:37:49.110 --> 00:37:50.740 align:middle line:90% There are only two electrodes. 00:37:50.740 --> 00:37:52.710 align:middle line:90% One is in, the other is out. 00:37:52.710 --> 00:37:56.820 align:middle line:84% So electrically, they are connected in series. 00:37:56.820 --> 00:38:03.150 align:middle line:84% And in fact, most of this device are made of opposite type, p 00:38:03.150 --> 00:38:07.470 align:middle line:84% and n together, a P type semiconductor, N type 00:38:07.470 --> 00:38:08.970 align:middle line:90% semiconductor. 00:38:08.970 --> 00:38:12.120 align:middle line:84% And in the N type is electron carry 00:38:12.120 --> 00:38:17.860 align:middle line:84% the current flow and P type is called the positive charge. 00:38:17.860 --> 00:38:22.080 align:middle line:84% So when I pass a current, of course current flow 00:38:22.080 --> 00:38:25.700 align:middle line:84% against the electron, along the positive charge direction, 00:38:25.700 --> 00:38:30.960 align:middle line:84% so you can say that's in terms of device how it works. 00:38:30.960 --> 00:38:34.050 align:middle line:84% They carry heat from one side to the other. 00:38:34.050 --> 00:38:36.300 align:middle line:84% And on this side, they reject the heat. 00:38:36.300 --> 00:38:37.860 align:middle line:84% On the other side, they cool down. 00:38:37.860 --> 00:38:44.200 align:middle line:84% So you can do the refrigeration as well as power production. 00:38:44.200 --> 00:38:49.270 align:middle line:84% We show the power, here is a simple demo of the cooling. 00:38:49.270 --> 00:38:56.680 align:middle line:84% That's the price, you convert the water into ice. 00:38:56.680 --> 00:39:02.950 align:middle line:84% OK, let's look at how the device performance depends on-- 00:39:02.950 --> 00:39:08.080 align:middle line:84% we show the summary, let's say three thermoelectric effect, 00:39:08.080 --> 00:39:11.230 align:middle line:84% but in reality, the solid state material, 00:39:11.230 --> 00:39:15.520 align:middle line:84% so there are other effects goes on, when I have 100 difference. 00:39:15.520 --> 00:39:17.640 align:middle line:84% And the first one is, of course heat conduction. 00:39:17.640 --> 00:39:22.850 align:middle line:84% On one side is hot, the other is cold, heat will flow. 00:39:22.850 --> 00:39:24.790 align:middle line:84% This heat could be heat conduction, 00:39:24.790 --> 00:39:30.110 align:middle line:84% electron can conduct heat, lattice also conduct heat. 00:39:30.110 --> 00:39:32.580 align:middle line:84% So you have both electron and lattice. 00:39:32.580 --> 00:39:38.270 align:middle line:84% This is different than just the Peltier coefficient or Seebeck 00:39:38.270 --> 00:39:39.350 align:middle line:90% coefficient. 00:39:39.350 --> 00:39:41.430 align:middle line:90% So we have the [INAUDIBLE] law. 00:39:41.430 --> 00:39:45.320 align:middle line:84% And if it's a 1b, I integrate it, 00:39:45.320 --> 00:39:49.460 align:middle line:84% I get the amount of heat transfer is proportional 00:39:49.460 --> 00:39:54.230 align:middle line:84% to the cross section area, thermal conductivity 00:39:54.230 --> 00:39:56.860 align:middle line:84% and the temperature difference divided by the length. 00:39:56.860 --> 00:39:59.830 align:middle line:90% 00:39:59.830 --> 00:40:02.440 align:middle line:90% You see this in [? 2005. ?] 00:40:02.440 --> 00:40:05.600 align:middle line:84% And if I group all those parameters together, 00:40:05.600 --> 00:40:10.060 align:middle line:84% AKL, I say this is the thermal conductance. 00:40:10.060 --> 00:40:13.060 align:middle line:84% We probably define thermal resistance before, 00:40:13.060 --> 00:40:16.060 align:middle line:84% but the resistance is just conductance is just 00:40:16.060 --> 00:40:20.800 align:middle line:90% the inverse of the resistance. 00:40:20.800 --> 00:40:26.230 align:middle line:84% So this is the definition of the thermal conductance in the KA 00:40:26.230 --> 00:40:28.560 align:middle line:90% or l. 00:40:28.560 --> 00:40:31.320 align:middle line:84% And just as a comment, very often we 00:40:31.320 --> 00:40:34.590 align:middle line:90% write it just look like math. 00:40:34.590 --> 00:40:39.330 align:middle line:84% But when you actually do it, it matters a lot because here, 00:40:39.330 --> 00:40:43.740 align:middle line:84% for example, the heat flow is inversely 00:40:43.740 --> 00:40:46.920 align:middle line:90% proportional to thickness, 00:40:46.920 --> 00:40:50.820 align:middle line:84% So in the technology development, if I use a film, 00:40:50.820 --> 00:40:53.370 align:middle line:90% l is of the order micron. 00:40:53.370 --> 00:40:56.880 align:middle line:84% And if I use a bulk material, l could be probably 00:40:56.880 --> 00:41:01.320 align:middle line:84% 100 microns or millimeters, and that heat flow 00:41:01.320 --> 00:41:05.410 align:middle line:84% is a 0 order of magnitude difference for the same delta t. 00:41:05.410 --> 00:41:09.520 align:middle line:84% So whether, in reality you have different problems, 00:41:09.520 --> 00:41:15.955 align:middle line:84% sometimes it's clearly space, like the solar, solar radiation 00:41:15.955 --> 00:41:18.520 align:middle line:90% clearly is fixed. 00:41:18.520 --> 00:41:22.300 align:middle line:84% And you want to build your system to create a delta t, 00:41:22.300 --> 00:41:24.220 align:middle line:84% because it's a thermoelectric device 00:41:24.220 --> 00:41:26.110 align:middle line:90% is proportional to delta t. 00:41:26.110 --> 00:41:29.320 align:middle line:90% So that's one type of problem. 00:41:29.320 --> 00:41:34.360 align:middle line:84% There are other cases where delta t is fixed. 00:41:34.360 --> 00:41:36.160 align:middle line:90% Give me give me an example. 00:41:36.160 --> 00:41:41.810 align:middle line:84% There are people looking to ocean geology generation. 00:41:41.810 --> 00:41:45.770 align:middle line:84% In the ocean, there is the top and bottom [INAUDIBLE] 00:41:45.770 --> 00:41:46.640 align:middle line:90% difference. 00:41:46.640 --> 00:41:48.560 align:middle line:84% You've got the different problems 00:41:48.560 --> 00:41:52.940 align:middle line:84% and you can go to back to the most basic picture 00:41:52.940 --> 00:41:54.650 align:middle line:84% to think about your system, sometimes 00:41:54.650 --> 00:41:56.530 align:middle line:90% that's always the first step. 00:41:56.530 --> 00:41:59.120 align:middle line:90% OK. 00:41:59.120 --> 00:42:03.980 align:middle line:90% Now let's look at the device. 00:42:03.980 --> 00:42:06.830 align:middle line:84% Again, the [INAUDIBLE] device has many repeat units 00:42:06.830 --> 00:42:09.440 align:middle line:90% of this t and n. 00:42:09.440 --> 00:42:14.330 align:middle line:84% And if I have just an ideal device, how much cooling I 00:42:14.330 --> 00:42:15.180 align:middle line:90% can create. 00:42:15.180 --> 00:42:20.390 align:middle line:84% I pass a current and the cooling is 00:42:20.390 --> 00:42:23.370 align:middle line:84% the difference and the junction of the two materials. 00:42:23.370 --> 00:42:26.540 align:middle line:84% So one possible material multiplication 00:42:26.540 --> 00:42:30.590 align:middle line:84% times a negative material coefficient times current. 00:42:30.590 --> 00:42:32.840 align:middle line:84% So that's how much cooling I can create. 00:42:32.840 --> 00:42:36.590 align:middle line:90% 00:42:36.590 --> 00:42:40.850 align:middle line:84% But in real situation, what happens 00:42:40.850 --> 00:42:44.390 align:middle line:84% is that when this site is cold, this site is hot, 00:42:44.390 --> 00:42:45.800 align:middle line:90% the heat will flow back. 00:42:45.800 --> 00:42:48.260 align:middle line:90% This is solid material. 00:42:48.260 --> 00:42:50.750 align:middle line:84% You can't get rid of that heat conduction. 00:42:50.750 --> 00:42:54.260 align:middle line:84% So it will diffuse back by conduction. 00:42:54.260 --> 00:42:56.880 align:middle line:90% That's one reality. 00:42:56.880 --> 00:42:59.870 align:middle line:90% That's a long idea factor. 00:42:59.870 --> 00:43:02.630 align:middle line:84% The other non-idea factor is when you pass the current 00:43:02.630 --> 00:43:04.730 align:middle line:90% through, I have [INAUDIBLE]. 00:43:04.730 --> 00:43:06.745 align:middle line:84% I didn't talk about [INAUDIBLE] here, right? 00:43:06.745 --> 00:43:09.680 align:middle line:90% That's unavoidable part. 00:43:09.680 --> 00:43:11.370 align:middle line:90% I don't have a superconductor. 00:43:11.370 --> 00:43:15.470 align:middle line:84% In fact, you don't want to use a superconductor here. 00:43:15.470 --> 00:43:18.560 align:middle line:84% Superconductor, electrical superconductor 00:43:18.560 --> 00:43:22.250 align:middle line:84% is only one quantum mechanical state. 00:43:22.250 --> 00:43:25.040 align:middle line:84% They introduce 0, doesn't carry heat. 00:43:25.040 --> 00:43:29.170 align:middle line:84% Electrons do not carry heat, in case, superconductor. 00:43:29.170 --> 00:43:32.800 align:middle line:84% OK, so there's a [INAUDIBLE] because 00:43:32.800 --> 00:43:34.900 align:middle line:90% the electric conductivity. 00:43:34.900 --> 00:43:39.077 align:middle line:84% And I have to consider both, reverse heat conduction 00:43:39.077 --> 00:43:40.270 align:middle line:90% and [INAUDIBLE]. 00:43:40.270 --> 00:43:44.440 align:middle line:84% Now, I think about [INAUDIBLE], the difference 00:43:44.440 --> 00:43:46.390 align:middle line:84% between conduction is this side is 00:43:46.390 --> 00:43:49.540 align:middle line:84% this side is called [INAUDIBLE] conduction. 00:43:49.540 --> 00:43:52.090 align:middle line:84% The [INAUDIBLE] is uniformly generated 00:43:52.090 --> 00:43:55.060 align:middle line:90% along the lag as approximation. 00:43:55.060 --> 00:43:58.460 align:middle line:84% So in that case, [INAUDIBLE] about half go this way. 00:43:58.460 --> 00:44:00.940 align:middle line:84% The other half goes the other way. 00:44:00.940 --> 00:44:04.980 align:middle line:84% You can solve the equation and you'll find that the answer. 00:44:04.980 --> 00:44:08.320 align:middle line:84% But that's the intuitive argument also. 00:44:08.320 --> 00:44:13.800 align:middle line:84% So in that case, the real net cooling I have is, 00:44:13.800 --> 00:44:18.250 align:middle line:84% in addition to calculate, I have half of the [INAUDIBLE]. 00:44:18.250 --> 00:44:20.250 align:middle line:90% This is electrical resistance. 00:44:20.250 --> 00:44:22.230 align:middle line:84% And I have a reverse heat conduction 00:44:22.230 --> 00:44:24.340 align:middle line:84% that the thermal conductance of the two legs. 00:44:24.340 --> 00:44:29.030 align:middle line:90% 00:44:29.030 --> 00:44:32.760 align:middle line:90% So that's the mathematics. 00:44:32.760 --> 00:44:35.220 align:middle line:84% The resistance, the electrical resistance 00:44:35.220 --> 00:44:39.380 align:middle line:84% is proportional to the resistivity of both legs 00:44:39.380 --> 00:44:44.810 align:middle line:84% area, that's and here are thermal conductance, they both p 00:44:44.810 --> 00:44:49.470 align:middle line:90% and n combine together. 00:44:49.470 --> 00:44:54.200 align:middle line:84% And now you can see the amount of heating 00:44:54.200 --> 00:44:59.960 align:middle line:84% or cooling I create depends on the current flow, right. 00:44:59.960 --> 00:45:03.800 align:middle line:84% I square, y is a linear, the other is square. 00:45:03.800 --> 00:45:08.450 align:middle line:84% If I drive the device too hard, I generate too much heat. 00:45:08.450 --> 00:45:12.500 align:middle line:84% I drive too little, doesn't have enough cooling. 00:45:12.500 --> 00:45:14.150 align:middle line:90% So there is an optimum. 00:45:14.150 --> 00:45:17.210 align:middle line:84% When you drive the device, there's an optimum there. 00:45:17.210 --> 00:45:18.490 align:middle line:90% It's easy to find the optimum. 00:45:18.490 --> 00:45:21.800 align:middle line:90% 00:45:21.800 --> 00:45:25.670 align:middle line:84% Firstly, I want to find out more not only for cooling but also 00:45:25.670 --> 00:45:27.020 align:middle line:90% for efficiency. 00:45:27.020 --> 00:45:33.740 align:middle line:84% So I have to calculate how much electrical energy I give in. 00:45:33.740 --> 00:45:36.380 align:middle line:90% You say. i square r. 00:45:36.380 --> 00:45:37.970 align:middle line:90% It's not that simple. 00:45:37.970 --> 00:45:39.830 align:middle line:90% There's a little trick here. 00:45:39.830 --> 00:45:44.300 align:middle line:84% Because there is a i square r, so voltage drop 00:45:44.300 --> 00:45:49.190 align:middle line:84% is i times r, that's the [INAUDIBLE] part. 00:45:49.190 --> 00:45:52.760 align:middle line:84% But when there is a temperature difference, 00:45:52.760 --> 00:45:56.390 align:middle line:90% there is also a Seebeck voltage. 00:45:56.390 --> 00:46:00.050 align:middle line:84% So when this side, one side is cold, the other side is hot, 00:46:00.050 --> 00:46:03.500 align:middle line:84% there is an additional voltage you have to overcome, 00:46:03.500 --> 00:46:06.710 align:middle line:84% the internal review voltage, Seebeck voltage. 00:46:06.710 --> 00:46:11.420 align:middle line:84% That's the Seebeck coefficient difference times delta t. 00:46:11.420 --> 00:46:13.550 align:middle line:84% That's the voltage you have to overcome 00:46:13.550 --> 00:46:16.740 align:middle line:90% in addition to resistance. 00:46:16.740 --> 00:46:23.610 align:middle line:84% So the electrical power is i times v. So 00:46:23.610 --> 00:46:25.710 align:middle line:90% that's the electrical I put in. 00:46:25.710 --> 00:46:29.070 align:middle line:84% So the efficiency, according to our definition, 00:46:29.070 --> 00:46:33.420 align:middle line:84% for refrigeration, we talk about coefficient of performance, 00:46:33.420 --> 00:46:35.100 align:middle line:90% We don't talk about efficiency. 00:46:35.100 --> 00:46:39.750 align:middle line:84% So this is what I want, the cooling, this is what I pay. 00:46:39.750 --> 00:46:43.050 align:middle line:84% The pay is the power, the power is the current times 00:46:43.050 --> 00:46:43.720 align:middle line:90% the voltage. 00:46:43.720 --> 00:46:47.250 align:middle line:84% So I have i square r, that's the [INAUDIBLE]. 00:46:47.250 --> 00:46:51.720 align:middle line:84% I have to overcome the Seebeck voltage. 00:46:51.720 --> 00:46:54.870 align:middle line:90% So that's the term there. 00:46:54.870 --> 00:46:56.470 align:middle line:90% So that's the bottom part. 00:46:56.470 --> 00:46:57.660 align:middle line:90% That's what I pay. 00:46:57.660 --> 00:47:02.890 align:middle line:84% And the numerator is what do we derive, the previous slide. 00:47:02.890 --> 00:47:07.370 align:middle line:84% Including is accounted for the reverse heat 00:47:07.370 --> 00:47:10.690 align:middle line:90% conduction and the [INAUDIBLE]. 00:47:10.690 --> 00:47:14.560 align:middle line:90% So now you go to optimize it. 00:47:14.560 --> 00:47:16.480 align:middle line:90% And this-- yes? 00:47:16.480 --> 00:47:18.650 align:middle line:84% AUDIENCE: Shouldn't Seebeck dominant be reversed? 00:47:18.650 --> 00:47:20.590 align:middle line:90% i squared r. 00:47:20.590 --> 00:47:22.870 align:middle line:84% GANG CHEN: No, you wish that's the case. 00:47:22.870 --> 00:47:24.340 align:middle line:90% You wish that's the case. 00:47:24.340 --> 00:47:29.050 align:middle line:84% But it's-- you are-- when you have a delta t, 00:47:29.050 --> 00:47:31.040 align:middle line:90% you have to push hard. 00:47:31.040 --> 00:47:36.310 align:middle line:84% You can say, OK, we'll have a hard flow for cooling. 00:47:36.310 --> 00:47:37.880 align:middle line:90% This is a t, this is n. 00:47:37.880 --> 00:47:40.030 align:middle line:90% I know [INAUDIBLE] this way. 00:47:40.030 --> 00:47:47.020 align:middle line:84% But this side is a hot, the voltage is against here. 00:47:47.020 --> 00:47:50.805 align:middle line:84% Otherwise, you get too easy, your problem. 00:47:50.805 --> 00:47:54.650 align:middle line:90% 00:47:54.650 --> 00:47:59.670 align:middle line:84% So you go to optimize your current, that's the arithmetic, 00:47:59.670 --> 00:48:05.360 align:middle line:84% you can divide ei for 0 and you find the optimal current, 00:48:05.360 --> 00:48:09.500 align:middle line:84% and then find the optimum, under optimal part 00:48:09.500 --> 00:48:14.330 align:middle line:84% you got to maximize efficiency or CLP. 00:48:14.330 --> 00:48:17.240 align:middle line:84% Of course, I dropped all the math. 00:48:17.240 --> 00:48:21.330 align:middle line:90% And let me again make a comment. 00:48:21.330 --> 00:48:25.050 align:middle line:84% You go to save your [INAUDIBLE], that's easy because there's 00:48:25.050 --> 00:48:27.330 align:middle line:90% no denominator here. 00:48:27.330 --> 00:48:31.590 align:middle line:84% You got the optimal current for maximum cooling power. 00:48:31.590 --> 00:48:35.760 align:middle line:84% Here you get an optimal current for maximum efficiency, 00:48:35.760 --> 00:48:39.240 align:middle line:84% but they two do not agree with each other. 00:48:39.240 --> 00:48:41.310 align:middle line:84% And in fact, in your operation, you 00:48:41.310 --> 00:48:45.720 align:middle line:84% want to adjust your current just between you can't satisfy, 00:48:45.720 --> 00:48:48.730 align:middle line:84% you go optimal current and you don't have much cooling power. 00:48:48.730 --> 00:48:52.190 align:middle line:90% 00:48:52.190 --> 00:48:54.690 align:middle line:84% The other point is, you look at this, 00:48:54.690 --> 00:48:57.690 align:middle line:90% you say, it's a linear term. 00:48:57.690 --> 00:49:01.800 align:middle line:90% This term is all thermal energy. 00:49:01.800 --> 00:49:06.270 align:middle line:84% That's a [INAUDIBLE] cycle for refrigeration. 00:49:06.270 --> 00:49:09.330 align:middle line:84% We wrote down [INAUDIBLE] for power generation. 00:49:09.330 --> 00:49:11.680 align:middle line:84% But this is a column so it's a column factor, 00:49:11.680 --> 00:49:13.320 align:middle line:90% it's a heat engine. 00:49:13.320 --> 00:49:18.080 align:middle line:84% And of course, you all make sure this term is less than 1. 00:49:18.080 --> 00:49:25.980 align:middle line:84% So you can't get column, and here came to this vector z. 00:49:25.980 --> 00:49:29.480 align:middle line:84% So every time people see, what's your zt? 00:49:29.480 --> 00:49:32.720 align:middle line:84% This is where it came from, z times temperature. 00:49:32.720 --> 00:49:35.780 align:middle line:84% And this t is the average temperature 00:49:35.780 --> 00:49:39.190 align:middle line:90% between the hot and cold side. 00:49:39.190 --> 00:49:42.490 align:middle line:84% And this is z, again, this is all 00:49:42.490 --> 00:49:45.580 align:middle line:84% coming from this mathematical derivative. 00:49:45.580 --> 00:49:49.960 align:middle line:84% And it's the Seebeck difference of the material. 00:49:49.960 --> 00:49:54.910 align:middle line:84% And the denominator is the conductance, thermal conductance 00:49:54.910 --> 00:49:57.190 align:middle line:90% times the electrical resistance. 00:49:57.190 --> 00:49:58.060 align:middle line:90% So look at it. 00:49:58.060 --> 00:50:01.520 align:middle line:84% It's not a material property at all, 00:50:01.520 --> 00:50:06.340 align:middle line:84% it'll equal the material property, Seebeck coefficient, 00:50:06.340 --> 00:50:09.430 align:middle line:84% electrical resistivity, thermal conductivity, 00:50:09.430 --> 00:50:12.810 align:middle line:84% but it also depends on the cross section area. 00:50:12.810 --> 00:50:15.600 align:middle line:90% 00:50:15.600 --> 00:50:17.730 align:middle line:84% And they look at this function, you 00:50:17.730 --> 00:50:21.930 align:middle line:84% want to maximize your zt to get a higher efficiency. 00:50:21.930 --> 00:50:24.330 align:middle line:84% So the first thing is that you go to maximize 00:50:24.330 --> 00:50:27.060 align:middle line:90% your z by geography. 00:50:27.060 --> 00:50:31.020 align:middle line:84% You can reduce the denominator by changing 00:50:31.020 --> 00:50:35.760 align:middle line:90% your l or a [INAUDIBLE], right? 00:50:35.760 --> 00:50:39.420 align:middle line:84% That's the least you can do if you don't work in the material. 00:50:39.420 --> 00:50:42.390 align:middle line:84% And that's what you want to minimize. 00:50:42.390 --> 00:50:47.040 align:middle line:84% And if you minimize it, it turns out this is what you have to do. 00:50:47.040 --> 00:50:50.370 align:middle line:84% The k times r is the minimum when 00:50:50.370 --> 00:50:54.570 align:middle line:84% they do lens cross-section area of the two legs. 00:50:54.570 --> 00:50:55.900 align:middle line:90% So you are engineer. 00:50:55.900 --> 00:51:01.250 align:middle line:84% This is where when you do the device, you optimize it. 00:51:01.250 --> 00:51:06.990 align:middle line:84% We then-- when we do that testing, own lab, sometimes just 00:51:06.990 --> 00:51:10.830 align:middle line:84% hand polishing, all this, trying to make it match to each other. 00:51:10.830 --> 00:51:13.180 align:middle line:84% So you want to get a better performance than others. 00:51:13.180 --> 00:51:16.050 align:middle line:90% 00:51:16.050 --> 00:51:22.920 align:middle line:84% OK, now you that your best case is an idea, 00:51:22.920 --> 00:51:24.750 align:middle line:90% that still is not a zt. 00:51:24.750 --> 00:51:27.870 align:middle line:84% That's still not the individual material property. 00:51:27.870 --> 00:51:33.330 align:middle line:84% It depends on both sides, here and the end materials. 00:51:33.330 --> 00:51:37.680 align:middle line:84% So basically, if I want to make a good device, 00:51:37.680 --> 00:51:43.770 align:middle line:84% I need a good n, a good p, and the two should match each other. 00:51:43.770 --> 00:51:52.080 align:middle line:84% One material you get, you do get the best performance, 00:51:52.080 --> 00:51:55.530 align:middle line:84% And you get about half of the performance 00:51:55.530 --> 00:51:57.810 align:middle line:90% if you have good one material. 00:51:57.810 --> 00:52:02.280 align:middle line:84% But because at the end, using the two 00:52:02.280 --> 00:52:04.920 align:middle line:84% means you have to make a lot of choices. 00:52:04.920 --> 00:52:08.430 align:middle line:84% In materials research, people just talk about one. 00:52:08.430 --> 00:52:13.350 align:middle line:84% You engineer, you know, you have to go to get both materials. 00:52:13.350 --> 00:52:14.960 align:middle line:90% Somebody has one. 00:52:14.960 --> 00:52:16.200 align:middle line:90% You say, do you have another? 00:52:16.200 --> 00:52:18.210 align:middle line:90% You're eager to us. 00:52:18.210 --> 00:52:20.670 align:middle line:84% We'll find others who has the other. 00:52:20.670 --> 00:52:23.400 align:middle line:84% So this is when material scientists just 00:52:23.400 --> 00:52:34.680 align:middle line:84% say, I discovered material with high z, That's s for sigma or k. 00:52:34.680 --> 00:52:40.170 align:middle line:84% You want pi, a material with a high electric conductivity. 00:52:40.170 --> 00:52:43.320 align:middle line:84% And so you want to minimize [INAUDIBLE]. 00:52:43.320 --> 00:52:47.610 align:middle line:84% You want a material with a high Seebeck coefficient. 00:52:47.610 --> 00:52:49.440 align:middle line:84% Seebeck coefficient fundamentally 00:52:49.440 --> 00:52:53.280 align:middle line:84% is the heat carried by per charge. 00:52:53.280 --> 00:52:56.040 align:middle line:84% OK, we'll talk more on that later. 00:52:56.040 --> 00:53:00.330 align:middle line:84% So average speaking per charge, how much heat it carrier. 00:53:00.330 --> 00:53:03.000 align:middle line:84% And then you want a thermal insulator, 00:53:03.000 --> 00:53:05.550 align:middle line:84% a low thermal conductivity because you don't 00:53:05.550 --> 00:53:06.880 align:middle line:90% want to heat reverse back. 00:53:06.880 --> 00:53:10.200 align:middle line:90% 00:53:10.200 --> 00:53:14.760 align:middle line:84% If you know any materials, let me know. 00:53:14.760 --> 00:53:19.200 align:middle line:84% People have been searching this for centuries, 00:53:19.200 --> 00:53:23.100 align:middle line:84% good material with a good electrical thermal conductivity, 00:53:23.100 --> 00:53:25.080 align:middle line:90% poor thermal conductivity. 00:53:25.080 --> 00:53:31.320 align:middle line:84% But also you want every electron carry a lot of heat. 00:53:31.320 --> 00:53:36.810 align:middle line:84% And this has to happen in one material, [INAUDIBLE] material. 00:53:36.810 --> 00:53:41.430 align:middle line:84% AUDIENCE: So we derived the Zmax for a junction. 00:53:41.430 --> 00:53:43.050 align:middle line:90% GANG CHEN: This is the only-- 00:53:43.050 --> 00:53:43.690 align:middle line:90% Zmax. 00:53:43.690 --> 00:53:49.110 align:middle line:84% You need a computer device in these two materials, 00:53:49.110 --> 00:53:51.670 align:middle line:84% Well, theoretically, you don't need two material, 00:53:51.670 --> 00:53:53.100 align:middle line:90% you can do one material. 00:53:53.100 --> 00:53:55.140 align:middle line:84% In fact, in that case, what people choose, 00:53:55.140 --> 00:53:58.530 align:middle line:84% the other material, they choose a superconductor. 00:53:58.530 --> 00:54:00.400 align:middle line:90% Just don't do anything. 00:54:00.400 --> 00:54:02.730 align:middle line:84% So that's how they characterize the one mature 00:54:02.730 --> 00:54:05.710 align:middle line:90% if you want to do a good job. 00:54:05.710 --> 00:54:10.820 align:middle line:84% All right, let's see, this one is immature research, 00:54:10.820 --> 00:54:17.555 align:middle line:84% you don't-- you can't wait to get too mature and positive, 00:54:17.555 --> 00:54:19.930 align:middle line:84% You get one but mature taking many years, 00:54:19.930 --> 00:54:22.840 align:middle line:84% so you do a simple material to say 00:54:22.840 --> 00:54:25.730 align:middle line:84% this is a measure of how good is this material. 00:54:25.730 --> 00:54:27.875 align:middle line:84% But as an engineer, you want to build a device, 00:54:27.875 --> 00:54:29.750 align:middle line:84% you have to say, where is the other material? 00:54:29.750 --> 00:54:31.370 align:middle line:90% I mean, I need both materials. 00:54:31.370 --> 00:54:34.340 align:middle line:90% 00:54:34.340 --> 00:54:41.420 align:middle line:84% So those are the comments that is made to optimize [INAUDIBLE] 00:54:41.420 --> 00:54:43.790 align:middle line:90% optimize index. 00:54:43.790 --> 00:54:46.730 align:middle line:90% And there is two types. 00:54:46.730 --> 00:54:49.340 align:middle line:84% And then you optimize the device performance, 00:54:49.340 --> 00:54:54.140 align:middle line:90% load matching by current. 00:54:54.140 --> 00:54:56.610 align:middle line:90% This is a [INAUDIBLE]. 00:54:56.610 --> 00:55:02.060 align:middle line:84% So here is some typical [INAUDIBLE] for the business, 00:55:02.060 --> 00:55:05.470 align:middle line:84% that's the commercial device mostly you buy. 00:55:05.470 --> 00:55:08.790 align:middle line:84% You can only buy this type of material based device. 00:55:08.790 --> 00:55:14.290 align:middle line:84% Seebeck [INAUDIBLE] is about 220 microwatts per kelvin. 00:55:14.290 --> 00:55:19.360 align:middle line:84% Electric [INAUDIBLE] fence is around 1.51 [INAUDIBLE]. 00:55:19.360 --> 00:55:21.490 align:middle line:90% This is all Si units. 00:55:21.490 --> 00:55:24.210 align:middle line:84% It's good to keep in mind, example of a micro 00:55:24.210 --> 00:55:30.470 align:middle line:84% [INAUDIBLE] including the [INAUDIBLE] zte is about 1. 00:55:30.470 --> 00:55:34.310 align:middle line:90% 00:55:34.310 --> 00:55:37.340 align:middle line:90% And we'll talk how good is that. 00:55:37.340 --> 00:55:38.990 align:middle line:90% Now, what's the problem? 00:55:38.990 --> 00:55:41.780 align:middle line:84% If you have all this library, you say, OK, this is-- 00:55:41.780 --> 00:55:45.840 align:middle line:84% I think, a [INAUDIBLE] 2 millimeter long electrical 00:55:45.840 --> 00:55:49.280 align:middle line:84% interface, cross-section, one millimeter square. 00:55:49.280 --> 00:55:52.100 align:middle line:84% So it's a small, if you look at the device that 00:55:52.100 --> 00:55:54.980 align:middle line:84% pass around, that's dimensioned roughly, 00:55:54.980 --> 00:55:58.160 align:middle line:84% each leg is only 20 million ohms, 00:55:58.160 --> 00:56:01.310 align:middle line:90% 20 million ohms, very small. 00:56:01.310 --> 00:56:03.080 align:middle line:84% You go to buy resistors, actually 00:56:03.080 --> 00:56:04.977 align:middle line:84% very hard to buy this small resistor. 00:56:04.977 --> 00:56:05.560 align:middle line:90% What it means? 00:56:05.560 --> 00:56:08.330 align:middle line:90% 00:56:08.330 --> 00:56:13.060 align:middle line:84% It means if you want to build a single device or two legs, 00:56:13.060 --> 00:56:16.840 align:middle line:84% because current is a voltage divided by resistance, 00:56:16.840 --> 00:56:20.050 align:middle line:84% It puts your [? heart, ?] huge [? heart, ?] 00:56:20.050 --> 00:56:22.510 align:middle line:90% you need a big power supply. 00:56:22.510 --> 00:56:27.490 align:middle line:84% So you go to look at you in your lab, have a big power 00:56:27.490 --> 00:56:32.070 align:middle line:84% supply, a small driver, small device. 00:56:32.070 --> 00:56:36.690 align:middle line:84% And at the end, that means cost, so everything 00:56:36.690 --> 00:56:38.160 align:middle line:90% you have to consider. 00:56:38.160 --> 00:56:41.080 align:middle line:84% And that's why some people do micro devices. 00:56:41.080 --> 00:56:44.040 align:middle line:84% You can actually shrink your area, 00:56:44.040 --> 00:56:46.350 align:middle line:84% You do a smaller cross-section area 00:56:46.350 --> 00:56:50.340 align:middle line:84% where you put a lot of those together, in that case, 00:56:50.340 --> 00:56:54.790 align:middle line:84% you get a higher resistance by putting more of the [INAUDIBLE] 00:56:54.790 --> 00:56:55.410 align:middle line:90% together. 00:56:55.410 --> 00:57:00.180 align:middle line:84% So in the device, I showed the cost around, this is about 100. 00:57:00.180 --> 00:57:05.130 align:middle line:84% So if you multiply, 100 is only two ohms, the total resistance 00:57:05.130 --> 00:57:06.930 align:middle line:90% if you own this sort of device. 00:57:06.930 --> 00:57:11.820 align:middle line:84% So it's a small resistance, current device. 00:57:11.820 --> 00:57:16.860 align:middle line:84% So that's the reason to put them in series 00:57:16.860 --> 00:57:21.600 align:middle line:84% is putting getting higher resistance so that they 00:57:21.600 --> 00:57:23.520 align:middle line:90% are supplied easier. 00:57:23.520 --> 00:57:26.130 align:middle line:84% Let's say it's still pretty large current. 00:57:26.130 --> 00:57:31.890 align:middle line:84% And then you put them ceremony in parallel, because the parity 00:57:31.890 --> 00:57:35.953 align:middle line:84% from one side to the other, electrically [INAUDIBLE]. 00:57:35.953 --> 00:57:37.620 align:middle line:84% AUDIENCE: When you optimize your system, 00:57:37.620 --> 00:57:43.020 align:middle line:84% then you really get that simple number, 1, 1, 2. 00:57:43.020 --> 00:57:44.940 align:middle line:84% GANG CHEN: Simple number of 1, 1? 00:57:44.940 --> 00:57:48.030 align:middle line:84% AUDIENCE: [? 100 ?] millimeter by [? 200 ?] millimeter. 00:57:48.030 --> 00:57:50.160 align:middle line:84% GANG CHEN: Oh, you mean-- no, no, no, no, no. 00:57:50.160 --> 00:57:51.580 align:middle line:90% This you can charge. 00:57:51.580 --> 00:57:53.950 align:middle line:84% You can make a long leg to test it. 00:57:53.950 --> 00:57:57.700 align:middle line:84% You will still get the same delta t. 00:57:57.700 --> 00:58:00.870 align:middle line:84% AUDIENCE: But when you optimize the system? 00:58:00.870 --> 00:58:04.890 align:middle line:84% GANG CHEN: Optimize means also material cost, The? 00:58:04.890 --> 00:58:10.830 align:middle line:84% Real world is not just you have to match to your application. 00:58:10.830 --> 00:58:15.090 align:middle line:84% You don't have to fix to the geometry I pass around. 00:58:15.090 --> 00:58:19.050 align:middle line:84% And that geometry is in commercial production 00:58:19.050 --> 00:58:24.300 align:middle line:84% because in fact, each application may be different, 00:58:24.300 --> 00:58:27.540 align:middle line:84% but the heart of the market is too small, 00:58:27.540 --> 00:58:30.870 align:middle line:84% so people are just selling more standard modules. 00:58:30.870 --> 00:58:32.920 align:middle line:84% Well, anything you go along a standard, 00:58:32.920 --> 00:58:34.420 align:middle line:84% you have to talk to the manufacturer 00:58:34.420 --> 00:58:36.140 align:middle line:84% and see whether they can manufacture. 00:58:36.140 --> 00:58:40.190 align:middle line:90% 00:58:40.190 --> 00:58:45.980 align:middle line:84% OK, so this is the example, this we built before. 00:58:45.980 --> 00:58:48.770 align:middle line:84% This is actually measuring two legs. 00:58:48.770 --> 00:58:51.740 align:middle line:84% There's a lot more difficult than measuring device, 00:58:51.740 --> 00:58:54.470 align:middle line:84% because any time you put a thermocouple there, 00:58:54.470 --> 00:58:56.210 align:middle line:90% you have a feed loss. 00:58:56.210 --> 00:58:58.410 align:middle line:84% Feed loss is your performance may diminish. 00:58:58.410 --> 00:59:01.850 align:middle line:84% If you want to say, what's your maximum delta t or that, 00:59:01.850 --> 00:59:08.030 align:middle line:84% so it's a lot of time brewing and doing the experiment, 00:59:08.030 --> 00:59:10.420 align:middle line:90% you have your leg is mediums. 00:59:10.420 --> 00:59:15.350 align:middle line:84% So anytime you have missing [INAUDIBLE] the industry, 00:59:15.350 --> 00:59:18.420 align:middle line:90% they do much more, much better. 00:59:18.420 --> 00:59:19.800 align:middle line:90% I look at a production. 00:59:19.800 --> 00:59:24.890 align:middle line:84% I was really amazed at what I'm seeing the worker can do, 00:59:24.890 --> 00:59:28.130 align:middle line:84% versus what we can do in the lab. 00:59:28.130 --> 00:59:32.450 align:middle line:90% That's a different environment. 00:59:32.450 --> 00:59:43.620 align:middle line:84% But this is the 1p1n, and this is a measurement curve. 00:59:43.620 --> 00:59:45.780 align:middle line:90% You can see it's a large term. 00:59:45.780 --> 00:59:49.680 align:middle line:84% In this case, we go one fatigue along the line 00:59:49.680 --> 00:59:51.600 align:middle line:90% through that device. 00:59:51.600 --> 00:59:56.010 align:middle line:84% By [? line ?] absent, the use of aggregate 1 million or 2. 00:59:56.010 --> 00:59:57.860 align:middle line:90% So these were-- 00:59:57.860 --> 01:00:01.050 align:middle line:84% What's amazing with that small thing, 01:00:01.050 --> 01:00:05.040 align:middle line:84% on this side is 100 degree, the other side is 0. 01:00:05.040 --> 01:00:09.270 align:middle line:84% So you can derive a lot of the other things you have. 01:00:09.270 --> 01:00:12.215 align:middle line:90% The efficiency is not very good. 01:00:12.215 --> 01:00:12.715 align:middle line:90% OK. 01:00:12.715 --> 01:00:15.250 align:middle line:90% 01:00:15.250 --> 01:00:18.550 align:middle line:84% The material is dependent-- mentioned this before. 01:00:18.550 --> 01:00:24.550 align:middle line:84% An the analysis I gave you is for constant temperature. 01:00:24.550 --> 01:00:27.940 align:middle line:84% So if you do real device design, you 01:00:27.940 --> 01:00:31.060 align:middle line:84% have to go solve differential equations 01:00:31.060 --> 01:00:34.330 align:middle line:84% and match the property, consider all the temperature 01:00:34.330 --> 01:00:39.700 align:middle line:84% dependent properties, and that I'm not going to cover in depth. 01:00:39.700 --> 01:00:43.900 align:middle line:84% Anybody wants to do that, you can just do the energy 01:00:43.900 --> 01:00:46.270 align:middle line:90% balance in differential form. 01:00:46.270 --> 01:00:48.490 align:middle line:84% And this is the heat conduction term. 01:00:48.490 --> 01:00:51.340 align:middle line:90% This is the constant term. 01:00:51.340 --> 01:00:54.010 align:middle line:90% This is [INAUDIBLE]. 01:00:54.010 --> 01:00:56.920 align:middle line:84% So that's a differential equation locally. 01:00:56.920 --> 01:01:00.610 align:middle line:84% And very often people use differential analysis 01:01:00.610 --> 01:01:02.770 align:middle line:90% to incorporate companies. 01:01:02.770 --> 01:01:06.370 align:middle line:84% And then the boundary has a plural term 01:01:06.370 --> 01:01:09.820 align:middle line:90% and the positive term. 01:01:09.820 --> 01:01:12.820 align:middle line:84% So you have a boundary condition and a differential equation. 01:01:12.820 --> 01:01:16.743 align:middle line:84% And so, again, this is a [INAUDIBLE]. 01:01:16.743 --> 01:01:17.410 align:middle line:90% Y'all know what. 01:01:17.410 --> 01:01:18.870 align:middle line:90% I want to talk in details. 01:01:18.870 --> 01:01:22.470 align:middle line:90% 01:01:22.470 --> 01:01:25.710 align:middle line:84% And now let's look at where those technologies are. 01:01:25.710 --> 01:01:29.160 align:middle line:84% I have the expression for CLT and you do 01:01:29.160 --> 01:01:31.710 align:middle line:90% the same analysis about power. 01:01:31.710 --> 01:01:37.170 align:middle line:84% And you get the efficiency for power generation. 01:01:37.170 --> 01:01:39.450 align:middle line:84% And we [INAUDIBLE] power generation 01:01:39.450 --> 01:01:43.650 align:middle line:84% and getting ZR inside, and this factor is slightly 01:01:43.650 --> 01:01:45.930 align:middle line:84% different from CLT, but you go to check, 01:01:45.930 --> 01:01:48.720 align:middle line:90% it's probably your first one. 01:01:48.720 --> 01:01:51.600 align:middle line:90% And this is a part of that, 01:01:51.600 --> 01:01:53.640 align:middle line:90% Again, it's a thermal engine. 01:01:53.640 --> 01:01:58.380 align:middle line:84% The [? power ?] pans to whatever your material. 01:01:58.380 --> 01:02:03.030 align:middle line:84% You can try to [? power, ?] you went big on this, you have 5gt, 01:02:03.030 --> 01:02:04.860 align:middle line:90% you can go to [INAUDIBLE]. 01:02:04.860 --> 01:02:12.040 align:middle line:84% And so this is not-- so I would say, not so accurate. 01:02:12.040 --> 01:02:16.080 align:middle line:84% I mean, it's like around 95 to 96. 01:02:16.080 --> 01:02:21.810 align:middle line:84% And this is the accurate ratio of hot to cold in Kelvin. 01:02:21.810 --> 01:02:24.600 align:middle line:90% And this is the efficiency. 01:02:24.600 --> 01:02:30.510 align:middle line:84% And what I put down here is the thermal activities 01:02:30.510 --> 01:02:33.060 align:middle line:90% at the bottom. 01:02:33.060 --> 01:02:36.170 align:middle line:84% OK, there's another [INAUDIBLE] picture. 01:02:36.170 --> 01:02:41.560 align:middle line:84% First, have to do a lot of research, 01:02:41.560 --> 01:02:46.210 align:middle line:84% And the power plant is about 40%. 01:02:46.210 --> 01:02:50.470 align:middle line:84% The normal coal fired power plant is 40%, 01:02:50.470 --> 01:02:53.670 align:middle line:84% Internal combustion engine is about 20%, 25%. 01:02:53.670 --> 01:02:56.450 align:middle line:90% 01:02:56.450 --> 01:02:57.380 align:middle line:90% OK. 01:02:57.380 --> 01:03:01.760 align:middle line:84% What I need now for the [INAUDIBLE] is [INAUDIBLE]. 01:03:01.760 --> 01:03:05.090 align:middle line:84% Depends on amount of silicon, about 6%, 01:03:05.090 --> 01:03:10.700 align:middle line:90% single crystal silicon about 18% 01:03:10.700 --> 01:03:14.900 align:middle line:84% Once you think about that, then your picture becomes a better. 01:03:14.900 --> 01:03:18.220 align:middle line:84% You can, in fact see the [INAUDIBLE] use 01:03:18.220 --> 01:03:22.520 align:middle line:84% a thermoelectric power generator and that's about 6% to 7% 01:03:22.520 --> 01:03:24.500 align:middle line:90% in the deep space missions. 01:03:24.500 --> 01:03:26.670 align:middle line:84% And now in the lab, there are people developing 01:03:26.670 --> 01:03:30.740 align:middle line:84% similar generator using a zt bottle, one material that 01:03:30.740 --> 01:03:36.680 align:middle line:84% is around 40%, copper, 40%, uranium 01:03:36.680 --> 01:03:42.660 align:middle line:84% 2 level of that's actually very attractive [INAUDIBLE]. 01:03:42.660 --> 01:03:46.440 align:middle line:84% So it really is an application because you don't-- 01:03:46.440 --> 01:03:49.740 align:middle line:84% at this stage, we're not thinking you can't it's not 01:03:49.740 --> 01:03:54.930 align:middle line:84% at that level to say I'm going to replace major form over 01:03:54.930 --> 01:03:58.620 align:middle line:84% in the sense of like, we're not dealing here 01:03:58.620 --> 01:04:02.230 align:middle line:84% with an internal combustion engine, 01:04:02.230 --> 01:04:05.280 align:middle line:84% but there are many different sources where you 01:04:05.280 --> 01:04:08.700 align:middle line:90% can potentially [INAUDIBLE]. 01:04:08.700 --> 01:04:15.990 align:middle line:84% And there is refrigeration on this before. 01:04:15.990 --> 01:04:21.880 align:middle line:84% and CLT, again, depends on temperature. 01:04:21.880 --> 01:04:30.690 align:middle line:84% And a CLT of thermal electric compared to fossil refrigerator 01:04:30.690 --> 01:04:32.320 align:middle line:90% is about a factor of 5. 01:04:32.320 --> 01:04:34.920 align:middle line:90% 01:04:34.920 --> 01:04:39.120 align:middle line:84% So that's actually probably the oddest really 01:04:39.120 --> 01:04:43.230 align:middle line:84% want to say the application, say really 01:04:43.230 --> 01:04:48.540 align:middle line:84% replacing the screwdriver, I think probably took a long time. 01:04:48.540 --> 01:04:53.070 align:middle line:84% But again, there may be other applications where you 01:04:53.070 --> 01:04:55.170 align:middle line:90% can think about [INAUDIBLE]. 01:04:55.170 --> 01:04:58.440 align:middle line:84% And in fact the current market, and I'll show later 01:04:58.440 --> 01:05:02.340 align:middle line:90% is mostly [INAUDIBLE]. 01:05:02.340 --> 01:05:10.560 align:middle line:84% So this is where really the engineers, you can really say, 01:05:10.560 --> 01:05:16.800 align:middle line:84% I know the technology is where it makes sense. 01:05:16.800 --> 01:05:21.930 align:middle line:84% There are different areas that it could make sense, 01:05:21.930 --> 01:05:28.710 align:middle line:84% and commercially, mostly standard size, standard size 01:05:28.710 --> 01:05:32.310 align:middle line:84% people offer different sides, but the geometry 01:05:32.310 --> 01:05:34.770 align:middle line:90% is very similar. 01:05:34.770 --> 01:05:39.900 align:middle line:84% The height could be in the case of our generator for about 5, 01:05:39.900 --> 01:05:44.340 align:middle line:84% 6 millimeters, and the coolers, the typical millimeter 01:05:44.340 --> 01:05:50.480 align:middle line:84% in height in the neck, and the top is a ceramic and copper 01:05:50.480 --> 01:05:51.540 align:middle line:90% bottomed ceramic. 01:05:51.540 --> 01:05:55.340 align:middle line:84% And [? the head, ?] the next the next are 01:05:55.340 --> 01:05:57.930 align:middle line:90% interconnected by copper. 01:05:57.930 --> 01:05:59.800 align:middle line:84% So the technology wise, they have 01:05:59.800 --> 01:06:03.940 align:middle line:84% to put a diffusion barrier between the copper and material, 01:06:03.940 --> 01:06:07.560 align:middle line:84% because copper easily get into the material that 01:06:07.560 --> 01:06:09.162 align:middle line:90% composes in the [INAUDIBLE]. 01:06:09.162 --> 01:06:12.290 align:middle line:90% 01:06:12.290 --> 01:06:20.960 align:middle line:84% In terms of applications, this has one standard small cooler, 01:06:20.960 --> 01:06:26.150 align:middle line:84% this is because when you reduce the compressor, 01:06:26.150 --> 01:06:29.720 align:middle line:84% the compressor actually, the smaller you make, the hotter-- 01:06:29.720 --> 01:06:32.480 align:middle line:90% the hotter you make it. 01:06:32.480 --> 01:06:36.410 align:middle line:84% When you make a very small compressor, of course, 01:06:36.410 --> 01:06:39.470 align:middle line:84% the northern part is [INAUDIBLE] and this 01:06:39.470 --> 01:06:44.890 align:middle line:84% becomes a more attractive, so this becomes more attractive. 01:06:44.890 --> 01:06:48.220 align:middle line:84% A lot of the dormitory [INAUDIBLE] refrigerators 01:06:48.220 --> 01:06:50.480 align:middle line:90% made for somewhere like this. 01:06:50.480 --> 01:06:52.790 align:middle line:84% And still the efficiency, I think, 01:06:52.790 --> 01:06:56.150 align:middle line:84% is still not as competitive, but the cost 01:06:56.150 --> 01:06:58.170 align:middle line:90% could be very attractive. 01:06:58.170 --> 01:07:00.720 align:middle line:90% 01:07:00.720 --> 01:07:04.980 align:middle line:84% And then it can be as small as just a little vial. 01:07:04.980 --> 01:07:09.300 align:middle line:84% And the people, in fact, that put a lot of multi-stage 01:07:09.300 --> 01:07:11.520 align:middle line:90% to create a lot of-- 01:07:11.520 --> 01:07:14.220 align:middle line:90% each stage is a maybe-- 01:07:14.220 --> 01:07:18.240 align:middle line:84% this to about six feet together, you 01:07:18.240 --> 01:07:23.670 align:middle line:84% can get a commercially at least 50, [INAUDIBLE] pounds. 01:07:23.670 --> 01:07:26.940 align:middle line:84% So the infrared detector were also 01:07:26.940 --> 01:07:29.580 align:middle line:84% needed to be cool with [INAUDIBLE]. 01:07:29.580 --> 01:07:32.130 align:middle line:90% 01:07:32.130 --> 01:07:36.630 align:middle line:84% But the main laser diode has a somewhat like a cooler. 01:07:36.630 --> 01:07:39.880 align:middle line:84% This is because the wavelengths in communication, 01:07:39.880 --> 01:07:42.870 align:middle line:84% telecommunication, the wavelengths of this laser 01:07:42.870 --> 01:07:45.660 align:middle line:90% are [INAUDIBLE]. 01:07:45.660 --> 01:07:50.070 align:middle line:84% So they actually use some energy to stabilize the temperature, 01:07:50.070 --> 01:07:55.050 align:middle line:84% not much for the [? human, ?] but for the [INAUDIBLE] 01:07:55.050 --> 01:07:59.340 align:middle line:84% macro DNA, we have to compare the initial [INAUDIBLE] 01:07:59.340 --> 01:08:03.600 align:middle line:90% naturalization and recycling. 01:08:03.600 --> 01:08:06.720 align:middle line:84% And probably a really good commercial example 01:08:06.720 --> 01:08:10.620 align:middle line:84% is this company for the American. 01:08:10.620 --> 01:08:15.600 align:middle line:84% And they started putting a device, 01:08:15.600 --> 01:08:20.609 align:middle line:84% this is where you have to look at where it makes sense, 01:08:20.609 --> 01:08:26.340 align:middle line:84% They started to manufacture around 2,000, 01:08:26.340 --> 01:08:32.170 align:middle line:84% somewhere like six, and in some high automobiles. 01:08:32.170 --> 01:08:35.430 align:middle line:84% Now they have a market, about 3 million models, 01:08:35.430 --> 01:08:39.630 align:middle line:90% include the car seats. 01:08:39.630 --> 01:08:42.310 align:middle line:90% I still have this in my car. 01:08:42.310 --> 01:08:54.460 align:middle line:84% It's a luxury item and but pretty well successful. 01:08:54.460 --> 01:08:57.810 align:middle line:84% And now the DOE is trying to even get rid 01:08:57.810 --> 01:09:00.040 align:middle line:90% of the main air conditioner. 01:09:00.040 --> 01:09:05.340 align:middle line:84% And the idea is that the main air conditioning automobile will 01:09:05.340 --> 01:09:08.370 align:middle line:90% require about 6, 7 kilowatt. 01:09:08.370 --> 01:09:12.390 align:middle line:84% And the purpose is to turn the engine on, 01:09:12.390 --> 01:09:13.450 align:middle line:90% the air conditioning on. 01:09:13.450 --> 01:09:18.870 align:middle line:84% You want to cool the whole compartment in about 5 minutes, 01:09:18.870 --> 01:09:22.770 align:middle line:84% but normally you do need a high compression, large compressor. 01:09:22.770 --> 01:09:28.800 align:middle line:84% So the question is whether they can use this distributed cooler 01:09:28.800 --> 01:09:31.770 align:middle line:90% into the automobile. 01:09:31.770 --> 01:09:34.455 align:middle line:84% I'm not sure whether it will be successful, but there 01:09:34.455 --> 01:09:35.760 align:middle line:90% [INAUDIBLE]. 01:09:35.760 --> 01:09:37.529 align:middle line:84% And in fact, this is a-- when you think 01:09:37.529 --> 01:09:39.310 align:middle line:90% about where they make sense. 01:09:39.310 --> 01:09:44.899 align:middle line:84% They find the seats, not your offices. 01:09:44.899 --> 01:09:47.390 align:middle line:90% Your offices, you move around. 01:09:47.390 --> 01:09:50.390 align:middle line:84% Once you get the car, it's there. 01:09:50.390 --> 01:09:54.820 align:middle line:84% They plug in the power because this means the power there. 01:09:54.820 --> 01:09:55.600 align:middle line:90% Right? 01:09:55.600 --> 01:10:02.202 align:middle line:84% So any other places it could be using that-- 01:10:02.202 --> 01:10:03.160 align:middle line:90% AUDIENCE: Movie theater 01:10:03.160 --> 01:10:06.130 align:middle line:84% GANG CHEN: Since that's probably too big. 01:10:06.130 --> 01:10:08.260 align:middle line:90% I was thinking about the bed. 01:10:08.260 --> 01:10:13.060 align:middle line:84% I say there are actual products there. 01:10:13.060 --> 01:10:17.650 align:middle line:84% You go, I was thinking before, I looked at the wrong products 01:10:17.650 --> 01:10:18.730 align:middle line:90% already. 01:10:18.730 --> 01:10:21.850 align:middle line:84% I guess the key there is whether it's a physiologically 01:10:21.850 --> 01:10:26.390 align:middle line:84% comfortable and also how you reject that. 01:10:26.390 --> 01:10:29.240 align:middle line:84% If you reject it to the same rule, 01:10:29.240 --> 01:10:32.720 align:middle line:90% does it make sense at the end? 01:10:32.720 --> 01:10:35.540 align:middle line:84% So there are-- those are all the places where 01:10:35.540 --> 01:10:37.400 align:middle line:84% if you're an engineer, you got to think 01:10:37.400 --> 01:10:41.780 align:middle line:84% about where it makes sense and where you 01:10:41.780 --> 01:10:45.550 align:middle line:90% have a product people accept. 01:10:45.550 --> 01:10:48.850 align:middle line:84% And with the more product into the market, of course 01:10:48.850 --> 01:10:52.000 align:middle line:84% there's a material is also improving 01:10:52.000 --> 01:10:59.050 align:middle line:84% that you have potential, further advancing the technology. 01:10:59.050 --> 01:11:02.540 align:middle line:84% Power generation, the main driver in the past 01:11:02.540 --> 01:11:04.850 align:middle line:90% is space missions. 01:11:04.850 --> 01:11:09.440 align:middle line:84% So in once you go beyond the Mars, 01:11:09.440 --> 01:11:11.510 align:middle line:90% the solar radiation diminishes. 01:11:11.510 --> 01:11:13.700 align:middle line:84% So in Mars, most of the power still 01:11:13.700 --> 01:11:16.820 align:middle line:84% come from the solar panels, although there 01:11:16.820 --> 01:11:21.120 align:middle line:84% are some electric cooler or thermoelectric generator. 01:11:21.120 --> 01:11:24.140 align:middle line:84% And sometimes those generator proposal 01:11:24.140 --> 01:11:29.240 align:middle line:84% was actually to keep the electronics warm, 01:11:29.240 --> 01:11:35.930 align:middle line:84% amazingly, in you go to say beyond in the-- 01:11:35.930 --> 01:11:37.790 align:middle line:90% it's very cold in the night. 01:11:37.790 --> 01:11:39.090 align:middle line:90% There's no power. 01:11:39.090 --> 01:11:42.290 align:middle line:84% You need the electrical power to heat up the electronics. 01:11:42.290 --> 01:11:47.540 align:middle line:84% So the space mission, most of the deep space mission 01:11:47.540 --> 01:11:49.430 align:middle line:90% are thermoelectric power. 01:11:49.430 --> 01:11:53.060 align:middle line:84% And that's a good news because Galileo, for example, 01:11:53.060 --> 01:11:57.480 align:middle line:84% send back signal for more than 20, close to 30 years. 01:11:57.480 --> 01:11:59.400 align:middle line:84% Galileo, eventually the signal was not 01:11:59.400 --> 01:12:01.900 align:middle line:84% lost a lot because the power generator, just because 01:12:01.900 --> 01:12:04.410 align:middle line:90% of the mission was abandoned. 01:12:04.410 --> 01:12:08.990 align:middle line:84% Voyager, all those were based on thermoelectric generator. 01:12:08.990 --> 01:12:11.810 align:middle line:84% And in there, they use a nuclear force. 01:12:11.810 --> 01:12:17.743 align:middle line:84% So actually, I went to one deep space conference in our pocket. 01:12:17.743 --> 01:12:19.910 align:middle line:84% That's interesting, in the conference outside, there 01:12:19.910 --> 01:12:22.970 align:middle line:90% are people, space missions. 01:12:22.970 --> 01:12:26.240 align:middle line:84% So there are outside people protesting, 01:12:26.240 --> 01:12:28.700 align:middle line:84% because it's the most of the space missions 01:12:28.700 --> 01:12:30.420 align:middle line:90% are nuclear power. 01:12:30.420 --> 01:12:33.750 align:middle line:90% 01:12:33.750 --> 01:12:34.250 align:middle line:90% OK. 01:12:34.250 --> 01:12:37.130 align:middle line:90% A terrestrial application. 01:12:37.130 --> 01:12:42.200 align:middle line:84% This is a standalone generator where, 01:12:42.200 --> 01:12:48.230 align:middle line:84% for example, this company, global thermoelectric 01:12:48.230 --> 01:12:53.060 align:middle line:84% they become good business because they sell those power 01:12:53.060 --> 01:12:57.110 align:middle line:84% generators along to big oil companies. 01:12:57.110 --> 01:13:01.190 align:middle line:84% The oil company needs to monitor their pipelines. 01:13:01.190 --> 01:13:04.850 align:middle line:84% The pipelines, let's say you go through Alaska. 01:13:04.850 --> 01:13:07.950 align:middle line:90% There's no electric power there. 01:13:07.950 --> 01:13:16.800 align:middle line:84% So they actually use the oil to generate the heat and the power 01:13:16.800 --> 01:13:17.470 align:middle line:90% generation. 01:13:17.470 --> 01:13:21.150 align:middle line:90% 01:13:21.150 --> 01:13:23.470 align:middle line:90% Body power watch. 01:13:23.470 --> 01:13:25.260 align:middle line:90% OK. 01:13:25.260 --> 01:13:28.350 align:middle line:84% I don't think it's very commercially successful. 01:13:28.350 --> 01:13:31.110 align:middle line:84% The company first company trying to market it 01:13:31.110 --> 01:13:36.630 align:middle line:90% was a Japan company, Seiko. 01:13:36.630 --> 01:13:40.180 align:middle line:84% I went to visit them at the time, 01:13:40.180 --> 01:13:46.720 align:middle line:84% and they said $3,000 is the modern power watch. 01:13:46.720 --> 01:13:48.140 align:middle line:90% I for one. 01:13:48.140 --> 01:13:53.400 align:middle line:84% I say it's amazing that the watch only 01:13:53.400 --> 01:13:57.358 align:middle line:84% 1 microwatt, 1 microwatt, that's what 01:13:57.358 --> 01:13:58.650 align:middle line:90% I learned from the [INAUDIBLE]. 01:13:58.650 --> 01:14:04.380 align:middle line:84% The temperature difference is 1 degree Kelvin, 01:14:04.380 --> 01:14:07.950 align:middle line:84% a degree Celsius to develop for this watch. 01:14:07.950 --> 01:14:09.770 align:middle line:84% And there was a lot of companies who 01:14:09.770 --> 01:14:13.370 align:middle line:84% see, [? Carlheim ?] I think I didn't go to check her watch, 01:14:13.370 --> 01:14:16.800 align:middle line:84% but I heard now they are still on the market. 01:14:16.800 --> 01:14:18.400 align:middle line:90% They are selling $300. 01:14:18.400 --> 01:14:19.430 align:middle line:90% This one, went to-- 01:14:19.430 --> 01:14:22.220 align:middle line:84% I visited and they say, well, what's in the Smithsonian? 01:14:22.220 --> 01:14:24.150 align:middle line:90% So today it's free. 01:14:24.150 --> 01:14:29.570 align:middle line:84% But I think [? Carlheim ?] it's is still about $300. 01:14:29.570 --> 01:14:30.680 align:middle line:90% I don't have much. 01:14:30.680 --> 01:14:33.260 align:middle line:90% I don't need a watch. 01:14:33.260 --> 01:14:39.350 align:middle line:84% But some people are developing body power 01:14:39.350 --> 01:14:46.730 align:middle line:84% for, you think about the low power electronics. 01:14:46.730 --> 01:14:51.020 align:middle line:84% Some of these devices don't really require a lot of people. 01:14:51.020 --> 01:14:54.750 align:middle line:84% At the other day, I met an MIT professor in the department, 01:14:54.750 --> 01:14:56.720 align:middle line:84% I know [INAUDIBLE] student there. 01:14:56.720 --> 01:15:01.100 align:middle line:84% He has-- he said that he can generate 300 microwatts, which 01:15:01.100 --> 01:15:03.110 align:middle line:90% is pretty good. 01:15:03.110 --> 01:15:11.280 align:middle line:84% And I saw Philips trying to also develop it, the body power. 01:15:11.280 --> 01:15:17.310 align:middle line:84% And in fact, it might be worth the calculation to say, 01:15:17.310 --> 01:15:20.610 align:middle line:84% I think Philips is trying to develop a few, 01:15:20.610 --> 01:15:24.210 align:middle line:84% where you put the body the delta t right. 01:15:24.210 --> 01:15:32.520 align:middle line:84% And one of the prototype I saw is more like around the head. 01:15:32.520 --> 01:15:35.490 align:middle line:84% Maybe it's good if you generate enough power for the poor kids 01:15:35.490 --> 01:15:41.820 align:middle line:84% to read like LED, now, how much power LED is. 01:15:41.820 --> 01:15:43.020 align:middle line:90% It's interesting to check. 01:15:43.020 --> 01:15:46.870 align:middle line:90% 01:15:46.870 --> 01:15:51.700 align:middle line:84% This we were actually talked a lot recently, 01:15:51.700 --> 01:15:54.670 align:middle line:84% not because this will create a lot of [INAUDIBLE] 01:15:54.670 --> 01:15:58.000 align:middle line:84% in the thermoelectric generator, but this 01:15:58.000 --> 01:16:01.000 align:middle line:84% will be a technology that will really 01:16:01.000 --> 01:16:04.270 align:middle line:84% make the full area of people [? burn. ?] 01:16:04.270 --> 01:16:09.520 align:middle line:84% Because look, a lot of places, people 01:16:09.520 --> 01:16:11.980 align:middle line:90% are still cooking using wood. 01:16:11.980 --> 01:16:16.300 align:middle line:84% I know where I grew up, say not my place 01:16:16.300 --> 01:16:20.290 align:middle line:84% now, but when I grew up, I used the wood. 01:16:20.290 --> 01:16:23.140 align:middle line:84% And in this wood, if you ever use a wood cooking, 01:16:23.140 --> 01:16:28.120 align:middle line:84% you will know that the smoke doesn't burn efficient 01:16:28.120 --> 01:16:34.630 align:middle line:84% And what the [? Phillip ?] develop is a fan generated power 01:16:34.630 --> 01:16:37.420 align:middle line:84% from the temperature difference of the burning 01:16:37.420 --> 01:16:41.320 align:middle line:84% and then drive the burning process clean. 01:16:41.320 --> 01:16:46.690 align:middle line:84% So it's a clean, clean wood-burning, wood-burner. 01:16:46.690 --> 01:16:51.940 align:middle line:84% And now they-- I heard that they're trying to market, 01:16:51.940 --> 01:16:55.180 align:middle line:84% but they still, this is about 10 to 20 bucks 01:16:55.180 --> 01:16:59.980 align:middle line:84% and people still couldn't afford it and $20. 01:16:59.980 --> 01:17:03.780 align:middle line:84% And so their market is now first person 01:17:03.780 --> 01:17:05.740 align:middle line:84% to get to world health organization 01:17:05.740 --> 01:17:09.070 align:middle line:90% by giving the people free. 01:17:09.070 --> 01:17:10.630 align:middle line:90% So there are a lot of-- 01:17:10.630 --> 01:17:13.360 align:middle line:84% this one, if we can gather, all the people 01:17:13.360 --> 01:17:20.320 align:middle line:84% use it, it's a tremendous, their analysis actually of CO2 problem 01:17:20.320 --> 01:17:25.390 align:middle line:84% right, because about 2 billion people are out 01:17:25.390 --> 01:17:27.800 align:middle line:90% of Greek in the world. 01:17:27.800 --> 01:17:30.520 align:middle line:90% A lot of people burn this. 01:17:30.520 --> 01:17:33.400 align:middle line:84% And if you make those who still efficient, 01:17:33.400 --> 01:17:38.140 align:middle line:84% reduce a lot significantly CO2 consumption. 01:17:38.140 --> 01:17:42.760 align:middle line:84% So the point is, at this stage, you 01:17:42.760 --> 01:17:47.800 align:middle line:84% have to think about where it can make sense technologically. 01:17:47.800 --> 01:17:51.160 align:middle line:84% Well, at the same time, of course, none of you 01:17:51.160 --> 01:17:54.550 align:middle line:84% are interested in developing more efficient, 01:17:54.550 --> 01:17:57.390 align:middle line:90% better materials. 01:17:57.390 --> 01:18:02.760 align:middle line:84% So I go to a lot of material conference, several industry 01:18:02.760 --> 01:18:04.290 align:middle line:90% conference. 01:18:04.290 --> 01:18:07.800 align:middle line:84% And one sense in the past, the last conference 01:18:07.800 --> 01:18:08.880 align:middle line:90% was very different. 01:18:08.880 --> 01:18:12.540 align:middle line:84% But in the past, you see more than 90% of the talk 01:18:12.540 --> 01:18:18.030 align:middle line:84% are materials, and not many talk on systems. 01:18:18.030 --> 01:18:20.440 align:middle line:84% So this is where I think the system, 01:18:20.440 --> 01:18:23.970 align:middle line:84% the engineering actually can make a good contribution there, 01:18:23.970 --> 01:18:25.920 align:middle line:84% because a lot of times people just say, 01:18:25.920 --> 01:18:28.450 align:middle line:84% I have the [INAUDIBLE] make a difference. 01:18:28.450 --> 01:18:32.280 align:middle line:84% But ZR is only half of the story. 01:18:32.280 --> 01:18:34.060 align:middle line:84% Because if you look at particular system, 01:18:34.060 --> 01:18:37.120 align:middle line:84% right, where the cost will come from, most likely 01:18:37.120 --> 01:18:41.500 align:middle line:90% it's not in the generator. 01:18:41.500 --> 01:18:44.600 align:middle line:84% It's an important part, but it will not be the dominant one. 01:18:44.600 --> 01:18:48.230 align:middle line:84% So this is an object to be cooled. 01:18:48.230 --> 01:18:50.630 align:middle line:84% The difference of similar electrics from solar 01:18:50.630 --> 01:18:54.340 align:middle line:84% is a solar cell, you put it in the sun, that's your system. 01:18:54.340 --> 01:18:55.700 align:middle line:90% You manufacture out. 01:18:55.700 --> 01:18:59.060 align:middle line:84% You just need a frame and put their electrical and the rest 01:18:59.060 --> 01:19:00.140 align:middle line:90% is-- 01:19:00.140 --> 01:19:04.220 align:middle line:84% it's about half the cost or balance of system, the inverters 01:19:04.220 --> 01:19:06.530 align:middle line:90% or those other stuff. 01:19:06.530 --> 01:19:08.360 align:middle line:84% But there's a much simpler system. 01:19:08.360 --> 01:19:12.590 align:middle line:84% Here for thermal system, you have to establish, 01:19:12.590 --> 01:19:16.790 align:middle line:84% you have to be able to maintain the temperature difference, 01:19:16.790 --> 01:19:21.760 align:middle line:84% so that means you have to take the heat out or put the heat in. 01:19:21.760 --> 01:19:27.430 align:middle line:84% And I once did a calculation for system for. 01:19:27.430 --> 01:19:30.670 align:middle line:84% And what I found is the electric, thermal electric 01:19:30.670 --> 01:19:35.380 align:middle line:84% material is only about a few cents per watt, electrical. 01:19:35.380 --> 01:19:38.620 align:middle line:84% But the cost come from all the aluminum 01:19:38.620 --> 01:19:41.860 align:middle line:84% that, I didn't do a very good thermal design, 01:19:41.860 --> 01:19:46.630 align:middle line:84% but that cost us a few dollars per watt 01:19:46.630 --> 01:19:51.640 align:middle line:84% because how you maintain the DC and do the cooling 01:19:51.640 --> 01:19:54.040 align:middle line:84% could be easily dominant in your cost. 01:19:54.040 --> 01:19:57.220 align:middle line:84% Not always, you have to do a good design. 01:19:57.220 --> 01:20:02.200 align:middle line:84% And the other is if you think about the temperature, 01:20:02.200 --> 01:20:07.240 align:middle line:84% so you need, for example, household temperature is 01:20:07.240 --> 01:20:08.920 align:middle line:90% about 22. 01:20:08.920 --> 01:20:11.020 align:middle line:90% Think about your refrigerator. 01:20:11.020 --> 01:20:13.690 align:middle line:84% And inside the refrigeration, refrigerator, 01:20:13.690 --> 01:20:16.150 align:middle line:84% let's suppose you want a 0 degree. 01:20:16.150 --> 01:20:20.290 align:middle line:84% So you say, I need a 22 degree solar heat. 01:20:20.290 --> 01:20:25.210 align:middle line:84% But that means you [INAUDIBLE] 22 is your refrigeration 01:20:25.210 --> 01:20:28.780 align:middle line:84% compartment inside, your air outside. 01:20:28.780 --> 01:20:31.700 align:middle line:84% Now you have to transfer the heat to the cold side. 01:20:31.700 --> 01:20:36.830 align:middle line:84% So this cold side must be lower temperature than 24, 01:20:36.830 --> 01:20:41.270 align:middle line:84% So let's suppose the 15 degrees, I give you degree. 01:20:41.270 --> 01:20:44.040 align:middle line:84% And then the far side, I rejected him. 01:20:44.040 --> 01:20:45.650 align:middle line:84% You don't want [INAUDIBLE] reject 01:20:45.650 --> 01:20:46.950 align:middle line:90% has to go through the error. 01:20:46.950 --> 01:20:51.800 align:middle line:84% So I have to have another theology from here to here. 01:20:51.800 --> 01:20:54.800 align:middle line:90% I give another 5 degrees. 01:20:54.800 --> 01:20:59.480 align:middle line:90% OK, that's 12 plus 22. 01:20:59.480 --> 01:21:03.740 align:middle line:84% So I need 39 degrees rather than 22 degrees. 01:21:03.740 --> 01:21:10.370 align:middle line:84% Now you go to 39, COP versus 22 COP will be very different. 01:21:10.370 --> 01:21:14.300 align:middle line:84% So your system is really a very critical part 01:21:14.300 --> 01:21:15.500 align:middle line:90% of the consideration. 01:21:15.500 --> 01:21:18.020 align:middle line:84% That's the significant difference 01:21:18.020 --> 01:21:20.240 align:middle line:84% of those thermal systems, it could 01:21:20.240 --> 01:21:25.220 align:middle line:84% be more expensive than the simulated side. 01:21:25.220 --> 01:21:28.790 align:middle line:84% Sensor, if you think about [INAUDIBLE], right? 01:21:28.790 --> 01:21:32.780 align:middle line:84% [INAUDIBLE], let's suppose you want-- 01:21:32.780 --> 01:21:37.340 align:middle line:84% this is a hot gas, and you put a similar [INAUDIBLE] 01:21:37.340 --> 01:21:41.780 align:middle line:84% exhaust and then you cool this side. 01:21:41.780 --> 01:21:44.690 align:middle line:84% And you see what temperature this system will offer. 01:21:44.690 --> 01:21:47.490 align:middle line:84% Then you suppose the device operate 01:21:47.490 --> 01:21:50.720 align:middle line:84% at a uniform temperature, not a good design. 01:21:50.720 --> 01:21:54.020 align:middle line:84% OK let's say, I suppose, the device offering 01:21:54.020 --> 01:21:57.290 align:middle line:84% uniform temperature, then the [INAUDIBLE] gas must have 01:21:57.290 --> 01:21:59.750 align:middle line:90% a higher temperature at exist. 01:21:59.750 --> 01:22:03.260 align:middle line:84% This temperature of the gas must be higher than this, 01:22:03.260 --> 01:22:08.870 align:middle line:84% otherwise heat cannot go from gas to the hot side. 01:22:08.870 --> 01:22:09.620 align:middle line:90% OK. 01:22:09.620 --> 01:22:11.360 align:middle line:84% Heat only go from high temperature 01:22:11.360 --> 01:22:13.550 align:middle line:90% to lower temperature. 01:22:13.550 --> 01:22:18.350 align:middle line:84% So that means if the gas is 600 degree, 01:22:18.350 --> 01:22:20.300 align:middle line:84% the amount of heat I can take out 01:22:20.300 --> 01:22:24.350 align:middle line:84% is from 600 degree to whatever this happened. 01:22:24.350 --> 01:22:28.040 align:middle line:84% So if you do an optimization, it's about half, 01:22:28.040 --> 01:22:30.470 align:middle line:84% because you need to take the heat out 01:22:30.470 --> 01:22:33.230 align:middle line:90% of the gas, put into the device. 01:22:33.230 --> 01:22:37.680 align:middle line:84% So that means your [? half-side ?] operator is 300. 01:22:37.680 --> 01:22:41.500 align:middle line:84% So you can't do your calculations, 600 degrees, 01:22:41.500 --> 01:22:42.930 align:middle line:90% t what's my [INAUDIBLE]? 01:22:42.930 --> 01:22:46.160 align:middle line:90% What's my efficiency? 01:22:46.160 --> 01:22:48.620 align:middle line:84% And of course, you can be more innovative. 01:22:48.620 --> 01:22:52.590 align:middle line:84% You say, OK, I don't operate at the same time, 01:22:52.590 --> 01:22:56.360 align:middle line:84% but actually I operate at a higher temperature 01:22:56.360 --> 01:23:00.080 align:middle line:84% and my efficiency system [INAUDIBLE]. 01:23:00.080 --> 01:23:02.600 align:middle line:84% So there you got a lot of system design 01:23:02.600 --> 01:23:07.160 align:middle line:84% that depends on material availability and cost, weight, 01:23:07.160 --> 01:23:09.890 align:middle line:84% particularly when you do automobile. 01:23:09.890 --> 01:23:17.360 align:middle line:84% And with that cost, and so a lot of really-- 01:23:17.360 --> 01:23:21.510 align:middle line:84% so what I say is there's space for both sides. 01:23:21.510 --> 01:23:23.210 align:middle line:90% There are a lot of problems. 01:23:23.210 --> 01:23:26.270 align:middle line:84% Engineers can make an important contribution 01:23:26.270 --> 01:23:30.500 align:middle line:84% and a lot of problems with the material, [INAUDIBLE] 01:23:30.500 --> 01:23:35.810 align:middle line:84% improvement of chemical conditions. 01:23:35.810 --> 01:23:41.720 align:middle line:84% You look at-- say this is not a serious work on the other side, 01:23:41.720 --> 01:23:45.260 align:middle line:84% because you look at where the potential to use it, 01:23:45.260 --> 01:23:47.780 align:middle line:84% but maybe car generation most people 01:23:47.780 --> 01:23:52.110 align:middle line:84% not working [INAUDIBLE] because it is too small. 01:23:52.110 --> 01:23:56.550 align:middle line:90% 01:23:56.550 --> 01:24:02.250 align:middle line:84% And the reality is automobile company says 3% fuel saving, 01:24:02.250 --> 01:24:04.290 align:middle line:84% you'll be happy to think about it. 01:24:04.290 --> 01:24:07.200 align:middle line:90% 3% fuel is less than 1% system. 01:24:07.200 --> 01:24:09.840 align:middle line:90% 01:24:09.840 --> 01:24:12.750 align:middle line:84% So if we are exhausted, one third 01:24:12.750 --> 01:24:17.280 align:middle line:84% of the wasted energy there, one third, 01:24:17.280 --> 01:24:19.830 align:middle line:84% let's take one half of the heat, if I can 01:24:19.830 --> 01:24:21.810 align:middle line:90% intercept the half of the heat. 01:24:21.810 --> 01:24:23.640 align:middle line:90% So that's one sixth. 01:24:23.640 --> 01:24:27.990 align:middle line:84% So my system efficiency, if it's 6%, which you usually 01:24:27.990 --> 01:24:34.100 align:middle line:84% can be done with a [INAUDIBLE] not system device, 6%. 01:24:34.100 --> 01:24:38.340 align:middle line:84% But then the question is, when you put all this together, 01:24:38.340 --> 01:24:40.570 align:middle line:84% your [? half-side ?] your co-side is really 01:24:40.570 --> 01:24:44.910 align:middle line:84% the temperature, you know, if you internalize naturally. 01:24:44.910 --> 01:24:48.720 align:middle line:84% So you have to think all this, put them together 01:24:48.720 --> 01:24:51.960 align:middle line:90% and make you have the impact. 01:24:51.960 --> 01:24:53.070 align:middle line:90% Yeah. 01:24:53.070 --> 01:24:56.810 align:middle line:84% So the [? BMW ?] is a very aggressive 01:24:56.810 --> 01:25:04.320 align:middle line:84% things, but if you put in a market when [INAUDIBLE] is 01:25:04.320 --> 01:25:08.160 align:middle line:90% before and after [INAUDIBLE]. 01:25:08.160 --> 01:25:13.180 align:middle line:84% It's really up to you to find that where 01:25:13.180 --> 01:25:16.160 align:middle line:90% it's not competitive against-- 01:25:16.160 --> 01:25:21.610 align:middle line:84% I say not competitive against main [INAUDIBLE]. 01:25:21.610 --> 01:25:24.618 align:middle line:84% Let's say there are a lot of places where you can be 01:25:24.618 --> 01:25:25.526 align:middle line:90% [INAUDIBLE]. 01:25:25.526 --> 01:25:28.195 align:middle line:90% 01:25:28.195 --> 01:25:29.360 align:middle line:90% Any questions? 01:25:29.360 --> 01:25:32.460 align:middle line:90% 01:25:32.460 --> 01:25:33.710 align:middle line:90% [INAUDIBLE] 01:25:33.710 --> 01:25:35.000 align:middle line:90%