WEBVTT 00:00:00.000 --> 00:00:05.210 align:middle line:90% 00:00:05.210 --> 00:00:07.700 align:middle line:84% The following content is provided under a Creative 00:00:07.700 --> 00:00:08.880 align:middle line:90% Commons license. 00:00:08.880 --> 00:00:11.300 align:middle line:84% Your support will help MIT OpenCourseWare 00:00:11.300 --> 00:00:14.930 align:middle line:84% continue to offer high quality educational resources for free. 00:00:14.930 --> 00:00:17.900 align:middle line:84% To make a donation or to view additional materials 00:00:17.900 --> 00:00:21.800 align:middle line:84% from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:21.800 --> 00:00:25.610 align:middle line:90% at ocw.mit.edu. 00:00:25.610 --> 00:00:28.100 align:middle line:84% GANG CHEN: [INAUDIBLE], we talk about solar cells. 00:00:28.100 --> 00:00:35.030 align:middle line:84% So in the rest of this course, we're now shifting our attention 00:00:35.030 --> 00:00:37.430 align:middle line:90% to solar power. 00:00:37.430 --> 00:00:42.680 align:middle line:84% We're combining solar to this engine and particularly 00:00:42.680 --> 00:00:47.300 align:middle line:84% solar thermoelectric and solar thermal [INAUDIBLE] state. 00:00:47.300 --> 00:00:54.620 align:middle line:84% And so the-- here, what's important is not, of course, 00:00:54.620 --> 00:00:57.310 align:middle line:84% the [INAUDIBLE], but really have a system perspective. 00:00:57.310 --> 00:00:59.960 align:middle line:84% You'll find out the spectral control 00:00:59.960 --> 00:01:04.459 align:middle line:84% is really crucial for the overall system efficiency 00:01:04.459 --> 00:01:07.740 align:middle line:84% if you want to achieve [INAUDIBLE]. 00:01:07.740 --> 00:01:11.310 align:middle line:84% So let's review the three modes of heat transfer. 00:01:11.310 --> 00:01:15.720 align:middle line:84% This is the first class for mechanical engineering 00:01:15.720 --> 00:01:16.830 align:middle line:90% is very simple. 00:01:16.830 --> 00:01:19.470 align:middle line:84% But if you come from other field, 00:01:19.470 --> 00:01:22.140 align:middle line:84% this is probably the best familiar. 00:01:22.140 --> 00:01:24.570 align:middle line:84% But see, we know there are three modes of heat type 00:01:24.570 --> 00:01:27.420 align:middle line:84% thermal conduction from [INAUDIBLE] radiation. 00:01:27.420 --> 00:01:29.670 align:middle line:84% And conduction is the fact that through [? the ?] 00:01:29.670 --> 00:01:34.875 align:middle line:84% thermal conductivity, heat transfer rate. that's the power, 00:01:34.875 --> 00:01:37.830 align:middle line:84% and then it's proportional to the [INAUDIBLE] gradient. 00:01:37.830 --> 00:01:42.530 align:middle line:84% And convection, we usually characterize 00:01:42.530 --> 00:01:44.880 align:middle line:84% with the [INAUDIBLE] coefficient h, 00:01:44.880 --> 00:01:47.200 align:middle line:84% so it's proportional to the [INAUDIBLE] difference 00:01:47.200 --> 00:01:52.350 align:middle line:84% between the wall and the fluids, which is away from the surface. 00:01:52.350 --> 00:01:55.980 align:middle line:84% And there are natural convection and forced convection. 00:01:55.980 --> 00:01:59.280 align:middle line:84% And then thermal radiation, we typically 00:01:59.280 --> 00:02:03.090 align:middle line:84% talk about the Stefan-Boltzmann law for blackbody radiation. 00:02:03.090 --> 00:02:06.060 align:middle line:84% And then we calculate the heat transfer relation-- heat 00:02:06.060 --> 00:02:09.600 align:middle line:84% transfer between surfaces in terms of view factor 00:02:09.600 --> 00:02:14.490 align:middle line:84% and [INAUDIBLE], which we'll go more into more detail 00:02:14.490 --> 00:02:20.430 align:middle line:84% since we're talking more now on the radiation part. 00:02:20.430 --> 00:02:25.170 align:middle line:84% So the thermal radiation, Planck's law, 00:02:25.170 --> 00:02:27.540 align:middle line:90% is usually considered a maximum. 00:02:27.540 --> 00:02:36.060 align:middle line:84% And we define the intensity as the power leaving the surface 00:02:36.060 --> 00:02:39.270 align:middle line:84% in certain directions, so that the intensity is 00:02:39.270 --> 00:02:41.340 align:middle line:90% different from power. 00:02:41.340 --> 00:02:44.700 align:middle line:84% So this is so that power in this direction 00:02:44.700 --> 00:02:48.300 align:middle line:84% that we will characterize by solid angle 00:02:48.300 --> 00:02:51.895 align:middle line:84% as a power in this direction per unit solid angle 00:02:51.895 --> 00:02:56.040 align:middle line:84% and per unit area normal to the direction of propagation per 00:02:56.040 --> 00:02:56.940 align:middle line:90% [INAUDIBLE]. 00:02:56.940 --> 00:02:59.360 align:middle line:90% So that's the intensity. 00:02:59.360 --> 00:03:02.310 align:middle line:84% So this is what we mean by intensity. 00:03:02.310 --> 00:03:04.350 align:middle line:84% It's propagating in this direction. 00:03:04.350 --> 00:03:07.880 align:middle line:84% And when we think about the area, 00:03:07.880 --> 00:03:10.580 align:middle line:84% this is the area, not this area, but the area 00:03:10.580 --> 00:03:13.230 align:middle line:84% projected in the direction of propagation. 00:03:13.230 --> 00:03:17.210 align:middle line:84% So [? ba ?] perpendicular has a cosine [INAUDIBLE] 00:03:17.210 --> 00:03:18.860 align:middle line:90% to the [? direction. ?] 00:03:18.860 --> 00:03:24.510 align:middle line:84% And the solid angle is a measure of the angle in space. 00:03:24.510 --> 00:03:29.420 align:middle line:84% So if you think about 2D, we use a polar angle. 00:03:29.420 --> 00:03:32.210 align:middle line:84% And a [? parallel ?] angle is the arc [INAUDIBLE] 00:03:32.210 --> 00:03:34.040 align:middle line:90% divided by radiance. 00:03:34.040 --> 00:03:38.390 align:middle line:84% Or solid angle is the area perpendicular 00:03:38.390 --> 00:03:41.510 align:middle line:84% to the direction of propagation, [? eaj ?] here, 00:03:41.510 --> 00:03:43.280 align:middle line:90% and divide by r squared. 00:03:43.280 --> 00:03:48.320 align:middle line:84% So if you take a sphere in space, that's 4 pi r squared, 00:03:48.320 --> 00:03:50.570 align:middle line:90% your solid angle is 4 pi. 00:03:50.570 --> 00:03:55.190 align:middle line:84% In 2D, polar angle, the maximum is 2 pi. 00:03:55.190 --> 00:03:58.230 align:middle line:84% So the solid angle is the space angle. 00:03:58.230 --> 00:04:02.250 align:middle line:84% And if we do [? a ?] into a polar spherical coordinates, 00:04:02.250 --> 00:04:06.710 align:middle line:84% this is theta, and [INAUDIBLE] with the direction to the phi, 00:04:06.710 --> 00:04:10.830 align:middle line:84% then you can show that this is a sine theta d theta d phi. 00:04:10.830 --> 00:04:17.550 align:middle line:84% So solid angle really including both theta and phi. 00:04:17.550 --> 00:04:22.710 align:middle line:84% So that's the definition in terms of intensity. 00:04:22.710 --> 00:04:26.580 align:middle line:84% And when we want to calculate-- so intensity 00:04:26.580 --> 00:04:28.950 align:middle line:90% is a user starting point. 00:04:28.950 --> 00:04:32.440 align:middle line:84% In fact, it will be really interesting to go back and read 00:04:32.440 --> 00:04:33.310 align:middle line:90% the Planck's law. 00:04:33.310 --> 00:04:35.865 align:middle line:84% He had a very interesting discussions, 00:04:35.865 --> 00:04:37.365 align:middle line:84% very careful, interesting discussion 00:04:37.365 --> 00:04:41.520 align:middle line:84% about [INAUDIBLE] radiation intensity. 00:04:41.520 --> 00:04:45.990 align:middle line:84% The immediate-- total immediate power of a surface 00:04:45.990 --> 00:04:48.450 align:middle line:84% normalized by surface area, that's 00:04:48.450 --> 00:04:50.520 align:middle line:84% what they call the emissive power. 00:04:50.520 --> 00:04:55.000 align:middle line:84% So now if you look at that, we normalize the emissive power. 00:04:55.000 --> 00:04:59.820 align:middle line:84% So power equals intensity times the area 00:04:59.820 --> 00:05:03.010 align:middle line:84% ea is perpendicular to the [? emissive ?] direction. 00:05:03.010 --> 00:05:04.900 align:middle line:90% So I have cosine theta. 00:05:04.900 --> 00:05:10.210 align:middle line:84% And d omega integration, so this is still per unit wavelength. 00:05:10.210 --> 00:05:14.530 align:middle line:90% So that's the initial power. 00:05:14.530 --> 00:05:19.630 align:middle line:84% And for blackbody radiation, the intensity is isotropic. 00:05:19.630 --> 00:05:21.670 align:middle line:90% It's the same in all directions. 00:05:21.670 --> 00:05:23.750 align:middle line:84% So it's independent of direction. 00:05:23.750 --> 00:05:25.810 align:middle line:84% You can take this out, blackbody. 00:05:25.810 --> 00:05:30.040 align:middle line:84% And then you have cosine theta, d omega is sine theta, d theta, 00:05:30.040 --> 00:05:30.650 align:middle line:90% d phi. 00:05:30.650 --> 00:05:33.020 align:middle line:90% So you go to do the integration. 00:05:33.020 --> 00:05:35.620 align:middle line:84% And if we think about the integration, 00:05:35.620 --> 00:05:39.190 align:middle line:90% theta is from 0 to 2 pi. 00:05:39.190 --> 00:05:40.630 align:middle line:90% That's 90 degree. 00:05:40.630 --> 00:05:44.710 align:middle line:84% And phi is azimuthal polar, say, coordinate, the spherical 00:05:44.710 --> 00:05:46.520 align:middle line:90% coordinate, that's a 2 pi. 00:05:46.520 --> 00:05:48.130 align:middle line:84% So if you do the integration, you 00:05:48.130 --> 00:05:50.890 align:middle line:84% find that the intensity for blackbody radiation 00:05:50.890 --> 00:05:54.655 align:middle line:84% for isotropic radiation, the intensity [INAUDIBLE] 00:05:54.655 --> 00:06:00.010 align:middle line:84% emissive power is a pi relationship. 00:06:00.010 --> 00:06:05.530 align:middle line:90% So that's the emissive power. 00:06:05.530 --> 00:06:09.100 align:middle line:84% And Planck's law of blackbody radiation 00:06:09.100 --> 00:06:13.570 align:middle line:84% could be either written in the intensity form 00:06:13.570 --> 00:06:17.140 align:middle line:90% or in the emissive power form. 00:06:17.140 --> 00:06:18.480 align:middle line:90% Apologize, I have a-- 00:06:18.480 --> 00:06:22.810 align:middle line:84% I missed the c square in my previous first lecture. 00:06:22.810 --> 00:06:25.240 align:middle line:84% If you go back to the notes, you can add that. 00:06:25.240 --> 00:06:30.960 align:middle line:84% So that's the intensity and the emissive power. 00:06:30.960 --> 00:06:35.560 align:middle line:90% And so, this is what we talked-- 00:06:35.560 --> 00:06:37.560 align:middle line:84% pretty much what we talked before. 00:06:37.560 --> 00:06:42.840 align:middle line:84% And if you plot the blackbody radiation curve 00:06:42.840 --> 00:06:46.140 align:middle line:84% as a function of wavelength, usually it 00:06:46.140 --> 00:06:50.820 align:middle line:84% is a unit of micro per unit micrometer. 00:06:50.820 --> 00:06:52.840 align:middle line:84% And you find out the [? multiplicity ?] peak 00:06:52.840 --> 00:06:56.550 align:middle line:84% for a [? shift. ?] As it goes to a higher temperature, 00:06:56.550 --> 00:07:00.030 align:middle line:84% the peak shifts to a shorter wavelength. 00:07:00.030 --> 00:07:03.750 align:middle line:84% So this is a Wien's displacement law states 00:07:03.750 --> 00:07:08.130 align:middle line:84% where this peak happens is the maximum radiation 00:07:08.130 --> 00:07:12.215 align:middle line:84% state of [INAUDIBLE] wavelength where [INAUDIBLE] happens. 00:07:12.215 --> 00:07:15.640 align:middle line:90% And temperature is about 3,000. 00:07:15.640 --> 00:07:17.850 align:middle line:90% So that's the [INAUDIBLE]. 00:07:17.850 --> 00:07:21.910 align:middle line:84% Remember, and hence the solar temperature, 00:07:21.910 --> 00:07:25.200 align:middle line:84% [? static ?] temperature in a vacuum is about 6,000. 00:07:25.200 --> 00:07:28.620 align:middle line:84% So that's why our [? highest ?] is [INAUDIBLE]. 00:07:28.620 --> 00:07:30.150 align:middle line:90% That's [INAUDIBLE]. 00:07:30.150 --> 00:07:32.740 align:middle line:84% The evolution works really well here. 00:07:32.740 --> 00:07:36.340 align:middle line:84% And we have not, say, [? adapted. ?] 00:07:36.340 --> 00:07:41.410 align:middle line:84% So it's interesting that the human adapted the sensitivity 00:07:41.410 --> 00:07:43.420 align:middle line:90% to the sun. 00:07:43.420 --> 00:07:45.920 align:middle line:84% Not a lot at night that you're probably sleeping. 00:07:45.920 --> 00:07:50.320 align:middle line:84% So if you think about the emission everybody 00:07:50.320 --> 00:07:53.020 align:middle line:90% has is [? 2 ?] micron. 00:07:53.020 --> 00:07:57.250 align:middle line:84% Because the 300 degree Kelvin has a peak around [? 2 ?] 00:07:57.250 --> 00:08:02.470 align:middle line:84% micron, which is equal to [INAUDIBLE]. 00:08:02.470 --> 00:08:08.170 align:middle line:84% So if you do integrate all the energy in this [? under all ?] 00:08:08.170 --> 00:08:12.670 align:middle line:84% wavelength, you get the Stefan-Boltzmann constant, 00:08:12.670 --> 00:08:17.020 align:middle line:90% 5.67 10 to the minus 8. 00:08:17.020 --> 00:08:19.840 align:middle line:84% So this is pretty much what we-- a review. 00:08:19.840 --> 00:08:25.750 align:middle line:84% And now, I want to plug this into a more convenient form, 00:08:25.750 --> 00:08:28.330 align:middle line:84% blackbody radiation, because it's 00:08:28.330 --> 00:08:32.559 align:middle line:84% a function of two parameter, wavelength and temperature. 00:08:32.559 --> 00:08:39.760 align:middle line:84% But if I normalize this emissive power by temperature phase 00:08:39.760 --> 00:08:45.430 align:middle line:84% power, I change it to a small e meter [INAUDIBLE] change. 00:08:45.430 --> 00:08:49.810 align:middle line:84% So if I normalize [INAUDIBLE] phase power, 00:08:49.810 --> 00:08:52.750 align:middle line:84% you find out this temperature phase power 00:08:52.750 --> 00:08:56.170 align:middle line:84% combined with lambda here is combined with lambda t. 00:08:56.170 --> 00:09:00.080 align:middle line:84% So now I only, I think about lambda t as one parameter. 00:09:00.080 --> 00:09:04.450 align:middle line:84% So this curve now, the blackbody [? uses ?] power [? localized ?] 00:09:04.450 --> 00:09:08.290 align:middle line:84% from pure phase power is [INAUDIBLE] function just lambda 00:09:08.290 --> 00:09:09.580 align:middle line:90% t. 00:09:09.580 --> 00:09:14.140 align:middle line:84% So I can have a universal curve rather than 00:09:14.140 --> 00:09:18.250 align:middle line:84% say each temperature have different blackbody curve. 00:09:18.250 --> 00:09:23.980 align:middle line:84% And in fact, if you take your maximum lambda t, you can say, 00:09:23.980 --> 00:09:26.890 align:middle line:84% if you think this [INAUDIBLE] at the x, 00:09:26.890 --> 00:09:29.150 align:middle line:90% you find out where maximum is. 00:09:29.150 --> 00:09:31.320 align:middle line:90% That's Wien's displacement law. 00:09:31.320 --> 00:09:34.000 align:middle line:90% Wien got this by experiment. 00:09:34.000 --> 00:09:36.550 align:middle line:84% And in fact, you will see that the Wien had 00:09:36.550 --> 00:09:41.470 align:middle line:84% an [INAUDIBLE] [? too. ?] But this is from Planck's theory you 00:09:41.470 --> 00:09:45.070 align:middle line:90% can derive these things. 00:09:45.070 --> 00:09:49.810 align:middle line:84% So now see, using this function, we 00:09:49.810 --> 00:09:54.160 align:middle line:84% can also calculate the fraction of energy. 00:09:54.160 --> 00:09:56.950 align:middle line:84% This is a very convenient [? particle. ?] In the old days, 00:09:56.950 --> 00:09:59.200 align:middle line:84% even now, for me, it's every time 00:09:59.200 --> 00:10:02.440 align:middle line:84% I want to see how much energy in certain wavelengths 00:10:02.440 --> 00:10:04.690 align:middle line:84% from the sun, I take this function 00:10:04.690 --> 00:10:06.950 align:middle line:90% and I look at table much faster. 00:10:06.950 --> 00:10:14.080 align:middle line:84% So this is the fraction of energy between 0 to lambda. 00:10:14.080 --> 00:10:18.460 align:middle line:84% That's the integrate between 0 to lambda. 00:10:18.460 --> 00:10:22.000 align:middle line:84% And of course, using this function, 00:10:22.000 --> 00:10:25.930 align:middle line:84% we can say that eventually we could write this 00:10:25.930 --> 00:10:30.050 align:middle line:90% into lambda t fifth power of-- 00:10:30.050 --> 00:10:30.880 align:middle line:90% this is a force. 00:10:30.880 --> 00:10:32.590 align:middle line:84% So there should be another t here. 00:10:32.590 --> 00:10:36.580 align:middle line:84% And then say lambda t, t [INAUDIBLE], 00:10:36.580 --> 00:10:38.560 align:middle line:84% because here is the fifth power, here 00:10:38.560 --> 00:10:40.180 align:middle line:90% is normalized the fifth power. 00:10:40.180 --> 00:10:42.370 align:middle line:84% Here I normalized it only to the fourth power, 00:10:42.370 --> 00:10:43.620 align:middle line:90% because this is the total. 00:10:43.620 --> 00:10:45.610 align:middle line:90% That's the Stefan-Boltzmann law. 00:10:45.610 --> 00:10:52.880 align:middle line:84% So after I write this, you can say, I can do this integration. 00:10:52.880 --> 00:10:56.440 align:middle line:84% this function is a function-- this integral 00:10:56.440 --> 00:10:58.796 align:middle line:90% is a function of lambda t only. 00:10:58.796 --> 00:11:00.970 align:middle line:84% Here is lambda t, lambda t, lambda t. 00:11:00.970 --> 00:11:03.150 align:middle line:90% So it's lambda t only. 00:11:03.150 --> 00:11:08.380 align:middle line:84% Again, so by doing this, I have a universal function 00:11:08.380 --> 00:11:12.220 align:middle line:84% that contains this is the fraction of energy 00:11:12.220 --> 00:11:16.330 align:middle line:84% with the wavelengths between 0 and lambda for any temperature 00:11:16.330 --> 00:11:17.560 align:middle line:90% t. 00:11:17.560 --> 00:11:21.190 align:middle line:84% So if you give me a temperature, I look at the wavelengths, 00:11:21.190 --> 00:11:24.340 align:middle line:84% I do the multiplication, I go to check the table, 00:11:24.340 --> 00:11:27.130 align:middle line:84% and usually quickly you find out. 00:11:27.130 --> 00:11:30.710 align:middle line:90% So this is the integrand. 00:11:30.710 --> 00:11:33.080 align:middle line:90% That's the small f. 00:11:33.080 --> 00:11:34.280 align:middle line:90% That's here. 00:11:34.280 --> 00:11:38.840 align:middle line:84% And as a function of lambda t, lambda t 00:11:38.840 --> 00:11:42.020 align:middle line:90% is written in micron Kelvin. 00:11:42.020 --> 00:11:44.570 align:middle line:90% And here is the integral. 00:11:44.570 --> 00:11:49.670 align:middle line:84% So that's the fraction of energy between 0 and lambda t. 00:11:49.670 --> 00:11:55.250 align:middle line:84% So you can quickly do an exercise. 00:11:55.250 --> 00:11:57.920 align:middle line:84% Again, let me take a solar energy, 00:11:57.920 --> 00:12:02.060 align:middle line:90% the sun at 606,000 Kelvin. 00:12:02.060 --> 00:12:06.410 align:middle line:84% A silicon bandgap is about 1.1 micron. 00:12:06.410 --> 00:12:11.960 align:middle line:90% So 6,000 times 1.1, 66, 6,600. 00:12:11.960 --> 00:12:14.360 align:middle line:90% So 6,600. 00:12:14.360 --> 00:12:16.520 align:middle line:90% If you look at this curve here-- 00:12:16.520 --> 00:12:19.130 align:middle line:84% this is a log scale, so it's harder to read. 00:12:19.130 --> 00:12:21.530 align:middle line:90% So the drop is 75%. 00:12:21.530 --> 00:12:27.770 align:middle line:84% So the other 25% of the solar energy beyond the-- 00:12:27.770 --> 00:12:31.570 align:middle line:84% below the bandgap, which is longer, is not used at all. 00:12:31.570 --> 00:12:34.590 align:middle line:84% So that's the case of when you use a photovoltaics, 00:12:34.590 --> 00:12:38.370 align:middle line:84% there's a bandgap, and the photons below the bandgap does 00:12:38.370 --> 00:12:41.610 align:middle line:84% not electron [INAUDIBLE]-- does not excite the electron 00:12:41.610 --> 00:12:42.390 align:middle line:90% [INAUDIBLE] pairs. 00:12:42.390 --> 00:12:44.010 align:middle line:90% So that part is completely gone. 00:12:44.010 --> 00:12:47.070 align:middle line:90% 00:12:47.070 --> 00:12:50.790 align:middle line:84% And in fact, you can also think for that part, 00:12:50.790 --> 00:12:55.330 align:middle line:84% it's better even just filter it out if you can do it cheaply. 00:12:55.330 --> 00:12:55.830 align:middle line:90% Why? 00:12:55.830 --> 00:13:00.930 align:middle line:84% Because if your solar cell absorb it, 00:13:00.930 --> 00:13:02.910 align:middle line:90% you will heat up the solar cell. 00:13:02.910 --> 00:13:06.520 align:middle line:84% And usually, solar cell heats up, the efficiency drop. 00:13:06.520 --> 00:13:10.600 align:middle line:90% 00:13:10.600 --> 00:13:12.730 align:middle line:90% So that's the flat body. 00:13:12.730 --> 00:13:15.450 align:middle line:84% Now let's look at the sun itself. 00:13:15.450 --> 00:13:17.320 align:middle line:90% And then, [INAUDIBLE]. 00:13:17.320 --> 00:13:25.820 align:middle line:84% So the distance diameter of the sun is 1.4 2 to the 9, 00:13:25.820 --> 00:13:30.100 align:middle line:84% [INAUDIBLE] about 1,000,000,000 meter. 00:13:30.100 --> 00:13:38.830 align:middle line:84% Remember, diameter of the Earth, that's a 12 million or 13 00:13:38.830 --> 00:13:41.110 align:middle line:90% million meters. 00:13:41.110 --> 00:13:49.540 align:middle line:84% And the distance is close to, what is it, 10 to the 11, 00:13:49.540 --> 00:13:50.440 align:middle line:90% 10 to 12. 00:13:50.440 --> 00:13:53.490 align:middle line:84% Is there a link for 10 to 12 for distance? 00:13:53.490 --> 00:13:55.780 align:middle line:90% [INAUDIBLE] 00:13:55.780 --> 00:13:59.930 align:middle line:84% [? Parameter. ?] So 1.5 10 to the 11 power. 00:13:59.930 --> 00:14:01.390 align:middle line:90% So that's the distance. 00:14:01.390 --> 00:14:08.650 align:middle line:84% And you look at the solar, of course, the orbital changes. 00:14:08.650 --> 00:14:13.490 align:middle line:84% The distance between the sun and the earth, slight change. 00:14:13.490 --> 00:14:18.410 align:middle line:90% But you see that this might be-- 00:14:18.410 --> 00:14:19.760 align:middle line:90% [INAUDIBLE] too large for you. 00:14:19.760 --> 00:14:23.190 align:middle line:84% But some of you may not be aware of this. 00:14:23.190 --> 00:14:27.340 align:middle line:84% Actually, in June and July, the solar flux is the lowest. 00:14:27.340 --> 00:14:31.690 align:middle line:90% 00:14:31.690 --> 00:14:37.870 align:middle line:84% From the distance, July is here, and it's the farthest 00:14:37.870 --> 00:14:41.270 align:middle line:90% away from the sun. 00:14:41.270 --> 00:14:45.190 align:middle line:84% Another thought is, this is the farthest. 00:14:45.190 --> 00:14:51.075 align:middle line:84% So we have the lowest flux, but we have the summer. 00:14:51.075 --> 00:14:53.760 align:middle line:90% 00:14:53.760 --> 00:14:58.260 align:middle line:84% And the reason is not due to the distance, 00:14:58.260 --> 00:15:03.480 align:middle line:84% it's because the Earth is wobbling a little bit. 00:15:03.480 --> 00:15:07.880 align:middle line:84% When you surround the sun, if you look at it, 00:15:07.880 --> 00:15:11.400 align:middle line:84% the Earth's axis is not perpendicular to the plane 00:15:11.400 --> 00:15:12.900 align:middle line:90% of rotation. 00:15:12.900 --> 00:15:21.360 align:middle line:90% And it has a 24 degree of-- 00:15:21.360 --> 00:15:22.950 align:middle line:90% 22 or 24? 00:15:22.950 --> 00:15:26.030 align:middle line:84% So this is the direction [INAUDIBLE]. 00:15:26.030 --> 00:15:29.280 align:middle line:90% 00:15:29.280 --> 00:15:37.840 align:middle line:84% --23.5 degree from the normal direction. 00:15:37.840 --> 00:15:40.020 align:middle line:90% So this is the normal direction. 00:15:40.020 --> 00:15:43.920 align:middle line:84% And because of that, on each side 00:15:43.920 --> 00:15:47.400 align:middle line:84% here, the sun's atmosphere facing the sun. 00:15:47.400 --> 00:15:49.320 align:middle line:84% And here, the northern hemisphere 00:15:49.320 --> 00:15:50.490 align:middle line:90% is [? facing ?] the sun. 00:15:50.490 --> 00:15:53.170 align:middle line:90% 00:15:53.170 --> 00:15:56.040 align:middle line:90% So that's the tilting. 00:15:56.040 --> 00:15:58.470 align:middle line:84% And this actually created a problem. 00:15:58.470 --> 00:16:01.860 align:middle line:84% Particularly, we want the [INAUDIBLE] sun. 00:16:01.860 --> 00:16:03.870 align:middle line:90% Say, some people do-- 00:16:03.870 --> 00:16:08.440 align:middle line:84% when we use concentration, you have to track your maximum. 00:16:08.440 --> 00:16:11.250 align:middle line:84% You want to maximize your intercepting area. 00:16:11.250 --> 00:16:13.690 align:middle line:90% And so, that's the tracking. 00:16:13.690 --> 00:16:18.741 align:middle line:84% You have to complete the rotation of the angle here 00:16:18.741 --> 00:16:22.700 align:middle line:84% of the Earth, of the [? orbit. ?] 00:16:22.700 --> 00:16:27.740 align:middle line:84% So here is the blackbody radiation 00:16:27.740 --> 00:16:30.990 align:middle line:84% coming from the sun reaching the earth's surface. 00:16:30.990 --> 00:16:33.560 align:middle line:90% It's the outside atmosphere. 00:16:33.560 --> 00:16:36.770 align:middle line:90% And it's close to 58. 00:16:36.770 --> 00:16:39.890 align:middle line:84% Different people have slightly different numbers. 00:16:39.890 --> 00:16:44.240 align:middle line:84% Later on, I will show if I use a 5777 Kelvin, 00:16:44.240 --> 00:16:48.980 align:middle line:84% I get a [INAUDIBLE] constant very close to [INAUDIBLE] 00:16:48.980 --> 00:16:50.210 align:middle line:90% solar constant. 00:16:50.210 --> 00:16:52.700 align:middle line:90% So this is the-- 00:16:52.700 --> 00:16:54.895 align:middle line:84% it's very close to blackbody overall. 00:16:54.895 --> 00:16:58.160 align:middle line:90% 00:16:58.160 --> 00:17:02.240 align:middle line:84% And of course, when the sun comes through the atmosphere, 00:17:02.240 --> 00:17:04.579 align:middle line:84% you have a lot of things happening. 00:17:04.579 --> 00:17:07.069 align:middle line:84% The solar radiation coming in, it 00:17:07.069 --> 00:17:09.770 align:middle line:84% will be reflected by the atmosphere. 00:17:09.770 --> 00:17:12.390 align:middle line:84% The clouds can scatter light to all directions. 00:17:12.390 --> 00:17:14.060 align:middle line:90% Some will go back. 00:17:14.060 --> 00:17:20.630 align:middle line:84% And the atmosphere itself will absorb the solar radiation. 00:17:20.630 --> 00:17:23.640 align:middle line:84% Depends on what molecular species. 00:17:23.640 --> 00:17:27.920 align:middle line:84% Those are the vibrational modes of the molecules. 00:17:27.920 --> 00:17:30.930 align:middle line:84% Typically it's of the few micron range. 00:17:30.930 --> 00:17:33.320 align:middle line:84% So it depends on what kind of molecule 00:17:33.320 --> 00:17:35.660 align:middle line:84% you will have different absorption bands. 00:17:35.660 --> 00:17:38.690 align:middle line:84% So if the molecules are happily absorbing, 00:17:38.690 --> 00:17:41.750 align:middle line:84% or shooting around all of those molecules, 00:17:41.750 --> 00:17:46.410 align:middle line:84% then say those photons cannot reach the surface, 00:17:46.410 --> 00:17:49.730 align:middle line:84% it's the heat up the molecules directly. 00:17:49.730 --> 00:17:53.200 align:middle line:84% But there are transparency windows. 00:17:53.200 --> 00:17:56.960 align:middle line:84% Again, this is a pretty lucky for us, for everything, 00:17:56.960 --> 00:17:59.730 align:middle line:84% just absorbed by all the molecules, 00:17:59.730 --> 00:18:04.570 align:middle line:84% we need to have direct sunlight and [INAUDIBLE] dark. 00:18:04.570 --> 00:18:08.930 align:middle line:84% And of course, there are also ways to reach surface. 00:18:08.930 --> 00:18:13.610 align:middle line:84% You will have the reflection from the surface of the Earth. 00:18:13.610 --> 00:18:19.250 align:middle line:84% So when you put a solar panel there, you have direct sunlight, 00:18:19.250 --> 00:18:23.480 align:middle line:84% you also have scattered light from the atmosphere 00:18:23.480 --> 00:18:24.630 align:middle line:90% and from the ground. 00:18:24.630 --> 00:18:27.420 align:middle line:90% 00:18:27.420 --> 00:18:34.290 align:middle line:84% So this is a [? characterize ?] solar cell. 00:18:34.290 --> 00:18:38.100 align:middle line:84% People have to compare orange to orange. 00:18:38.100 --> 00:18:42.600 align:middle line:84% So there are standard in terms of what you should compare. 00:18:42.600 --> 00:18:48.690 align:middle line:84% And this solar spectrum [INAUDIBLE] by the air mass, 00:18:48.690 --> 00:18:53.030 align:middle line:84% which is the ratio of the [? confidence ?] of the air, 00:18:53.030 --> 00:18:57.360 align:middle line:84% of the air [? being ?] travelled through to the shortest possible 00:18:57.360 --> 00:18:57.950 align:middle line:90% pathway. 00:18:57.950 --> 00:19:05.730 align:middle line:84% So if I-- the outside atmosphere is an a m 0. 00:19:05.730 --> 00:19:10.890 align:middle line:84% And then a m one, air mass one, occurs when the sun is directly 00:19:10.890 --> 00:19:12.960 align:middle line:90% overhead. 00:19:12.960 --> 00:19:22.500 align:middle line:84% And a m 1.5 occurs when the sun rays travel through roughly 50% 00:19:22.500 --> 00:19:26.990 align:middle line:84% more of the atmosphere than when the sun is directly overhead. 00:19:26.990 --> 00:19:33.340 align:middle line:84% So at an angle, there is, say, the confluence of the sun 00:19:33.340 --> 00:19:34.660 align:middle line:90% will be longer. 00:19:34.660 --> 00:19:39.340 align:middle line:84% And you can imagine, because the longer confluence, the spectrum 00:19:39.340 --> 00:19:41.800 align:middle line:84% of solar radiation reaching the surface 00:19:41.800 --> 00:19:45.730 align:middle line:84% will be different because the absorption of the atmosphere 00:19:45.730 --> 00:19:49.374 align:middle line:90% itself and scattering process. 00:19:49.374 --> 00:19:54.580 align:middle line:84% So you look at, let's say, 1.5, the angular relation, 00:19:54.580 --> 00:19:58.540 align:middle line:84% the actual distance is 1 over cosine theta. 00:19:58.540 --> 00:20:02.900 align:middle line:90% So cosine 48.2 gives you 1.5. 00:20:02.900 --> 00:20:07.540 align:middle line:84% So this is, of course, a m 1.5 [INAUDIBLE] solar in this angle, 00:20:07.540 --> 00:20:14.390 align:middle line:84% the angle away from the perpendicular is 48.2 degrees. 00:20:14.390 --> 00:20:22.430 align:middle line:84% So that's the-- but there are also different [INAUDIBLE]. 00:20:22.430 --> 00:20:26.510 align:middle line:84% Depends on whether the solar radiation we measure 00:20:26.510 --> 00:20:31.370 align:middle line:84% is directly coming from the sun or there are also scattered, 00:20:31.370 --> 00:20:32.450 align:middle line:90% diffuse light. 00:20:32.450 --> 00:20:38.520 align:middle line:84% So there are a m 1.5, there are different a m 1.5. 00:20:38.520 --> 00:20:45.050 align:middle line:84% I mentioned before, the a m 0 is the spectrum of the radiation 00:20:45.050 --> 00:20:47.630 align:middle line:90% outside the atmosphere. 00:20:47.630 --> 00:20:53.510 align:middle line:84% And a m one is directly 0 degree. 00:20:53.510 --> 00:21:02.870 align:middle line:84% And 1.5 has 1.5 [INAUDIBLE], g, and 1.5 direct [? path ?] 00:21:02.870 --> 00:21:04.490 align:middle line:90% circumsolar. 00:21:04.490 --> 00:21:11.690 align:middle line:84% So the direct one is really consider a small cone 00:21:11.690 --> 00:21:13.800 align:middle line:90% of solar radiation. 00:21:13.800 --> 00:21:22.580 align:middle line:84% And this cone is confined to 2.5 degree, let's say here. 00:21:22.580 --> 00:21:28.220 align:middle line:84% Let's say 2.5 up and the 2.5 degree is around the sun. 00:21:28.220 --> 00:21:34.370 align:middle line:84% And so, this is the a m 1.5 direct. 00:21:34.370 --> 00:21:40.980 align:middle line:84% And then a m 1.5g is the radiation from the sun. 00:21:40.980 --> 00:21:43.970 align:middle line:84% The entire sky is reflecting off the ground. 00:21:43.970 --> 00:21:49.040 align:middle line:84% And so, in this case, the solar [INAUDIBLE] is 1.5 to the 40-- 00:21:49.040 --> 00:21:50.360 align:middle line:90% 48.2. 00:21:50.360 --> 00:21:56.820 align:middle line:84% But also the panel itself is tilted at an angle of 37. 00:21:56.820 --> 00:22:00.110 align:middle line:84% So it's not a perpendicular incidence 00:22:00.110 --> 00:22:03.290 align:middle line:90% from the sun to the solar panel. 00:22:03.290 --> 00:22:05.340 align:middle line:90% Here is 37. 00:22:05.340 --> 00:22:12.750 align:middle line:84% So the angle of the incidence, angle of incidence is 11.2. 00:22:12.750 --> 00:22:17.915 align:middle line:84% And so, people are using 1.5g for solar cells. 00:22:17.915 --> 00:22:23.540 align:middle line:90% 00:22:23.540 --> 00:22:28.640 align:middle line:84% So that's just a property [INAUDIBLE]. 00:22:28.640 --> 00:22:32.770 align:middle line:90% 1.5 is the 40-- 00:22:32.770 --> 00:22:38.642 align:middle line:90% 48.1, 48.2. 00:22:38.642 --> 00:22:44.730 align:middle line:84% And so, the global equal the scattered light. 00:22:44.730 --> 00:22:52.800 align:middle line:84% And also, the panel is 11.1 degree away 00:22:52.800 --> 00:22:55.180 align:middle line:90% from the normal incidence. 00:22:55.180 --> 00:22:59.610 align:middle line:90% 00:22:59.610 --> 00:23:04.950 align:middle line:84% So if you look at the spectrum, this 00:23:04.950 --> 00:23:09.660 align:middle line:84% is how the different gases in the atmosphere absorbs. 00:23:09.660 --> 00:23:18.680 align:middle line:84% And water is actually really the absorption is the worst. 00:23:18.680 --> 00:23:23.350 align:middle line:84% So this is the water absorption spectrum different wavelengths. 00:23:23.350 --> 00:23:30.920 align:middle line:84% Carbon dioxide here is 10 micron, 00:23:30.920 --> 00:23:32.990 align:middle line:90% That's about a 10-micron range. 00:23:32.990 --> 00:23:38.240 align:middle line:84% Carbon dioxide in this band is what people worry the most 00:23:38.240 --> 00:23:40.900 align:middle line:84% because of the increased carbon dioxide, 00:23:40.900 --> 00:23:46.360 align:middle line:84% the 10-micron radiation from the Earth cannot escape. 00:23:46.360 --> 00:23:49.840 align:middle line:84% And in fact, if you combine all this, 00:23:49.840 --> 00:23:53.370 align:middle line:84% let's say the Earth warms a little bit more. 00:23:53.370 --> 00:23:57.990 align:middle line:84% In this, there are more water evaporate from the ocean, 00:23:57.990 --> 00:24:02.160 align:middle line:84% and more water will attract more radiation. 00:24:02.160 --> 00:24:07.740 align:middle line:84% So there is-- say, that's why it's a very complex problem. 00:24:07.740 --> 00:24:14.730 align:middle line:84% And methane [INAUDIBLE] oxide scattering is-- 00:24:14.730 --> 00:24:19.350 align:middle line:84% the scattering is the most severe in the blue region. 00:24:19.350 --> 00:24:24.300 align:middle line:84% And that's why the sky is blue, because the scattering 00:24:24.300 --> 00:24:27.960 align:middle line:84% proportional of omega fourth power, frequency fourth power. 00:24:27.960 --> 00:24:32.470 align:middle line:84% So the short wavelength scatter more, and the sky is blue. 00:24:32.470 --> 00:24:34.550 align:middle line:90% We look at only scatter light. 00:24:34.550 --> 00:24:38.010 align:middle line:84% We don't directly look in the sun. 00:24:38.010 --> 00:24:40.950 align:middle line:84% So that's the solar spectrum, say, 00:24:40.950 --> 00:24:43.920 align:middle line:84% in terms of the absorption characteristics. 00:24:43.920 --> 00:24:49.120 align:middle line:90% And here is the spectrum. 00:24:49.120 --> 00:24:55.680 align:middle line:84% So outside the Earth, you can see the blue curve here. 00:24:55.680 --> 00:24:59.940 align:middle line:84% And let's say when the radiation goes 00:24:59.940 --> 00:25:04.680 align:middle line:84% through the atmosphere, the absorption bands, 00:25:04.680 --> 00:25:08.990 align:middle line:84% different absorption bands here, will kick in, 00:25:08.990 --> 00:25:13.488 align:middle line:84% and the radiation is diminished when 00:25:13.488 --> 00:25:14.780 align:middle line:90% they reach the Earth's surface. 00:25:14.780 --> 00:25:18.540 align:middle line:90% 00:25:18.540 --> 00:25:25.680 align:middle line:84% And if you integrate all the solar radiation here. 00:25:25.680 --> 00:25:30.480 align:middle line:84% And you get that the total radiation energy in the solar 00:25:30.480 --> 00:25:36.785 align:middle line:84% spectrum, and the a m 0 that's outside the atmosphere is 1,366 00:25:36.785 --> 00:25:38.850 align:middle line:90% [? Watt ?] meter square. 00:25:38.850 --> 00:25:47.280 align:middle line:84% So you go to, say, probably I think Professor Ely Sachs, 00:25:47.280 --> 00:25:51.170 align:middle line:84% he has a startup company called 1366. 00:25:51.170 --> 00:25:52.790 align:middle line:84% Next time you can [? tell ?] when 00:25:52.790 --> 00:25:58.800 align:middle line:84% you saw him, that you know that's the solar [INAUDIBLE]. 00:25:58.800 --> 00:26:08.680 align:middle line:84% And this is a [INAUDIBLE] 577 Kelvin, so that's about a 00:26:08.680 --> 00:26:09.560 align:middle line:90% [INAUDIBLE], solar. 00:26:09.560 --> 00:26:12.550 align:middle line:84% Now let's talk about the surface itself. 00:26:12.550 --> 00:26:17.300 align:middle line:84% And I'm giving you the next few slides of definitions. 00:26:17.300 --> 00:26:21.910 align:middle line:84% And the key point I want to [INAUDIBLE] not 00:26:21.910 --> 00:26:24.940 align:middle line:84% say you need to know all the details. 00:26:24.940 --> 00:26:29.440 align:middle line:84% But the key point is that the surface properties, radiation 00:26:29.440 --> 00:26:32.350 align:middle line:84% surface properties, is spectral dependent, 00:26:32.350 --> 00:26:36.670 align:middle line:84% depends on wavelengths, it's also directional dependent. 00:26:36.670 --> 00:26:42.940 align:middle line:84% So those particular data, we'll talk a lot on selective surface. 00:26:42.940 --> 00:26:44.770 align:middle line:90% That's the spectral dependence. 00:26:44.770 --> 00:26:47.230 align:middle line:84% And in fact, they're also directionally [INAUDIBLE]. 00:26:47.230 --> 00:26:50.710 align:middle line:84% So control spectral and directional property 00:26:50.710 --> 00:26:51.820 align:middle line:90% of the surfaces. 00:26:51.820 --> 00:26:57.650 align:middle line:84% So the appreciation I want you to have is those are-- 00:26:57.650 --> 00:27:01.640 align:middle line:84% you can start with the basic property. 00:27:01.640 --> 00:27:04.520 align:middle line:84% When I look at the vicinity of a surface, 00:27:04.520 --> 00:27:06.980 align:middle line:84% I can look at the different direction 00:27:06.980 --> 00:27:11.000 align:middle line:84% on different wavelengths, how it's emitting the emission 00:27:11.000 --> 00:27:11.990 align:middle line:90% characteristics. 00:27:11.990 --> 00:27:15.320 align:middle line:84% So this is the light coming, the intensity 00:27:15.320 --> 00:27:17.390 align:middle line:90% emitted in a certain direction. 00:27:17.390 --> 00:27:20.180 align:middle line:84% And I normalize the blackbody intensity. 00:27:20.180 --> 00:27:24.290 align:middle line:84% That's the-- usually we consider that as the maximum. 00:27:24.290 --> 00:27:29.780 align:middle line:84% So this normalization is the directional, which I 00:27:29.780 --> 00:27:33.710 align:middle line:90% put a prime, so notation-wise. 00:27:33.710 --> 00:27:36.740 align:middle line:84% And the spectrum, which I put a lambda, 00:27:36.740 --> 00:27:40.220 align:middle line:84% so directional spectral emissivity. 00:27:40.220 --> 00:27:43.400 align:middle line:84% And it's a function of the temperature 00:27:43.400 --> 00:27:45.980 align:middle line:90% of the surface, the material. 00:27:45.980 --> 00:27:47.840 align:middle line:84% Temperature depends on temperature, 00:27:47.840 --> 00:27:53.060 align:middle line:84% depends on material, and also depends on surface finish. 00:27:53.060 --> 00:27:56.840 align:middle line:84% That's how we control the properties. 00:27:56.840 --> 00:28:00.140 align:middle line:84% You can have a piece of aluminum, 00:28:00.140 --> 00:28:03.860 align:middle line:84% which is a very shiny low emissivity, but you rough it, 00:28:03.860 --> 00:28:10.370 align:middle line:84% then your emissivity will change into much higher values. 00:28:10.370 --> 00:28:14.090 align:middle line:84% So that's a spectral direction or spectral. 00:28:14.090 --> 00:28:19.460 align:middle line:84% And then you also allow you to integrate all the energy. 00:28:19.460 --> 00:28:20.930 align:middle line:90% So this is intensity. 00:28:20.930 --> 00:28:23.450 align:middle line:84% Here I'm talking about the energy 00:28:23.450 --> 00:28:26.700 align:middle line:84% now because it's a emitted [? in all ?] direction. 00:28:26.700 --> 00:28:29.150 align:middle line:84% If I integrate together all the energy 00:28:29.150 --> 00:28:32.420 align:middle line:84% going [INAUDIBLE] the surface, but still 00:28:32.420 --> 00:28:34.760 align:middle line:84% at a certain wavelength interval, 00:28:34.760 --> 00:28:39.290 align:middle line:84% only at a certain wavelength, then I get a half spherical. 00:28:39.290 --> 00:28:44.350 align:middle line:84% So that's an all directions, that's spectral. 00:28:44.350 --> 00:28:46.190 align:middle line:90% And you can calculate. 00:28:46.190 --> 00:28:49.600 align:middle line:84% You can calculate from here to here if you know this, 00:28:49.600 --> 00:28:50.630 align:middle line:90% you know everything. 00:28:50.630 --> 00:28:54.970 align:middle line:84% We just want to go through the concept. 00:28:54.970 --> 00:28:59.560 align:middle line:84% And then you can also say, in this direction 00:28:59.560 --> 00:29:01.640 align:middle line:84% you integrate the whole spectrum. 00:29:01.640 --> 00:29:07.030 align:middle line:84% So we call that total, total is all the wavelengths. 00:29:07.030 --> 00:29:09.760 align:middle line:84% Hemispherical means all the angle. 00:29:09.760 --> 00:29:13.120 align:middle line:90% So you have direction total. 00:29:13.120 --> 00:29:16.720 align:middle line:84% And then formally, when you take an undergraduate course, you 00:29:16.720 --> 00:29:19.940 align:middle line:84% define emissivity, we typically talk about hemispherical 00:29:19.940 --> 00:29:21.070 align:middle line:90% [INAUDIBLE]. 00:29:21.070 --> 00:29:22.580 align:middle line:90% That's the typical [INAUDIBLE]. 00:29:22.580 --> 00:29:24.370 align:middle line:90% You look at a table [INAUDIBLE]. 00:29:24.370 --> 00:29:26.110 align:middle line:90% 00:29:26.110 --> 00:29:32.300 align:middle line:84% So that's the all direction, all wavelengths. 00:29:32.300 --> 00:29:35.510 align:middle line:90% So those are the definitions. 00:29:35.510 --> 00:29:40.640 align:middle line:84% And surface, when we say [? alpha, ?] it's 00:29:40.640 --> 00:29:43.400 align:middle line:84% in terms of the emission characteristics. 00:29:43.400 --> 00:29:48.870 align:middle line:84% If it goes all immediately in all directions isotropically, 00:29:48.870 --> 00:29:50.850 align:middle line:84% intensity is the same in all directions. 00:29:50.850 --> 00:29:52.970 align:middle line:90% Blackbody is the one example. 00:29:52.970 --> 00:29:57.690 align:middle line:84% It is a diffuse emitter, so it goes isotropic all directions. 00:29:57.690 --> 00:30:01.210 align:middle line:84% And if the emission is independent of wavelength, 00:30:01.210 --> 00:30:06.360 align:middle line:84% So the directional emissivity is same 00:30:06.360 --> 00:30:09.060 align:middle line:84% as if we integrate all wavelengths 00:30:09.060 --> 00:30:10.270 align:middle line:90% in the same direction. 00:30:10.270 --> 00:30:15.060 align:middle line:84% So that's the [INAUDIBLE], the independent-- radiance 00:30:15.060 --> 00:30:16.920 align:middle line:90% independent of wavelength. 00:30:16.920 --> 00:30:18.690 align:middle line:90% Diffuse means isotropic. 00:30:18.690 --> 00:30:22.860 align:middle line:84% So diffuse grade means the [INAUDIBLE]. 00:30:22.860 --> 00:30:26.040 align:middle line:84% So if it's diffuse grade, then in all direction, 00:30:26.040 --> 00:30:29.490 align:middle line:84% all wavelengths is the same, and then all those emissivity 00:30:29.490 --> 00:30:30.930 align:middle line:90% are the same. 00:30:30.930 --> 00:30:34.320 align:middle line:84% But fundamentally, you can start from here 00:30:34.320 --> 00:30:37.290 align:middle line:84% and write the relation between all these properties 00:30:37.290 --> 00:30:41.790 align:middle line:84% to calculate all other properties in all this. 00:30:41.790 --> 00:30:44.920 align:middle line:84% But this one doesn't always equal to the others. 00:30:44.920 --> 00:30:47.640 align:middle line:90% 00:30:47.640 --> 00:30:51.600 align:middle line:90% So that's the emissivity. 00:30:51.600 --> 00:30:57.960 align:middle line:84% And the inverse of emission is absorption. 00:30:57.960 --> 00:31:03.210 align:middle line:84% So if the light comes in, and the thermal radiation of light, 00:31:03.210 --> 00:31:08.940 align:middle line:90% and then the power, really-- 00:31:08.940 --> 00:31:11.820 align:middle line:84% I think I probably should have written d omega 00:31:11.820 --> 00:31:15.150 align:middle line:84% then in a small form how much radiation come in 00:31:15.150 --> 00:31:18.600 align:middle line:84% and then power absorbed in this-- 00:31:18.600 --> 00:31:20.640 align:middle line:84% the fraction of the power that's being 00:31:20.640 --> 00:31:22.260 align:middle line:90% absorbed in this small form. 00:31:22.260 --> 00:31:25.200 align:middle line:90% That's the absorptivity. 00:31:25.200 --> 00:31:30.600 align:middle line:84% And again, here we have, coming from a certain direction, 00:31:30.600 --> 00:31:31.890 align:middle line:90% so that's prime. 00:31:31.890 --> 00:31:36.630 align:middle line:84% And at specific wavelength, that's lambda. 00:31:36.630 --> 00:31:40.020 align:middle line:84% So we define directional spectral, 00:31:40.020 --> 00:31:41.850 align:middle line:90% and then you do the same thing. 00:31:41.850 --> 00:31:45.390 align:middle line:84% You integrate [? all ?] angle of incidence. 00:31:45.390 --> 00:31:49.950 align:middle line:84% They absorb as hemispherical, spherical spectral. 00:31:49.950 --> 00:31:51.990 align:middle line:84% And then all in the same direction, 00:31:51.990 --> 00:31:56.250 align:middle line:84% integrate all wavelengths, or you integrate both wavelengths 00:31:56.250 --> 00:32:00.510 align:middle line:84% and direction, same analogous to emission, 00:32:00.510 --> 00:32:05.670 align:middle line:84% except now the reference is what comes in. 00:32:05.670 --> 00:32:10.170 align:middle line:84% But let me just make one comment here. 00:32:10.170 --> 00:32:15.510 align:middle line:84% Although what comes in, the overall spectrum of-- so, 00:32:15.510 --> 00:32:18.120 align:middle line:84% for example, solar coming into the surface 00:32:18.120 --> 00:32:21.180 align:middle line:84% depends on temperature of the sun. 00:32:21.180 --> 00:32:24.940 align:middle line:84% But the spectral here doesn't depend on temperature. 00:32:24.940 --> 00:32:28.170 align:middle line:84% I can have the surface, this is [? thermal ?] radiating, 00:32:28.170 --> 00:32:30.240 align:middle line:84% coming to the surface, or this laser beam 00:32:30.240 --> 00:32:31.210 align:middle line:90% coming to the surface. 00:32:31.210 --> 00:32:34.170 align:middle line:90% That's my intensity. 00:32:34.170 --> 00:32:38.970 align:middle line:84% And this temperature is really the temperature of the material. 00:32:38.970 --> 00:32:42.380 align:middle line:84% But it's not a temperature of the source. 00:32:42.380 --> 00:32:44.660 align:middle line:90% So this is the absorptivity. 00:32:44.660 --> 00:32:50.030 align:middle line:84% And then the next is a very important-- second law. 00:32:50.030 --> 00:32:56.480 align:middle line:84% Second law relation for emissivity and absorptivity. 00:32:56.480 --> 00:32:59.520 align:middle line:90% That's Kirchhoff's law. 00:32:59.520 --> 00:33:04.490 align:middle line:84% And Kirchhoff's law say, this is the same character 00:33:04.490 --> 00:33:10.520 align:middle line:84% of the object, the directional spectral absorptivity utility 00:33:10.520 --> 00:33:13.625 align:middle line:84% inverse directional spectral absorption. 00:33:13.625 --> 00:33:17.090 align:middle line:90% 00:33:17.090 --> 00:33:21.500 align:middle line:84% Blackbody radiation is not a second law. 00:33:21.500 --> 00:33:25.610 align:middle line:84% The Kirchhoff's law is a [INAUDIBLE]. 00:33:25.610 --> 00:33:27.260 align:middle line:84% The [? maxima ?] of the Planck's law, 00:33:27.260 --> 00:33:29.093 align:middle line:84% [? I am going to ?] say blackbody radiation, 00:33:29.093 --> 00:33:30.740 align:middle line:90% I mean Planck's law. 00:33:30.740 --> 00:33:32.330 align:middle line:90% You can break it. 00:33:32.330 --> 00:33:36.410 align:middle line:84% Kirchhoff's law, you cannot break it. 00:33:36.410 --> 00:33:41.000 align:middle line:84% This is the second law of thermodynamics. 00:33:41.000 --> 00:33:45.260 align:middle line:84% Fundamental, but remember, I'm putting down, 00:33:45.260 --> 00:33:48.290 align:middle line:90% again, directional, spectral. 00:33:48.290 --> 00:33:52.070 align:middle line:84% I don't mean the outer properties are the same. 00:33:52.070 --> 00:33:55.040 align:middle line:84% Now if you have a diffuse surface, 00:33:55.040 --> 00:33:59.020 align:middle line:84% diffuse emitter, diffuse absorber, then this is fine. 00:33:59.020 --> 00:34:01.500 align:middle line:84% Then say all the other property-- 00:34:01.500 --> 00:34:05.960 align:middle line:84% the higher level properties are also equal. 00:34:05.960 --> 00:34:09.449 align:middle line:84% But in general, they are not equal for higher order. 00:34:09.449 --> 00:34:12.295 align:middle line:84% It's only at this fundamental level, directional spectral. 00:34:12.295 --> 00:34:15.370 align:middle line:90% 00:34:15.370 --> 00:34:19.630 align:middle line:84% So like I said, the message is, it's 00:34:19.630 --> 00:34:22.270 align:middle line:84% dependent on wavelength and angle. 00:34:22.270 --> 00:34:24.909 align:middle line:84% And if you think about the reflectivity, 00:34:24.909 --> 00:34:29.679 align:middle line:84% transmissivity, so you have a piece of glass. 00:34:29.679 --> 00:34:31.960 align:middle line:84% So light passing, you have reflection, 00:34:31.960 --> 00:34:33.639 align:middle line:90% and the light can go through. 00:34:33.639 --> 00:34:36.639 align:middle line:84% Of course, there are also [INAUDIBLE] here inside. 00:34:36.639 --> 00:34:39.639 align:middle line:90% And then the light comes in. 00:34:39.639 --> 00:34:42.820 align:middle line:84% The reflectivity is usually more complicated 00:34:42.820 --> 00:34:46.159 align:middle line:84% because you can go other directions. 00:34:46.159 --> 00:34:49.790 align:middle line:84% You can go-- when light comes to a surface-- 00:34:49.790 --> 00:34:52.630 align:middle line:84% and this is relatively smooth, but you 00:34:52.630 --> 00:34:56.020 align:middle line:84% can go to diffuse it to other directions. 00:34:56.020 --> 00:35:01.330 align:middle line:84% So we then have to say, incoming is one direction, 00:35:01.330 --> 00:35:02.550 align:middle line:90% outgoing is another. 00:35:02.550 --> 00:35:07.330 align:middle line:84% So the fundamental definition is the actual despite directional, 00:35:07.330 --> 00:35:12.050 align:middle line:84% what comes in, what goes out is [INAUDIBLE] the intensity. 00:35:12.050 --> 00:35:13.210 align:middle line:90% So you have two angle. 00:35:13.210 --> 00:35:15.220 align:middle line:84% One is the angle of incident, the other 00:35:15.220 --> 00:35:17.410 align:middle line:90% is the angle of reflection. 00:35:17.410 --> 00:35:19.990 align:middle line:84% It's a bi-directional reflectivity. 00:35:19.990 --> 00:35:24.520 align:middle line:84% Let's say, now, if you integrate the whole reflected intensity, 00:35:24.520 --> 00:35:31.420 align:middle line:84% you get, say, the directional, when I say directional spectral. 00:35:31.420 --> 00:35:34.600 align:middle line:84% So that's coming in and integrate all angles. 00:35:34.600 --> 00:35:38.320 align:middle line:84% So if, here, when I do bi-directional, 00:35:38.320 --> 00:35:42.310 align:middle line:90% notation-wise I have 2 prime. 00:35:42.310 --> 00:35:48.280 align:middle line:84% And when I integrate all angle of reflection, 00:35:48.280 --> 00:35:50.080 align:middle line:90% I get directional spectral. 00:35:50.080 --> 00:35:52.750 align:middle line:84% So this direction only means the incoming 00:35:52.750 --> 00:35:56.110 align:middle line:84% because I integrate the reflection over all angle ray. 00:35:56.110 --> 00:35:58.030 align:middle line:84% And then I have [? transferred. ?] 00:35:58.030 --> 00:36:00.910 align:middle line:84% So this now from here I can do the rest similar 00:36:00.910 --> 00:36:05.860 align:middle line:84% as I did for emissivity and [INAUDIBLE]. 00:36:05.860 --> 00:36:07.570 align:middle line:90% So in fact, there are eight. 00:36:07.570 --> 00:36:09.340 align:middle line:84% You can start with more fundamental 00:36:09.340 --> 00:36:13.790 align:middle line:84% and define all those other properties. 00:36:13.790 --> 00:36:20.690 align:middle line:84% And you can do the same for transmissivity, bi-directional 00:36:20.690 --> 00:36:23.030 align:middle line:84% transmissivity, and then integrate over 00:36:23.030 --> 00:36:25.760 align:middle line:90% all transmitted light. 00:36:25.760 --> 00:36:30.080 align:middle line:84% And that's only one direction that angle of incidence. 00:36:30.080 --> 00:36:33.770 align:middle line:84% So all these are [INAUDIBLE] properties. 00:36:33.770 --> 00:36:36.650 align:middle line:84% Now, the energy conservation will tell us, 00:36:36.650 --> 00:36:40.220 align:middle line:84% if I think about the light comes in, 00:36:40.220 --> 00:36:42.200 align:middle line:90% and it's [INAUDIBLE] reflected. 00:36:42.200 --> 00:36:48.560 align:middle line:84% That's the reflection of all angles incident at one angle, 00:36:48.560 --> 00:36:52.670 align:middle line:84% and absorbed it inside the material 00:36:52.670 --> 00:36:56.720 align:middle line:84% or transmit it to the other side. 00:36:56.720 --> 00:36:58.650 align:middle line:90% So that's an energy conversion. 00:36:58.650 --> 00:36:59.580 align:middle line:90% That's the first law. 00:36:59.580 --> 00:37:02.630 align:middle line:84% So in those relations, I've told you 00:37:02.630 --> 00:37:04.700 align:middle line:90% the first law and second law. 00:37:04.700 --> 00:37:09.940 align:middle line:84% Can't violate them in any of those-- in any cases. 00:37:09.940 --> 00:37:15.120 align:middle line:84% So you've used reflector, so similar to the model 00:37:15.120 --> 00:37:20.310 align:middle line:84% we talked about, the emitter is when one light comes in, 00:37:20.310 --> 00:37:25.200 align:middle line:84% the reflected light go all directions, a really bad, say, 00:37:25.200 --> 00:37:28.990 align:middle line:84% surface in the sense of light goes all direction. 00:37:28.990 --> 00:37:31.200 align:middle line:84% But in fact, a lot of times you do 00:37:31.200 --> 00:37:35.490 align:middle line:84% want this, particularly in some illumination. 00:37:35.490 --> 00:37:37.080 align:middle line:84% You actually want the diffuse light 00:37:37.080 --> 00:37:39.900 align:middle line:84% that go to make the room feel comfortable. 00:37:39.900 --> 00:37:45.150 align:middle line:84% And so a re-emitter is [INAUDIBLE] one wavelengths, 00:37:45.150 --> 00:37:50.250 align:middle line:84% and diffuse reflector is both isotropic and 00:37:50.250 --> 00:37:52.220 align:middle line:90% frequency-independent. 00:37:52.220 --> 00:37:55.940 align:middle line:84% So if you-- some of you, to the undergraduate heat transfer, 00:37:55.940 --> 00:38:01.100 align:middle line:84% learn diffuse [? resurface ?] means diffusive re-emitter 00:38:01.100 --> 00:38:03.830 align:middle line:90% and diffuse re-reflector. 00:38:03.830 --> 00:38:04.940 align:middle line:90% So it means both. 00:38:04.940 --> 00:38:08.640 align:middle line:84% We have come back to a solid diffuse re-emitter 00:38:08.640 --> 00:38:10.616 align:middle line:90% here with this [INAUDIBLE]. 00:38:10.616 --> 00:38:13.650 align:middle line:90% 00:38:13.650 --> 00:38:15.160 align:middle line:90% Now the definitions. 00:38:15.160 --> 00:38:16.480 align:middle line:90% We're not going to use much. 00:38:16.480 --> 00:38:23.610 align:middle line:84% I just want to make you aware that the surface properties are 00:38:23.610 --> 00:38:25.890 align:middle line:84% frequency-dependent, wavelength-dependent, 00:38:25.890 --> 00:38:28.700 align:middle line:90% and directional. 00:38:28.700 --> 00:38:32.010 align:middle line:84% And now, there's another key concept. 00:38:32.010 --> 00:38:34.710 align:middle line:84% When I want to calculate how much 00:38:34.710 --> 00:38:38.670 align:middle line:84% radiation goes if I have an emitter. 00:38:38.670 --> 00:38:42.250 align:middle line:84% Really, how much of my radiation get to you? 00:38:42.250 --> 00:38:47.820 align:middle line:84% So that's the concept of view factor. 00:38:47.820 --> 00:38:53.040 align:middle line:84% If I have one surface here, another surface here, 00:38:53.040 --> 00:39:00.420 align:middle line:84% view factor is defined the power leaving this surface. 00:39:00.420 --> 00:39:02.970 align:middle line:84% That's the total power leave this surface, 00:39:02.970 --> 00:39:06.615 align:middle line:90% and intercepted by this surface. 00:39:06.615 --> 00:39:11.220 align:middle line:84% I didn't say absorbed by the other surface, 00:39:11.220 --> 00:39:13.650 align:middle line:84% it's just reaching the other surface. 00:39:13.650 --> 00:39:20.490 align:middle line:84% After which you could reflect it, transmit it, that's not 00:39:20.490 --> 00:39:23.220 align:middle line:84% including [? the power-- ?] say, the view factor. 00:39:23.220 --> 00:39:25.470 align:middle line:84% Just to say diffraction [? reached ?] [INAUDIBLE]. 00:39:25.470 --> 00:39:29.350 align:middle line:84% So that gives you a way of, if you 00:39:29.350 --> 00:39:32.410 align:middle line:84% think about the previous reflectivity transmissivity, 00:39:32.410 --> 00:39:33.760 align:middle line:90% that's near the surface. 00:39:33.760 --> 00:39:37.850 align:middle line:84% This is just saying how much goes to that surface. 00:39:37.850 --> 00:39:46.550 align:middle line:84% And if I use this definition, the power within the surface 00:39:46.550 --> 00:39:51.800 align:middle line:90% here is the i [INAUDIBLE]. 00:39:51.800 --> 00:39:55.160 align:middle line:90% So that's the-- 00:39:55.160 --> 00:40:00.281 align:middle line:84% I should have multiplied the pi, I think. 00:40:00.281 --> 00:40:04.550 align:middle line:84% Yeah, so pi, that's because the intensity affects pi, 00:40:04.550 --> 00:40:07.580 align:middle line:84% the diffuse surface give me the total radiation 00:40:07.580 --> 00:40:08.810 align:middle line:90% leaving the surface. 00:40:08.810 --> 00:40:12.200 align:middle line:84% And then this is the radiation, if I go back 00:40:12.200 --> 00:40:14.090 align:middle line:84% to the definition of the intensity. 00:40:14.090 --> 00:40:18.770 align:middle line:84% So this is the power in the cone times the solid angle 00:40:18.770 --> 00:40:27.080 align:middle line:84% that this area, eaj, suspended with respect to this point here. 00:40:27.080 --> 00:40:30.030 align:middle line:90% So that's eaj cosine theta. 00:40:30.030 --> 00:40:32.120 align:middle line:90% That's the lower area. 00:40:32.120 --> 00:40:35.120 align:middle line:84% And divided by r squared, that's the distance 00:40:35.120 --> 00:40:36.950 align:middle line:90% between the two surfaces. 00:40:36.950 --> 00:40:40.410 align:middle line:84% And this is what's the power in this cone 00:40:40.410 --> 00:40:43.170 align:middle line:90% and reaching that area. 00:40:43.170 --> 00:40:50.025 align:middle line:84% So this with this definition, I have-- 00:40:50.025 --> 00:40:54.062 align:middle line:84% I still [INAUDIBLE], I still think that needs a pi, 00:40:54.062 --> 00:40:55.950 align:middle line:90% but I will check that. 00:40:55.950 --> 00:41:02.970 align:middle line:84% So I have a pi r squared cosine theta i, cosine theta j, eaj. 00:41:02.970 --> 00:41:08.860 align:middle line:84% So that's a differential, small area, the two surface are small. 00:41:08.860 --> 00:41:10.693 align:middle line:84% Does anybody remember if this is pi? 00:41:10.693 --> 00:41:17.295 align:middle line:90% 00:41:17.295 --> 00:41:20.430 align:middle line:84% And if I integrate both surfaces, 00:41:20.430 --> 00:41:22.170 align:middle line:90% I get a total [INAUDIBLE]. 00:41:22.170 --> 00:41:24.840 align:middle line:84% The surface is a uniformly [? medium. ?] 00:41:24.840 --> 00:41:28.470 align:middle line:90% And so, that's the view factor. 00:41:28.470 --> 00:41:33.780 align:middle line:84% Those kind of view factor, again, you can look for tables. 00:41:33.780 --> 00:41:36.620 align:middle line:84% One way to look is go to do this calculation, 00:41:36.620 --> 00:41:39.390 align:middle line:84% but a lot of standard geometry, people 00:41:39.390 --> 00:41:40.930 align:middle line:90% have done the calculation. 00:41:40.930 --> 00:41:44.470 align:middle line:90% So it's calculated. 00:41:44.470 --> 00:41:49.600 align:middle line:84% And the assumption I made is that, over this surface, 00:41:49.600 --> 00:41:52.530 align:middle line:90% the radiation is diffuse. 00:41:52.530 --> 00:41:55.390 align:middle line:90% So I said I have a pi times i. 00:41:55.390 --> 00:41:58.030 align:middle line:84% And then radiation given the surface, 00:41:58.030 --> 00:42:00.190 align:middle line:90% the whole surface is uniform. 00:42:00.190 --> 00:42:03.730 align:middle line:84% So that's the assumption [INAUDIBLE]. 00:42:03.730 --> 00:42:06.760 align:middle line:84% And I said, you can look at the tables. 00:42:06.760 --> 00:42:08.540 align:middle line:84% But there are also relationships. 00:42:08.540 --> 00:42:11.120 align:middle line:84% If you look at the definition, it's very symmetric. 00:42:11.120 --> 00:42:18.460 align:middle line:84% So from this, you will see the reciprocity relation 00:42:18.460 --> 00:42:26.980 align:middle line:84% from view factor from a to j is times the area i. 00:42:26.980 --> 00:42:33.030 align:middle line:84% And then [? increase ?] from j to i times the area j. 00:42:33.030 --> 00:42:36.600 align:middle line:90% That's a reciprocity relation. 00:42:36.600 --> 00:42:41.720 align:middle line:90% And if you do the [INAUDIBLE]. 00:42:41.720 --> 00:42:43.660 align:middle line:90% And then the summation. 00:42:43.660 --> 00:42:45.920 align:middle line:84% Summation is basically the energy balance. 00:42:45.920 --> 00:42:49.670 align:middle line:84% The energy leaving surface i will reach 00:42:49.670 --> 00:42:53.510 align:middle line:90% j, combined surface i plus k. 00:42:53.510 --> 00:42:57.290 align:middle line:84% Then it's the same as leaving i [? plus ?] j and leaving 00:42:57.290 --> 00:42:59.170 align:middle line:90% i plus k. 00:42:59.170 --> 00:43:01.010 align:middle line:90% First [INAUDIBLE]. 00:43:01.010 --> 00:43:02.300 align:middle line:90% First one. 00:43:02.300 --> 00:43:07.340 align:middle line:84% So with those relation, the view factors, most of time 00:43:07.340 --> 00:43:10.670 align:middle line:84% you can, for simple geometry, you can find it from table, 00:43:10.670 --> 00:43:12.530 align:middle line:84% or you calculate using this relation 00:43:12.530 --> 00:43:15.800 align:middle line:84% rather than doing those complicated [INAUDIBLE] 00:43:15.800 --> 00:43:18.890 align:middle line:90% calculation. 00:43:18.890 --> 00:43:22.430 align:middle line:84% Let's go look at the Earth and the sun. 00:43:22.430 --> 00:43:27.890 align:middle line:84% So the Earth and sun, because they are so far apart, 00:43:27.890 --> 00:43:31.400 align:middle line:84% essentially I can treat them a very small surface 00:43:31.400 --> 00:43:35.510 align:middle line:84% relative to each other, so the d area. 00:43:35.510 --> 00:43:38.228 align:middle line:84% And rather than look at the curvature, 00:43:38.228 --> 00:43:39.770 align:middle line:84% because if want to look at curvature, 00:43:39.770 --> 00:43:42.290 align:middle line:84% each point will be different angle-wise, 00:43:42.290 --> 00:43:43.940 align:middle line:90% perpendicular surface. 00:43:43.940 --> 00:43:47.240 align:middle line:84% And in fact, you can just treat this as a disk and this 00:43:47.240 --> 00:43:48.140 align:middle line:90% as a disk. 00:43:48.140 --> 00:43:50.660 align:middle line:90% It's the equivalent. 00:43:50.660 --> 00:43:55.640 align:middle line:84% The disk area of which pi d squared over 4. 00:43:55.640 --> 00:43:57.650 align:middle line:84% And then I look at the view factor 00:43:57.650 --> 00:44:00.410 align:middle line:90% from the sun to the Earth. 00:44:00.410 --> 00:44:04.450 align:middle line:84% It's the Earth's area divided by the distance. 00:44:04.450 --> 00:44:08.190 align:middle line:90% So very small. 00:44:08.190 --> 00:44:12.410 align:middle line:84% And from Earth to the sun, so how much radiation 00:44:12.410 --> 00:44:13.840 align:middle line:90% leaving Earth reach the sun? 00:44:13.840 --> 00:44:15.660 align:middle line:90% That's the fraction. 00:44:15.660 --> 00:44:20.460 align:middle line:84% This is the fraction, radiation leaving the sun reach the Earth. 00:44:20.460 --> 00:44:21.990 align:middle line:90% That's here. 00:44:21.990 --> 00:44:23.250 align:middle line:90% There is the reverse. 00:44:23.250 --> 00:44:26.530 align:middle line:84% And because the sun cross-section area is larger, 00:44:26.530 --> 00:44:29.490 align:middle line:84% the view factor from Earth to the sun 00:44:29.490 --> 00:44:32.790 align:middle line:84% is larger, fraction-wise more radiation 00:44:32.790 --> 00:44:34.626 align:middle line:90% leaving here than here. 00:44:34.626 --> 00:44:37.370 align:middle line:90% 00:44:37.370 --> 00:44:40.700 align:middle line:84% So that's the [INAUDIBLE] first [INAUDIBLE] 00:44:40.700 --> 00:44:45.680 align:middle line:84% check the reciprocity is satisfied. 00:44:45.680 --> 00:44:51.590 align:middle line:84% Now I want to calculate the solar constant. 00:44:51.590 --> 00:44:54.950 align:middle line:84% I said the 1,366, [INAUDIBLE] check. 00:44:54.950 --> 00:44:58.910 align:middle line:84% Radiation reaching the Earth from the sun, 00:44:58.910 --> 00:45:05.000 align:middle line:84% so this is the blackbody from the sun 00:45:05.000 --> 00:45:09.890 align:middle line:84% definitely by approximately the blackbody, times the surface 00:45:09.890 --> 00:45:15.200 align:middle line:84% area that is the area, a s, times the view factor 00:45:15.200 --> 00:45:18.730 align:middle line:90% from the sun to the Earth. 00:45:18.730 --> 00:45:25.410 align:middle line:84% So that's the total radiation from the sun reaching the Earth, 00:45:25.410 --> 00:45:28.780 align:middle line:90% intercepted by Earth. 00:45:28.780 --> 00:45:33.890 align:middle line:84% And I can use the reciprocity to get a per unit area. 00:45:33.890 --> 00:45:38.900 align:middle line:84% Because the a s times the se, a s, se, 00:45:38.900 --> 00:45:44.980 align:middle line:84% [? fs ?] ae versus ae Earth, [? fe, es. ?] So when I do per 00:45:44.980 --> 00:45:49.240 align:middle line:84% unit area, I normalize, I use the reciprocity, 00:45:49.240 --> 00:45:54.850 align:middle line:84% I will actually write this as the sun emissive power times 00:45:54.850 --> 00:45:57.130 align:middle line:90% the Earth to sun-- 00:45:57.130 --> 00:45:59.320 align:middle line:84% here it's sun to Earth, but the area gives me 00:45:59.320 --> 00:46:04.090 align:middle line:90% the Earth to sun view factor. 00:46:04.090 --> 00:46:07.810 align:middle line:90% Oops, I forgot this number. 00:46:07.810 --> 00:46:11.230 align:middle line:84% So this is a step, of course, [INAUDIBLE] minus 8. 00:46:11.230 --> 00:46:12.550 align:middle line:90% I was distributing an area. 00:46:12.550 --> 00:46:13.510 align:middle line:90% Sorry about that. 00:46:13.510 --> 00:46:19.030 align:middle line:84% Minus 8, 10 to the fourth power, that's this side, 5.67 10 00:46:19.030 --> 00:46:25.630 align:middle line:84% to the minus 8, 577, that's the sun temperature, times 00:46:25.630 --> 00:46:28.130 align:middle line:90% this factor here, [INAUDIBLE]. 00:46:28.130 --> 00:46:29.490 align:middle line:90% I did the calculation. 00:46:29.490 --> 00:46:33.620 align:middle line:84% What I got is the 1,365, pretty close. 00:46:33.620 --> 00:46:36.710 align:middle line:84% And solar is constantly integrated. 00:46:36.710 --> 00:46:38.990 align:middle line:90% It's not exactly blackbody. 00:46:38.990 --> 00:46:46.556 align:middle line:84% So this is why some people say the equivalent is 5777. 00:46:46.556 --> 00:46:56.780 align:middle line:90% Solar constant is 1,366. 00:46:56.780 --> 00:46:59.270 align:middle line:90% Now let's look at-- 00:46:59.270 --> 00:47:05.510 align:middle line:84% so that's the energy coming from the sun to the Earth. 00:47:05.510 --> 00:47:09.600 align:middle line:84% What's the maximum efficiency I potentially can get? 00:47:09.600 --> 00:47:16.280 align:middle line:84% What's my best [? luck? ?] If I can convert the solar energy 00:47:16.280 --> 00:47:26.240 align:middle line:84% into mechanical or electrical energy, the maximum using 00:47:26.240 --> 00:47:28.430 align:middle line:90% thermal process, thermal energy. 00:47:28.430 --> 00:47:30.140 align:middle line:84% Thermal energy, of course, is limited 00:47:30.140 --> 00:47:34.880 align:middle line:84% by the Planck's law-- or no, the [INAUDIBLE] efficiency. 00:47:34.880 --> 00:47:41.450 align:middle line:84% So you can always say, it's the Earth's temperature and the sun 00:47:41.450 --> 00:47:42.470 align:middle line:90% temperature. 00:47:42.470 --> 00:47:47.330 align:middle line:84% You drive a power efficiency between the 2, 00:47:47.330 --> 00:47:51.560 align:middle line:84% and you will get 1 minus 300 divided 00:47:51.560 --> 00:47:56.390 align:middle line:90% by 5777, which is about 9%. 00:47:56.390 --> 00:48:00.600 align:middle line:84% That's an upper absolute, absolute possible [INAUDIBLE] 00:48:00.600 --> 00:48:05.292 align:middle line:84% you can somehow [? tap ?] into the sun directly. 00:48:05.292 --> 00:48:11.290 align:middle line:84% Of course, we can't put anything in contact with the sun. 00:48:11.290 --> 00:48:15.920 align:middle line:84% And so, let's dream up this process. 00:48:15.920 --> 00:48:23.635 align:middle line:84% I have a blackbody of the sun very close to my absorber. 00:48:23.635 --> 00:48:26.420 align:middle line:90% 00:48:26.420 --> 00:48:29.074 align:middle line:90% Let's say, this is the-- 00:48:29.074 --> 00:48:33.650 align:middle line:84% I have a very close, because in reality, it can be close. 00:48:33.650 --> 00:48:38.390 align:middle line:84% But I can focus it, focus the solar radiation. 00:48:38.390 --> 00:48:43.730 align:middle line:84% And it turns out that if you do the full version, 00:48:43.730 --> 00:48:49.070 align:middle line:84% and the maximum you can get is something 00:48:49.070 --> 00:48:51.440 align:middle line:90% like the solar temperature. 00:48:51.440 --> 00:48:56.990 align:middle line:84% So the blackbody at the sun, and the absorber, 00:48:56.990 --> 00:49:00.530 align:middle line:84% if I absorb all the solar radiation, so here 00:49:00.530 --> 00:49:04.560 align:middle line:84% the absorber is also a blackbody. 00:49:04.560 --> 00:49:08.340 align:middle line:84% And then say, I discovered a t, and then 00:49:08.340 --> 00:49:12.120 align:middle line:84% I put a engine in between this absorber 00:49:12.120 --> 00:49:16.050 align:middle line:90% and the ambient and the output. 00:49:16.050 --> 00:49:21.030 align:middle line:84% And then I can imagine this engine is a perfect car engine. 00:49:21.030 --> 00:49:26.975 align:middle line:84% So what will be the efficiency of such a, say, system? 00:49:26.975 --> 00:49:30.350 align:middle line:90% 00:49:30.350 --> 00:49:35.570 align:middle line:84% And first I want to see how much heat can go from the sun 00:49:35.570 --> 00:49:38.960 align:middle line:90% to this absorber. 00:49:38.960 --> 00:49:43.880 align:middle line:84% Here, I'm doing to blackbody, so blackbody radiation 00:49:43.880 --> 00:49:46.410 align:middle line:84% is from sensing my T fourth power. 00:49:46.410 --> 00:49:51.440 align:middle line:84% You can see, now I don't have this very small view factor. 00:49:51.440 --> 00:49:54.740 align:middle line:84% I'm just doing two parallel plates. 00:49:54.740 --> 00:50:01.570 align:middle line:84% So sigma T fourth area is an [? no ?] area difference 00:50:01.570 --> 00:50:02.540 align:middle line:90% anymore. 00:50:02.540 --> 00:50:06.670 align:middle line:84% Sigma T fourth power minus this radiation, 00:50:06.670 --> 00:50:10.700 align:middle line:84% now the absorber will radiate it back. 00:50:10.700 --> 00:50:14.310 align:middle line:90% So [? minus ?] T fourth power. 00:50:14.310 --> 00:50:21.350 align:middle line:84% So that's the heat transfer from the sun to this absorber, 00:50:21.350 --> 00:50:24.770 align:middle line:90% maximum you can get. 00:50:24.770 --> 00:50:33.620 align:middle line:84% And so, that means the thermal efficiency, what comes in, 00:50:33.620 --> 00:50:36.350 align:middle line:84% this order, this sigma T fourth power, 00:50:36.350 --> 00:50:39.740 align:middle line:84% and the amount of heat transfer that actually should happen 00:50:39.740 --> 00:50:42.590 align:middle line:84% is T fourth plus [INAUDIBLE] fourth 00:50:42.590 --> 00:50:47.990 align:middle line:84% must T fourth The thermal efficiency to the 1 minus 00:50:47.990 --> 00:50:49.561 align:middle line:84% [? come ?] to the fourth power ratio. 00:50:49.561 --> 00:50:52.270 align:middle line:90% 00:50:52.270 --> 00:50:57.820 align:middle line:84% So the higher the temperature the absorber, the lower 00:50:57.820 --> 00:50:59.620 align:middle line:90% is the thermal efficiency. 00:50:59.620 --> 00:51:02.440 align:middle line:90% 00:51:02.440 --> 00:51:06.360 align:middle line:90% And now, [INAUDIBLE]. 00:51:06.360 --> 00:51:12.170 align:middle line:90% So the power efficiency is here. 00:51:12.170 --> 00:51:16.710 align:middle line:84% And in fact, as I move on, you should ask questions. 00:51:16.710 --> 00:51:22.760 align:middle line:84% Because what are the questions, what if I use selective surface? 00:51:22.760 --> 00:51:27.690 align:middle line:90% Why you put a blackbody here? 00:51:27.690 --> 00:51:31.980 align:middle line:84% And this will be related to what kind of concentration, 00:51:31.980 --> 00:51:33.690 align:middle line:90% how you concentrate. 00:51:33.690 --> 00:51:38.940 align:middle line:84% Because here I'm really putting the maximum temperature. 00:51:38.940 --> 00:51:41.365 align:middle line:84% Really, this is the sun, this is blackbody, 00:51:41.365 --> 00:51:43.380 align:middle line:90% and they are facing each other. 00:51:43.380 --> 00:51:49.470 align:middle line:84% And that will require you to put your maximum concentration. 00:51:49.470 --> 00:51:51.930 align:middle line:84% And in the case of maximum concentration, 00:51:51.930 --> 00:51:58.050 align:middle line:84% the emission of this surface becomes not important. 00:51:58.050 --> 00:52:01.560 align:middle line:84% It's really the absorption that's most important. 00:52:01.560 --> 00:52:05.370 align:middle line:84% Absorption, the higher the better, the best is 1. 00:52:05.370 --> 00:52:07.560 align:middle line:90% So you get a blackbody. 00:52:07.560 --> 00:52:08.060 align:middle line:90% That's why. 00:52:08.060 --> 00:52:11.570 align:middle line:90% 00:52:11.570 --> 00:52:15.260 align:middle line:84% So now I have a thermal efficiency, 00:52:15.260 --> 00:52:19.070 align:middle line:84% I have a power efficiency, and the product of the two 00:52:19.070 --> 00:52:21.610 align:middle line:90% gives me the maximum-- 00:52:21.610 --> 00:52:23.570 align:middle line:90% the combined efficiency. 00:52:23.570 --> 00:52:25.880 align:middle line:84% So this is the thermal efficiency. 00:52:25.880 --> 00:52:28.310 align:middle line:90% This is the power efficiency. 00:52:28.310 --> 00:52:30.080 align:middle line:84% Of course, the power efficiency, you 00:52:30.080 --> 00:52:34.760 align:middle line:84% want to operate your engine as high temperature as possible. 00:52:34.760 --> 00:52:37.880 align:middle line:84% The thermal efficiency, as you operate the higher temperature, 00:52:37.880 --> 00:52:40.010 align:middle line:90% radiation loss increase. 00:52:40.010 --> 00:52:43.670 align:middle line:90% So you have a maximum here. 00:52:43.670 --> 00:52:50.990 align:middle line:84% So this is the maximum efficiency you can get about 85% 00:52:50.990 --> 00:52:54.980 align:middle line:90% of efficiency out of this. 00:52:54.980 --> 00:53:01.145 align:middle line:84% And this happens around 2,450 Kelvin when you have 00:53:01.145 --> 00:53:04.130 align:middle line:90% [INAUDIBLE]. 00:53:04.130 --> 00:53:06.470 align:middle line:84% And what's interesting is that, actually, there 00:53:06.470 --> 00:53:08.070 align:middle line:90% is a pretty wide range. 00:53:08.070 --> 00:53:14.450 align:middle line:84% The efficiency, this is actually really good, pretty flat, 00:53:14.450 --> 00:53:15.280 align:middle line:90% relatively flat. 00:53:15.280 --> 00:53:17.900 align:middle line:90% 00:53:17.900 --> 00:53:22.100 align:middle line:84% And so, if you operate, if you think about here, 00:53:22.100 --> 00:53:24.920 align:middle line:90% it's only about 1,000 degree. 00:53:24.920 --> 00:53:27.800 align:middle line:90% Here is the 4,000 degree. 00:53:27.800 --> 00:53:31.910 align:middle line:90% And this is a 7%. 00:53:31.910 --> 00:53:34.310 align:middle line:84% Pretty good if you can get there. 00:53:34.310 --> 00:53:36.140 align:middle line:90% And we know the solar-- 00:53:36.140 --> 00:53:41.240 align:middle line:90% the coal plant is only 40%. 00:53:41.240 --> 00:53:45.590 align:middle line:84% The combined, that's the coal burning plant. 00:53:45.590 --> 00:53:47.930 align:middle line:90% Coal plant is about 40%. 00:53:47.930 --> 00:53:51.740 align:middle line:84% And if you combine gas turbines, [? and a ?] 00:53:51.740 --> 00:53:55.940 align:middle line:84% combined cycle, combined gas turbine with a steam turbine. 00:53:55.940 --> 00:54:01.620 align:middle line:84% So you burn fuel, so you generate hot gas, and gas 00:54:01.620 --> 00:54:04.880 align:middle line:84% profile turbine, say, a gas turbine 00:54:04.880 --> 00:54:06.800 align:middle line:90% and exhaust generate steam. 00:54:06.800 --> 00:54:09.290 align:middle line:90% Steam drive a steam turbine. 00:54:09.290 --> 00:54:12.710 align:middle line:90% That combined about 60%. 00:54:12.710 --> 00:54:17.540 align:middle line:84% That's the best you can do with the fuels. 00:54:17.540 --> 00:54:20.870 align:middle line:84% And an internal combustion engine, the car 00:54:20.870 --> 00:54:23.900 align:middle line:90% is about 25% to 30%. 00:54:23.900 --> 00:54:29.340 align:middle line:84% So that's the-- so this is a pretty optimistic value here. 00:54:29.340 --> 00:54:31.490 align:middle line:90% So if you put your solar-- 00:54:31.490 --> 00:54:33.800 align:middle line:84% if you put your thermal engine between the 00:54:33.800 --> 00:54:35.700 align:middle line:90% using the heat from the sun. 00:54:35.700 --> 00:54:39.390 align:middle line:84% But of course, there are many limitations. 00:54:39.390 --> 00:54:43.610 align:middle line:90% 00:54:43.610 --> 00:54:46.790 align:middle line:84% Now, the next question I want to ask 00:54:46.790 --> 00:54:52.940 align:middle line:84% is, if I put the material here, under the sun, 00:54:52.940 --> 00:54:55.400 align:middle line:90% how far they can get? 00:54:55.400 --> 00:54:57.690 align:middle line:84% What's the maximum temperature you can get? 00:54:57.690 --> 00:55:01.652 align:middle line:90% 00:55:01.652 --> 00:55:06.860 align:middle line:84% And I could imagine a case where you could potentially 00:55:06.860 --> 00:55:10.010 align:middle line:90% get to a very high temperature. 00:55:10.010 --> 00:55:11.420 align:middle line:90% And this is the-- 00:55:11.420 --> 00:55:14.790 align:middle line:84% radiation comes in, you will be up [INAUDIBLE]. 00:55:14.790 --> 00:55:16.500 align:middle line:84% I don't think about the direction. 00:55:16.500 --> 00:55:18.920 align:middle line:84% Let me just say all direction the same. 00:55:18.920 --> 00:55:21.410 align:middle line:84% And again, this is, because of that, maybe 00:55:21.410 --> 00:55:24.660 align:middle line:84% you have ways to do better, I don't know yet. 00:55:24.660 --> 00:55:28.260 align:middle line:90% So radiation comes in. 00:55:28.260 --> 00:55:31.200 align:middle line:84% These absorptivity of the surface 00:55:31.200 --> 00:55:34.760 align:middle line:84% is a function of lambda wavelengths. 00:55:34.760 --> 00:55:39.560 align:middle line:84% And then, also, the emission, you will re-radiate. 00:55:39.560 --> 00:55:42.680 align:middle line:84% So absorption, if I put the [? rationale, ?] 00:55:42.680 --> 00:55:44.780 align:middle line:84% I know the Kirchhoff's law tells me, 00:55:44.780 --> 00:55:48.590 align:middle line:84% absorption equals emission for wavelengths at least. 00:55:48.590 --> 00:55:51.710 align:middle line:84% At least if I say the rationale one is the same. 00:55:51.710 --> 00:55:55.135 align:middle line:84% So it's all diffuse, you can imagine that. 00:55:55.135 --> 00:55:57.734 align:middle line:90% 00:55:57.734 --> 00:56:09.060 align:middle line:84% So when I do this, I will have the absorbed energy, 00:56:09.060 --> 00:56:10.190 align:middle line:90% this is the-- 00:56:10.190 --> 00:56:13.940 align:middle line:84% you can see, this is the spectrum from the sun, 00:56:13.940 --> 00:56:17.001 align:middle line:90% and the times absorptivity. 00:56:17.001 --> 00:56:20.870 align:middle line:84% [INAUDIBLE] I have integrated the [INAUDIBLE] angle 00:56:20.870 --> 00:56:23.720 align:middle line:90% and integrated over d lambda. 00:56:23.720 --> 00:56:27.380 align:middle line:84% So that's all the energy comes in. 00:56:27.380 --> 00:56:33.920 align:middle line:84% And then, this is the energy that is re-radiated. 00:56:33.920 --> 00:56:36.710 align:middle line:90% One is the surface radiation. 00:56:36.710 --> 00:56:40.460 align:middle line:84% In [INAUDIBLE] times blackbody emission, 00:56:40.460 --> 00:56:42.770 align:middle line:84% this blackbody emission [INAUDIBLE]. 00:56:42.770 --> 00:56:46.260 align:middle line:84% But also the ambient is [INAUDIBLE]. 00:56:46.260 --> 00:56:49.970 align:middle line:84% So you have a [INAUDIBLE] change between here and the ambient. 00:56:49.970 --> 00:56:53.600 align:middle line:84% So this is the radiation to the ambient. 00:56:53.600 --> 00:56:58.340 align:middle line:90% t should not be t, a, t0, ta. 00:56:58.340 --> 00:57:01.760 align:middle line:90% And here I have concentration. 00:57:01.760 --> 00:57:03.500 align:middle line:90% As I said, this may not be-- 00:57:03.500 --> 00:57:05.990 align:middle line:84% I think this probably is not the maximum. 00:57:05.990 --> 00:57:08.595 align:middle line:84% Well, as I talk, I'm just making comments. 00:57:08.595 --> 00:57:11.340 align:middle line:90% 00:57:11.340 --> 00:57:16.840 align:middle line:84% Because the radiation from the sun is in a very small angle. 00:57:16.840 --> 00:57:21.030 align:middle line:84% It's almost lower-- you say lower incidence. 00:57:21.030 --> 00:57:24.570 align:middle line:84% And when I write this emission, I 00:57:24.570 --> 00:57:30.810 align:middle line:84% am writing the emissivity isotropic. 00:57:30.810 --> 00:57:36.540 align:middle line:84% I could potentially design a surface emission only also 00:57:36.540 --> 00:57:39.690 align:middle line:84% in the same angle where the sun has. 00:57:39.690 --> 00:57:42.330 align:middle line:84% Then I have to do angular integration. 00:57:42.330 --> 00:57:45.150 align:middle line:84% That probably will go even higher temperature 00:57:45.150 --> 00:57:47.060 align:middle line:84% than this if I just make that guess. 00:57:47.060 --> 00:57:52.308 align:middle line:90% 00:57:52.308 --> 00:58:00.540 align:middle line:84% So once the-- in terms of how I-- the spectral 00:58:00.540 --> 00:58:01.330 align:middle line:90% characteristics. 00:58:01.330 --> 00:58:06.630 align:middle line:84% So if you look at, this is the radiation from the sun. 00:58:06.630 --> 00:58:09.600 align:middle line:84% And this might be the radiation emission 00:58:09.600 --> 00:58:12.440 align:middle line:90% from [INAUDIBLE] the surface. 00:58:12.440 --> 00:58:19.100 align:middle line:84% And at each wavelength, so you can 00:58:19.100 --> 00:58:21.530 align:middle line:90% design your selective surface. 00:58:21.530 --> 00:58:26.390 align:middle line:84% Ideally, you can design [INAUDIBLE] if you could. 00:58:26.390 --> 00:58:32.270 align:middle line:84% Seriously, [? no, ?] seriously, you [? cannot. ?] But it's hard 00:58:32.270 --> 00:58:33.500 align:middle line:90% to do. 00:58:33.500 --> 00:58:40.220 align:middle line:84% But let's just say, imagine I have that [INAUDIBLE] surface 00:58:40.220 --> 00:58:42.830 align:middle line:90% that I have a sharp cutoff. 00:58:42.830 --> 00:58:49.850 align:middle line:84% So below certain wavelengths, all the radiation is absorbed. 00:58:49.850 --> 00:58:53.810 align:middle line:84% So that could be the solar radiation. 00:58:53.810 --> 00:59:01.380 align:middle line:84% And then, beyond that, all radiation is rejected. 00:59:01.380 --> 00:59:08.700 align:middle line:84% So that's a spectral idea 1, 0 spectral properties, 00:59:08.700 --> 00:59:11.070 align:middle line:90% selective surfaces. 00:59:11.070 --> 00:59:15.210 align:middle line:84% And so, if this selective surface is a 1, 0, 00:59:15.210 --> 00:59:19.950 align:middle line:84% and I can look at, if I design the selective wavelengths here, 00:59:19.950 --> 00:59:24.510 align:middle line:84% if you look at it, this blackbody from emission 00:59:24.510 --> 00:59:26.190 align:middle line:90% reduces rapidly. 00:59:26.190 --> 00:59:30.000 align:middle line:84% So if I make my wavelengths here, this radiation, 00:59:30.000 --> 00:59:31.170 align:middle line:90% Kirchhoff's law-- 00:59:31.170 --> 00:59:35.490 align:middle line:84% and now I have to remind you of Kirchhoff's law. 00:59:35.490 --> 00:59:40.680 align:middle line:84% When I see this spectrum, this absorption is 1, 00:59:40.680 --> 00:59:45.780 align:middle line:84% I also mean the emission is also 1. 00:59:45.780 --> 00:59:47.910 align:middle line:90% I can't violate that. 00:59:47.910 --> 00:59:51.670 align:middle line:84% So this radiation will be going out. 00:59:51.670 --> 00:59:59.250 align:middle line:84% This blue in this region will be emitted if I absorb everything 00:59:59.250 --> 01:00:01.320 align:middle line:90% from the sun. 01:00:01.320 --> 01:00:03.090 align:middle line:90% That's the second law tells me. 01:00:03.090 --> 01:00:07.500 align:middle line:90% So if I have-- 01:00:07.500 --> 01:00:09.300 align:middle line:90% I check this wavelength. 01:00:09.300 --> 01:00:09.840 align:middle line:90% You can say. 01:00:09.840 --> 01:00:12.420 align:middle line:84% Now I make the wavelength shorter, 01:00:12.420 --> 01:00:16.020 align:middle line:84% there's less emission from the blue curve. 01:00:16.020 --> 01:00:17.880 align:middle line:90% So here is almost 0. 01:00:17.880 --> 01:00:20.940 align:middle line:84% But there's still a fraction of the solar radiation 01:00:20.940 --> 01:00:23.340 align:middle line:90% that comes in absorbed. 01:00:23.340 --> 01:00:27.060 align:middle line:84% So I want to do my energy balance and say, 01:00:27.060 --> 01:00:30.420 align:middle line:84% what's the maximum temperature I can get just 01:00:30.420 --> 01:00:34.760 align:middle line:84% with a flat surface, one [? sun? ?] 01:00:34.760 --> 01:00:36.660 align:middle line:90% So c equal to 1. 01:00:36.660 --> 01:00:41.070 align:middle line:84% And I do, rather than do a blackbody spectrum here, 01:00:41.070 --> 01:00:43.830 align:middle line:90% I was trying to do this by hand. 01:00:43.830 --> 01:00:45.643 align:middle line:84% And then later on I found that I still 01:00:45.643 --> 01:00:46.810 align:middle line:90% couldn't solve the equation. 01:00:46.810 --> 01:00:49.240 align:middle line:84% So I get [INAUDIBLE] that came into my office. 01:00:49.240 --> 01:00:52.470 align:middle line:84% He has a code that you possibly [INAUDIBLE] you'll see later on. 01:00:52.470 --> 01:00:59.100 align:middle line:84% So here is the radiation from the sun. 01:00:59.100 --> 01:01:03.090 align:middle line:84% And I say absorption is 1 becomes 0 lambda. 01:01:03.090 --> 01:01:07.620 align:middle line:84% So this is 1 times whatever comes from the sun. 01:01:07.620 --> 01:01:11.040 align:middle line:84% So view factor from the sun to Earth's surface, 01:01:11.040 --> 01:01:15.530 align:middle line:84% the surface area of the sun, blackbody emission of the sun, 01:01:15.530 --> 01:01:19.140 align:middle line:84% t lambda, that's what comes to the Earth's surface. 01:01:19.140 --> 01:01:24.210 align:middle line:84% And this is the emission radiation out from the surface. 01:01:24.210 --> 01:01:27.990 align:middle line:84% So assuming this surface is facing the sun directly, 01:01:27.990 --> 01:01:33.820 align:middle line:84% there's no angle [INAUDIBLE], and emission out 01:01:33.820 --> 01:01:39.402 align:middle line:84% and the emission to the ambient, [INAUDIBLE] ambient. 01:01:39.402 --> 01:01:42.320 align:middle line:90% 01:01:42.320 --> 01:01:46.100 align:middle line:84% And of course, let's say, I've used this trick before. 01:01:46.100 --> 01:01:50.360 align:middle line:84% This area times view factor is the same area on Earth 01:01:50.360 --> 01:01:52.900 align:middle line:84% times the view factor from Earth to the sun 01:01:52.900 --> 01:01:55.360 align:middle line:90% so that I can cancel the area. 01:01:55.360 --> 01:01:57.850 align:middle line:84% So it's the independent of area here. 01:01:57.850 --> 01:02:02.060 align:middle line:90% 01:02:02.060 --> 01:02:03.950 align:middle line:90% I can cancel the area. 01:02:03.950 --> 01:02:09.110 align:middle line:84% And that's why I was doing the universal blackbody curve. 01:02:09.110 --> 01:02:12.140 align:middle line:84% So if I do my universal blackbody curve, 01:02:12.140 --> 01:02:16.175 align:middle line:84% this is the radiation between the sun temperature-- 01:02:16.175 --> 01:02:20.120 align:middle line:84% I mean, wavelengths normalized to sun 10 to the fourth power. 01:02:20.120 --> 01:02:23.210 align:middle line:84% This is the function I want to find the time temperature. 01:02:23.210 --> 01:02:25.430 align:middle line:84% I thought I could do this by hand. 01:02:25.430 --> 01:02:27.560 align:middle line:84% Again, this function is not [INAUDIBLE]. 01:02:27.560 --> 01:02:30.770 align:middle line:84% I can't-- you have to do a [INAUDIBLE] to solve 01:02:30.770 --> 01:02:33.680 align:middle line:90% for the [INAUDIBLE]. 01:02:33.680 --> 01:02:36.600 align:middle line:84% So but this is definitely solvable. 01:02:36.600 --> 01:02:39.080 align:middle line:84% You can go to solve the equation. 01:02:39.080 --> 01:02:41.060 align:middle line:84% You can even take the real spectrum 01:02:41.060 --> 01:02:45.080 align:middle line:84% to solve it rather than doing blackbody spectrum as I'm 01:02:45.080 --> 01:02:46.460 align:middle line:90% doing here. 01:02:46.460 --> 01:02:50.060 align:middle line:84% I've written down, in fact, that's what [? King ?] has done. 01:02:50.060 --> 01:02:52.670 align:middle line:90% 01:02:52.670 --> 01:02:57.470 align:middle line:84% This is the curve a m 0 condition. 01:02:57.470 --> 01:02:59.900 align:middle line:84% And if you choose your wavelengths, 01:02:59.900 --> 01:03:02.450 align:middle line:84% it's interesting that the shorter the wavelengths 01:03:02.450 --> 01:03:06.350 align:middle line:84% you choose, the higher the temperature you get. 01:03:06.350 --> 01:03:10.640 align:middle line:84% That's because the loss is smaller. 01:03:10.640 --> 01:03:14.120 align:middle line:84% You look at it, you go to shift to small wavelengths, 01:03:14.120 --> 01:03:17.570 align:middle line:84% you absorb the radiation, but you lose very small. 01:03:17.570 --> 01:03:21.260 align:middle line:84% Because this curve, once you go to very short, 01:03:21.260 --> 01:03:25.850 align:middle line:84% this curve is always below the blackbody curve 01:03:25.850 --> 01:03:27.030 align:middle line:90% of the re-emission. 01:03:27.030 --> 01:03:32.130 align:middle line:90% 01:03:32.130 --> 01:03:36.720 align:middle line:84% And so you-- but see, isn't this amazing 01:03:36.720 --> 01:03:40.000 align:middle line:90% if you have that surface here? 01:03:40.000 --> 01:03:42.760 align:middle line:84% AUDIENCE: My old house, I think I bought 01:03:42.760 --> 01:03:45.680 align:middle line:90% my [INAUDIBLE] something. 01:03:45.680 --> 01:03:47.953 align:middle line:90% GANG CHEN: [INAUDIBLE] 01:03:47.953 --> 01:03:48.995 align:middle line:90% AUDIENCE: No, it's black. 01:03:48.995 --> 01:03:51.520 align:middle line:90% [INAUDIBLE] 01:03:51.520 --> 01:03:57.890 align:middle line:84% Yeah, no conservation, and no, let's say, no optical treatment, 01:03:57.890 --> 01:03:58.745 align:middle line:90% no filters. 01:03:58.745 --> 01:03:59.660 align:middle line:90% GANG CHEN: Right. 01:03:59.660 --> 01:04:01.850 align:middle line:84% AUDIENCE: It's definitely not 600 Kelvin. 01:04:01.850 --> 01:04:02.640 align:middle line:90% GANG CHEN: No, no. 01:04:02.640 --> 01:04:04.660 align:middle line:90% AUDIENCE: It's 81 Celsius. 01:04:04.660 --> 01:04:08.850 align:middle line:84% GANG CHEN: Yes, what is that, is it a flat panel? 01:04:08.850 --> 01:04:09.590 align:middle line:90% AUDIENCE: Yeah. 01:04:09.590 --> 01:04:10.507 align:middle line:90% GANG CHEN: Flat panel? 01:04:10.507 --> 01:04:13.090 align:middle line:84% Yeah, flat panel, you got a lot of losses. 01:04:13.090 --> 01:04:15.090 align:middle line:90% Firstly, the surface is not bad. 01:04:15.090 --> 01:04:17.990 align:middle line:84% The [INAUDIBLE] industry has done a pretty good job. 01:04:17.990 --> 01:04:21.860 align:middle line:90% And you can buy-- 01:04:21.860 --> 01:04:23.780 align:middle line:84% I visit-- this is the part of the things I'm 01:04:23.780 --> 01:04:25.340 align:middle line:90% going to talk later. 01:04:25.340 --> 01:04:31.280 align:middle line:84% You can buy commercial this hot water surfaces, 01:04:31.280 --> 01:04:36.080 align:middle line:84% have a 95% absorption, 5% emission, 01:04:36.080 --> 01:04:39.260 align:middle line:84% not a [? shock ?] [? product. ?] We'll have an example later on. 01:04:39.260 --> 01:04:42.620 align:middle line:84% And another flat panel, it's not a vacuum. 01:04:42.620 --> 01:04:45.260 align:middle line:84% You take a vacuum tube that the channel use, 01:04:45.260 --> 01:04:51.410 align:middle line:84% you put it inside, you go to 200 degrees Celsius. 01:04:51.410 --> 01:04:55.710 align:middle line:84% That's when you don't have water inside it, just dry 01:04:55.710 --> 01:04:56.880 align:middle line:90% in [INAUDIBLE]. 01:04:56.880 --> 01:05:03.640 align:middle line:90% 01:05:03.640 --> 01:05:07.210 align:middle line:90% Yeah, so this is the-- 01:05:07.210 --> 01:05:13.780 align:middle line:84% I guess the point is, if you can design, in here is-- 01:05:13.780 --> 01:05:20.500 align:middle line:84% if you recall, for thermal engine, 85% efficiency range, 01:05:20.500 --> 01:05:27.040 align:middle line:84% or 70 to 85, you need 1,000 to 4,000 temperature range, 01:05:27.040 --> 01:05:28.540 align:middle line:90% theoretically. 01:05:28.540 --> 01:05:32.710 align:middle line:84% And here, it doesn't seem to be that hard 01:05:32.710 --> 01:05:34.570 align:middle line:90% if you've got that surface. 01:05:34.570 --> 01:05:37.756 align:middle line:84% Of course, that's a really ideal surface. 01:05:37.756 --> 01:05:41.410 align:middle line:84% If you can get it to the 1,000 degree, even with one sun, 01:05:41.410 --> 01:05:45.370 align:middle line:90% [? flat-- ?] sorry. 01:05:45.370 --> 01:05:47.390 align:middle line:90% And here is another example. 01:05:47.390 --> 01:05:51.010 align:middle line:84% [? In ?] 1.5, that's the [INAUDIBLE] Earth. 01:05:51.010 --> 01:05:54.390 align:middle line:90% And again, [INAUDIBLE]. 01:05:54.390 --> 01:05:58.630 align:middle line:90% 01:05:58.630 --> 01:06:03.940 align:middle line:84% Now, for those ideal situation, you can do almost-- 01:06:03.940 --> 01:06:07.120 align:middle line:90% this doesn't give you any power. 01:06:07.120 --> 01:06:12.040 align:middle line:84% What we did is just to say, it's something 01:06:12.040 --> 01:06:14.590 align:middle line:90% equal to the loss, no power. 01:06:14.590 --> 01:06:21.490 align:middle line:84% So now let's look at the more realistic case where this is 01:06:21.490 --> 01:06:23.210 align:middle line:90% still-- the surface is ideal. 01:06:23.210 --> 01:06:28.690 align:middle line:84% But I don't optimize the temperature, trying 01:06:28.690 --> 01:06:30.910 align:middle line:90% to reach maximum temperature. 01:06:30.910 --> 01:06:35.690 align:middle line:84% I try to say, given a temperature of [? operation, ?] 01:06:35.690 --> 01:06:37.010 align:middle line:90% what's the-- 01:06:37.010 --> 01:06:39.230 align:middle line:90% I choose the wavelength. 01:06:39.230 --> 01:06:42.320 align:middle line:84% So the way I choose the wavelength, if I say, 01:06:42.320 --> 01:06:44.640 align:middle line:84% this is the curve here, then what 01:06:44.640 --> 01:06:46.640 align:middle line:90% radiation come in from the sun? 01:06:46.640 --> 01:06:50.660 align:middle line:84% And at this wavelength, the blackbody, at this temperature, 01:06:50.660 --> 01:06:54.485 align:middle line:84% the blackbody intersect the solar radiation 01:06:54.485 --> 01:06:56.780 align:middle line:84% at this temperature, at this wavelength. 01:06:56.780 --> 01:06:59.450 align:middle line:90% So I cut out this point. 01:06:59.450 --> 01:07:05.690 align:middle line:84% And then, below this wavelength I have 1 above, I have 0. 01:07:05.690 --> 01:07:08.210 align:middle line:84% So the difference from the previous discussion 01:07:08.210 --> 01:07:12.090 align:middle line:84% is, previously I say that each wavelength 01:07:12.090 --> 01:07:14.300 align:middle line:90% what's the maximum temperature? 01:07:14.300 --> 01:07:17.760 align:middle line:84% And here is, I gave a temperature, 01:07:17.760 --> 01:07:20.510 align:middle line:90% I choose my wavelength. 01:07:20.510 --> 01:07:25.850 align:middle line:84% And then I say, if I operate this engine 01:07:25.850 --> 01:07:29.730 align:middle line:84% at this temperature, what's the efficiency I can get? 01:07:29.730 --> 01:07:33.390 align:middle line:90% 01:07:33.390 --> 01:07:39.580 align:middle line:84% And so, this is the, again, the same picture 01:07:39.580 --> 01:07:43.370 align:middle line:84% here other than any of this [INAUDIBLE] 01:07:43.370 --> 01:07:46.960 align:middle line:84% and the blackbody, two blackbody working together, 01:07:46.960 --> 01:07:51.190 align:middle line:84% I'd say I'm looking at the one sun [INAUDIBLE]. 01:07:51.190 --> 01:07:53.800 align:middle line:90% Again, like what I said. 01:07:53.800 --> 01:07:58.150 align:middle line:84% Now, in this case, the thermal efficiency 01:07:58.150 --> 01:08:04.960 align:middle line:84% is what comes in at the total, and then this part is lost. 01:08:04.960 --> 01:08:08.890 align:middle line:90% The blue curve part is lost. 01:08:08.890 --> 01:08:14.110 align:middle line:84% So if I calculate the thermal efficiency, 01:08:14.110 --> 01:08:19.330 align:middle line:84% and this is the [INAUDIBLE] mechanics calculation. 01:08:19.330 --> 01:08:24.680 align:middle line:84% And as you-- here is the thermal efficiency. 01:08:24.680 --> 01:08:30.950 align:middle line:90% So the loss, this is a larger-- 01:08:30.950 --> 01:08:34.720 align:middle line:84% the blue-- the purple area is the-- 01:08:34.720 --> 01:08:39.560 align:middle line:84% or dark area, this is a 0.9 [? high ?] thermal efficiency. 01:08:39.560 --> 01:08:44.330 align:middle line:84% So naturally, if you want to have a good thermal efficiency, 01:08:44.330 --> 01:08:47.040 align:middle line:84% if you want to [INAUDIBLE] out [INAUDIBLE]. 01:08:47.040 --> 01:08:50.899 align:middle line:84% So you want to operate, again, at a low temperature. 01:08:50.899 --> 01:08:53.630 align:middle line:84% You go the low temperature, [INAUDIBLE]. 01:08:53.630 --> 01:08:58.649 align:middle line:84% So that's the-- but of course, you get a 0 power efficiency. 01:08:58.649 --> 01:09:02.540 align:middle line:84% So you still got the more optimum. 01:09:02.540 --> 01:09:07.130 align:middle line:84% So you multiply this to the power efficiency, 01:09:07.130 --> 01:09:12.529 align:middle line:84% and this is the transition wavelengths are here. 01:09:12.529 --> 01:09:19.189 align:middle line:84% And so, this is the-- in this case, what you have is 0.5. 01:09:19.189 --> 01:09:24.759 align:middle line:84% So still pretty ideal, pretty good, very good 01:09:24.759 --> 01:09:28.910 align:middle line:84% if you can get even half of that. 01:09:28.910 --> 01:09:33.649 align:middle line:84% Because 50%, let's assume you have a thermal engine, a power 01:09:33.649 --> 01:09:37.130 align:middle line:84% engine operating between, in this case, 01:09:37.130 --> 01:09:41.840 align:middle line:84% let's say, here is a 50%, it's a power engine operating 01:09:41.840 --> 01:09:48.189 align:middle line:84% between 800 Kelvin to room temperature. 01:09:48.189 --> 01:09:52.149 align:middle line:84% And of course, if you have a real efficiency, [INAUDIBLE] 01:09:52.149 --> 01:09:55.930 align:middle line:84% that's the power of-- so most likely 01:09:55.930 --> 01:09:58.434 align:middle line:84% you're shifted to lower temperature. 01:09:58.434 --> 01:10:01.640 align:middle line:90% 01:10:01.640 --> 01:10:06.920 align:middle line:84% This is actually a real selective surface. 01:10:06.920 --> 01:10:11.420 align:middle line:84% With selective surfaces from [? sun ?] [? select, ?] this is 01:10:11.420 --> 01:10:15.710 align:middle line:84% the emissivity, the absorber in the solar region, 01:10:15.710 --> 01:10:18.830 align:middle line:90% and in the IR region. 01:10:18.830 --> 01:10:24.240 align:middle line:84% Problem is, nobody could make this really sharp I think. 01:10:24.240 --> 01:10:25.630 align:middle line:90% And it's a transition. 01:10:25.630 --> 01:10:30.430 align:middle line:84% There are always a transition, the sharper, the better. 01:10:30.430 --> 01:10:36.160 align:middle line:84% And so, if you use this surface to do the calculation, 01:10:36.160 --> 01:10:41.860 align:middle line:84% real surface to do calculation, and then, again, assuming 01:10:41.860 --> 01:10:44.020 align:middle line:90% a [? power ?] efficiency. 01:10:44.020 --> 01:10:54.100 align:middle line:84% So here is the system efficiency now becomes about 30%. 01:10:54.100 --> 01:10:59.330 align:middle line:84% And the operator, you don't want to operate at high temperature. 01:10:59.330 --> 01:11:02.350 align:middle line:84% You can see here, the [? upper ?] one is actually 01:11:02.350 --> 01:11:04.480 align:middle line:84% pretty low temperature, except that you 01:11:04.480 --> 01:11:09.670 align:middle line:84% need a device converter that work by the power efficiency 01:11:09.670 --> 01:11:12.070 align:middle line:90% here. 01:11:12.070 --> 01:11:16.720 align:middle line:84% If you recall, the solar cell, [INAUDIBLE] 01:11:16.720 --> 01:11:19.420 align:middle line:84% sharpening [INAUDIBLE] paper, [INAUDIBLE] 01:11:19.420 --> 01:11:25.050 align:middle line:84% limit for single junction solar cell, silicon solar cell, 01:11:25.050 --> 01:11:27.313 align:middle line:84% the maximum efficiency is about 28%. 01:11:27.313 --> 01:11:29.912 align:middle line:90% 01:11:29.912 --> 01:11:31.190 align:middle line:90% Now look at this. 01:11:31.190 --> 01:11:32.540 align:middle line:90% Yeah, this is very good. 01:11:32.540 --> 01:11:35.920 align:middle line:90% 01:11:35.920 --> 01:11:46.320 align:middle line:84% And of course, solar cell is also all thermal energy. 01:11:46.320 --> 01:11:49.320 align:middle line:84% It is limited by this efficiency, 01:11:49.320 --> 01:11:52.780 align:middle line:84% power efficiency of whatever limit 01:11:52.780 --> 01:11:54.930 align:middle line:90% that we're discussing here. 01:11:54.930 --> 01:11:56.640 align:middle line:84% Except that the emission [INAUDIBLE]. 01:11:56.640 --> 01:11:58.650 align:middle line:90% So not this one, I'm sorry. 01:11:58.650 --> 01:12:02.910 align:middle line:84% The emission, solar cell do not have a re-emission problem. 01:12:02.910 --> 01:12:08.820 align:middle line:84% So it's a matter of the what's above the bandgap times the-- 01:12:08.820 --> 01:12:11.610 align:middle line:84% the current efficiency limit of solar cell 01:12:11.610 --> 01:12:18.480 align:middle line:84% is the solar cell is itself operating at low temperature. 01:12:18.480 --> 01:12:21.210 align:middle line:84% So the current efficiency limit is really 01:12:21.210 --> 01:12:25.440 align:middle line:84% from the sun temperature as an [INAUDIBLE]. 01:12:25.440 --> 01:12:28.110 align:middle line:84% And if you do-- it turns out that if you 01:12:28.110 --> 01:12:31.260 align:middle line:84% do infinite multi-junction solar cell, 01:12:31.260 --> 01:12:36.160 align:middle line:84% the maximum efficiency is still that 85%, same upper limit. 01:12:36.160 --> 01:12:43.492 align:middle line:90% 01:12:43.492 --> 01:12:46.090 align:middle line:84% So those were-- the previous discussion 01:12:46.090 --> 01:12:50.440 align:middle line:84% were done for the concentration in first one, one [? sun ?] 01:12:50.440 --> 01:12:51.340 align:middle line:90% condition. 01:12:51.340 --> 01:12:55.780 align:middle line:84% And you can add other concentrations and the-- 01:12:55.780 --> 01:12:58.540 align:middle line:90% use various kind of absorbers. 01:12:58.540 --> 01:13:02.440 align:middle line:90% And this is the-- 01:13:02.440 --> 01:13:08.410 align:middle line:84% we have a blackbody absorber, these different 01:13:08.410 --> 01:13:12.400 align:middle line:84% [? conservation ?] [INAUDIBLE] [? concentration. ?] 01:13:12.400 --> 01:13:17.050 align:middle line:84% And that's the temperature of operation here is 01:13:17.050 --> 01:13:20.020 align:middle line:90% the efficiency. 01:13:20.020 --> 01:13:27.730 align:middle line:84% And now you use a more realistic absorber. 01:13:27.730 --> 01:13:31.580 align:middle line:84% The blackbody is [INAUDIBLE] overall spectrum. 01:13:31.580 --> 01:13:35.170 align:middle line:84% Let's say here is a selective absorber. 01:13:35.170 --> 01:13:37.930 align:middle line:84% Let's say you get the higher efficiency. 01:13:37.930 --> 01:13:40.700 align:middle line:84% And if you compare these two, you also 01:13:40.700 --> 01:13:43.370 align:middle line:90% operate at higher temperature. 01:13:43.370 --> 01:13:46.380 align:middle line:84% So here you got to operate at a higher temperature. 01:13:46.380 --> 01:13:49.130 align:middle line:84% If you selectivity do it, you can 01:13:49.130 --> 01:13:50.720 align:middle line:90% push to a higher temperature. 01:13:50.720 --> 01:13:55.130 align:middle line:84% If your selectivity is not good, spectrum is not good, 01:13:55.130 --> 01:13:56.780 align:middle line:84% then the blackbody, you don't want 01:13:56.780 --> 01:13:57.800 align:middle line:90% to operate at high temperature. 01:13:57.800 --> 01:14:00.050 align:middle line:84% You want to operate the low temperature because you're 01:14:00.050 --> 01:14:01.280 align:middle line:90% losing too much heat. 01:14:01.280 --> 01:14:04.350 align:middle line:84% So the solar thermal energy is always 01:14:04.350 --> 01:14:06.650 align:middle line:84% the fight between the losing heat 01:14:06.650 --> 01:14:09.670 align:middle line:84% by radiation and the [INAUDIBLE], 01:14:09.670 --> 01:14:12.690 align:middle line:84% the thermal energy you want to operate 01:14:12.690 --> 01:14:15.500 align:middle line:84% at higher temperature, your surface 01:14:15.500 --> 01:14:19.700 align:middle line:84% you want to operate at higher temperature, so optimum there. 01:14:19.700 --> 01:14:23.720 align:middle line:84% And now, if you go back to the ideal absorber, 01:14:23.720 --> 01:14:29.330 align:middle line:84% ideal absorber means 1 and 0 selectivity spectrum, 01:14:29.330 --> 01:14:31.310 align:middle line:84% you push to higher and higher temperature 01:14:31.310 --> 01:14:33.450 align:middle line:84% depends on your concentration ratio. 01:14:33.450 --> 01:14:37.684 align:middle line:90% 01:14:37.684 --> 01:14:45.740 align:middle line:84% So those were generally [INAUDIBLE] 01:14:45.740 --> 01:14:47.970 align:middle line:90% I think the messages. 01:14:47.970 --> 01:14:51.900 align:middle line:84% If you can do good spectral control, 01:14:51.900 --> 01:14:54.840 align:middle line:84% you can get the high [INAUDIBLE]. 01:14:54.840 --> 01:14:57.510 align:middle line:84% So that's to say, spectral control 01:14:57.510 --> 01:15:00.360 align:middle line:90% is really a critical problem. 01:15:00.360 --> 01:15:03.390 align:middle line:84% And we're [? finding ?] out, doing 01:15:03.390 --> 01:15:07.360 align:middle line:84% Department of Energy Research Center, we have two parts. 01:15:07.360 --> 01:15:09.840 align:middle line:84% One is we look at the, for example, [INAUDIBLE]. 01:15:09.840 --> 01:15:14.040 align:middle line:84% The other is really look at the spectral control. 01:15:14.040 --> 01:15:19.290 align:middle line:84% And in fact, later on, we talk more to thermal [INAUDIBLE]. 01:15:19.290 --> 01:15:25.440 align:middle line:84% And you realize that you're transforming one difficulty 01:15:25.440 --> 01:15:27.840 align:middle line:90% into another difficulty. 01:15:27.840 --> 01:15:30.930 align:middle line:84% In solar cell, the difficulty is the single-junction cell 01:15:30.930 --> 01:15:33.990 align:middle line:90% is limited to sharp [INAUDIBLE]. 01:15:33.990 --> 01:15:37.570 align:middle line:84% So you try to do multi-junction cell, which people have reached 01:15:37.570 --> 01:15:41.080 align:middle line:90% about 41% three-junction. 01:15:41.080 --> 01:15:45.400 align:middle line:84% But say, infinite junction you can get to 85%. 01:15:45.400 --> 01:15:50.290 align:middle line:84% So but the growing material to more than three junction 01:15:50.290 --> 01:15:52.290 align:middle line:90% is very difficult. 01:15:52.290 --> 01:15:57.060 align:middle line:84% And now we transform one problem into one-- 01:15:57.060 --> 01:16:00.050 align:middle line:84% this difficulty into another difficulty. 01:16:00.050 --> 01:16:06.510 align:middle line:84% If I can have a selective surface, really ideal, that 01:16:06.510 --> 01:16:08.640 align:middle line:84% work at a high temperature, then I 01:16:08.640 --> 01:16:10.930 align:middle line:84% can [INAUDIBLE] get high efficiency, 01:16:10.930 --> 01:16:13.640 align:middle line:90% even with single junctions. 01:16:13.640 --> 01:16:20.960 align:middle line:84% So but of course, this has now a lot of engineering aspects. 01:16:20.960 --> 01:16:27.910 align:middle line:84% Because let's suppose, when I have this ideal surface, 01:16:27.910 --> 01:16:29.760 align:middle line:84% selective surface of absorptivity, 01:16:29.760 --> 01:16:32.450 align:middle line:84% emissivity, on the other side, that you can probably 01:16:32.450 --> 01:16:34.820 align:middle line:84% design a surface of really 0 emissions. 01:16:34.820 --> 01:16:37.520 align:middle line:84% So this side I will lose radiation. 01:16:37.520 --> 01:16:41.840 align:middle line:84% And also, you have to hold it somehow, 1,000 degree, 01:16:41.840 --> 01:16:44.960 align:middle line:84% 2,000 degree, you have to hold it. 01:16:44.960 --> 01:16:49.430 align:middle line:84% And of course, you can use, let's say, a suspension. 01:16:49.430 --> 01:16:52.040 align:middle line:84% You can use this thing called-- this is actually, 01:16:52.040 --> 01:16:57.920 align:middle line:84% if you do the solar in that, this is the one, and the one 01:16:57.920 --> 01:17:00.020 align:middle line:90% that I consider solar. 01:17:00.020 --> 01:17:05.320 align:middle line:84% If you do with a combustion chamber, 01:17:05.320 --> 01:17:07.970 align:middle line:84% it has to [? gas ?] contact [INAUDIBLE] 01:17:07.970 --> 01:17:12.430 align:middle line:90% or a very sturdy structure. 01:17:12.430 --> 01:17:15.110 align:middle line:84% At least in the case of the sun, what comes in, 01:17:15.110 --> 01:17:18.240 align:middle line:84% let's suppose this is a vacuum chamber. 01:17:18.240 --> 01:17:20.580 align:middle line:90% What comes in, then it goes-- 01:17:20.580 --> 01:17:23.430 align:middle line:90% photon can go through the glass. 01:17:23.430 --> 01:17:28.710 align:middle line:84% Today you have much less in terms of the complexity 01:17:28.710 --> 01:17:32.200 align:middle line:84% in dealing with the [? top ?] gas, the physical contact. 01:17:32.200 --> 01:17:34.880 align:middle line:90% I think you can use a really-- 01:17:34.880 --> 01:17:38.880 align:middle line:84% say, very small [? stream ?] to suspend your surface. 01:17:38.880 --> 01:17:42.180 align:middle line:84% So that's one advantage, that [? view, ?] 01:17:42.180 --> 01:17:46.830 align:middle line:84% which is probably better, they do the solar 01:17:46.830 --> 01:17:50.220 align:middle line:90% compared to thermal source. 01:17:50.220 --> 01:17:51.780 align:middle line:90% So here is the suspension. 01:17:51.780 --> 01:17:54.180 align:middle line:84% And of course, if you have suspension, 01:17:54.180 --> 01:17:56.340 align:middle line:90% then you have heat loss. 01:17:56.340 --> 01:18:01.770 align:middle line:84% You have to account for other heat loss, suspension, 01:18:01.770 --> 01:18:03.810 align:middle line:90% and other emission losses. 01:18:03.810 --> 01:18:08.800 align:middle line:84% And so it's a, say, then becomes a careful engineering problem. 01:18:08.800 --> 01:18:14.700 align:middle line:84% That's why at the end, now even you work on the [INAUDIBLE] 01:18:14.700 --> 01:18:17.920 align:middle line:84% thermophotovoltaic, you have to go back to basics on how 01:18:17.920 --> 01:18:20.380 align:middle line:84% the conduction, [? key ?] leakage through-- 01:18:20.380 --> 01:18:22.132 align:middle line:84% any [? key ?] leakage [INAUDIBLE]. 01:18:22.132 --> 01:18:25.150 align:middle line:90% 01:18:25.150 --> 01:18:29.860 align:middle line:84% --degree making factor for your system applications. 01:18:29.860 --> 01:18:31.950 align:middle line:90% Any questions?