WEBVTT 00:01.233 --> 00:06.073 RONALD SMITH: So last time, upstairs, we did this systems 00:06.067 --> 00:08.867 experiment where we had a tank of water. 00:08.867 --> 00:13.127 We tried to analyze it and its three components-- 00:13.133 --> 00:16.833 the reservoir, the input, and the output. 00:16.833 --> 00:20.473 We talked about things like steady state balance, 00:20.467 --> 00:25.827 transient response to changes in the input and the output. 00:25.833 --> 00:29.233 We derived a little mathematical relationship 00:29.233 --> 00:32.803 describing how the outflow depends on the 00:32.800 --> 00:34.600 depth of the water. 00:34.600 --> 00:37.300 We put those equations together, we came up with a 00:37.300 --> 00:41.230 prediction of what the equilibrium water level would 00:41.233 --> 00:45.003 be for various values of flow inputs. 00:45.000 --> 00:45.970 It worked out pretty well. 00:45.967 --> 00:47.967 We got fairly good quantitative 00:47.967 --> 00:48.827 agreement on that. 00:48.833 --> 00:50.373 Are there any questions on any of that? 00:53.400 --> 00:55.500 So that's basic system analysis. 00:55.500 --> 01:00.200 We're going to apply that idea today to the energy 01:00.200 --> 01:02.370 budget of the Earth. 01:02.367 --> 01:05.667 And we'll be applying it later in the course to other simple 01:05.667 --> 01:08.397 systems relating to the Earth. 01:08.400 --> 01:11.530 In this one, the input is going to 01:11.533 --> 01:13.273 be the solar radiation. 01:13.267 --> 01:17.297 Sometimes it's called insolation, with an o, not 01:17.300 --> 01:18.800 insulation, but insolation. 01:18.800 --> 01:22.700 That's the rate at which solar energy is approaching and then 01:22.700 --> 01:26.370 finally being absorbed by the Earth. 01:26.367 --> 01:30.367 The loss is going to be the infrared radiation to space. 01:30.367 --> 01:34.267 We'll talk about the laws that govern that today. 01:34.267 --> 01:38.727 And the heat storage will be not the whole Earth, because 01:38.733 --> 01:41.833 it takes too long for heat to conduct in and 01:41.833 --> 01:43.433 out of a whole Earth-- 01:43.433 --> 01:46.103 millions, if not hundreds of millions of years. 01:46.100 --> 01:49.530 So really the system we're talking about is just the skin 01:49.533 --> 01:53.403 of the Earth, the first few meters are in the ocean, the 01:53.400 --> 01:56.200 first five kilometers or so. 01:56.200 --> 02:00.730 The part that is responsive to the heat that's being put in 02:00.733 --> 02:01.673 and taken out. 02:01.667 --> 02:05.027 So we will have a reservoir. 02:05.033 --> 02:06.603 We'll have inputs, we'll have outputs. 02:06.600 --> 02:09.600 Now, there's one input we're going to neglect. 02:09.600 --> 02:12.500 There is some heat in the deep interior of the Earth that 02:12.500 --> 02:17.830 comes from the decay of uranium that makes the 02:17.833 --> 02:19.533 interior of the Earth quite hot. 02:19.533 --> 02:23.903 And that heat can leak out to the surface of the Earth. 02:23.900 --> 02:27.130 That's called geothermal heat. 02:27.133 --> 02:30.333 That can be important for certain subjects, but for 02:30.333 --> 02:33.173 climate studies that is negligible. 02:33.167 --> 02:37.927 That's only a few-- a tiny fraction of a watt per square 02:37.933 --> 02:41.373 meter that reaches the Earth's surface from the interior. 02:41.367 --> 02:43.827 And we'll see, these fluxes are orders of 02:43.833 --> 02:45.233 magnitude larger than that. 02:45.233 --> 02:47.503 So we're going to neglect geothermal radiation-- 02:50.633 --> 02:52.073 geothermal heat from the interior. 02:52.067 --> 02:55.697 We're also going to assume that the Earth has a uniform 02:55.700 --> 02:57.400 temperature. 02:57.400 --> 03:00.130 That's not a great assumption, but in the beginning we're 03:00.133 --> 03:03.873 going to just try to find a formula that describes the 03:03.867 --> 03:06.367 average temperature of the Earth. 03:06.367 --> 03:09.427 Later on we'll be dealing with the pole to equator 03:09.433 --> 03:10.373 temperature gradients. 03:10.367 --> 03:12.467 But for now, the Earth will have a 03:12.467 --> 03:15.127 single temperature today. 03:15.133 --> 03:18.803 And of course, we're going to assume steady state. 03:18.800 --> 03:21.070 So we're going to use the kind of formulation we did with the 03:21.067 --> 03:24.197 water tank where we understand the inputs and outputs. 03:24.200 --> 03:26.770 Sometimes they'll be out of balance, but we're going to 03:26.767 --> 03:29.597 make the assumption they'll be in balance and use that to 03:29.600 --> 03:34.370 solve for certain properties of the system. 03:34.367 --> 03:39.197 So that's the goal today, but before I do that I've got to 03:39.200 --> 03:43.070 talk to you about the fundamental laws of radiation. 03:53.733 --> 03:55.833 Now, I mentioned this the other day when we were talking 03:55.833 --> 04:00.803 about the stratosphere and the thermosphere. 04:00.800 --> 04:05.800 If you have an object like anything in this room, or the 04:05.800 --> 04:15.800 Sun, or any object at all, and you plot the emitted radiation 04:15.800 --> 04:18.330 as a function of wavelengths-- 04:18.333 --> 04:22.273 I'll use the Greek letter lambda to represent 04:22.267 --> 04:24.197 wavelength. 04:24.200 --> 04:33.600 That's the distance from the crest to crest of the wave. It 04:33.600 --> 04:34.930 looks something like this. 04:34.933 --> 04:36.673 I'm going to draw a bunch of curves for different 04:36.667 --> 04:37.897 temperatures. 04:46.700 --> 04:48.270 These are called black body curves. 04:55.133 --> 04:56.903 It's also referred to sometimes 04:56.900 --> 04:58.170 as the Plank Function. 05:01.600 --> 05:05.930 So if you've got a book on physics, look up black body or 05:05.933 --> 05:09.803 look up the Plank Function and read what it says about this. 05:09.800 --> 05:13.770 Now, this would be for a cooler temperature. 05:13.767 --> 05:17.697 This would be for some intermediate temperature. 05:17.700 --> 05:19.230 And this would be for a high temperature. 05:22.533 --> 05:25.803 So for example, this might be the surface of the Earth with 05:25.800 --> 05:28.470 the temperature at 288 Kelvin. 05:28.467 --> 05:31.327 This might be for the surface of the Sun with the 05:31.333 --> 05:34.703 temperature of 6,000 degrees Kelvin. 05:34.700 --> 05:36.000 Notice two things about this. 05:36.000 --> 05:39.630 When you make the temperature greater, of course, you're 05:39.633 --> 05:42.273 increasing the amount of radiation that's coming out at 05:42.267 --> 05:45.527 every wavelength. 05:45.533 --> 05:52.173 Every wavelength the intensity of the emitted radiation 05:52.167 --> 05:55.127 increases with temperature. 05:55.133 --> 05:57.433 As does the integral under the curve. 05:57.433 --> 06:01.303 The total sum of all the radiation is the area under 06:01.300 --> 06:02.670 each of these curves. 06:02.667 --> 06:05.827 That total increases as well. 06:05.833 --> 06:09.833 Furthermore, notice that the peak of the curve shifts with 06:09.833 --> 06:11.003 temperature. 06:11.000 --> 06:14.670 It's there for the cooler temperature, there for the 06:14.667 --> 06:17.267 intermediate temperature, and there for the higher 06:17.267 --> 06:18.197 temperature. 06:18.200 --> 06:23.830 So the color, if you like, the color of the radiation changes 06:23.833 --> 06:28.033 as the temperature of the object changes. 06:28.033 --> 06:32.903 Now, there are names for these particular aspects of the 06:32.900 --> 06:34.300 radiation law. 06:34.300 --> 06:37.900 The shift in the peak is referred to as Wien's law. 06:41.967 --> 06:44.897 And it's given as by the following formula. 06:44.900 --> 06:50.070 Lambda max is equal to a constant divided by the 06:50.067 --> 06:51.967 temperature expressed in Kelvins. 06:54.700 --> 07:00.130 And this lambda is going to be in units of microns. 07:00.133 --> 07:03.703 A micron is 10 to the minus 6 meters. 07:12.933 --> 07:17.203 Before I compute an example of that, let me just remind you 07:17.200 --> 07:19.370 of the electromagnetic spectrum for a second. 07:29.100 --> 07:31.330 Wavelength increasing to the right. 07:31.333 --> 07:33.733 There's a range we call the visible part of the spectrum 07:33.733 --> 07:39.003 that runs from 0.4 to 0.7 microns. 07:39.000 --> 07:42.930 The human eye is sensitive to those waves. 07:42.933 --> 07:46.503 Then, as we spoke about last time, the ultraviolet is over 07:46.500 --> 07:49.800 here, and the infrared is over there. 07:49.800 --> 07:57.730 Microwave is further over, and then radio waves are further 07:57.733 --> 08:00.533 over to the right, and X-rays are here. 08:05.333 --> 08:08.473 So just to remind you, you might want to remember 0.4 and 08:08.467 --> 08:12.767 0.7 as the range of the visible part of the spectrum. 08:12.767 --> 08:14.797 Now, let's do a calculation here. 08:14.800 --> 08:18.300 For the Sun, the surface of the Sun is 08:18.300 --> 08:23.030 approximately 6,000 Kelvin. 08:23.033 --> 08:27.473 If I plug into that formula to get lambda max, it's going to 08:27.467 --> 08:32.327 be 2897 over 6,000. 08:32.333 --> 08:37.573 That's approximately 0.48 microns. 08:37.567 --> 08:42.397 I'll write it here as mu m, micrometers. 08:42.400 --> 08:50.600 And that is going to lie right about there, roughly in the 08:50.600 --> 08:54.130 middle of the visible range of the spectrum. 08:54.133 --> 08:56.333 That's kind of interesting, and you might want to think is 08:56.333 --> 08:59.573 that just an accident? 08:59.567 --> 09:01.167 I'll say more about that later. 09:01.167 --> 09:02.927 But make a little question mark there. 09:02.933 --> 09:04.473 Why does it happen-- yeah? 09:04.467 --> 09:06.427 STUDENT: What is the 6,000 again? 09:06.433 --> 09:10.133 PROFESSOR: The surface temperature of the Sun. 09:10.133 --> 09:11.273 Is it just an accident? 09:11.267 --> 09:13.267 That's my question to you for thought. 09:13.267 --> 09:17.067 Is it just an accident that the Sun's peak radiation 09:17.067 --> 09:23.297 happens to fall in the human range of high sensitivity? 09:23.300 --> 09:24.730 Interesting question. 09:24.733 --> 09:26.433 Let's do the same thing for Earth. 09:29.267 --> 09:33.767 Typical temperature for Earth is about 288 Kelvin. 09:33.767 --> 09:39.967 Lambda max then is 2897 over 288. 09:39.967 --> 09:40.967 That's an easy one to do. 09:40.967 --> 09:44.167 That's approximately 10 microns. 09:44.167 --> 09:47.427 That is way out-- 09:47.433 --> 09:49.203 no, that's in the infrared. 09:49.200 --> 09:51.370 Let me not exaggerate this. 09:51.367 --> 09:52.767 That is somewhere-- 09:52.767 --> 09:54.697 this is kind of a log scale I've got here. 09:54.700 --> 09:58.100 That's in the infrared part of the spectrum, the so-called 09:58.100 --> 09:59.400 thermal infrared. 09:59.400 --> 10:00.130 Question? 10:00.133 --> 10:01.103 STUDENT: Is that the surface temperature? 10:01.100 --> 10:02.500 PROFESSOR: This is the surface temperature of 10:02.500 --> 10:03.900 the Earth, 288 Kelvin. 10:03.900 --> 10:05.070 We've used it before. 10:05.067 --> 10:06.867 It's 15 degrees Celsius-- 10:06.867 --> 10:08.327 it's like the temperature in this room. 10:08.333 --> 10:11.403 Maybe we're a few degrees warmer than that, but this is 10:11.400 --> 10:15.700 a typical Earth-type temperature. 10:15.700 --> 10:17.670 So this makes a big difference. 10:17.667 --> 10:21.597 This means that the radiation coming from the Sun is in one 10:21.600 --> 10:22.900 wavelength. 10:22.900 --> 10:25.800 And the radiation emitted by the Earth is quite a different 10:25.800 --> 10:26.970 wavelength altogether. 10:26.967 --> 10:27.997 So remember that. 10:28.000 --> 10:30.730 That's going to be a key for understanding 10:30.733 --> 10:33.873 the greenhouse effect. 10:33.867 --> 10:37.727 The other law that arises from this is called the 10:37.733 --> 10:39.003 Stefan-Boltzmann Law. 10:49.767 --> 10:54.727 And it relates to the total power, the area under the 10:54.733 --> 11:03.303 curve, power per unit area of an object-- 11:06.000 --> 11:08.730 an object emitting-- 11:08.733 --> 11:11.473 is given by a constant-- 11:11.467 --> 11:14.867 I'll use a Greek letter sigma for that-- 11:14.867 --> 11:17.567 times the temperature to the fourth power. 11:17.567 --> 11:20.627 This constant is the Stefan-Boltzmann constant. 11:23.433 --> 11:27.173 It's derived in physics classes from first principles. 11:27.167 --> 11:38.097 And the value is 5.735 times 10 to the minus 8 watts per 11:38.100 --> 11:43.230 meter squared per Kelvins to the fourth power. 11:43.233 --> 11:44.433 You could look it up. 11:44.433 --> 11:45.473 You can Google it. 11:45.467 --> 11:48.167 If you ever forget it, you can find it very easily. 11:48.167 --> 11:50.367 It's a very famous physical constant, the 11:50.367 --> 11:52.527 Stefan-Boltzmann constant. 11:52.533 --> 11:55.133 It will never be any problem with knowing 11:55.133 --> 11:56.403 what that value is. 11:58.833 --> 12:02.233 Now before we go any further, let's see if these two laws 12:02.233 --> 12:03.073 make any sense. 12:03.067 --> 12:06.697 The Stefan-Boltzmann law that says that the total power goes 12:06.700 --> 12:09.570 like the fourth power of the temperature. 12:09.567 --> 12:13.527 If I were to double the temperature, the power would 12:13.533 --> 12:19.033 go up by a factor of not two, not four, not eight, but 16. 12:19.033 --> 12:23.503 So you'd increase the power by a factor of 16 by doubling the 12:23.500 --> 12:24.700 temperature. 12:24.700 --> 12:28.630 Very powerful sensitivity to temperature. 12:28.633 --> 12:31.133 And then Wein's law that says that the 12:31.133 --> 12:32.903 wavelength goes inversely. 12:32.900 --> 12:37.030 The wavelength of maximum radiation goes inversely with 12:37.033 --> 12:38.603 the temperature. 12:38.600 --> 12:41.430 The higher the temperature, the shorter is the wavelength 12:41.433 --> 12:43.633 that's being strongly emitted. 12:43.633 --> 12:49.203 Now, I've got this little light bulb over here. 12:49.200 --> 12:50.700 And I'm just going to hit some lights. 12:54.533 --> 12:58.533 I've got a variable transformer, and I've got a 12:58.533 --> 13:03.203 light bulb that has no frost on the glass, so you can see 13:03.200 --> 13:04.500 the filament in there. 13:04.500 --> 13:07.600 I can change the temperature of the filament by how much 13:07.600 --> 13:09.970 electrical current I pass through it. 13:09.967 --> 13:14.397 So when, of course, it's at room temperature like that, 13:14.400 --> 13:16.770 it's radiating a little bit, but it's radiating at 13:16.767 --> 13:19.567 wavelengths in the infrared for which 13:19.567 --> 13:22.567 the eye is not sensitive. 13:22.567 --> 13:26.267 Then as I gradually increase the temperature, you can begin 13:26.267 --> 13:27.497 to see it there. 13:27.500 --> 13:29.400 There's a little bit now in the visible part of the 13:29.400 --> 13:34.600 spectrum, but it's red. 13:34.600 --> 13:35.600 Remember that diagram-- 13:35.600 --> 13:36.600 I should have put-- 13:36.600 --> 13:39.470 let me just back up and get that up here for a second. 13:39.467 --> 13:47.327 On this end of the spectrum is the red, and this is the blue. 13:47.333 --> 13:51.233 So originally the wavelength being emitted is here, now it 13:51.233 --> 13:52.433 begins to move over. 13:52.433 --> 13:56.103 As I increase the temperature you begin to see some red. 13:56.100 --> 13:58.630 Then as I continue to move it over, at some point you'll be 13:58.633 --> 14:01.333 seeing equal amounts in all of the-- 14:05.633 --> 14:06.933 in all the parts of the visible spectrum. 14:06.933 --> 14:10.433 So there it's becoming white. 14:10.433 --> 14:15.173 Because that peak has moved over, centered on the visible 14:15.167 --> 14:16.327 part of the spectrum. 14:16.333 --> 14:18.173 Notice it's also very much brighter. 14:18.167 --> 14:22.927 So with this one little device, we are looking at both 14:22.933 --> 14:25.073 the Stefan-Boltzmann law and Wien's law. 14:25.067 --> 14:28.967 They're both illustrated by this little experiment. 14:28.967 --> 14:31.567 Any questions on that? 14:31.567 --> 14:33.627 So all I'm doing is changing the temperature of the 14:33.633 --> 14:37.103 filament and what I'm seeing is an increase in power and a 14:37.100 --> 14:41.730 shift in the wavelength from the red into the center of the 14:41.733 --> 14:43.033 visible part of the spectrum. 14:45.667 --> 14:46.327 Yes, question. 14:46.333 --> 14:49.903 STUDENT: Why does it appear to turn white when it does, 14:49.900 --> 14:51.930 directly after going to yellow? 14:51.933 --> 14:55.933 PROFESSOR: Well remember, think of this 14:55.933 --> 14:59.873 peak sliding over. 14:59.867 --> 15:03.267 So first you see only the red, then you begin to see some red 15:03.267 --> 15:05.397 and some green is in the middle. 15:05.400 --> 15:07.100 That's going to give you yellow when you get the red 15:07.100 --> 15:08.230 and the green together. 15:08.233 --> 15:12.073 Then finally, when you get an equal set of all red, green 15:12.067 --> 15:13.467 and blue, that looks white. 15:13.467 --> 15:16.567 So white light, as Newton figured out, is the sum, an 15:16.567 --> 15:19.567 equal sum of all the visible parts of the spectrum. 15:19.567 --> 15:22.867 So we're just seeing that happen as we shift that peak 15:22.867 --> 15:27.627 over and center it on the visible part of the spectrum. 15:27.633 --> 15:28.033 Yes. 15:28.033 --> 15:28.633 STUDENT: Does the Stefan-Boltzmann Law give 15:28.633 --> 15:28.773 brightness or power? 15:28.767 --> 15:30.027 What is power? 15:33.067 --> 15:35.767 PROFESSOR: Power is the emitted power, it's the power 15:35.767 --> 15:36.967 in that radiation. 15:36.967 --> 15:41.097 It's the rate at which energy is being sent from the object 15:41.100 --> 15:44.500 out into space with electromagnetic radiation. 15:44.500 --> 15:47.470 You can think of as brightness if you like, but brightness 15:47.467 --> 15:50.227 usually refers to how something is perceived by the 15:50.233 --> 15:53.233 human eye, and that's not our context here. 15:53.233 --> 15:55.533 Our context here is an energy budget. 15:55.533 --> 15:58.273 How much energy is being lost. So I'm going to use the word 15:58.267 --> 16:02.527 power there instead of brightness. 16:02.533 --> 16:05.803 Anything else on this? 16:05.800 --> 16:07.500 Well now I think we're ready to do-- 16:10.200 --> 16:16.370 oh, well there is one other thing maybe we should do while 16:16.367 --> 16:18.627 we remember. 16:18.633 --> 16:22.003 Some of you may not even believe me when I tell you 16:22.000 --> 16:25.130 that all the objects in this room are emitting. 16:25.133 --> 16:28.433 They're just not emitting at a wavelength that the 16:28.433 --> 16:29.403 human eye can see. 16:29.400 --> 16:30.500 What do you see? 16:30.500 --> 16:34.470 You see light reflecting off various objects. 16:34.467 --> 16:36.467 That's not what I'm talking about here. 16:36.467 --> 16:39.627 Objects yes, objects can reflect light coming from 16:39.633 --> 16:41.133 light bulbs and so on. 16:41.133 --> 16:44.233 But I'm talking about the emission of radiation. 16:44.233 --> 16:47.633 That's a different process than reflection. 16:47.633 --> 16:50.733 So this is just an infrared thermometer. 16:50.733 --> 16:53.303 It's not much different than the one you use to take your 16:53.300 --> 16:56.300 own temperature or the temperature of a child. 16:56.300 --> 17:00.130 It measures the temperature of an object by measuring the 17:00.133 --> 17:03.533 intensity of the radiation that's being emitted. 17:03.533 --> 17:05.603 So it measures emitted radiation. 17:05.600 --> 17:08.370 Then from this curve, it figures out what the 17:08.367 --> 17:10.527 temperature must have been in order to 17:10.533 --> 17:13.273 radiate that intensely. 17:13.267 --> 17:16.927 So when I look at this table-- 17:16.933 --> 17:18.703 by the way, I have to warn you of something. 17:18.700 --> 17:21.570 There is a little laser in there. 17:21.567 --> 17:22.927 See the red dot? 17:22.933 --> 17:25.703 But that's just to help you aim it. 17:25.700 --> 17:29.000 It doesn't play any role in the measurement whatsoever. 17:29.000 --> 17:31.830 It just aims so you know what object it is that 17:31.833 --> 17:33.173 you're aiming at. 17:33.167 --> 17:35.397 But please don't aim this in your eye. 17:35.400 --> 17:40.400 So anyway, the temperature of this table is 24 Celsius. 17:40.400 --> 17:44.630 Temperature of my hand is 30 Celsius. 17:44.633 --> 17:45.333 Try it yourself. 17:45.333 --> 17:46.933 I'll pass that around. 17:46.933 --> 17:50.303 Anyway, that little gadget is a perfect illustration of the 17:50.300 --> 17:52.830 physical process I'm talking about. 17:52.833 --> 17:57.033 It's an object emitting radiation in proportion to its 17:57.033 --> 17:58.273 temperature-- 17:58.267 --> 18:00.427 in proportion to its temperature. 18:00.433 --> 18:05.103 Higher temperature, more radiation is being emitted. 18:08.533 --> 18:12.403 Now I think we're ready to do the main part of the 18:12.400 --> 18:13.630 derivation. 18:33.900 --> 18:37.770 I'm going to re-draw the Earth here a little smaller. 18:37.767 --> 18:41.197 We're going to assume that the Sun's radiation-- 18:41.200 --> 18:44.530 radiant beams are coming in parallel to each other. 18:44.533 --> 18:48.803 Because the Sun is so far away from us, we can assume that 18:48.800 --> 18:51.800 those rays are actually parallel by the time they 18:51.800 --> 18:52.930 reach the Earth. 18:52.933 --> 18:56.903 Therefore, they're going to hit the Earth and cast a 18:56.900 --> 19:06.700 shadow out into outer space behind the Earth. 19:06.700 --> 19:10.330 The radiation that's missing there is going to be the 19:10.333 --> 19:13.073 radiation that hits the Earth. 19:13.067 --> 19:15.867 Now, the reason I'm saying it that way is that you might be 19:15.867 --> 19:18.697 a little bit confused because this Earth's surface is a 19:18.700 --> 19:22.100 sphere, and some of the radiation is hitting it in a 19:22.100 --> 19:24.900 normal direction, some of it is hitting it 19:24.900 --> 19:26.830 in a oblique direction. 19:26.833 --> 19:28.603 For the moment, I don't care about that. 19:28.600 --> 19:32.130 I just want to know the total amount of radiation that hits 19:32.133 --> 19:34.573 the object independent of where it hits and 19:34.567 --> 19:36.167 what angle it hits. 19:36.167 --> 19:40.867 The easiest way to do that is just to imagine that the Earth 19:40.867 --> 19:45.127 is casting a shadow and has removed that amount of 19:45.133 --> 19:47.603 radiation from the beam. 19:47.600 --> 19:55.000 So the solar constant, the intensity of the radiation 19:55.000 --> 19:59.470 from the Sun at the orbital position of the Earth is about 19:59.467 --> 20:04.397 1,380 watts per square meter. 20:04.400 --> 20:07.630 In other words, if you go outside the atmosphere facing 20:07.633 --> 20:13.803 the Sun and draw a square meter, there's 1,380 watts of 20:13.800 --> 20:17.300 radiant energy passing through that square meter. 20:17.300 --> 20:19.870 If you had two square meters, it would be twice that value. 20:19.867 --> 20:23.727 So that's on a per unit area basis. 20:23.733 --> 20:26.903 The area of this shadow then is just a circle. 20:26.900 --> 20:33.070 It's pi r squared where r is the radius of the planet. 20:36.367 --> 20:47.867 So the intercepted radiation is given by the product of S 20:47.867 --> 20:49.397 pi r squared. 20:49.400 --> 20:52.130 S is a solar constant, pi r squared is 20:52.133 --> 20:55.673 the intercepted area. 20:55.667 --> 20:58.627 I want to illustrate that for a second. 20:58.633 --> 21:00.373 I'm going to hit the lights again here. 21:04.667 --> 21:09.397 I just have a source of light that's nearly parallel and I 21:09.400 --> 21:12.530 have my globe here. 21:12.533 --> 21:16.133 Now the Earth is spinning on its axis of course, and its 21:16.133 --> 21:19.003 tilt may change with the seasons, but basically it's 21:19.000 --> 21:21.970 casting a shadow as you see there. 21:21.967 --> 21:27.427 That shadow is just related to the projected area of this 21:27.433 --> 21:30.803 sphere, which is pi r squared, the area of a circle. 21:30.800 --> 21:33.870 So that's all I've done here is just to compute the total 21:33.867 --> 21:36.567 radiation hitting that globe by using the idea 21:36.567 --> 21:39.927 of casting a shadow. 21:39.933 --> 21:43.233 Questions on that? 21:43.233 --> 21:46.703 Pretty simple idea. 21:46.700 --> 21:51.670 Now, some of that radiation, however, 21:51.667 --> 21:52.927 is going to be reflected. 21:56.967 --> 22:02.067 And we define here something called the albedo. 22:02.067 --> 22:04.927 Albedo is the average reflectivity of a planet. 22:16.700 --> 22:19.370 It can be expressed as a decimal or as a percent. 22:22.067 --> 22:26.367 I'll give you a number for Earth. 22:26.367 --> 22:31.927 For planet Earth the albedo is approximately 0.33, or you 22:31.933 --> 22:33.503 could call that 33%. 22:33.500 --> 22:37.400 Approximately 33% of the radiation that hits the Earth 22:37.400 --> 22:39.570 reflects off. 22:39.567 --> 22:41.997 And because that heat then doesn't really enter the 22:42.000 --> 22:46.800 Earth, doesn't really add energy to the Earth, we're 22:46.800 --> 22:47.700 going to drop that off. 22:47.700 --> 22:51.130 So that was the intercepted radiation. 22:51.133 --> 23:08.003 The absorbed radiation then is S pi r squared times 1 minus 23:08.000 --> 23:09.270 the albedo. 23:11.000 --> 23:18.600 If 33% is reflected, well then, 67% is absorbed. 23:18.600 --> 23:20.870 That's the 1 minus the albedo. 23:20.867 --> 23:22.097 It's the other part. 23:24.700 --> 23:30.170 The amount reflected is S pi r squared A, and the part 23:30.167 --> 23:34.127 absorbed is S pi r squared 1 minus A. So we've just 23:34.133 --> 23:40.333 partitioned that radiation, the part that is absorbed and 23:40.333 --> 23:43.403 the part that is reflected. 23:43.400 --> 23:46.700 Now, let's try to compute what the emitted radiation is. 23:53.933 --> 23:55.903 We're going to assume that the surface of the earth is a 23:55.900 --> 23:58.000 black body. 23:58.000 --> 24:02.170 It emits according to the Stefan-Boltzmann law. 24:02.167 --> 24:05.067 So we have to get the area-- 24:05.067 --> 24:07.027 remember, this is per unit area-- 24:07.033 --> 24:10.933 we need to find the area that is emitting. 24:10.933 --> 24:14.773 The area that is emitting is not the 24:14.767 --> 24:16.897 projected area of the sphere. 24:16.900 --> 24:21.030 It's the actual area of a sphere. 24:21.033 --> 24:25.633 What is the expression for the surface area of a sphere? 24:25.633 --> 24:27.233 Anybody remember? 24:27.233 --> 24:28.503 STUDENT: 4 pi r squared. 24:31.533 --> 24:33.373 PROFESSOR: 4 pi r squared, right. 24:33.367 --> 24:41.827 So the area we're talking about here is 4 pi r squared, 24:41.833 --> 24:46.973 and so the emitted radiation then is going to be 4 pi r 24:46.967 --> 24:53.027 squared times sigma times T to the fourth using the 24:53.033 --> 24:54.303 Stefan-Boltzmann law. 25:01.033 --> 25:03.103 Questions so far? 25:03.100 --> 25:03.600 Yes. 25:03.600 --> 25:07.300 STUDENT: For the surface area thing, we're including the 25:07.300 --> 25:09.170 entire Earth, even though the Sun's only 25:09.167 --> 25:10.227 shining on half of it? 25:10.233 --> 25:11.273 PROFESSOR: That's right. 25:11.267 --> 25:11.667 That's right. 25:11.667 --> 25:15.527 Remember, I've assumed here that the Earth has a uniform 25:15.533 --> 25:19.103 temperature, and since the emission depends only on the 25:19.100 --> 25:23.300 temperature, we're going to use the entire 25:23.300 --> 25:25.530 surface of the Earth. 25:25.533 --> 25:29.703 After all, even in the real world, when expressed in 25:29.700 --> 25:33.970 Kelvins, that temperature is not so different. 25:33.967 --> 25:40.667 This might be 310 Kelvin, this might be 250 Kelvin, but out 25:40.667 --> 25:43.367 of a range of 300, so that's not a huge difference. 25:43.367 --> 25:45.227 So this is not a huge problem. 25:45.233 --> 25:47.933 It's not great, but it's not a huge problem, the assumption 25:47.933 --> 25:51.003 of uniform temperature. 25:51.000 --> 25:53.530 Well, I think you know what I'm going to do now because of 25:53.533 --> 25:57.403 what I did in the tank experiment. 25:57.400 --> 26:03.670 I have laws that govern the input and the output, and I'm 26:03.667 --> 26:06.427 going to assume steady state and see what kind of a-- how 26:06.433 --> 26:09.073 does a system come into equilibrium? 26:09.067 --> 26:11.567 So I'm making the steady state assumption. 26:15.600 --> 26:21.400 Simply, all I have to do is balance the emitted radiation, 26:21.400 --> 26:30.900 which has units, by the way, of watts with the intercepted 26:30.900 --> 26:36.000 or the absorbed radiation, which has units of watts. 26:36.000 --> 26:37.570 So I will simply equate those two. 26:37.567 --> 26:42.297 I'm going to write S pi r squared 1 minus the albedo is 26:42.300 --> 26:47.200 now equal to, this is the statement of steady state, 4 26:47.200 --> 26:53.800 pi r squared sigma T to the fourth. 26:53.800 --> 26:57.330 That's the profound and very useful step. 27:01.933 --> 27:05.533 And I could then go the next step and solve mathematically 27:05.533 --> 27:07.103 for the temperature of the planet. 27:07.100 --> 27:08.970 So let me do that. 27:08.967 --> 27:12.197 First of all, notice that the pi r squares are going to 27:12.200 --> 27:16.000 cancel out from both sides of the equation. 27:16.000 --> 27:19.500 In other words, the result is not going to depend on the 27:19.500 --> 27:20.770 radius of the planet. 27:20.767 --> 27:21.397 Why is that? 27:21.400 --> 27:25.700 Well, the larger the planet is, the more radiation it 27:25.700 --> 27:29.330 receives from the Sun, but the more effectively 27:29.333 --> 27:31.473 it radiates to space. 27:31.467 --> 27:34.227 And those two things exactly cancel out. 27:34.233 --> 27:38.903 So there's no direct impact of the size of the planet. 27:38.900 --> 27:42.170 Notice that four remains, however. 27:42.167 --> 27:44.827 That important difference between the projected area of 27:44.833 --> 27:48.873 a sphere and the surface area of the sphere, that stays in 27:48.867 --> 27:50.127 our calculation. 27:52.133 --> 27:55.333 Now let me bring T to the fourth over here on the 27:55.333 --> 27:56.133 left-hand side. 27:56.133 --> 28:03.733 That's going to be S times 1 minus albedo over 4 sigma. 28:03.733 --> 28:06.373 Have I done that right? 28:06.367 --> 28:08.797 Divide through by 4 sigma. 28:08.800 --> 28:12.500 Then the final step would be to take the fourth root of 28:12.500 --> 28:13.230 that equation. 28:13.233 --> 28:18.303 So I'm going to write it as T equals bracket 1 minus the 28:18.300 --> 28:24.000 albedo over 4 sigma to the 1/4 power. 28:28.433 --> 28:33.333 That is a prediction based on some simple laws of physics 28:33.333 --> 28:37.203 for how hot each temperature in the solar-- each planet in 28:37.200 --> 28:39.470 the solar system will be. 28:39.467 --> 28:44.267 You need to know the solar constant for that planet, and 28:44.267 --> 28:47.467 of course, the further away from the Sun you are, the 28:47.467 --> 28:50.097 smaller will be that value. 28:50.100 --> 28:54.070 You need to know the albedo of the planet, how much radiation 28:54.067 --> 28:56.627 does it reflect. 28:56.633 --> 28:59.373 And then you need to know the Stefan-Boltzmann constant, but 28:59.367 --> 29:02.767 that's a universal constant so that doesn't change from 29:02.767 --> 29:05.397 planet to planet. 29:05.400 --> 29:07.430 STUDENT: And the sigma is the Stefan-Boltzmann-- 29:10.967 --> 29:12.727 PROFESSOR: So let's put some numbers in here for Earth. 29:17.900 --> 29:20.300 What am I using for solar constant? 29:20.300 --> 29:24.670 1,380. 29:24.667 --> 29:42.867 The albedo for Earth is 0.33. 29:42.867 --> 29:44.297 This is a formula for which you're going to want 29:44.300 --> 29:46.100 to check the units. 29:46.100 --> 29:48.270 I haven't put the units up here, but you should do that 29:48.267 --> 29:50.367 to be sure all the units are going to work out. 29:50.367 --> 29:52.227 That should be just in Kelvins. 29:52.233 --> 29:57.503 So when you do all the unit crossings out, you should get 29:57.500 --> 29:59.000 something just in units of Kelvin. 29:59.000 --> 30:03.970 Leave an inch in your notes to check on that. 30:03.967 --> 30:11.397 I worked this out and that's about 252 Kelvins, predicted 30:11.400 --> 30:13.030 temperature for Earth. 30:16.233 --> 30:18.573 Questions on that calculation? 30:18.567 --> 30:22.797 Remember all the assumptions that went into it. 30:22.800 --> 30:25.800 These, as well as assuming that the Earth emits like a 30:25.800 --> 30:28.900 black body, because we used that. 30:34.200 --> 30:40.870 Now, if you convert that to Celsius, that's minus 21 30:40.867 --> 30:44.067 degrees Celsius. 30:44.067 --> 30:46.167 That's a little too cold, right? 30:46.167 --> 30:51.027 Remember, the actual temperature for Earth is 30:51.033 --> 30:55.503 something around 288 Kelvin, which is 30:55.500 --> 31:01.400 about 15 degrees Celsius. 31:01.400 --> 31:06.870 Now if you look at this in the Celsius-- in the Kelvin scale, 31:06.867 --> 31:13.697 252 versus 288, that seems like a pretty good estimate. 31:13.700 --> 31:18.130 It's only off by 10% or 15%, something like that. 31:18.133 --> 31:22.173 But if you look at it in terms of Celsius, it looks like a 31:22.167 --> 31:25.397 bad approximation. 31:25.400 --> 31:26.070 Why is that? 31:26.067 --> 31:28.397 Because remember, the Celsius scale-- 31:28.400 --> 31:31.000 zero on the Celsius scale is based at the 31:31.000 --> 31:34.370 freezing point for water. 31:34.367 --> 31:38.397 Whether water is frozen or not is a big deal for us on Earth. 31:38.400 --> 31:44.070 So this prediction with the assumptions I made indicates 31:44.067 --> 31:46.767 the earth would be in a permanently frozen state. 31:46.767 --> 31:49.867 All the water on it would be frozen, whereas this would say 31:49.867 --> 31:51.797 most of the water's going to be in the liquid state. 31:51.800 --> 31:55.070 So it's a big deal to think of it in terms of Celsius or in 31:55.067 --> 31:58.997 terms of water, but it's not such a bad approximation if 31:59.000 --> 32:02.700 you think of it in terms of absolute temperature. 32:02.700 --> 32:05.030 Now what do you think is the reason for the error? 32:05.033 --> 32:08.273 Where have I gone wrong with this calculation? 32:08.267 --> 32:09.527 Anybody in the back? 32:11.967 --> 32:12.467 Yeah. 32:12.467 --> 32:13.697 STUDENT: You're assuming no geothermal heat? 32:16.300 --> 32:16.930 PROFESSOR: No. 32:16.933 --> 32:20.733 I did make that assumption, but it turns out that that's a 32:20.733 --> 32:21.903 very good assumption. 32:21.900 --> 32:23.400 So that's not the problem. 32:23.400 --> 32:23.830 Yes. 32:23.833 --> 32:25.103 STUDENT: Are you assuming that it's like a black body? 32:27.600 --> 32:28.900 PROFESSOR: Yeah. 32:28.900 --> 32:32.570 What's the catch word there? 32:32.567 --> 32:33.997 So yeah, the greenhouse effect. 32:34.000 --> 32:35.970 So the planet has an atmosphere. 32:35.967 --> 32:38.767 I've neglected the atmosphere here. 32:38.767 --> 32:43.067 What the atmosphere does on our planet and others is that 32:43.067 --> 32:46.527 when the radiation is emitted from the Earth's surface, 32:46.533 --> 32:50.233 instead of letting all of that escape, it stops some of it, 32:50.233 --> 32:55.003 it absorbs it, and sends some of it back to Earth again. 32:55.000 --> 32:59.770 It's as if that object is not able to radiate with its full 32:59.767 --> 33:01.797 black body potential. 33:01.800 --> 33:05.100 Something's holding that heat in, and it's the greenhouse 33:05.100 --> 33:08.130 gases in the atmosphere. 33:08.133 --> 33:11.033 So obviously, we're going to be coming back to this time 33:11.033 --> 33:12.133 and time again in the course. 33:12.133 --> 33:17.603 But this important discrepancy is largely due to our neglect 33:17.600 --> 33:21.500 of the atmosphere, that is to say our neglect of the 33:21.500 --> 33:22.770 greenhouse effect. 33:29.000 --> 33:34.070 Let me give a very brief description of how the 33:34.067 --> 33:38.167 greenhouse effect works on planet Earth. 33:38.167 --> 33:40.967 And then we'll take a quick look at some other planets to 33:40.967 --> 33:44.267 see if other planets have a greenhouse effect as well. 33:51.567 --> 33:56.567 So once again, this is wavelength versus intensity of 33:56.567 --> 33:58.527 radiation emitted. 34:04.133 --> 34:10.933 For Earth's temperature, the curve looks 34:10.933 --> 34:12.603 something like that. 34:12.600 --> 34:19.200 For the Sun's temperature it looks something like that. 34:19.200 --> 34:22.970 We've already talked about this shift in the wavelength 34:22.967 --> 34:25.127 of maximum emission. 34:25.133 --> 34:27.573 But let me put underneath this some of the absorptive 34:27.567 --> 34:31.627 properties of the Earth's atmosphere. 34:31.633 --> 34:37.503 On the same wavelength scale, I'm going to draw here the 34:37.500 --> 34:45.270 percent absorbed as radiation tries to pass through the 34:45.267 --> 34:45.897 atmosphere. 34:45.900 --> 34:49.130 In other words, I'm looking at a segment of the atmosphere 34:49.133 --> 34:52.933 and imagining radiation is either coming in and trying to 34:52.933 --> 34:55.873 penetrate to the Earth's surface, or it's trying to get 34:55.867 --> 34:56.897 out and escape. 34:56.900 --> 34:58.970 Either one, it doesn't matter what direction it's moving, 34:58.967 --> 35:01.197 but some fraction of the radiation's going to be 35:01.200 --> 35:06.000 absorbed as it tries to pass through the atmosphere. 35:06.000 --> 35:09.300 That's the faction I'm going to plot on the y-axis here. 35:12.167 --> 35:15.597 Now, the visible part of the spectrum is about here. 35:15.600 --> 35:18.370 Let's call that the visible part. 35:18.367 --> 35:19.767 I'm going to need these guidelines 35:19.767 --> 35:22.927 to help me be accurate. 35:22.933 --> 35:25.473 Here's 100%. 35:25.467 --> 35:27.227 Basically, this absorption curve looks 35:27.233 --> 35:28.473 something like this. 35:34.300 --> 35:36.970 I'm just making some random wiggles here. 35:36.967 --> 35:40.167 There are a few areas that are nearly transparent in the 35:40.167 --> 35:41.397 wavelength spectrum. 35:44.033 --> 35:46.573 And then you get to the radio waves and it comes way down. 35:49.300 --> 35:50.600 So this is very schematic. 35:50.600 --> 35:53.930 I haven't meant to be quantitative on this. 35:53.933 --> 35:59.533 The point is that most of the Sun's radiation falls in a 35:59.533 --> 36:03.503 part of the spectrum for which the Earth's atmosphere is 36:03.500 --> 36:04.870 transparent. 36:04.867 --> 36:07.867 When this percent absorption is low, that means the 36:07.867 --> 36:09.127 atmosphere is transparent. 36:12.467 --> 36:15.697 On the other hand, when the Earth tries to radiate back 36:15.700 --> 36:21.030 out to space, because it's cooler, it radiates at a 36:21.033 --> 36:24.073 longer wavelength. 36:24.067 --> 36:27.167 That wavelength tends to fall in a region where there's a 36:27.167 --> 36:30.167 lot of atmospheric absorption. 36:30.167 --> 36:35.397 The atmosphere is almost opaque at those longer 36:35.400 --> 36:38.000 wavelengths. 36:38.000 --> 36:41.270 So it's a bit like a one-way valve. 36:41.267 --> 36:43.167 I don't like that analogy, but let me say it and 36:43.167 --> 36:44.827 then correct it. 36:44.833 --> 36:46.503 It's really like a one-way valve. 36:46.500 --> 36:49.730 The radiation coming from the Sun can pass through the 36:49.733 --> 36:52.703 atmosphere and heat the Earth. 36:52.700 --> 36:56.930 Now I'm neglecting the little bit that's ultraviolet that 36:56.933 --> 37:00.073 heats the stratosphere, a little bit of the X-rays that 37:00.067 --> 37:00.967 heats the thermosphere. 37:00.967 --> 37:03.627 The bulk of the radiation comes right on through and 37:03.633 --> 37:05.073 hits the surface of the Earth. 37:05.067 --> 37:08.997 But when the Earth tries to radiate out to space, most of 37:09.000 --> 37:13.500 that radiation is absorbed and it has to be re-emitted before 37:13.500 --> 37:15.930 it can finally escape from the planet. 37:15.933 --> 37:19.433 Now, I don't like the term one-way valve because that 37:19.433 --> 37:22.833 implies that it makes a difference what direction the 37:22.833 --> 37:27.003 radiation is moving in, and that's not the point at all. 37:27.000 --> 37:31.430 The point is that these are at two different wavelengths. 37:31.433 --> 37:34.173 Absorption doesn't depend on what direction the photons are 37:34.167 --> 37:36.367 moving, but it does depend on their wavelength. 37:36.367 --> 37:39.527 So the short wavelength can penetrate, the longer 37:39.533 --> 37:42.033 wavelengths cannot. 37:42.033 --> 37:45.333 And that's the origin, or that's the physics behind the 37:45.333 --> 37:46.073 greenhouse effect. 37:46.067 --> 37:46.397 Yes. 37:46.400 --> 37:47.630 STUDENT: Does it enter the atmosphere and then--? 37:49.900 --> 37:52.870 PROFESSOR: Enter and penetrate through. 37:52.867 --> 37:53.567 When I say penetrate-- 37:53.567 --> 37:55.267 STUDENT: And hit the surface? 37:55.267 --> 37:55.697 PROFESSOR: That's right. 37:55.700 --> 37:57.900 So this radiation will come through all the way to the 37:57.900 --> 37:58.570 Earth's surface. 37:58.567 --> 38:00.797 There it will be absorbed. 38:00.800 --> 38:02.970 It'll heat the Earth's surface and then that heat will come 38:02.967 --> 38:05.167 back up and heat the atmosphere and so on. 38:05.167 --> 38:08.527 But the point is it gets all the way through the atmosphere 38:08.533 --> 38:09.673 without being absorbed. 38:09.667 --> 38:11.797 It isn't until it hits the Earth's surface 38:11.800 --> 38:12.800 that it gets absorbed. 38:12.800 --> 38:14.100 Thanks for that clarification. 38:14.100 --> 38:16.530 This is the atmosphere only I'm talking about. 38:16.533 --> 38:20.303 All those radiations, of course, cannot 38:20.300 --> 38:21.470 penetrate into the Earth. 38:21.467 --> 38:23.127 They're absorbed immediately when they 38:23.133 --> 38:23.933 hit the Earth's surface. 38:23.933 --> 38:24.233 Yes. 38:24.233 --> 38:25.473 STUDENT: So you're saying that the longer wavelengths--? 38:30.867 --> 38:32.897 PROFESSOR: Cannot penetrate through the atmosphere. 38:32.900 --> 38:35.700 STUDENT: So they don't go through-- do they get into the 38:35.700 --> 38:36.370 atmosphere? 38:36.367 --> 38:36.967 PROFESSOR: They do. 38:36.967 --> 38:38.367 They get part way-- 38:38.367 --> 38:40.867 for example, this happens to be radiation trying to get 38:40.867 --> 38:42.627 out, because it's the longer stuff. 38:42.633 --> 38:45.603 So let's just imagine for a moment, you've got the Earth's 38:45.600 --> 38:49.300 surface radiating at, say, 10 microns, 38:49.300 --> 38:51.130 wavelength of 10 microns. 38:51.133 --> 38:53.873 It'll penetrate up a few hundred meters or maybe even a 38:53.867 --> 38:57.597 kilometer into the atmosphere, but it'll get absorbed. 38:57.600 --> 39:01.230 It'll heat the air there, the air will then re-radiate some 39:01.233 --> 39:03.003 up and some down. 39:03.000 --> 39:05.800 And some of the down will come all the way back and add a 39:05.800 --> 39:08.170 source of heat to the surface. 39:08.167 --> 39:09.467 So the fact that-- 39:09.467 --> 39:11.997 I'm not saying it can't penetrate a little bit. 39:12.000 --> 39:15.670 It'll penetrate on average tens, hundreds, maybe even a 39:15.667 --> 39:19.427 few thousand meters, but it won't get all the way out for 39:19.433 --> 39:20.673 the most part. 39:20.667 --> 39:22.767 That's not 100%. 39:22.767 --> 39:25.527 Some will get out, but most will not. 39:25.533 --> 39:30.803 There are few special parts of the spectrum that are 39:30.800 --> 39:36.200 transparent, even to these longer waves, and we refer to 39:36.200 --> 39:39.100 those as windows. 39:39.100 --> 39:42.100 For example, the most famous one, the so-called infrared 39:42.100 --> 39:45.970 window is from 8 to 12 microns. 39:45.967 --> 39:47.167 It's a fairly narrow window. 39:47.167 --> 39:49.797 It's only 4 microns in width. 39:49.800 --> 39:52.130 And out there that's not very much. 39:52.133 --> 39:55.403 But there, that particular wavelength 39:55.400 --> 39:56.570 can penetrate through. 39:56.567 --> 40:00.497 And this gadget, by the way, you might ask 40:00.500 --> 40:01.700 why does this work? 40:01.700 --> 40:04.530 If there's such a thing as atmospheric absorption, then 40:04.533 --> 40:07.803 how come the radiation emitted from the surface hasn't been 40:07.800 --> 40:09.970 absorbed before it gets to the instrument? 40:09.967 --> 40:12.267 This instrument is designed to work in 40:12.267 --> 40:14.397 that particular window. 40:14.400 --> 40:17.670 But it's a narrow window, and I had to use special optics to 40:17.667 --> 40:20.897 get it just to work in that window. 40:20.900 --> 40:25.200 So be careful, the atmosphere is not opaque to every 40:25.200 --> 40:28.270 wavelength, but to most wavelengths out in the 40:28.267 --> 40:30.297 infrared part of the spectrum. 40:35.233 --> 40:36.503 Any questions there? 40:39.300 --> 40:42.600 I think I have time to put up a small table. 40:50.133 --> 40:54.033 I'm going to keep this final formula here because that's 40:54.033 --> 40:56.073 the one that I used to construct the table. 41:01.200 --> 41:14.100 Planet, albedo, predicted temperature, and the actual 41:14.100 --> 41:19.530 temperature, and something about the 41:19.533 --> 41:24.233 atmosphere of the planet. 41:24.233 --> 41:30.133 Venus, Earth, and Mars. 41:30.133 --> 41:32.073 We'll just do those three Earth-like planets. 41:35.400 --> 41:46.300 The albedo for these planets are 0.71, 0.33, and 0.17. 41:46.300 --> 41:50.930 Venus is a very bright planet, if you look at in the sky. 41:50.933 --> 41:53.233 It's very often the brightest object in the sky because it 41:53.233 --> 41:56.173 reflects radiation so strongly. 41:56.167 --> 42:00.997 We see that represented by that high albedo number there. 42:01.000 --> 42:02.800 The Earth we've already spoken about. 42:02.800 --> 42:07.470 Some of that reflectivity comes from the clouds in our 42:07.467 --> 42:10.097 atmosphere, which are quite bright. 42:10.100 --> 42:15.170 Mars is a rather dark planet, Mars with an s, because there 42:15.167 --> 42:16.997 are very few clouds in its atmosphere. 42:17.000 --> 42:20.500 So it's only the surface itself that we're dealing with 42:20.500 --> 42:21.770 when we're computing the albedo. 42:24.567 --> 42:24.867 When I put the-- 42:24.867 --> 42:26.027 I haven't written the solar constant. 42:26.033 --> 42:28.573 Remember, S is different for each of these planets as well, 42:28.567 --> 42:31.597 but when I put the appropriate S in there and use that 42:31.600 --> 42:35.570 albedo, here's what I get from this formula. 42:35.567 --> 42:40.197 I get 244, 252-- 42:40.200 --> 42:41.870 we've done that one-- 42:41.867 --> 42:46.227 and 216. 42:46.233 --> 42:47.503 And here's the actual. 42:55.767 --> 42:59.667 The actual observed surface temperature for these planets. 42:59.667 --> 43:00.727 Mars is pretty good. 43:00.733 --> 43:05.573 We predict 216, the actual is 230. 43:05.567 --> 43:08.527 There is a little bit of a greenhouse effect on Mars, but 43:08.533 --> 43:10.273 it's not terribly strong. 43:10.267 --> 43:12.127 The Earth we've already spoken about. 43:12.133 --> 43:15.173 That's a pretty big difference when you express it in Celsius 43:15.167 --> 43:16.867 and think about the properties of water. 43:16.867 --> 43:19.427 But look at Venus. 43:19.433 --> 43:20.533 We are not even close. 43:20.533 --> 43:22.473 Not even in a Kelvin scale does that look like a 43:22.467 --> 43:24.627 reasonable estimate. 43:24.633 --> 43:27.073 That's because Venus has the granddaddy of 43:27.067 --> 43:29.667 all greenhouse effects. 43:29.667 --> 43:33.327 That huge difference is due to the effect of Venus's 43:33.333 --> 43:37.333 atmosphere trapping infrared radiation as it tries to leave 43:37.333 --> 43:38.403 the surface. 43:38.400 --> 43:44.030 Let me just mention here, Venus has a massive CO2 43:44.033 --> 43:46.733 atmosphere. 43:46.733 --> 43:52.733 Earth has a moderate intensity, mostly air, but 43:52.733 --> 43:59.503 with some greenhouse gases like H20, CO2, et cetera. 43:59.500 --> 44:01.400 I have to erase this now. 44:01.400 --> 44:08.270 And Mars has a thin CO2 atmosphere. 44:08.267 --> 44:13.797 CO2 is a greenhouse gas, but because the atmosphere of Mars 44:13.800 --> 44:17.130 is so thin, the greenhouse effect is not particularly 44:17.133 --> 44:19.803 strong on Mars. 44:19.800 --> 44:21.870 So there we have it. 44:21.867 --> 44:26.427 We have the fact that the greenhouse effect is-- occurs 44:26.433 --> 44:29.803 on all planets that have atmospheres. 44:29.800 --> 44:33.830 It tends to make the planet's surface temperature warmer 44:33.833 --> 44:36.233 than it would otherwise be. 44:36.233 --> 44:40.703 The physics of it has to do with radiation being able to 44:40.700 --> 44:44.230 penetrate through the atmosphere. 44:44.233 --> 44:47.833 The Sun's radiation versus the radiation that's emitted by 44:47.833 --> 44:49.533 the planet. 44:49.533 --> 44:53.803 Then it depends on the nature of the atmosphere how much of 44:53.800 --> 44:58.830 a greenhouse gas you're going to have. CO2's 44:58.833 --> 45:00.133 a greenhouse gas. 45:02.233 --> 45:07.003 The surface pressure on Venus is something like 60 times 45:07.000 --> 45:08.570 that of Earth. 45:08.567 --> 45:11.927 Has a very massive atmosphere, and it's almost all CO2. 45:11.933 --> 45:14.303 You can just imagine you're going to-- 45:14.300 --> 45:19.570 kind of like the worst possible scenario for having a 45:19.567 --> 45:20.897 very strong greenhouse gas. 45:20.900 --> 45:24.130 Not only is there a lot of it, but almost all of it is an 45:24.133 --> 45:25.233 absorbing gas. 45:25.233 --> 45:26.903 I have to say a few words-- 45:26.900 --> 45:29.170 I think I can squeeze it in-- 45:29.167 --> 45:32.627 about what is a greenhouse gas because I use that term 45:32.633 --> 45:33.933 loosely now. 45:33.933 --> 45:35.203 It needs to be defined. 45:43.867 --> 45:51.597 It's basically a gas that can absorb and 45:51.600 --> 45:58.830 emit infrared radiation. 46:07.900 --> 46:10.470 What determines whether a gas can do that is 46:10.467 --> 46:13.327 its molecular structure. 46:13.333 --> 46:20.133 So for example, an Argon atom just by itself, because it's 46:20.133 --> 46:24.873 only a single point mass, it cannot rotate, it can't 46:24.867 --> 46:27.367 vibrate, it can just move around. 46:27.367 --> 46:32.967 And by moving around, it doesn't radiate any energy. 46:32.967 --> 46:42.027 Nitrogen, N2, two point masses held by a chemical bond. 46:42.033 --> 46:46.873 It can rotate, it can vibrate, but because it's a symmetric 46:46.867 --> 46:52.697 molecule, it's electrical charge distribution is 46:52.700 --> 46:56.730 symmetric and it has no dipole moment. 46:59.633 --> 47:05.203 A dipole moment is a separation of charges. 47:05.200 --> 47:07.600 If I've got a positive and a negative charge and they've 47:07.600 --> 47:12.700 been moved apart, then we say that object 47:12.700 --> 47:15.800 has a dipole moment. 47:15.800 --> 47:20.130 But you need to break symmetry in the molecule before you can 47:20.133 --> 47:22.603 have a dipole moment, and nitrogen is a perfectly 47:22.600 --> 47:24.900 symmetric molecule. 47:24.900 --> 47:29.470 Nitrogen, nitrogen, symmetry, no dipole moment. 47:29.467 --> 47:32.797 Oxygen, same problem, right? 47:32.800 --> 47:36.430 Perfectly symmetric molecule, no dipole moment. 47:36.433 --> 47:37.603 Look at this. 47:37.600 --> 47:41.170 The primary constituents of our atmosphere, nitrogen 47:41.167 --> 47:45.697 first, oxygen second, Argon third, none of them have a 47:45.700 --> 47:48.000 dipole moment, none of them can absorb or 47:48.000 --> 47:49.330 emit infrared radiation. 47:49.333 --> 47:51.173 These are not greenhouse gases. 47:51.167 --> 47:55.327 It doesn't matter much how much of these you have. What 47:55.333 --> 47:56.673 are the greenhouse gases then? 47:56.667 --> 48:02.897 Well CO2, which has a structure like this. 48:02.900 --> 48:04.770 That's a greenhouse gas. 48:04.767 --> 48:05.397 Why, do you say? 48:05.400 --> 48:07.100 It looks symmetric, doesn't it? 48:07.100 --> 48:10.270 But it can vibrate. 48:10.267 --> 48:14.027 If that carbon vibrates to the left and that oxygen vibrates 48:14.033 --> 48:17.573 to the right, suddenly I've broken symmetry. 48:17.567 --> 48:20.897 And I can have a dipole moment, and that will absorb 48:20.900 --> 48:22.430 and emit infrared radiation. 48:22.433 --> 48:24.033 What about water vapor? 48:24.033 --> 48:26.203 H2O. 48:26.200 --> 48:29.100 Oxygen, two hydrogens. 48:29.100 --> 48:31.330 Well, that's symmetric, isn't it? 48:31.333 --> 48:34.633 Well no, not about that axis. 48:34.633 --> 48:36.133 It's not symmetric about that axis. 48:36.133 --> 48:38.533 So it'll have a dipole moment. 48:38.533 --> 48:41.603 And it will absorb and emit radiation. 48:41.600 --> 48:45.100 So see, the distinction I want to make here is between gases 48:45.100 --> 48:49.070 that are so simple in their structure that they can never, 48:49.067 --> 48:51.667 no matter what they do, they can't generate a dipole 48:51.667 --> 48:54.727 moment, they can't get a charge separation. 48:54.733 --> 48:57.173 Remember, when you're talking on your cell phone, you're 48:57.167 --> 48:58.727 transmitting radiation. 48:58.733 --> 49:01.833 There's an antenna in there that's creating a dipole 49:01.833 --> 49:04.273 moment-- positive, negative, positive, negative, positive, 49:04.267 --> 49:08.027 negative, and that is what is emitting the radiation. 49:08.033 --> 49:10.203 When you're listening, the same thing is happening. 49:10.200 --> 49:11.870 That radiation is coming to you. 49:11.867 --> 49:15.867 It's being captured by the antenna in the cell phone with 49:15.867 --> 49:17.927 a dipole moment. 49:17.933 --> 49:19.903 So it's exactly the same physics. 49:19.900 --> 49:23.100 In all cases, you have to have an oscillating dipole moment 49:23.100 --> 49:26.730 if you want to absorb or emit radiation. 49:26.733 --> 49:32.573 Air cannot do it, but these greenhouse gases can. 49:32.567 --> 49:34.127 We're out of time, but we'll pick up on 49:34.133 --> 49:36.133 the theme next meeting.