2 00:00:10,036 --> 00:00:12,663 To understand how convection sets up this 3 00:00:12,663 --> 00:00:16,781 temperature difference between the ground and the upper atmosphere 4 00:00:16,781 --> 00:00:19,834 that drives the Greenhouse Effect, we need to talk about 5 00:00:19,834 --> 00:00:23,440 three or four separate pieces of physics. 6 00:00:23,440 --> 00:00:26,350 It may seem kind of unrelated and off the wall to 7 00:00:26,350 --> 00:00:31,110 you, but we'll put them all together when we get there. 8 00:00:31,110 --> 00:00:35,500 The first is about pressure in a standing fluid. 9 00:00:35,500 --> 00:00:37,750 If you stand here in the atmosphere, or if we were 10 00:00:37,750 --> 00:00:40,860 to stand at the bottom of a swimming pool, we feel pressure. 11 00:00:40,860 --> 00:00:48,870 And the pressure that we feel is due to the weight of the material over our heads, pushing down. 13 00:00:48,870 --> 00:00:50,550 Standing at the bottom of a swimming pool 14 00:00:50,550 --> 00:00:53,240 we've got this water over our heads, and the 15 00:00:53,240 --> 00:00:56,790 gravitational from the water is what we feel 16 00:00:56,790 --> 00:01:00,030 as pressure, and the same is true of the atmosphere. 17 00:01:00,030 --> 00:01:03,320 But the difference between the water and the 19 00:01:03,320 --> 00:01:06,330 air is that water is basically incompressible. 20 00:01:06,330 --> 00:01:09,020 So it's basically all the same density, 21 00:01:09,020 --> 00:01:11,434 all the way up to the top, whereas gasses 22 00:01:11,434 --> 00:01:14,629 expand if they're not under pressure, 23 00:01:14,629 --> 00:01:17,185 so, the gas is much thicker close to the ground 24 00:01:17,185 --> 00:01:20,450 and then it gets thinner as you go up in the atmosphere. 25 00:01:20,450 --> 00:01:25,840 What that means for pressure in an incompressible medium like water, 26 00:01:25,840 --> 00:01:29,590 if you start at the surface of a swimming pool, 27 00:01:29,590 --> 00:01:35,710 and you swim down, the pressure is going to increase linearly with the depth, 28 00:01:35,710 --> 00:01:39,760 so the pressure will be equal to some pressure at the top plus a constant 29 00:01:39,760 --> 00:01:44,380 times the depth, and so this describes a straight line. 30 00:01:44,380 --> 00:01:46,920 That's because if you start at the top and you swim down a meter 31 00:01:46,920 --> 00:01:51,340 you've got one meter's worth of water over your head. 32 00:01:51,340 --> 00:01:53,940 And you do it all the way at the bottom of the pool, one more meter. 33 00:01:53,940 --> 00:01:56,830 The water has the same density at the top as at the bottom 34 00:01:56,830 --> 00:02:03,015 so the slope of this line is constant, meaning it's a straight line. 35 00:02:03,015 --> 00:02:10,570 Whereas in a compressible medium like a column of air, the pressure 36 00:02:10,570 --> 00:02:16,440 change, if you climb up a little ways in the atmosphere, 37 00:02:16,440 --> 00:02:20,300 is more intense than if you're already at the top of a mountain and you go up a little bit higher, 38 00:02:20,300 --> 00:02:24,480 because the air is so much thinner up at the top of a mountain. So if you climb up 39 00:02:24,480 --> 00:02:28,690 say 100 meters at the top of the mountain, you don't leave behind as much air as if 40 00:02:28,690 --> 00:02:31,010 you were at the ground or sea level, 41 00:02:31,010 --> 00:02:34,510 and if you climb up 100 meters, you're leaving behind more air. 42 00:02:34,510 --> 00:02:38,230 That means that the pressure isn't linear with altitude like 43 00:02:38,230 --> 00:02:41,490 it is in water, but it gets more and more gradual 44 00:02:41,490 --> 00:02:47,140 as you go up. It follows an exponential profile. 45 00:02:47,140 --> 00:02:51,870 The pressure at some height is equal to the pressure at the ground times 46 00:02:51,870 --> 00:02:57,470 e, which is a number raised to the power of 47 00:02:57,470 --> 00:03:02,429 the height divided by a value of about eight kilometers. 48 00:03:03,490 --> 00:03:07,440 One thing to note about this atmospheric 49 00:03:07,440 --> 00:03:12,040 pressure profile, is it never actually really reaches zero. 50 00:03:12,040 --> 00:03:15,736 Mathematically it gets closer, and closer, and closer but it's 51 00:03:15,736 --> 00:03:19,300 as if the pressure of the earth's atmosphere extends out, 52 00:03:19,300 --> 00:03:22,732 forever into the entire galaxy, which is kind of, 53 00:03:22,732 --> 00:03:26,992 an idea that only a mathematician could love probably. 54 00:03:26,992 --> 00:03:31,540 But it might give you the impression that the atmosphere is infinitely thick. 55 00:03:31,540 --> 00:03:37,320 But this multiplier here in the exponent is an important number and 57 00:03:37,320 --> 00:03:40,900 it sort of sets the height of the atmosphere in some way. 58 00:03:40,900 --> 00:03:43,160 It's called a scale height. 59 00:03:43,160 --> 00:03:48,390 So that number is about eight kilometers and it turns out that if you could make 60 00:03:48,390 --> 00:03:53,740 the air all have the same density as air at the ground, 61 00:03:55,070 --> 00:03:59,850 so that it was like incompressible water 63 00:03:59,850 --> 00:04:04,090 then the atmosphere would run out at eight kilometers high. 64 00:04:04,090 --> 00:04:08,790 Eight kilometers is kind of like how thick the atmosphere is, 65 00:04:08,790 --> 00:04:13,000 even though mathematically it kind of is infinitely thick. 66 00:04:13,000 --> 00:04:17,680 But, this tells you a scale height. 67 00:04:17,680 --> 00:04:20,600 When you're actually at eight kilometers 68 00:04:20,600 --> 00:04:23,700 the pressure is a factor of one over e 69 00:04:23,700 --> 00:04:27,470 times this pressure, which is about 30% or something like that. 70 00:04:27,470 --> 00:04:31,610 It sets the height scale of the atmosphere. 71 00:04:33,470 --> 00:04:38,870 The next thing that we need to worry about, is what happens 72 00:04:38,870 --> 00:04:44,030 to the heat when this gas expands as it rises up, 73 00:04:44,030 --> 00:04:49,690 or when it gets compressed, when it comes down toward the Earth under higher pressure. 75 00:04:49,690 --> 00:04:52,840 Because it affects the temperature of the gas, actually. 76 00:04:52,840 --> 00:04:58,900 And you can think of this by imagining a piston that's 77 00:04:58,900 --> 00:05:05,220 got a sleeve that's insulated here so that no heat can cross the walls. 78 00:05:05,220 --> 00:05:07,880 And then you've got this plunger that you 79 00:05:07,880 --> 00:05:11,800 can push in there to compress the gas. 80 00:05:11,800 --> 00:05:14,760 So you push on this plunger and 81 00:05:14,760 --> 00:05:19,650 you're actually doing work to do that. You're pushing the gas molecules together. 82 00:05:19,650 --> 00:05:23,450 It turns out that where that energy goes from doing the 83 00:05:23,450 --> 00:05:28,850 work is to make the temperature of those gas molecules higher. 84 00:05:28,850 --> 00:05:30,520 So you may have encountered this if you've ever 85 00:05:30,520 --> 00:05:33,180 gone to a dive shop to go scuba diving. 86 00:05:33,180 --> 00:05:36,100 You take a scuba tank and you need to 87 00:05:36,100 --> 00:05:39,480 get your tank filled up and so they could just, 88 00:05:39,480 --> 00:05:40,820 pump air into it. 89 00:05:40,820 --> 00:05:43,940 But when they do that it gets very hot 90 00:05:43,940 --> 00:05:47,660 and the tank doesn't want to hold more than a certain amount of pressure. 91 00:05:47,660 --> 00:05:53,250 Hot gas is exerting more pressure and so if you went to a cheap dive shop. 92 00:05:53,250 --> 00:05:57,390 and they just put air in your tank and let it get hot, 93 00:05:57,390 --> 00:05:59,580 you would then take the tank and go jump in 94 00:05:59,580 --> 00:06:01,860 the cold water, and the pressure would go way down. 95 00:06:01,860 --> 00:06:05,190 You'd only have a half a tank of air to breathe. 96 00:06:05,190 --> 00:06:07,580 A good dive shop will put the scuba tank 97 00:06:07,580 --> 00:06:10,310 into a big tub of water and cool it down as 98 00:06:10,310 --> 00:06:13,290 you put the gas in, to prevent the heating 99 00:06:13,290 --> 00:06:16,230 up of the gas from affecting how much gas you take. 100 00:06:16,230 --> 00:06:20,570 Or you can feel it if you ever let the air out of a bicycle tire. 101 00:06:20,570 --> 00:06:23,490 You can feel the expansion of the gas as it's 102 00:06:23,490 --> 00:06:26,970 coming out of the tire, makes it get really cold. 103 00:06:26,970 --> 00:06:28,979 You can feel it on your thumbnail when you do that. 104 00:06:30,020 --> 00:06:32,380 The air when it was inside the tire was at 105 00:06:32,380 --> 00:06:35,350 the same temperature as the air outside, but just because it 106 00:06:35,350 --> 00:06:41,010 expands, the fact that it's expanding decreases the average kinetic energy 107 00:06:41,010 --> 00:06:43,835 of the molecules of gas and so it makes it colder. 109 00:06:44,790 --> 00:06:49,374 Convection is the process of 110 00:06:49,374 --> 00:06:54,149 heating a fluid from below and 111 00:06:54,149 --> 00:06:59,879 causing it to overturn, or warming 112 00:06:59,879 --> 00:07:05,100 it or cooling it from above. 113 00:07:05,100 --> 00:07:10,250 If you heat from below you make the fluid at the bottom expand 114 00:07:10,250 --> 00:07:12,410 because it's warmer. 115 00:07:12,410 --> 00:07:17,710 And when it expands, it's less dense, and it will tend to rise up. 116 00:07:17,710 --> 00:07:21,630 Or if you cool it from above, it will contract, and that 117 00:07:21,630 --> 00:07:24,550 makes it more dense, then it will tend to fall down. 118 00:07:24,550 --> 00:07:27,240 This is a picture of a lava lamp. 119 00:07:27,240 --> 00:07:30,230 You have to have the light bulb at the bottom to heat it from below. 120 00:07:30,230 --> 00:07:31,650 If you had a light bulb at the top, it 121 00:07:31,650 --> 00:07:35,420 wouldn't convect, it wouldn't be any fun, 122 00:07:35,420 --> 00:07:36,160 it wouldn't work. 123 00:07:37,260 --> 00:07:40,770 So this happens in the real world when sunlight hits the 124 00:07:40,770 --> 00:07:45,170 ground, it warms the atmosphere from below and that causes the atmosphere 125 00:07:45,170 --> 00:07:49,820 to convect, or the ocean can convect 126 00:07:49,820 --> 00:07:54,350 upside down, if you cool it from the top, like around Antarctica. 127 00:07:54,350 --> 00:07:57,110 Up in the North Atlantic, you make the water at the 128 00:07:57,110 --> 00:08:00,870 top denser and so it sinks and you do this overturning thing. 129 00:08:02,530 --> 00:08:08,880 It's easiest to understand convection 130 00:08:08,880 --> 00:08:13,990 first in the incompressible case, because it's simpler. 131 00:08:13,990 --> 00:08:17,640 We'll start from a case where let's say we've got a pan of water 132 00:08:17,640 --> 00:08:21,370 on a stove and we're heating it from below so it's going to be convecting. 133 00:08:21,370 --> 00:08:24,330 So let's start out and say that the water is 134 00:08:24,330 --> 00:08:27,270 well mixed in the pan. 136 00:08:29,050 --> 00:08:32,630 That means that it will all be the same temperature, 137 00:08:32,630 --> 00:08:35,680 because there isn't any expansion of the 138 00:08:35,680 --> 00:08:40,340 (liquid) that makes it change its temperature 140 00:08:40,340 --> 00:08:44,540 liquid I mean, because liquids are not compressible. 141 00:08:44,540 --> 00:08:47,340 So it's all the same temperature just like 142 00:08:47,340 --> 00:08:49,300 if you put some sugar into your coffee and 143 00:08:49,300 --> 00:08:51,230 then stir it, it would all have the same amount 144 00:08:51,230 --> 00:08:54,140 of sugar all through the the column. 145 00:08:55,330 --> 00:08:59,600 So then we heat it from below, if this is the 146 00:08:59,600 --> 00:09:03,880 temperature, we make a little blob of hot water at the bottom, but 147 00:09:03,880 --> 00:09:07,320 that's going to expand, and it's going to be less dense than the 148 00:09:07,320 --> 00:09:10,800 water above it, and that's not the way it wants to be. 149 00:09:10,800 --> 00:09:12,780 So it's going to rise up. 150 00:09:12,780 --> 00:09:16,530 Now, in the lava lamp, they have two different 151 00:09:16,530 --> 00:09:20,770 kinds of fluids that can't mix, it's like oil and water. 152 00:09:20,770 --> 00:09:24,660 So the blob from the bottom gets hot and it rises, goes all the way to 153 00:09:24,660 --> 00:09:28,340 the top and then it cools down and comes all the way to the bottom again. 154 00:09:28,340 --> 00:09:34,500 But what tends to happen in the atmosphere is that when this blob of hot stuff rises. 155 00:09:34,500 --> 00:09:38,580 It mixes with everything above it and so it tends to move the 156 00:09:38,580 --> 00:09:46,340 temperature of the whole column to a higher value, instead of just this blob 157 00:09:46,340 --> 00:09:49,190 going up to the top like it would in a lava lamp. 158 00:09:49,190 --> 00:09:53,250 Now in a compressible column of fluid, of 159 00:09:53,250 --> 00:09:58,450 gas, we start out with a well-mixed profile. 160 00:09:58,450 --> 00:10:00,910 But now here's the tricky part. 161 00:10:00,910 --> 00:10:04,390 A well mixed profile is not all the same temperature. 162 00:10:04,390 --> 00:10:07,930 Because this gas up here is under lower pressure. 163 00:10:07,930 --> 00:10:11,440 If you were to take this gas and pull 164 00:10:11,440 --> 00:10:16,690 it down to the bottom of the column so that it was under higher pressure, that 165 00:10:16,690 --> 00:10:21,830 would make it warm up because it's being compressed, and it would, if this 166 00:10:21,830 --> 00:10:24,120 is a well-mixed profile, it would just 167 00:10:24,120 --> 00:10:27,845 exactly follow this trajectory going down, 168 00:10:27,845 --> 00:10:31,130 so a well-mixed profile of gas is not all 169 00:10:31,130 --> 00:10:33,940 the same temperature because of this expansion effect. 170 00:10:35,690 --> 00:10:38,030 And then the rest of it is pretty easy. 172 00:10:38,030 --> 00:10:42,193 We heat it from below and mix it, and it goes to another well-mixed profile. 173 00:10:42,193 --> 00:10:48,056 Which is parallel to the first, pretty much, but warmed up. 174 00:10:48,056 --> 00:10:53,120 The whole thing is kind of just tilted over by this expansion effect of the gas.