WEBVTT 00:00:00.000 --> 00:00:02.640 align:middle line:84% NARRATOR: The following content is provided under a Creative 00:00:02.640 --> 00:00:04.000 align:middle line:90% Commons license. 00:00:04.000 --> 00:00:06.400 align:middle line:84% Your support will help MIT OpenCourseWare 00:00:06.400 --> 00:00:10.080 align:middle line:84% continue to offer high quality educational resources for free. 00:00:10.080 --> 00:00:13.320 align:middle line:84% To make a donation or view additional materials 00:00:13.320 --> 00:00:17.280 align:middle line:84% from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:17.280 --> 00:00:20.860 align:middle line:90% at ocw.mit.edu. 00:00:20.860 --> 00:00:24.520 align:middle line:90% PROFESSOR: So gas exchange. 00:00:24.520 --> 00:00:29.680 align:middle line:84% So this is the last lecture on how does stuff 00:00:29.680 --> 00:00:32.400 align:middle line:90% get into and out of the ocean. 00:00:32.400 --> 00:00:34.160 align:middle line:84% And then after the midterm, we'll 00:00:34.160 --> 00:00:36.840 align:middle line:84% deal a lot more with what goes on 00:00:36.840 --> 00:00:40.720 align:middle line:84% within the ocean in terms of internal cycling and dynamics. 00:00:40.720 --> 00:00:47.120 align:middle line:84% And so what we're interested in is, for soluble gases, 00:00:47.120 --> 00:00:51.040 align:middle line:84% there's going to be fluxes in and out of across the RC 00:00:51.040 --> 00:00:57.760 align:middle line:84% interface, and we're interested in these fluxes, which 00:00:57.760 --> 00:01:00.140 align:middle line:90% we're going to call of f. 00:01:00.140 --> 00:01:05.239 align:middle line:90% 00:01:05.239 --> 00:01:10.400 align:middle line:84% Typically, the way this is formulated or discussed 00:01:10.400 --> 00:01:13.120 align:middle line:90% is in terms of two components. 00:01:13.120 --> 00:01:17.280 align:middle line:84% It's going to be the flux is going 00:01:17.280 --> 00:01:36.680 align:middle line:84% to equal a kinetic component times a thermodynamic component. 00:01:36.680 --> 00:01:39.840 align:middle line:84% And if any of you have had transport theory, 00:01:39.840 --> 00:01:45.720 align:middle line:84% like diffusion, thermal conductivity, 00:01:45.720 --> 00:01:47.260 align:middle line:90% this should look very familiar. 00:01:47.260 --> 00:01:51.320 align:middle line:84% It's basically, almost everything in this formulation 00:01:51.320 --> 00:01:54.600 align:middle line:84% has been stolen from physical chemistry and chemical 00:01:54.600 --> 00:01:56.960 align:middle line:90% engineering adapted. 00:01:56.960 --> 00:02:01.030 align:middle line:84% And there's a lot of crossover between the chemical engineering 00:02:01.030 --> 00:02:03.590 align:middle line:84% and the environmental communities 00:02:03.590 --> 00:02:06.750 align:middle line:90% in terms of gas exchange. 00:02:06.750 --> 00:02:12.470 align:middle line:84% The kinetic component is going to depend 00:02:12.470 --> 00:02:21.830 align:middle line:84% on things like properties of the water and turbulence. 00:02:21.830 --> 00:02:23.870 align:middle line:84% So this kinetic component we're going 00:02:23.870 --> 00:02:28.750 align:middle line:84% to try to set up so that lots of the kinetic component 00:02:28.750 --> 00:02:31.950 align:middle line:84% are independent of the particular gas. 00:02:31.950 --> 00:02:41.750 align:middle line:84% And we'll also show you how to reference 00:02:41.750 --> 00:02:45.690 align:middle line:90% gas one to, say, gas two. 00:02:45.690 --> 00:02:49.710 align:middle line:90% 00:02:49.710 --> 00:02:54.070 align:middle line:84% The thermodynamic component is going to depend specifically 00:02:54.070 --> 00:03:03.070 align:middle line:84% on individual gases, and is essentially 00:03:03.070 --> 00:03:06.270 align:middle line:84% a measure of things like the solubility 00:03:06.270 --> 00:03:14.450 align:middle line:84% of the gas, the atmospheric and ocean concentrations. 00:03:14.450 --> 00:03:17.965 align:middle line:90% 00:03:17.965 --> 00:03:19.090 align:middle line:90% Oh, do you want me to move? 00:03:19.090 --> 00:03:19.830 align:middle line:90% I can move. 00:03:19.830 --> 00:03:22.270 align:middle line:90% Well, I can't anymore. 00:03:22.270 --> 00:03:25.050 align:middle line:84% I was just going to move the tip for you guys right there. 00:03:25.050 --> 00:03:31.785 align:middle line:90% 00:03:31.785 --> 00:03:35.870 align:middle line:84% And this is pretty standard, this separation 00:03:35.870 --> 00:03:39.728 align:middle line:84% into a kinetic component and a thermodynamic component. 00:03:39.728 --> 00:03:41.270 align:middle line:84% So we're going to-- first we're going 00:03:41.270 --> 00:03:45.750 align:middle line:84% to talk about solubilities and the thermodynamic component. 00:03:45.750 --> 00:03:50.990 align:middle line:84% So you need to know a little bit about the composition 00:03:50.990 --> 00:03:56.820 align:middle line:84% of the air, and there's some notes or a table in the notes. 00:03:56.820 --> 00:04:03.260 align:middle line:84% Most of the atmosphere is nitrogen. It's about 78%. 00:04:03.260 --> 00:04:10.620 align:middle line:84% Next comes oxygen, which is 21% And then everything else, 00:04:10.620 --> 00:04:16.240 align:middle line:84% argon is 1%, and then everything else, if you look at this well, 00:04:16.240 --> 00:04:19.860 align:middle line:84% it actually looks like it already adds up to 100%. 00:04:19.860 --> 00:04:22.860 align:middle line:84% Everything else in the atmosphere is small. 00:04:22.860 --> 00:04:31.236 align:middle line:84% It's either in parts per billion or parts per trillion. 00:04:31.236 --> 00:04:33.500 align:middle line:90% STUDENT: Parts by volume? 00:04:33.500 --> 00:04:36.980 align:middle line:84% PROFESSOR: Well, yeah, I'll get there in a second. 00:04:36.980 --> 00:04:39.900 align:middle line:84% The way these are usually reported 00:04:39.900 --> 00:04:43.040 align:middle line:90% are as partial pressures. 00:04:43.040 --> 00:04:46.580 align:middle line:90% 00:04:46.580 --> 00:04:50.440 align:middle line:84% So you guys all remember PV equals nRT? 00:04:50.440 --> 00:04:56.020 align:middle line:90% 00:04:56.020 --> 00:04:59.140 align:middle line:84% The partial pressure is the pressure 00:04:59.140 --> 00:05:05.020 align:middle line:84% that a gas would exert, independent of the other gases 00:05:05.020 --> 00:05:09.660 align:middle line:84% all by itself at that particular concentration or molar 00:05:09.660 --> 00:05:12.900 align:middle line:90% ratio and temperature. 00:05:12.900 --> 00:05:15.000 align:middle line:84% You'll see it traded back and forth, 00:05:15.000 --> 00:05:22.420 align:middle line:84% whether it's reported as parts per million or mole fraction, 00:05:22.420 --> 00:05:26.380 align:middle line:84% because the pressure that a gas exerts 00:05:26.380 --> 00:05:28.360 align:middle line:84% depends upon how many moles are there, 00:05:28.360 --> 00:05:31.820 align:middle line:90% not on its molecular weight. 00:05:31.820 --> 00:05:37.580 align:middle line:84% So PV n is either the mole fraction 00:05:37.580 --> 00:05:41.900 align:middle line:84% or it's the partial pressure relative to the total pressure. 00:05:41.900 --> 00:05:45.780 align:middle line:84% For most gases, you can assume ideal behavior. 00:05:45.780 --> 00:05:51.770 align:middle line:84% That is that you can actually use PV equals nRT 00:05:51.770 --> 00:05:53.810 align:middle line:90% without any corrections. 00:05:53.810 --> 00:05:56.730 align:middle line:90% For some gases, example, CO2. 00:05:56.730 --> 00:05:59.870 align:middle line:84% You actually need to look at the fugacity. 00:05:59.870 --> 00:06:02.970 align:middle line:90% 00:06:02.970 --> 00:06:05.970 align:middle line:84% It's a fairly minor correction, but it's basically 00:06:05.970 --> 00:06:10.090 align:middle line:84% deviation from the ideal gas law associated with the fact 00:06:10.090 --> 00:06:13.470 align:middle line:84% that CO2 is interacting with the other gases. 00:06:13.470 --> 00:06:16.250 align:middle line:90% 00:06:16.250 --> 00:06:19.850 align:middle line:84% Also, almost all the air-sea gas exchange measurements 00:06:19.850 --> 00:06:24.090 align:middle line:90% are reported for dry air. 00:06:24.090 --> 00:06:27.890 align:middle line:84% So they've actually dried the air and removed the water vapor. 00:06:27.890 --> 00:06:34.730 align:middle line:84% So it would be PPM, parts per million relative to dry air, not 00:06:34.730 --> 00:06:35.750 align:middle line:90% the total pressure. 00:06:35.750 --> 00:06:38.030 align:middle line:84% And so when you go back and apply total pressure, 00:06:38.030 --> 00:06:42.050 align:middle line:84% you just have to make sure you know what's-- you just need 00:06:42.050 --> 00:06:44.330 align:middle line:84% to keep track of what's been done with the water vapor 00:06:44.330 --> 00:06:46.930 align:middle line:84% because it can be several percent, 00:06:46.930 --> 00:06:48.430 align:middle line:90% particularly in the tropics. 00:06:48.430 --> 00:06:56.138 align:middle line:90% 00:06:56.138 --> 00:07:03.890 align:middle line:84% Usually, we're going to formulate our equation 00:07:03.890 --> 00:07:06.630 align:middle line:84% in terms of not the partial pressure, 00:07:06.630 --> 00:07:17.522 align:middle line:84% but the concentration that would be in-- 00:07:17.522 --> 00:07:19.710 align:middle line:84% I'm trying to see what the convention is. 00:07:19.710 --> 00:07:22.370 align:middle line:90% 00:07:22.370 --> 00:07:29.210 align:middle line:84% It would be the concentration in the air-sea surface that 00:07:29.210 --> 00:07:31.850 align:middle line:84% would be in equilibrium with the atmosphere. 00:07:31.850 --> 00:07:35.370 align:middle line:84% So if you have, say, a partial pressure of some gas 00:07:35.370 --> 00:07:40.730 align:middle line:84% C we want to find out right at the air-sea surface what 00:07:40.730 --> 00:07:43.810 align:middle line:84% would be the concentration that would 00:07:43.810 --> 00:07:48.970 align:middle line:84% be in solubility equilibrium with that partial pressure. 00:07:48.970 --> 00:07:51.930 align:middle line:84% So rather than working in partial pressure in one side 00:07:51.930 --> 00:07:53.850 align:middle line:84% and concentration in the other, we're 00:07:53.850 --> 00:07:55.890 align:middle line:84% going to convert partial pressure 00:07:55.890 --> 00:08:02.250 align:middle line:84% into a corresponding solubility equilibrium concentration. 00:08:02.250 --> 00:08:05.810 align:middle line:84% Now, there's a couple ways of doing that, 00:08:05.810 --> 00:08:14.770 align:middle line:84% and I will warn you that the literature is not consistent. 00:08:14.770 --> 00:08:17.650 align:middle line:84% If you remember from physical chemistry [INAUDIBLE] 00:08:17.650 --> 00:08:23.730 align:middle line:84% one form of Henry's law, it's basically 00:08:23.730 --> 00:08:28.250 align:middle line:84% relating the partial pressure of a gas 00:08:28.250 --> 00:08:32.530 align:middle line:84% to a solubility concentration as a function of an equilibrium 00:08:32.530 --> 00:08:38.130 align:middle line:84% constant, temperature in the ideal gas constant. 00:08:38.130 --> 00:08:44.130 align:middle line:84% You'll also see things often recorded 00:08:44.130 --> 00:08:58.400 align:middle line:84% like this, which is technically the Bunsen solubility law, where 00:08:58.400 --> 00:09:01.600 align:middle line:84% this k equilibrium is now actually a Bunsen solubility 00:09:01.600 --> 00:09:03.840 align:middle line:90% coefficient. 00:09:03.840 --> 00:09:07.600 align:middle line:84% But in the literature, people are very sloppy, 00:09:07.600 --> 00:09:09.620 align:middle line:90% and sometimes you see it. 00:09:09.620 --> 00:09:11.840 align:middle line:84% Sometimes you see Bunsen solubility law 00:09:11.840 --> 00:09:14.900 align:middle line:90% written as Henry's law. 00:09:14.900 --> 00:09:18.760 align:middle line:90% 00:09:18.760 --> 00:09:23.800 align:middle line:84% So they go back and forth, and you just have to be very aware. 00:09:23.800 --> 00:09:27.560 align:middle line:84% Sometimes this is also written as a beta. 00:09:27.560 --> 00:09:32.920 align:middle line:84% You just need to be aware of where the beta is coming from 00:09:32.920 --> 00:09:34.380 align:middle line:90% and what they're talking about. 00:09:34.380 --> 00:09:36.760 align:middle line:84% STUDENT: And units will help with that. 00:09:36.760 --> 00:09:38.160 align:middle line:90% PROFESSOR: Yes. 00:09:38.160 --> 00:09:39.720 align:middle line:90% Wel, units. 00:09:39.720 --> 00:09:41.060 align:middle line:90% STUDENT: Well if you use them. 00:09:41.060 --> 00:09:42.700 align:middle line:84% PROFESSOR: Yeah, if they use them. 00:09:42.700 --> 00:09:46.440 align:middle line:90% 00:09:46.440 --> 00:09:47.440 align:middle line:90% Yeah. 00:09:47.440 --> 00:09:50.260 align:middle line:84% STUDENT: You mean pressure of your gas 00:09:50.260 --> 00:09:55.000 align:middle line:84% C in those last questions, not pressure gas A? 00:09:55.000 --> 00:09:57.620 align:middle line:84% PROFESSOR: Oh, this is supposed to be-- yeah, sorry. 00:09:57.620 --> 00:10:01.920 align:middle line:84% It's pressure of-- if the atmospheric pressure of C. 00:10:01.920 --> 00:10:04.880 align:middle line:84% So I guess I could put a little C here if you wanted. 00:10:04.880 --> 00:10:08.880 align:middle line:84% It is the pressure of C, but it's the-- yeah, sorry. 00:10:08.880 --> 00:10:10.840 align:middle line:90% I didn't match those very well. 00:10:10.840 --> 00:10:15.680 align:middle line:84% It's the atmospheric pressure of those of compound C. Yes, that's 00:10:15.680 --> 00:10:16.340 align:middle line:90% a good point. 00:10:16.340 --> 00:10:18.000 align:middle line:90% It's not total pressure. 00:10:18.000 --> 00:10:23.820 align:middle line:84% It's the partial pressure of that particular gas. 00:10:23.820 --> 00:10:24.320 align:middle line:90% Thanks. 00:10:24.320 --> 00:10:29.640 align:middle line:90% 00:10:29.640 --> 00:10:30.420 align:middle line:90% Units. 00:10:30.420 --> 00:10:33.000 align:middle line:90% 00:10:33.000 --> 00:10:41.910 align:middle line:84% The modern standard for gas exchange literature 00:10:41.910 --> 00:10:48.270 align:middle line:84% is, gases are reported in micromoles per kilogram. 00:10:48.270 --> 00:10:53.030 align:middle line:84% Unfortunately, you will see all sorts of things. 00:10:53.030 --> 00:10:55.110 align:middle line:84% The most confusing, particularly if you go back 00:10:55.110 --> 00:10:59.470 align:middle line:84% in the older literature, is that oxygen, 00:10:59.470 --> 00:11:02.070 align:middle line:84% which is ubiquitous not just for gas exchange, 00:11:02.070 --> 00:11:06.150 align:middle line:84% but for hydrography and for biology, 00:11:06.150 --> 00:11:11.710 align:middle line:84% was often reported as milliliters per liter. 00:11:11.710 --> 00:11:15.070 align:middle line:90% And you say milliliters of what? 00:11:15.070 --> 00:11:20.910 align:middle line:84% It's actually milliliters at STP, standard temperature 00:11:20.910 --> 00:11:22.270 align:middle line:90% and pressure. 00:11:22.270 --> 00:11:25.630 align:middle line:84% And there's a conversion in the notes, 00:11:25.630 --> 00:11:28.710 align:middle line:84% but it's essentially 1 milliliter per liter 00:11:28.710 --> 00:11:36.790 align:middle line:84% equals about 43.6 micromoles per kilogram. 00:11:36.790 --> 00:11:39.470 align:middle line:84% And since we're assuming ideal gas behavior 00:11:39.470 --> 00:11:42.170 align:middle line:84% and it's at standard temperature and pressure, this-- 00:11:42.170 --> 00:11:45.110 align:middle line:90% 00:11:45.110 --> 00:11:47.750 align:middle line:90% you're using. 00:11:47.750 --> 00:11:52.030 align:middle line:84% But so you'll often see the older literature oxygen values 00:11:52.030 --> 00:11:54.670 align:middle line:84% that are about a factor of 50 lower than 00:11:54.670 --> 00:11:56.850 align:middle line:84% if you had them in micromoles per kilogram. 00:11:56.850 --> 00:12:09.070 align:middle line:90% 00:12:09.070 --> 00:12:18.110 align:middle line:84% So what determines this Bunsen coefficient or the Henry's law 00:12:18.110 --> 00:12:19.950 align:middle line:90% coefficient? 00:12:19.950 --> 00:12:24.110 align:middle line:84% Well, there's essentially three things. 00:12:24.110 --> 00:12:28.610 align:middle line:84% You've got a gas that you're trying to stick into water. 00:12:28.610 --> 00:12:31.990 align:middle line:84% So we've got all these water molecules that are happily 00:12:31.990 --> 00:12:33.050 align:middle line:90% bound to each other. 00:12:33.050 --> 00:12:35.470 align:middle line:84% Remember they're all sitting there undergoing 00:12:35.470 --> 00:12:40.380 align:middle line:90% their lovely little hydrogen-- 00:12:40.380 --> 00:12:42.120 align:middle line:84% have all their little hydrogen bonds. 00:12:42.120 --> 00:12:43.300 align:middle line:90% They're quite happy. 00:12:43.300 --> 00:12:48.500 align:middle line:84% You gotta put a hole in the water in order to put a gas in. 00:12:48.500 --> 00:12:52.740 align:middle line:84% And so the first thing is going to be the energy 00:12:52.740 --> 00:12:56.380 align:middle line:90% to create a cavity. 00:12:56.380 --> 00:12:59.980 align:middle line:84% And that's going to just depend upon the solvent. 00:12:59.980 --> 00:13:02.740 align:middle line:84% It's just basically, you gotta break the water, 00:13:02.740 --> 00:13:08.340 align:middle line:84% break those hydrogen bonds and make room to stick your gas in. 00:13:08.340 --> 00:13:13.580 align:middle line:84% The second thing is the energy to keep 00:13:13.580 --> 00:13:17.880 align:middle line:90% the solute in the cavity. 00:13:17.880 --> 00:13:20.900 align:middle line:90% 00:13:20.900 --> 00:13:24.820 align:middle line:84% And that's going to depend upon the solute. 00:13:24.820 --> 00:13:28.540 align:middle line:84% For example, a big solute might bounce around 00:13:28.540 --> 00:13:31.880 align:middle line:84% more slowly so it stays in the cavity more easily. 00:13:31.880 --> 00:13:35.660 align:middle line:84% A smaller solute has a much harder time 00:13:35.660 --> 00:13:37.860 align:middle line:84% and has a higher diffusion rate, and it's 00:13:37.860 --> 00:13:41.060 align:middle line:84% going to bounce out quite quickly. 00:13:41.060 --> 00:13:48.620 align:middle line:84% And then the third component is the solute-solvent interaction, 00:13:48.620 --> 00:13:53.220 align:middle line:84% which of course, depends upon both the solute and the solvent. 00:13:53.220 --> 00:13:57.220 align:middle line:84% And this is things like, we know that water is polar, 00:13:57.220 --> 00:14:01.780 align:middle line:84% unless it's 400 degrees and 5,000 bars. 00:14:01.780 --> 00:14:06.220 align:middle line:84% Water is going to be polar, and so polar gas molecules 00:14:06.220 --> 00:14:11.720 align:middle line:84% are going to be more soluble than non-polar gas molecules, 00:14:11.720 --> 00:14:13.500 align:middle line:90% because it's easier. 00:14:13.500 --> 00:14:18.620 align:middle line:84% You gain energy back from the solute-solvent interaction, 00:14:18.620 --> 00:14:21.380 align:middle line:84% and it helps if things are polar. 00:14:21.380 --> 00:14:27.020 align:middle line:84% Now, there's some examples in the notes. 00:14:27.020 --> 00:14:32.500 align:middle line:84% We're going to do a fair amount of stuff looking at noble gases. 00:14:32.500 --> 00:14:38.250 align:middle line:84% So the noble gases are helium up to xenon. 00:14:38.250 --> 00:14:40.090 align:middle line:90% Yeah. 00:14:40.090 --> 00:14:42.490 align:middle line:84% And a lot of the gas exchange work 00:14:42.490 --> 00:14:46.050 align:middle line:84% has focused on those, because those are the geochemical things 00:14:46.050 --> 00:14:48.370 align:middle line:90% that you want to know. 00:14:48.370 --> 00:14:53.010 align:middle line:84% But they don't have other physical and biological sources 00:14:53.010 --> 00:14:53.930 align:middle line:90% and sinks. 00:14:53.930 --> 00:14:58.010 align:middle line:84% And so you can isolate using the noble gases, what's 00:14:58.010 --> 00:14:59.670 align:middle line:90% going on with gas exchange. 00:14:59.670 --> 00:15:02.110 align:middle line:84% And then you can apply them to your molecule of interest, 00:15:02.110 --> 00:15:08.690 align:middle line:84% whether it's dimethyl sulfide, or CO2, or oxygen, or something 00:15:08.690 --> 00:15:09.390 align:middle line:90% like that. 00:15:09.390 --> 00:15:12.050 align:middle line:90% 00:15:12.050 --> 00:15:17.070 align:middle line:84% So a couple of rules about solubility. 00:15:17.070 --> 00:15:22.290 align:middle line:84% If we were to plot now the Bunsen solubility 00:15:22.290 --> 00:15:25.930 align:middle line:84% against temperature, what we would see 00:15:25.930 --> 00:15:32.156 align:middle line:84% is that helium would be down here, 00:15:32.156 --> 00:15:36.450 align:middle line:90% and xenon would be up here. 00:15:36.450 --> 00:15:37.590 align:middle line:90% So there's a couple things. 00:15:37.590 --> 00:15:45.050 align:middle line:90% One is, solubility-- sorry-- 00:15:45.050 --> 00:15:50.650 align:middle line:84% increases as you decrease temperature. 00:15:50.650 --> 00:15:51.830 align:middle line:90% And that makes sense. 00:15:51.830 --> 00:15:53.550 align:middle line:84% Colder water is going to hold more gas. 00:15:53.550 --> 00:15:57.410 align:middle line:84% If anybody's ever played with a soda can or a soda bottle, 00:15:57.410 --> 00:16:01.350 align:middle line:84% if it's warm, you open it up, it spills all over the place. 00:16:01.350 --> 00:16:05.010 align:middle line:84% Well, that's because a lot of the CO2 in the carbonated water 00:16:05.010 --> 00:16:07.570 align:middle line:84% has degassed and is sitting over the lid, where 00:16:07.570 --> 00:16:10.530 align:middle line:84% if you cool it down, put it in the refrigerator, 00:16:10.530 --> 00:16:12.330 align:middle line:84% more of that gas goes into the water 00:16:12.330 --> 00:16:14.450 align:middle line:90% and you have less pressure-- 00:16:14.450 --> 00:16:18.810 align:middle line:84% a smaller pressure then built up underneath the cap. 00:16:18.810 --> 00:16:21.850 align:middle line:84% The other thing is that there tends 00:16:21.850 --> 00:16:25.030 align:middle line:84% to be a relationship in this case for the noble gases, 00:16:25.030 --> 00:16:33.390 align:middle line:84% where the larger gases are more soluble. 00:16:33.390 --> 00:16:43.210 align:middle line:90% 00:16:43.210 --> 00:16:48.990 align:middle line:84% And if you want details on that, there's more. 00:16:48.990 --> 00:16:50.530 align:middle line:84% There's a nice figure in your notes, 00:16:50.530 --> 00:16:54.930 align:middle line:84% and tables and the references to go look up coefficients. 00:16:54.930 --> 00:16:59.450 align:middle line:84% I should warn you that often these betas, just 00:16:59.450 --> 00:17:04.450 align:middle line:84% like what we saw for, say, temperature and salinity, 00:17:04.450 --> 00:17:11.250 align:middle line:84% where you're given an equation, a very complicated polynomial. 00:17:11.250 --> 00:17:14.890 align:middle line:84% That's also the way that these are calculated for seawater 00:17:14.890 --> 00:17:17.550 align:middle line:84% because of salinity effects and temperature effects, 00:17:17.550 --> 00:17:19.849 align:middle line:84% as you will usually be some long polynomial 00:17:19.849 --> 00:17:21.970 align:middle line:84% as a function of temperature and salinity 00:17:21.970 --> 00:17:24.690 align:middle line:84% that will give you an exact value. 00:17:24.690 --> 00:17:28.569 align:middle line:84% But there are tables and curves you can pick up. 00:17:28.569 --> 00:17:33.240 align:middle line:84% The other thing is that salinity-- 00:17:33.240 --> 00:17:37.920 align:middle line:84% salinity works to disrupt some of these solute-solvent 00:17:37.920 --> 00:17:43.800 align:middle line:84% interactions because of all the large ion charges bouncing 00:17:43.800 --> 00:17:48.920 align:middle line:90% around and all of the-- 00:17:48.920 --> 00:17:52.760 align:middle line:84% basically, yeah, because of all the high ionic strength. 00:17:52.760 --> 00:17:55.300 align:middle line:84% It disrupts some of the solute-solvent interactions, 00:17:55.300 --> 00:17:58.400 align:middle line:84% which actually help make the gas more soluble. 00:17:58.400 --> 00:18:05.320 align:middle line:84% And so as you increase salinity, you decrease solubility. 00:18:05.320 --> 00:18:08.580 align:middle line:90% And this is often written as-- 00:18:08.580 --> 00:18:11.640 align:middle line:90% 00:18:11.640 --> 00:18:14.400 align:middle line:84% I'm not going to test you on spelling on this one 00:18:14.400 --> 00:18:15.800 align:middle line:90% because I never-- 00:18:15.800 --> 00:18:21.080 align:middle line:84% It's the [INAUDIBLE] relation, which 00:18:21.080 --> 00:18:27.280 align:middle line:84% basically says if you had your Bunsen coefficient 00:18:27.280 --> 00:18:31.680 align:middle line:84% for fresh water and your Bunsen coefficient for whatever 00:18:31.680 --> 00:18:38.720 align:middle line:84% salinity, those are related, and you can actually calculate them 00:18:38.720 --> 00:18:40.480 align:middle line:90% as a function of salinity. 00:18:40.480 --> 00:18:42.360 align:middle line:90% This is an approximation. 00:18:42.360 --> 00:18:45.160 align:middle line:84% In reality, we're going to use the full polynomials. 00:18:45.160 --> 00:18:47.780 align:middle line:84% But it basically says that if salinity goes up, 00:18:47.780 --> 00:18:50.320 align:middle line:90% solubility goes down. 00:18:50.320 --> 00:18:52.640 align:middle line:84% And it's a fairly substantial effect. 00:18:52.640 --> 00:18:55.800 align:middle line:90% It's order of 20%, 30%. 00:18:55.800 --> 00:18:58.260 align:middle line:84% STUDENT: Does that also hold for nonpolar gases 00:18:58.260 --> 00:19:01.200 align:middle line:84% that [INAUDIBLE] be for solubility [INAUDIBLE]? 00:19:01.200 --> 00:19:05.760 align:middle line:84% PROFESSOR: Well, even like the noble gases can 00:19:05.760 --> 00:19:08.720 align:middle line:90% have small inducible polarity. 00:19:08.720 --> 00:19:10.880 align:middle line:90% STUDENT: Something like methane? 00:19:10.880 --> 00:19:12.540 align:middle line:84% PROFESSOR: Oh, yeah, methane, as well. 00:19:12.540 --> 00:19:15.360 align:middle line:84% But even like xenon has a salting out effect 00:19:15.360 --> 00:19:20.080 align:middle line:84% because it can be inducibly polar, which 00:19:20.080 --> 00:19:21.840 align:middle line:84% is why you can actually make some-- 00:19:21.840 --> 00:19:24.780 align:middle line:84% you can actually do some stuff with noble gases. 00:19:24.780 --> 00:19:28.710 align:middle line:90% 00:19:28.710 --> 00:19:34.550 align:middle line:84% So that's all we're going to cover on solubility. 00:19:34.550 --> 00:19:36.870 align:middle line:90% Any questions on that? 00:19:36.870 --> 00:19:40.070 align:middle line:84% If anybody wants, we got one of the world's experts 00:19:40.070 --> 00:19:42.130 align:middle line:84% on this of stuff here, Bill Jenkins. 00:19:42.130 --> 00:19:45.510 align:middle line:84% And he you can go talk to him, and have coffee 00:19:45.510 --> 00:19:47.450 align:middle line:90% and spend the afternoon. 00:19:47.450 --> 00:19:50.270 align:middle line:90% 00:19:50.270 --> 00:19:51.430 align:middle line:90% Great. 00:19:51.430 --> 00:20:00.110 align:middle line:84% So we'll go back to our simple flux model for the flux. 00:20:00.110 --> 00:20:03.310 align:middle line:84% We're going to start to delve into what we're going 00:20:03.310 --> 00:20:05.510 align:middle line:90% to call the kinetic component. 00:20:05.510 --> 00:20:09.870 align:middle line:84% It's often approximated by this coefficient, little k. 00:20:09.870 --> 00:20:14.430 align:middle line:84% And sorry, this is just notational. 00:20:14.430 --> 00:20:16.310 align:middle line:90% Gas exchanges notational help. 00:20:16.310 --> 00:20:18.990 align:middle line:84% These come from so many different fields. 00:20:18.990 --> 00:20:23.750 align:middle line:84% The [INAUDIBLE] relation uses a little k with an S. k 00:20:23.750 --> 00:20:26.790 align:middle line:84% is just what is typically used for the kinetic component in gas 00:20:26.790 --> 00:20:30.910 align:middle line:84% exchange, and I think I've kept it straight in the notes. 00:20:30.910 --> 00:20:33.590 align:middle line:84% But usually, it's going to be formulated as something 00:20:33.590 --> 00:20:42.150 align:middle line:84% like a kinetic component times the concentration in the water. 00:20:42.150 --> 00:20:46.530 align:middle line:84% So I'm going to use C is the concentration in the bulk water. 00:20:46.530 --> 00:20:51.510 align:middle line:90% 00:20:51.510 --> 00:21:00.670 align:middle line:84% And C0 is the atmospheric equilibrium concentration. 00:21:00.670 --> 00:21:04.770 align:middle line:90% So C0 is a fictional quantity. 00:21:04.770 --> 00:21:09.070 align:middle line:84% It would be what the water right at the very surface that's 00:21:09.070 --> 00:21:12.990 align:middle line:84% just touching the gas would have as a concentration. 00:21:12.990 --> 00:21:15.790 align:middle line:90% You don't actually measure C0. 00:21:15.790 --> 00:21:18.870 align:middle line:84% What you do is you measure the atmospheric partial pressure, 00:21:18.870 --> 00:21:20.990 align:middle line:90% and then you compute C0. 00:21:20.990 --> 00:21:26.100 align:middle line:84% So C0 would be that Bunsen coefficient times the pressure 00:21:26.100 --> 00:21:27.040 align:middle line:90% in the atmosphere. 00:21:27.040 --> 00:21:33.100 align:middle line:90% 00:21:33.100 --> 00:21:35.220 align:middle line:84% So this is kind of going back to, 00:21:35.220 --> 00:21:38.540 align:middle line:84% remember, the kinetic component and the thermodynamic component. 00:21:38.540 --> 00:21:40.580 align:middle line:84% This is going to be the kinetic component. 00:21:40.580 --> 00:21:43.740 align:middle line:84% This is going to be the thermodynamic component. 00:21:43.740 --> 00:21:46.140 align:middle line:84% So the thermodynamic component, you go out 00:21:46.140 --> 00:21:48.680 align:middle line:84% and you make measurements [INAUDIBLE]. 00:21:48.680 --> 00:21:51.338 align:middle line:90% 00:21:51.338 --> 00:21:53.380 align:middle line:84% And you make measurements of the partial pressure 00:21:53.380 --> 00:21:54.480 align:middle line:90% in the atmosphere. 00:21:54.480 --> 00:22:01.340 align:middle line:90% 00:22:01.340 --> 00:22:03.780 align:middle line:84% Now, one confusing thing is often, 00:22:03.780 --> 00:22:06.140 align:middle line:84% the way people make concentration measurements 00:22:06.140 --> 00:22:11.180 align:middle line:84% in the water is they take a bottle-- a blob. 00:22:11.180 --> 00:22:14.780 align:middle line:84% A blob-- a blob of water, a parcel of water. 00:22:14.780 --> 00:22:19.060 align:middle line:84% And then the way they instead of making concentration 00:22:19.060 --> 00:22:24.420 align:middle line:84% measurements, they may take this and actually compute 00:22:24.420 --> 00:22:28.020 align:middle line:90% its own partial pressure-- 00:22:28.020 --> 00:22:30.540 align:middle line:90% seawater partial pressure. 00:22:30.540 --> 00:22:35.060 align:middle line:84% So sometimes you'll see this instead of being written as k, C 00:22:35.060 --> 00:22:41.340 align:middle line:84% minus C0, you might see it as k, P minus P0, where 00:22:41.340 --> 00:22:46.460 align:middle line:90% or PSW minus PA. 00:22:46.460 --> 00:22:48.780 align:middle line:84% Just for some gases it's instead of-- it's easier 00:22:48.780 --> 00:22:52.100 align:middle line:84% to make partial pressure measurements for the seawater, 00:22:52.100 --> 00:22:54.780 align:middle line:84% rather than to make concentration measurements. 00:22:54.780 --> 00:22:57.640 align:middle line:84% Just depends upon what the easiest chemical technique is. 00:22:57.640 --> 00:23:03.380 align:middle line:90% 00:23:03.380 --> 00:23:06.580 align:middle line:90% Everybody set with that? 00:23:06.580 --> 00:23:08.100 align:middle line:90% OK. 00:23:08.100 --> 00:23:13.440 align:middle line:84% So there are several models of gas exchange, 00:23:13.440 --> 00:23:16.100 align:middle line:84% and these are really simple conceptual models 00:23:16.100 --> 00:23:24.500 align:middle line:84% to give you some framework in which to interpret observations. 00:23:24.500 --> 00:23:28.680 align:middle line:84% The first one is called the stagnant film model. 00:23:28.680 --> 00:23:36.900 align:middle line:90% 00:23:36.900 --> 00:23:39.460 align:middle line:84% And the stagnant film model is going 00:23:39.460 --> 00:23:43.300 align:middle line:84% to try to simplify everything by saying 00:23:43.300 --> 00:23:50.100 align:middle line:84% that if we were to plot depth, and we're 00:23:50.100 --> 00:23:52.820 align:middle line:90% going to plot concentration. 00:23:52.820 --> 00:23:54.660 align:middle line:84% So we're going to start off with at C0. 00:23:54.660 --> 00:23:58.060 align:middle line:90% 00:23:58.060 --> 00:24:02.980 align:middle line:84% We're going to say that the atmosphere is well mixed. 00:24:02.980 --> 00:24:04.620 align:middle line:84% And for most of the gases we're going 00:24:04.620 --> 00:24:06.540 align:middle line:84% to be talking about in this class, 00:24:06.540 --> 00:24:09.420 align:middle line:84% it's a pretty good assumption that most 00:24:09.420 --> 00:24:12.840 align:middle line:84% of the resistance to gas exchange is on the water side, 00:24:12.840 --> 00:24:15.380 align:middle line:84% not on the air side, because they're 00:24:15.380 --> 00:24:24.970 align:middle line:84% what are called sparingly soluble gases, so 00:24:24.970 --> 00:24:30.710 align:middle line:84% things like CO2, O2, N2, the noble gases. 00:24:30.710 --> 00:24:33.970 align:middle line:90% 00:24:33.970 --> 00:24:37.190 align:middle line:84% They're soluble in seawater, but they're not significant. 00:24:37.190 --> 00:24:41.370 align:middle line:84% It's not significantly soluble in seawater. 00:24:41.370 --> 00:24:45.530 align:middle line:84% So you can basically make the assumption 00:24:45.530 --> 00:24:48.530 align:middle line:84% that the atmosphere, the transport 00:24:48.530 --> 00:24:54.770 align:middle line:84% is so quick that the atmosphere is a well-mixed box. 00:24:54.770 --> 00:24:57.630 align:middle line:84% So this C0, you make an atmospheric measurement, 00:24:57.630 --> 00:24:59.490 align:middle line:84% and then you can say, OK, I'm going 00:24:59.490 --> 00:25:01.730 align:middle line:84% to know what the concentration and equilibrium is 00:25:01.730 --> 00:25:04.130 align:middle line:90% right at the surface. 00:25:04.130 --> 00:25:08.570 align:middle line:84% For the stagnant film model, it's just like what it says. 00:25:08.570 --> 00:25:13.690 align:middle line:84% Stagnant film where the only processes going on 00:25:13.690 --> 00:25:16.750 align:middle line:84% are diffusion, molecular diffusion. 00:25:16.750 --> 00:25:22.530 align:middle line:90% 00:25:22.530 --> 00:25:26.030 align:middle line:90% So we have that relationship. 00:25:26.030 --> 00:25:30.130 align:middle line:90% Remember, we have flux, right? 00:25:30.130 --> 00:25:35.123 align:middle line:84% The flux across this stagnant film is going to be constant. 00:25:35.123 --> 00:25:37.290 align:middle line:84% We're going to assume there's no chemical reactions, 00:25:37.290 --> 00:25:38.710 align:middle line:90% no biological reactions. 00:25:38.710 --> 00:25:40.810 align:middle line:90% There's a very small film. 00:25:40.810 --> 00:25:45.410 align:middle line:84% So if you have molecular diffusion going on, 00:25:45.410 --> 00:25:47.210 align:middle line:84% and you have no sources and sinks, 00:25:47.210 --> 00:25:49.730 align:middle line:84% and you have a constant flux, can anybody 00:25:49.730 --> 00:25:51.650 align:middle line:84% tell me what the profile is going 00:25:51.650 --> 00:25:55.250 align:middle line:84% to look through that stagnant film layer? 00:25:55.250 --> 00:25:56.910 align:middle line:84% You may have molecular diffusion. 00:25:56.910 --> 00:26:00.530 align:middle line:90% 00:26:00.530 --> 00:26:01.390 align:middle line:90% Straight line. 00:26:01.390 --> 00:26:02.410 align:middle line:90% Good guess. 00:26:02.410 --> 00:26:03.990 align:middle line:90% Well, or good knowledge. 00:26:03.990 --> 00:26:06.470 align:middle line:90% [LAUGHING] 00:26:06.470 --> 00:26:08.450 align:middle line:90% 00:26:08.450 --> 00:26:10.730 align:middle line:84% Across that stagnant film, there's actually 00:26:10.730 --> 00:26:12.810 align:middle line:90% going to be a straight line. 00:26:12.810 --> 00:26:14.543 align:middle line:90% And then there's going to be-- 00:26:14.543 --> 00:26:15.960 align:middle line:84% we're going to assume that there's 00:26:15.960 --> 00:26:22.680 align:middle line:84% some bulk concentration, C, and that the Oceanside is actually 00:26:22.680 --> 00:26:24.320 align:middle line:90% well mixed, as well. 00:26:24.320 --> 00:26:27.440 align:middle line:84% So all the turbulence that's going on down here 00:26:27.440 --> 00:26:29.880 align:middle line:84% keeps this infinitely well mixed. 00:26:29.880 --> 00:26:32.240 align:middle line:84% There's this stagnant film layer and then 00:26:32.240 --> 00:26:35.640 align:middle line:84% an infinitely well mixed atmosphere. 00:26:35.640 --> 00:26:38.340 align:middle line:84% The reason why this is a straight line, if you remember, 00:26:38.340 --> 00:26:50.840 align:middle line:84% from Fickian diffusion, Fickian diffusion or molecular diffusion 00:26:50.840 --> 00:26:53.760 align:middle line:84% says that the flux is simply equal to a diffusion 00:26:53.760 --> 00:26:56.400 align:middle line:90% coefficient times the gradient. 00:26:56.400 --> 00:27:01.340 align:middle line:84% Well, if the flux is fixed and the diffusivity is fixed, 00:27:01.340 --> 00:27:02.540 align:middle line:90% you have a constant flux. 00:27:02.540 --> 00:27:05.520 align:middle line:84% Otherwise, you'd be draining or adding gas in and out 00:27:05.520 --> 00:27:06.780 align:middle line:90% of the stagnant film layer. 00:27:06.780 --> 00:27:10.402 align:middle line:90% 00:27:10.402 --> 00:27:12.120 align:middle line:84% But the only way for that to occur 00:27:12.120 --> 00:27:15.500 align:middle line:84% is if you have a constant gradient and a constant gradient 00:27:15.500 --> 00:27:16.485 align:middle line:90% [INAUDIBLE]. 00:27:16.485 --> 00:27:20.920 align:middle line:90% 00:27:20.920 --> 00:27:23.440 align:middle line:84% Where the stagnant film comes in is 00:27:23.440 --> 00:27:27.720 align:middle line:84% we're going to say that this stagnant film has a thickness 00:27:27.720 --> 00:27:28.620 align:middle line:90% delta z. 00:27:28.620 --> 00:27:32.200 align:middle line:90% 00:27:32.200 --> 00:27:35.720 align:middle line:84% So we're going to approximate the Fickian diffusion 00:27:35.720 --> 00:27:47.920 align:middle line:84% as flux equals minus D, delta C, over delta z. 00:27:47.920 --> 00:27:51.640 align:middle line:84% So we're just turning the little d DC and Dz 00:27:51.640 --> 00:27:55.160 align:middle line:90% into delta C and delta z. 00:27:55.160 --> 00:27:59.680 align:middle line:84% Then we're going to say, well, we have minus D, delta z. 00:27:59.680 --> 00:28:05.060 align:middle line:84% And then the delta C is just the C minus C0. 00:28:05.060 --> 00:28:09.440 align:middle line:90% 00:28:09.440 --> 00:28:12.010 align:middle line:90% So these things we can measure. 00:28:12.010 --> 00:28:15.630 align:middle line:90% 00:28:15.630 --> 00:28:19.430 align:middle line:84% We know D. We can look that up in a table. 00:28:19.430 --> 00:28:20.650 align:middle line:90% It's a diffusivity. 00:28:20.650 --> 00:28:26.270 align:middle line:90% 00:28:26.270 --> 00:28:31.710 align:middle line:84% So we could rearrange this equation. 00:28:31.710 --> 00:28:36.830 align:middle line:84% If we could estimate f from some measurements, 00:28:36.830 --> 00:28:41.910 align:middle line:84% we could then turn around and calculate delta z. 00:28:41.910 --> 00:28:46.910 align:middle line:84% It's like, well, I'm not really interested in delta C or delta z 00:28:46.910 --> 00:28:47.830 align:middle line:90% per se. 00:28:47.830 --> 00:28:53.750 align:middle line:84% But if I had a set of gases for which I could measure the fluxes 00:28:53.750 --> 00:28:56.790 align:middle line:84% and then compute delta z, I could then 00:28:56.790 --> 00:29:00.630 align:middle line:84% use that delta z for other gases for which I couldn't 00:29:00.630 --> 00:29:02.010 align:middle line:90% make flux measurements. 00:29:02.010 --> 00:29:04.870 align:middle line:90% 00:29:04.870 --> 00:29:06.690 align:middle line:90% That make sense? 00:29:06.690 --> 00:29:10.590 align:middle line:90% 00:29:10.590 --> 00:29:17.850 align:middle line:84% And often-- oh, yeah, let's do one thing-- 00:29:17.850 --> 00:29:26.150 align:middle line:84% the diffusivities, the units on those 00:29:26.150 --> 00:29:29.390 align:middle line:90% are length squared over time. 00:29:29.390 --> 00:29:32.970 align:middle line:84% So meters squared per second, for example, 00:29:32.970 --> 00:29:35.830 align:middle line:90% is a typical diffusivity. 00:29:35.830 --> 00:29:44.070 align:middle line:84% It depends upon temperature, and the solute and the solvent. 00:29:44.070 --> 00:29:47.950 align:middle line:84% So you actually need to know what gas it is 00:29:47.950 --> 00:29:51.390 align:middle line:90% and whether it's in water. 00:29:51.390 --> 00:29:53.830 align:middle line:84% Water has different diffusivities 00:29:53.830 --> 00:29:57.670 align:middle line:90% than magma or methanol. 00:29:57.670 --> 00:30:00.710 align:middle line:84% And you also know the temperature. 00:30:00.710 --> 00:30:05.790 align:middle line:84% D tends to increase with increasing temperature. 00:30:05.790 --> 00:30:12.420 align:middle line:84% So if warmer waters, diffusion tends to occur faster. 00:30:12.420 --> 00:30:21.580 align:middle line:84% And also, as molecular weight goes up, diffusivity goes down. 00:30:21.580 --> 00:30:28.740 align:middle line:84% So bigger molecules tend to diffuse slower. 00:30:28.740 --> 00:30:31.740 align:middle line:84% Now, for the noble gases, there's 00:30:31.740 --> 00:30:33.500 align:middle line:90% nice sets of relationships. 00:30:33.500 --> 00:30:38.740 align:middle line:84% As soon as you get a molecule that is not spherical, then 00:30:38.740 --> 00:30:40.240 align:middle line:90% it's not just molecular weight. 00:30:40.240 --> 00:30:45.340 align:middle line:84% It's also its polarity and its actual shape. 00:30:45.340 --> 00:30:48.660 align:middle line:84% But these can be-- these are recorded, 00:30:48.660 --> 00:30:50.080 align:middle line:90% have been measured in the lab. 00:30:50.080 --> 00:30:52.122 align:middle line:84% They've been measured in the lab for fresh water. 00:30:52.122 --> 00:30:54.780 align:middle line:84% They've been measured in the lab as a function of salinity 00:30:54.780 --> 00:30:56.180 align:middle line:90% and temperature. 00:30:56.180 --> 00:30:59.020 align:middle line:90% 00:30:59.020 --> 00:31:05.420 align:middle line:84% So let's show an example of how you might do this. 00:31:05.420 --> 00:31:11.240 align:middle line:84% So we're going to talk about radon. 00:31:11.240 --> 00:31:13.820 align:middle line:90% 00:31:13.820 --> 00:31:16.420 align:middle line:84% Everybody remembers from Bill Martin's lecture 00:31:16.420 --> 00:31:21.700 align:middle line:84% on radioactive isotopes and radionuclides. 00:31:21.700 --> 00:31:26.640 align:middle line:84% Everybody remembers that radon 222 is a daughter of what? 00:31:26.640 --> 00:31:32.940 align:middle line:90% 00:31:32.940 --> 00:31:34.340 align:middle line:90% STUDENT: Radium 226. 00:31:34.340 --> 00:31:36.480 align:middle line:90% PROFESSOR: Right. 00:31:36.480 --> 00:31:44.700 align:middle line:84% Radon 222 is the daughter of radium 226, or yeah, radium 226. 00:31:44.700 --> 00:31:48.780 align:middle line:90% And so this is a gas. 00:31:48.780 --> 00:31:52.020 align:middle line:90% This is not a gas. 00:31:52.020 --> 00:31:59.220 align:middle line:84% And so, because the radium is always decaying to radon 222, 00:31:59.220 --> 00:32:04.140 align:middle line:84% we can look at the imbalance between how much radon 00:32:04.140 --> 00:32:07.260 align:middle line:84% you would expect to see based on how much radium 00:32:07.260 --> 00:32:10.780 align:middle line:84% is there versus how much is actually there. 00:32:10.780 --> 00:32:16.740 align:middle line:84% Remember, we would expect the activity of radon 222 00:32:16.740 --> 00:32:21.660 align:middle line:84% to equal the activity of radium 226, 00:32:21.660 --> 00:32:24.980 align:middle line:84% unless there's some process that's removing the radium. 00:32:24.980 --> 00:32:30.060 align:middle line:84% This is the secular equilibrium that Bill 00:32:30.060 --> 00:32:33.620 align:middle line:90% talked about quite a bit. 00:32:33.620 --> 00:32:39.500 align:middle line:84% So if you were to look in the field, what you'll often see 00:32:39.500 --> 00:32:49.460 align:middle line:84% is that in the deep water, this would be depth 00:32:49.460 --> 00:32:53.860 align:middle line:84% and this would be, say, 100 meters. 00:32:53.860 --> 00:33:05.490 align:middle line:84% What you might see is that the activity of radon 222 00:33:05.490 --> 00:33:10.370 align:middle line:84% is low in the surface, and then tends to increase at depth, 00:33:10.370 --> 00:33:15.530 align:middle line:84% and this dashed line is the activity of 226. 00:33:15.530 --> 00:33:18.130 align:middle line:84% And so deep in the water column, they 00:33:18.130 --> 00:33:20.610 align:middle line:84% are in secular equilibrium with each other. 00:33:20.610 --> 00:33:25.090 align:middle line:84% And right up near the surface in the mixed layer, 00:33:25.090 --> 00:33:30.690 align:middle line:84% there tends to be a deficit of radon. 00:33:30.690 --> 00:33:34.790 align:middle line:84% And that's simply because radon has been lifting out the top. 00:33:34.790 --> 00:33:38.010 align:middle line:90% 00:33:38.010 --> 00:33:42.670 align:middle line:90% Now, everybody have that? 00:33:42.670 --> 00:33:45.490 align:middle line:90% Can I switch? 00:33:45.490 --> 00:33:47.290 align:middle line:90% You guys studied at MIT? 00:33:47.290 --> 00:33:48.450 align:middle line:90% OK. 00:33:48.450 --> 00:34:02.930 align:middle line:84% So what we want to do is set up a mass balance for radon 222, 00:34:02.930 --> 00:34:06.950 align:middle line:84% and we're going to do it over the mixed layer. 00:34:06.950 --> 00:34:12.850 align:middle line:90% 00:34:12.850 --> 00:34:21.510 align:middle line:84% So remember the little diagram I had, where that's radon 222, 00:34:21.510 --> 00:34:24.050 align:middle line:90% and this is the radon 226. 00:34:24.050 --> 00:34:27.130 align:middle line:84% We're going to approximate and say that there's going 00:34:27.130 --> 00:34:30.050 align:middle line:90% to be some mixed layer depth h. 00:34:30.050 --> 00:34:32.570 align:middle line:84% And we're just going to look at the mixed layer, 00:34:32.570 --> 00:34:34.650 align:middle line:84% and we're going to assume that everything is well 00:34:34.650 --> 00:34:36.770 align:middle line:90% mixed within that mixed layer. 00:34:36.770 --> 00:34:38.730 align:middle line:84% If you had to do the calculation for real, 00:34:38.730 --> 00:34:42.489 align:middle line:84% you could integrate over that and find out 00:34:42.489 --> 00:34:43.550 align:middle line:90% averages and all that. 00:34:43.550 --> 00:34:47.090 align:middle line:84% But typically, things are pretty well mixed in the mixed layer, 00:34:47.090 --> 00:34:52.730 align:middle line:84% and for first order, that's a good assumption. 00:34:52.730 --> 00:35:03.520 align:middle line:84% So we're going to say we want to know the first look 00:35:03.520 --> 00:35:07.120 align:middle line:90% at the production terms. 00:35:07.120 --> 00:35:10.560 align:middle line:84% The production term of radon 222 is simply 00:35:10.560 --> 00:35:21.000 align:middle line:84% going to be the mixed layer depth times the activity of 226. 00:35:21.000 --> 00:35:25.160 align:middle line:84% So radioactive decay is producing radon, 00:35:25.160 --> 00:35:29.520 align:middle line:84% and if we know the radium activity, 00:35:29.520 --> 00:35:35.120 align:middle line:84% that gives us the production rate of radon. 00:35:35.120 --> 00:35:39.520 align:middle line:84% There's going to be two loss terms. 00:35:39.520 --> 00:35:44.360 align:middle line:84% One is simply going to be the mixed layer depth 00:35:44.360 --> 00:35:53.920 align:middle line:90% times the activity of 222. 00:35:53.920 --> 00:35:59.000 align:middle line:84% The second one is going to be a flux term, which 00:35:59.000 --> 00:36:09.800 align:middle line:84% is going to depend upon a piston velocity, which 00:36:09.800 --> 00:36:15.420 align:middle line:84% I'll get to in a minute, times a delta concentration. 00:36:15.420 --> 00:36:21.080 align:middle line:84% Remember, that was the flux form that we showed previously. 00:36:21.080 --> 00:36:27.400 align:middle line:84% So from the stagnant film model, this 00:36:27.400 --> 00:36:31.960 align:middle line:84% is going to be-- this term stays the same. 00:36:31.960 --> 00:36:39.320 align:middle line:84% We're going to assume that the atmosphere has no radon 222. 00:36:39.320 --> 00:36:40.980 align:middle line:90% And that's not a bad assumption. 00:36:40.980 --> 00:36:44.800 align:middle line:84% The half life for radon is about four days. 00:36:44.800 --> 00:36:46.560 align:middle line:84% And so over the open [INAUDIBLE], 00:36:46.560 --> 00:36:49.140 align:middle line:84% the amount of radon in the atmosphere is really small. 00:36:49.140 --> 00:36:52.840 align:middle line:84% That's not true over land because you 00:36:52.840 --> 00:36:58.790 align:middle line:84% have outgassing of-- you have uranium-rich soils and rocks, 00:36:58.790 --> 00:37:02.590 align:middle line:84% have a lot of radium, and you get a lot of radon out. 00:37:02.590 --> 00:37:05.470 align:middle line:84% Fills up your basement, fills up your shower. 00:37:05.470 --> 00:37:12.070 align:middle line:84% So we're going to assume that the sea-atmosphere for radon 00:37:12.070 --> 00:37:13.050 align:middle line:90% goes to zero. 00:37:13.050 --> 00:37:16.070 align:middle line:90% 00:37:16.070 --> 00:37:21.870 align:middle line:84% And we're also going to assume a stagnant film. 00:37:21.870 --> 00:37:25.670 align:middle line:84% So then what we would need to know 00:37:25.670 --> 00:37:36.270 align:middle line:84% is simply the diffusion rate of radon over the stagnant film 00:37:36.270 --> 00:37:37.270 align:middle line:90% depth-- 00:37:37.270 --> 00:37:39.110 align:middle line:84% remember that's the piston velocity-- 00:37:39.110 --> 00:37:42.820 align:middle line:90% 00:37:42.820 --> 00:37:50.150 align:middle line:84% times the concentration of radon 222. 00:37:50.150 --> 00:37:56.830 align:middle line:84% Now, usually, this is formulated in terms of [INAUDIBLE] 00:37:56.830 --> 00:38:03.550 align:middle line:90% 00:38:03.550 --> 00:38:09.950 align:middle line:84% --constant number of molecules that are there. 00:38:09.950 --> 00:38:11.030 align:middle line:90% Yep. 00:38:11.030 --> 00:38:12.250 align:middle line:90% Oh, did I drop out? 00:38:12.250 --> 00:38:14.990 align:middle line:90% 00:38:14.990 --> 00:38:16.950 align:middle line:90% STUDENT: We lost them too. 00:38:16.950 --> 00:38:18.490 align:middle line:84% PROFESSOR: We can't hear you either, 00:38:18.490 --> 00:38:21.150 align:middle line:90% so we'll give it a second. 00:38:21.150 --> 00:38:23.110 align:middle line:90% The answers to the midterm are-- 00:38:23.110 --> 00:38:25.370 align:middle line:90% [LAUGHING] 00:38:25.370 --> 00:38:27.522 align:middle line:90% 00:38:27.522 --> 00:38:29.230 align:middle line:84% STUDENT: I think she said she heard that. 00:38:29.230 --> 00:38:31.476 align:middle line:90% STUDENT: Do we have you back? 00:38:31.476 --> 00:38:32.670 align:middle line:90% I'm out. 00:38:32.670 --> 00:38:36.590 align:middle line:90% PROFESSOR: OK, cool. 00:38:36.590 --> 00:38:38.010 align:middle line:90% How far back did you miss? 00:38:38.010 --> 00:38:40.630 align:middle line:90% 00:38:40.630 --> 00:38:43.870 align:middle line:84% STUDENT: I'm below the word loss. 00:38:43.870 --> 00:38:44.910 align:middle line:90% PROFESSOR: OK. 00:38:44.910 --> 00:38:47.870 align:middle line:84% So what I was saying was that there's two components 00:38:47.870 --> 00:38:49.530 align:middle line:90% to the loss term. 00:38:49.530 --> 00:38:53.150 align:middle line:84% There's going to be radioactive decay for radon, 00:38:53.150 --> 00:38:56.790 align:middle line:84% and then there's going to be gas exchange. 00:38:56.790 --> 00:39:00.590 align:middle line:84% And the gas exchange is going to depend upon the concentration 00:39:00.590 --> 00:39:05.350 align:middle line:84% difference across the interface and a piston velocity. 00:39:05.350 --> 00:39:09.030 align:middle line:84% We're going to assume that the concentration of radon-- 00:39:09.030 --> 00:39:12.310 align:middle line:90% so this would be for radon-- 00:39:12.310 --> 00:39:14.150 align:middle line:90% is going to be zero. 00:39:14.150 --> 00:39:18.470 align:middle line:84% And so all you need to know is the concentration of radon 00:39:18.470 --> 00:39:21.270 align:middle line:84% in the water because that's going to drive gas 00:39:21.270 --> 00:39:24.190 align:middle line:90% exchange across the interface. 00:39:24.190 --> 00:39:27.580 align:middle line:84% So all I did was then expand this lost term, 00:39:27.580 --> 00:39:30.710 align:middle line:90% so this would still be loss. 00:39:30.710 --> 00:39:33.910 align:middle line:84% It's going to equal the radioactive loss term, 00:39:33.910 --> 00:39:37.670 align:middle line:84% and we're going to replace this k by the stagnant film model. 00:39:37.670 --> 00:39:41.390 align:middle line:84% So we have the diffusivity of radon. 00:39:41.390 --> 00:39:44.550 align:middle line:84% We have the thickness of the stagnant film. 00:39:44.550 --> 00:39:49.910 align:middle line:90% So this is that stagnant film. 00:39:49.910 --> 00:39:52.080 align:middle line:84% And then we need a concentration. 00:39:52.080 --> 00:39:55.180 align:middle line:90% 00:39:55.180 --> 00:39:59.100 align:middle line:84% And the way we're going to get that concentration is we're 00:39:59.100 --> 00:40:01.980 align:middle line:84% going to go back and remember what the definition of activity 00:40:01.980 --> 00:40:04.620 align:middle line:84% is, because usually, these are measured and reported 00:40:04.620 --> 00:40:06.060 align:middle line:90% in activities. 00:40:06.060 --> 00:40:09.580 align:middle line:84% So we want n, and n is just going 00:40:09.580 --> 00:40:13.820 align:middle line:84% to be the activity over the decay constant. 00:40:13.820 --> 00:40:15.500 align:middle line:84% So then this would be the activity 00:40:15.500 --> 00:40:20.680 align:middle line:90% of radon over lambda for radon. 00:40:20.680 --> 00:40:24.220 align:middle line:90% 00:40:24.220 --> 00:40:31.980 align:middle line:84% So if we assume steady state, which for when they first went 00:40:31.980 --> 00:40:35.540 align:middle line:84% out and started to do these experiments in the '60s, they 00:40:35.540 --> 00:40:38.300 align:middle line:84% weren't able to make the experiments long enough to see 00:40:38.300 --> 00:40:40.240 align:middle line:84% what actually was changing over time, 00:40:40.240 --> 00:40:42.523 align:middle line:90% so that's something [INAUDIBLE]. 00:40:42.523 --> 00:40:47.620 align:middle line:90% 00:40:47.620 --> 00:40:52.540 align:middle line:84% Steady state is that production equals loss. 00:40:52.540 --> 00:40:57.660 align:middle line:84% And I won't go through, but what you can find if you notes, 00:40:57.660 --> 00:41:01.980 align:middle line:84% well, is you can rearrange the equation for delta 00:41:01.980 --> 00:41:08.420 align:middle line:84% z, because everything else in here is known. 00:41:08.420 --> 00:41:11.300 align:middle line:84% H is known from your measurements. 00:41:11.300 --> 00:41:14.260 align:middle line:84% The activity of 226 is known, the activity 00:41:14.260 --> 00:41:19.540 align:middle line:84% of 222, diffusion coefficients, lambdas, et cetera. 00:41:19.540 --> 00:41:22.340 align:middle line:84% And so you can rearrange and find delta 00:41:22.340 --> 00:41:28.260 align:middle line:84% z as some function of the activities of 222 00:41:28.260 --> 00:41:32.340 align:middle line:90% and the activities of 226. 00:41:32.340 --> 00:41:37.620 align:middle line:84% And what they found was that the delta zs 00:41:37.620 --> 00:41:48.050 align:middle line:84% tended to be in the tens of microns for stagnant films. 00:41:48.050 --> 00:41:51.030 align:middle line:84% And you can go through the whole calculation in the notes, 00:41:51.030 --> 00:41:53.610 align:middle line:84% and I would recommend it because it's a pretty useful, 00:41:53.610 --> 00:41:57.210 align:middle line:84% both in terms of remembering secular equilibrium 00:41:57.210 --> 00:42:00.590 align:middle line:84% and radioactive decay, and also gas exchange. 00:42:00.590 --> 00:42:04.250 align:middle line:90% 00:42:04.250 --> 00:42:05.750 align:middle line:84% STUDENT: Can I ask a quick question? 00:42:05.750 --> 00:42:06.417 align:middle line:90% PROFESSOR: Sure. 00:42:06.417 --> 00:42:08.570 align:middle line:90% STUDENT: What's system velocity? 00:42:08.570 --> 00:42:11.130 align:middle line:90% PROFESSOR: Ah. 00:42:11.130 --> 00:42:11.750 align:middle line:90% Good question. 00:42:11.750 --> 00:42:13.203 align:middle line:90% I should have covered that. 00:42:13.203 --> 00:42:14.870 align:middle line:84% I'm going to slide this up a little bit. 00:42:14.870 --> 00:42:18.210 align:middle line:90% Do you guys have everything? 00:42:18.210 --> 00:42:24.930 align:middle line:84% Remember I wrote f equals k delta C at the very beginning? 00:42:24.930 --> 00:42:28.810 align:middle line:84% And this k can also be it's the D over delta delta 00:42:28.810 --> 00:42:30.630 align:middle line:90% z for the stagnant film model. 00:42:30.630 --> 00:42:33.610 align:middle line:90% 00:42:33.610 --> 00:42:40.770 align:middle line:84% I think I wrote it as kC minus C0, but that's the same thing. 00:42:40.770 --> 00:42:45.570 align:middle line:84% If you look at the units D has units of meters squared 00:42:45.570 --> 00:42:47.930 align:middle line:84% per second, length squared time because it's 00:42:47.930 --> 00:42:50.370 align:middle line:90% a molecular diffusivity. 00:42:50.370 --> 00:42:58.330 align:middle line:84% Z has units of 1 over m, or 1 over length. 00:42:58.330 --> 00:43:03.650 align:middle line:84% So this term k, or capital D over delta z, 00:43:03.650 --> 00:43:07.170 align:middle line:90% has units of meters per second. 00:43:07.170 --> 00:43:11.630 align:middle line:84% And it's often called a transfer velocity. 00:43:11.630 --> 00:43:14.170 align:middle line:90% 00:43:14.170 --> 00:43:16.250 align:middle line:84% I actually like transfer velocity 00:43:16.250 --> 00:43:20.490 align:middle line:84% because it so hearkens back to transport theory, transport 00:43:20.490 --> 00:43:21.570 align:middle line:90% phenomenon. 00:43:21.570 --> 00:43:24.890 align:middle line:84% But for reasons that escape me, it's 00:43:24.890 --> 00:43:27.890 align:middle line:90% also called a piston velocity. 00:43:27.890 --> 00:43:31.770 align:middle line:84% And I think the idea was that you can imagine that 00:43:31.770 --> 00:43:36.170 align:middle line:84% as this piston sitting at the bottom of the bottom 00:43:36.170 --> 00:43:39.770 align:middle line:84% of the mixed layer, pushing up, pushing the gas from the mixed 00:43:39.770 --> 00:43:41.810 align:middle line:84% layer into the atmosphere, or similarly, 00:43:41.810 --> 00:43:45.400 align:middle line:84% pushing gas from the atmosphere down into the ocean. 00:43:45.400 --> 00:43:46.920 align:middle line:90% It's really terrible. 00:43:46.920 --> 00:43:48.940 align:middle line:84% It's really terrible nomenclature, 00:43:48.940 --> 00:43:57.440 align:middle line:84% but it has leaked into the notation. 00:43:57.440 --> 00:43:59.340 align:middle line:84% But essentially, this is the kinetic. 00:43:59.340 --> 00:44:00.740 align:middle line:90% It's the kinetic. 00:44:00.740 --> 00:44:03.480 align:middle line:90% 00:44:03.480 --> 00:44:09.160 align:middle line:84% The stagnant film model is not the best model. 00:44:09.160 --> 00:44:13.280 align:middle line:84% Oh, and I should say these are order of tens-- 00:44:13.280 --> 00:44:19.120 align:middle line:84% k is typically tens of centimeters per hour. 00:44:19.120 --> 00:44:23.920 align:middle line:84% And that's just also a historical thing 00:44:23.920 --> 00:44:26.600 align:middle line:84% that ks are often reported at centimeters per hour 00:44:26.600 --> 00:44:28.740 align:middle line:90% rather than meters per second. 00:44:28.740 --> 00:44:33.460 align:middle line:84% And that's just so the units look more closer to 1. 00:44:33.460 --> 00:44:41.160 align:middle line:90% 00:44:41.160 --> 00:44:47.800 align:middle line:84% So the stagnant film model is a really good pedagogical tool 00:44:47.800 --> 00:44:50.680 align:middle line:84% and useful for the initial interpretation. 00:44:50.680 --> 00:44:53.680 align:middle line:84% But what was found was it's actually not a very good model 00:44:53.680 --> 00:44:55.742 align:middle line:90% for open ocean conditions. 00:44:55.742 --> 00:44:57.700 align:middle line:84% If you think about it, you've got this little-- 00:44:57.700 --> 00:45:03.070 align:middle line:90% 00:45:03.070 --> 00:45:05.320 align:middle line:84% you're supposed to have this little stagnant film that 00:45:05.320 --> 00:45:08.120 align:middle line:84% just sits there, and nothing happens to it. 00:45:08.120 --> 00:45:10.140 align:middle line:84% Well, if anybody's gone out to the open ocean, 00:45:10.140 --> 00:45:12.360 align:middle line:84% particularly when the wind picks up, 00:45:12.360 --> 00:45:15.440 align:middle line:84% it's hard to imagine a little constant film that 00:45:15.440 --> 00:45:18.960 align:middle line:90% stays there indefinitely. 00:45:18.960 --> 00:45:26.520 align:middle line:84% So a new model or a competing model, if you like, 00:45:26.520 --> 00:45:34.200 align:middle line:90% is the film replacement model. 00:45:34.200 --> 00:45:36.320 align:middle line:84% And the argument for the film replacement 00:45:36.320 --> 00:45:40.230 align:middle line:84% is that let's say you have some stagnant film sitting up 00:45:40.230 --> 00:45:41.090 align:middle line:90% at the surface. 00:45:41.090 --> 00:45:44.970 align:middle line:84% So it would be if you were to do this in cartoon, 00:45:44.970 --> 00:45:48.910 align:middle line:84% you might have some stagnant film that then stays there 00:45:48.910 --> 00:45:51.630 align:middle line:84% for some length of time, but then some eddy 00:45:51.630 --> 00:45:56.590 align:middle line:84% comes along and pulls that film off. 00:45:56.590 --> 00:45:59.070 align:middle line:84% And you'd have no stagnant for a while, 00:45:59.070 --> 00:46:01.950 align:middle line:84% and then a new stagnant film would develop. 00:46:01.950 --> 00:46:07.430 align:middle line:84% So that film basically gets wholesale replaced every so 00:46:07.430 --> 00:46:09.190 align:middle line:90% often. 00:46:09.190 --> 00:46:12.150 align:middle line:84% And so then the problem becomes, you're 00:46:12.150 --> 00:46:17.070 align:middle line:84% going to have, say, a diffusional flux into that film 00:46:17.070 --> 00:46:23.270 align:middle line:84% over time, and then whatever gas has built up, it's one, 00:46:23.270 --> 00:46:26.510 align:middle line:84% and then maybe you got lots of gas that's built up. 00:46:26.510 --> 00:46:28.950 align:middle line:84% All of that gas gets transported down 00:46:28.950 --> 00:46:33.670 align:middle line:84% into the interior when that film gets replaced or overturned. 00:46:33.670 --> 00:46:37.310 align:middle line:84% And then you start off with no gas, 00:46:37.310 --> 00:46:40.750 align:middle line:84% and then it would build up with time. 00:46:40.750 --> 00:46:46.350 align:middle line:84% This would be time in this direction. 00:46:46.350 --> 00:46:50.710 align:middle line:84% So then we no longer have a steady state problem, 00:46:50.710 --> 00:47:01.138 align:middle line:84% and we need to look at the flux into the film 00:47:01.138 --> 00:47:02.850 align:middle line:90% as a function of time. 00:47:02.850 --> 00:47:09.030 align:middle line:90% 00:47:09.030 --> 00:47:15.110 align:middle line:84% So f as a function of time into a infinite slab. 00:47:15.110 --> 00:47:17.550 align:middle line:84% So we'll assume that the film is thick enough 00:47:17.550 --> 00:47:21.090 align:middle line:84% that we can treat it as an infinite slab. 00:47:21.090 --> 00:47:24.190 align:middle line:84% It's going to equal, again, the concentration difference, where 00:47:24.190 --> 00:47:27.950 align:middle line:84% this is the concentration difference from the atmosphere 00:47:27.950 --> 00:47:31.150 align:middle line:90% to the bulk fluid. 00:47:31.150 --> 00:47:34.950 align:middle line:84% Same thing that we've been approximating before. 00:47:34.950 --> 00:47:41.110 align:middle line:84% And it's going to depend upon diffusivity in the water. 00:47:41.110 --> 00:47:43.030 align:middle line:84% Except now it's going to depend-- instead 00:47:43.030 --> 00:47:46.530 align:middle line:84% of being depending upon linearly on diffusivity, 00:47:46.530 --> 00:47:51.790 align:middle line:84% it's going to depend upon the square root of diffusivity. 00:47:51.790 --> 00:47:53.350 align:middle line:84% It's going to depend on pi, which 00:47:53.350 --> 00:47:58.310 align:middle line:90% is just a constant, and time. 00:47:58.310 --> 00:48:01.790 align:middle line:84% And that says that when you bring this-- 00:48:01.790 --> 00:48:08.590 align:middle line:84% when you bring this parcel up, what you'll notice 00:48:08.590 --> 00:48:13.470 align:middle line:84% is that this equation is actually unstable. 00:48:13.470 --> 00:48:18.470 align:middle line:84% At zero time, it says you have this infinite flux. 00:48:18.470 --> 00:48:20.910 align:middle line:84% And that says that right when you bring it up, 00:48:20.910 --> 00:48:25.630 align:middle line:84% you're exposing water that has had-- that essentially has 00:48:25.630 --> 00:48:29.150 align:middle line:84% zero perturbation to the gas concentration 00:48:29.150 --> 00:48:30.090 align:middle line:90% right at the surface. 00:48:30.090 --> 00:48:33.310 align:middle line:84% So you're exposing it across just that molecular layer 00:48:33.310 --> 00:48:37.340 align:middle line:84% of the atmosphere spirit to the water. 00:48:37.340 --> 00:48:40.780 align:middle line:84% And so you have this very, very rapid rate 00:48:40.780 --> 00:48:42.780 align:middle line:90% for a very short period of time. 00:48:42.780 --> 00:48:46.010 align:middle line:84% But as time progresses-- the square root 00:48:46.010 --> 00:48:48.780 align:middle line:84% should be all the way down, by the way. 00:48:48.780 --> 00:48:51.660 align:middle line:84% As time progresses, this term gets smaller. 00:48:51.660 --> 00:48:54.460 align:middle line:84% And it basically says as this film-- 00:48:54.460 --> 00:48:57.700 align:middle line:84% as time progresses, this film fills up with gas, 00:48:57.700 --> 00:48:59.560 align:middle line:84% and so the flux gets less and less, 00:48:59.560 --> 00:49:02.340 align:middle line:84% because this film starts to become equilibrated 00:49:02.340 --> 00:49:05.340 align:middle line:90% with the atmosphere. 00:49:05.340 --> 00:49:06.980 align:middle line:90% That make sense? 00:49:06.980 --> 00:49:08.540 align:middle line:84% And the only way to increase the flux 00:49:08.540 --> 00:49:11.060 align:middle line:84% is then to rip that film off, put it down, and then bring up 00:49:11.060 --> 00:49:15.000 align:middle line:84% a new film from a new, uncontaminated film. 00:49:15.000 --> 00:49:18.620 align:middle line:90% 00:49:18.620 --> 00:49:24.646 align:middle line:84% What we actually want to know is the mean flux 00:49:24.646 --> 00:49:28.420 align:middle line:90% over some time theta. 00:49:28.420 --> 00:49:30.600 align:middle line:84% That's going to be the mean life. 00:49:30.600 --> 00:49:33.420 align:middle line:90% 00:49:33.420 --> 00:49:36.100 align:middle line:90% The mean life of the film. 00:49:36.100 --> 00:49:38.320 align:middle line:90% And that's just going to be-- 00:49:38.320 --> 00:49:41.940 align:middle line:90% 00:49:41.940 --> 00:49:45.020 align:middle line:84% the mean flux is going to be 1 over theta. 00:49:45.020 --> 00:49:47.820 align:middle line:84% I'm just going to integrate from zero to theta, 00:49:47.820 --> 00:49:49.120 align:middle line:90% integrate the flux. 00:49:49.120 --> 00:49:55.900 align:middle line:90% 00:49:55.900 --> 00:49:59.780 align:middle line:84% And that just has a very similar form, 00:49:59.780 --> 00:50:06.280 align:middle line:84% except now instead of having t, I have theta in the denominator. 00:50:06.280 --> 00:50:10.780 align:middle line:90% 00:50:10.780 --> 00:50:12.860 align:middle line:84% And so what we've done is, instead 00:50:12.860 --> 00:50:14.760 align:middle line:84% of having-- remember in stagnant film, 00:50:14.760 --> 00:50:17.020 align:middle line:90% we had the transfer velocity. 00:50:17.020 --> 00:50:22.620 align:middle line:84% Piston velocity was equal to D over delta z. 00:50:22.620 --> 00:50:24.860 align:middle line:84% And the film replacement model, it's 00:50:24.860 --> 00:50:33.330 align:middle line:84% now 2 over the square root of diffusivity 00:50:33.330 --> 00:50:35.310 align:middle line:90% times pi times theta. 00:50:35.310 --> 00:50:37.890 align:middle line:90% 00:50:37.890 --> 00:50:41.210 align:middle line:84% Now, there's a very useful non-dimensional coefficient 00:50:41.210 --> 00:50:44.390 align:middle line:84% that we use a lot, which is the Schmidt number. 00:50:44.390 --> 00:50:50.410 align:middle line:90% 00:50:50.410 --> 00:50:59.290 align:middle line:84% And the Schmidt number, SH equals the viscosity of water 00:50:59.290 --> 00:51:02.730 align:middle line:90% over the diffusivity of a gas. 00:51:02.730 --> 00:51:15.950 align:middle line:84% So this is the viscosity of water, and diffusivity of a gas. 00:51:15.950 --> 00:51:19.450 align:middle line:90% 00:51:19.450 --> 00:51:21.050 align:middle line:84% Now, the nice thing about this is 00:51:21.050 --> 00:51:24.650 align:middle line:84% that this gives you some information 00:51:24.650 --> 00:51:26.830 align:middle line:90% about relative transport. 00:51:26.830 --> 00:51:30.210 align:middle line:84% If the viscosity of the-- if the viscosity of the fluid 00:51:30.210 --> 00:51:33.130 align:middle line:84% were to go up, you'd expect turbulence to be damped, 00:51:33.130 --> 00:51:36.490 align:middle line:84% so it gives some measure of turbulence. 00:51:36.490 --> 00:51:39.130 align:middle line:84% And if the diffusivity of the gas goes up, 00:51:39.130 --> 00:51:46.850 align:middle line:84% you'd expect the gas to be more effectively transported. 00:51:46.850 --> 00:51:53.690 align:middle line:84% The Schmidt number looks a lot like you've got a D term. 00:51:53.690 --> 00:51:57.170 align:middle line:84% We can then, instead of just computing D, 00:51:57.170 --> 00:52:02.170 align:middle line:84% we'll actually report these ks in terms of Schmidt numbers. 00:52:02.170 --> 00:52:03.690 align:middle line:84% And remember at the beginning, I was 00:52:03.690 --> 00:52:05.330 align:middle line:84% saying one of the things we want to do 00:52:05.330 --> 00:52:14.850 align:middle line:84% is how to go from compute k or one gas, 00:52:14.850 --> 00:52:17.030 align:middle line:90% and then go to a second gas. 00:52:17.030 --> 00:52:20.107 align:middle line:90% 00:52:20.107 --> 00:52:21.190 align:middle line:90% That was one of the goals. 00:52:21.190 --> 00:52:23.650 align:middle line:84% We're going to try to compute gas exchange with things 00:52:23.650 --> 00:52:26.330 align:middle line:84% we can measure, and then we're going 00:52:26.330 --> 00:52:28.960 align:middle line:90% to apply those to other gases. 00:52:28.960 --> 00:52:31.280 align:middle line:84% The way we're going to relate them 00:52:31.280 --> 00:52:33.180 align:middle line:90% is through the Schmidt numbers. 00:52:33.180 --> 00:52:36.200 align:middle line:90% 00:52:36.200 --> 00:52:39.880 align:middle line:84% So we have for the stagnant film model, 00:52:39.880 --> 00:52:43.360 align:middle line:84% we're going to say we have some-- 00:52:43.360 --> 00:52:51.400 align:middle line:84% we're going to have k is proportional to D to the one 00:52:51.400 --> 00:52:51.900 align:middle line:90% half. 00:52:51.900 --> 00:52:54.560 align:middle line:90% 00:52:54.560 --> 00:52:57.840 align:middle line:90% That's what this says up here. 00:52:57.840 --> 00:53:01.440 align:middle line:90% Well, and this is proportional. 00:53:01.440 --> 00:53:05.360 align:middle line:84% Well, that's also proportional to Schmidt number 00:53:05.360 --> 00:53:11.560 align:middle line:84% to the minus one half, because D is in the denominator 00:53:11.560 --> 00:53:14.680 align:middle line:90% of the Schmitt number. 00:53:14.680 --> 00:53:18.760 align:middle line:84% So one of the things you will see a lot-- 00:53:18.760 --> 00:53:22.800 align:middle line:84% and did we put it on the top set? 00:53:22.800 --> 00:53:25.720 align:middle line:84% I can't remember if we made it switch Schmidt numbers. 00:53:25.720 --> 00:53:27.540 align:middle line:84% STUDENT: I haven't done the last question. 00:53:27.540 --> 00:53:30.280 align:middle line:90% [INAUDIBLE] 00:53:30.280 --> 00:53:32.280 align:middle line:90% PROFESSOR: OK. 00:53:32.280 --> 00:53:35.440 align:middle line:84% Is that the generalized forms of the flux 00:53:35.440 --> 00:53:40.920 align:middle line:84% equation for the replacement model is k0. 00:53:40.920 --> 00:53:43.140 align:middle line:84% So this might be some piston velocity 00:53:43.140 --> 00:53:51.360 align:middle line:84% you measure, say, with radon or some other noble gas. 00:53:51.360 --> 00:53:54.940 align:middle line:84% Would then be, you'd have a Schmidt number correction. 00:53:54.940 --> 00:53:57.800 align:middle line:90% 00:53:57.800 --> 00:54:00.280 align:middle line:84% So you'd have the Schmidt number that you originally 00:54:00.280 --> 00:54:03.560 align:middle line:84% made the reference measurement with for k0, and then 00:54:03.560 --> 00:54:05.000 align:middle line:84% the new Schmidt number, where this 00:54:05.000 --> 00:54:07.480 align:middle line:84% is the Schmidt number for whatever gas 00:54:07.480 --> 00:54:08.920 align:middle line:90% that you're interested in. 00:54:08.920 --> 00:54:13.280 align:middle line:84% So this would be the flux you're trying 00:54:13.280 --> 00:54:21.900 align:middle line:84% to compute for new gas times the concentration gradient. 00:54:21.900 --> 00:54:23.960 align:middle line:84% STUDENT: Is that with your subscripts, 00:54:23.960 --> 00:54:25.875 align:middle line:90% the words in parentheses. 00:54:25.875 --> 00:54:28.000 align:middle line:84% PROFESSOR: That's a these are both Schmidt numbers, 00:54:28.000 --> 00:54:30.020 align:middle line:84% and that's just supposed to be a Zero. 00:54:30.020 --> 00:54:34.480 align:middle line:84% So it's the same k0, Schmidt number zero. 00:54:34.480 --> 00:54:37.480 align:middle line:84% So if I had made a measurement with radon, 00:54:37.480 --> 00:54:40.240 align:middle line:84% I would plug in the piston velocity 00:54:40.240 --> 00:54:44.340 align:middle line:84% for radon, the Schmidt number for radon-- oh, excuse me-- 00:54:44.340 --> 00:54:49.980 align:middle line:84% and then minus 0.5 for the replacement of the model. 00:54:49.980 --> 00:54:55.520 align:middle line:90% 00:54:55.520 --> 00:54:58.440 align:middle line:84% And that's simply because the piston velocity 00:54:58.440 --> 00:55:01.260 align:middle line:84% is proportional to Schmidt number to the minus one half. 00:55:01.260 --> 00:55:05.120 align:middle line:90% 00:55:05.120 --> 00:55:06.340 align:middle line:90% Have I lost you guys? 00:55:06.340 --> 00:55:09.720 align:middle line:90% How you guys doing up at MIT? 00:55:09.720 --> 00:55:10.760 align:middle line:90% Yeah? 00:55:10.760 --> 00:55:13.337 align:middle line:90% Riveting stuff, huh? 00:55:13.337 --> 00:55:13.920 align:middle line:90% STUDENT: Yeah. 00:55:13.920 --> 00:55:19.880 align:middle line:90% 00:55:19.880 --> 00:55:23.732 align:middle line:84% PROFESSOR: Sometimes you'll see this written as-- 00:55:23.732 --> 00:55:25.190 align:middle line:84% people will say, well, I don't know 00:55:25.190 --> 00:55:27.590 align:middle line:84% whether it's whether I believe the stagnant film 00:55:27.590 --> 00:55:31.510 align:middle line:84% model or some other model, and they will write it 00:55:31.510 --> 00:55:34.610 align:middle line:90% as same general form. 00:55:34.610 --> 00:55:38.910 align:middle line:84% Schmidt number over Schmidt number reference to the minus n, 00:55:38.910 --> 00:55:41.510 align:middle line:84% where n might be the exponent that they're actually trying 00:55:41.510 --> 00:55:43.290 align:middle line:90% to find from their experiment. 00:55:43.290 --> 00:55:51.858 align:middle line:90% 00:55:51.858 --> 00:55:52.650 align:middle line:90% STUDENT: I'm sorry. 00:55:52.650 --> 00:55:54.430 align:middle line:84% Because for the standard film model, 00:55:54.430 --> 00:55:56.043 align:middle line:90% it's going to be one thing. 00:55:56.043 --> 00:55:56.710 align:middle line:90% PROFESSOR: Yeah. 00:55:56.710 --> 00:56:00.750 align:middle line:84% If we were to go back, remember, k-- 00:56:00.750 --> 00:56:04.910 align:middle line:90% 00:56:04.910 --> 00:56:09.270 align:middle line:84% k was proportional to diffusivity 00:56:09.270 --> 00:56:11.950 align:middle line:90% for the stagnant film model. 00:56:11.950 --> 00:56:14.710 align:middle line:84% So if we come down here, that would 00:56:14.710 --> 00:56:19.390 align:middle line:84% say that k for stagnant film model would be proportional to 1 00:56:19.390 --> 00:56:22.830 align:middle line:84% over the Schmidt number, so Schmidt number to the minus 1. 00:56:22.830 --> 00:56:26.150 align:middle line:84% So if the stagnant film model were dominant, 00:56:26.150 --> 00:56:31.550 align:middle line:84% then n would be 1, where for the film replacement model, 00:56:31.550 --> 00:56:39.535 align:middle line:90% it's 0.5. 00:56:39.535 --> 00:56:40.410 align:middle line:90% STUDENT: That's good. 00:56:40.410 --> 00:56:42.230 align:middle line:90% Just a quick clarification. 00:56:42.230 --> 00:56:54.470 align:middle line:84% For the equations up there, the 2 pi theta not z, right? 00:56:54.470 --> 00:56:55.630 align:middle line:90% You were pointing out. 00:56:55.630 --> 00:56:56.213 align:middle line:90% STUDENT: Yeah. 00:56:56.213 --> 00:56:57.070 align:middle line:90% Oh, that's 2, right? 00:56:57.070 --> 00:56:57.987 align:middle line:90% PROFESSOR: That's a 2. 00:56:57.987 --> 00:56:59.570 align:middle line:90% Yeah. 00:56:59.570 --> 00:57:00.970 align:middle line:90% STUDENT: I thought it was. 00:57:00.970 --> 00:57:02.910 align:middle line:84% PROFESSOR: Yeah, I tried to cross my Zs. 00:57:02.910 --> 00:57:07.990 align:middle line:84% So yeah, I usually am pretty good about that. 00:57:07.990 --> 00:57:11.310 align:middle line:84% Makes up for some of my poor handwriting. 00:57:11.310 --> 00:57:16.247 align:middle line:84% STUDENT: So this is the flux from the atmosphere to the bulk. 00:57:16.247 --> 00:57:16.830 align:middle line:90% PROFESSOR: Oh. 00:57:16.830 --> 00:57:18.870 align:middle line:84% STUDENT: [INAUDIBLE] the atmosphere. 00:57:18.870 --> 00:57:22.040 align:middle line:84% PROFESSOR: Yeah, it just depends upon the concentration gradient, 00:57:22.040 --> 00:57:23.820 align:middle line:84% whether it's going to be from the atmospheric to water, 00:57:23.820 --> 00:57:25.200 align:middle line:84% from the water to the atmosphere. 00:57:25.200 --> 00:57:31.140 align:middle line:90% 00:57:31.140 --> 00:57:39.680 align:middle line:84% So now, I've told you how I have computed a k0. 00:57:39.680 --> 00:57:44.140 align:middle line:84% We went through an example with radon. 00:57:44.140 --> 00:57:47.880 align:middle line:84% We've now gone through how to transfer from gas to gas, 00:57:47.880 --> 00:57:52.180 align:middle line:84% and there's actually a table of Schmidt numbers for seawater 00:57:52.180 --> 00:57:55.460 align:middle line:84% in your notes that you can look at. 00:57:55.460 --> 00:57:57.580 align:middle line:84% It's basically 1 over-- you can think 00:57:57.580 --> 00:57:59.820 align:middle line:90% of it as 1 over diffusivity. 00:57:59.820 --> 00:58:02.500 align:middle line:84% So just invert everything we said 00:58:02.500 --> 00:58:04.860 align:middle line:84% about diffusivities in terms of sensitivity 00:58:04.860 --> 00:58:07.180 align:middle line:84% to temperature and molecular weight. 00:58:07.180 --> 00:58:10.720 align:middle line:84% But what does k-- what else does k depend upon? 00:58:10.720 --> 00:58:13.220 align:middle line:84% It depends upon the solute, but it also 00:58:13.220 --> 00:58:17.900 align:middle line:84% depends upon other environmental conditions. 00:58:17.900 --> 00:58:23.020 align:middle line:84% And there's a fairly long-running debate 00:58:23.020 --> 00:58:26.340 align:middle line:84% in the literature about the values of k 00:58:26.340 --> 00:58:28.940 align:middle line:90% and how to measure them. 00:58:28.940 --> 00:58:30.740 align:middle line:90% And I don't know whether-- 00:58:30.740 --> 00:58:34.660 align:middle line:84% I don't know whether it's actually getting resolved or not 00:58:34.660 --> 00:58:39.060 align:middle line:84% with time or whether we're just headed into some more confusion. 00:58:39.060 --> 00:58:46.980 align:middle line:84% So we had flux equals k, Schmidt number, Schmidt number, 00:58:46.980 --> 00:58:59.780 align:middle line:84% zero to some exponent delta C. There's a couple of things 00:58:59.780 --> 00:59:02.940 align:middle line:90% that we think increase k or k0. 00:59:02.940 --> 00:59:06.020 align:middle line:90% 00:59:06.020 --> 00:59:09.780 align:middle line:90% Would be wind speed. 00:59:09.780 --> 00:59:14.520 align:middle line:84% So higher wind leads to more gas exchange. 00:59:14.520 --> 00:59:16.730 align:middle line:90% Well, that makes sense. 00:59:16.730 --> 00:59:19.570 align:middle line:84% Higher wind leads to a lot more turbulence. 00:59:19.570 --> 00:59:22.870 align:middle line:84% It leads to wave breaking, bubbles, 00:59:22.870 --> 00:59:24.530 align:middle line:90% all sorts of things like that. 00:59:24.530 --> 00:59:31.250 align:middle line:84% So that kinetically makes some intuitive sense. 00:59:31.250 --> 00:59:33.430 align:middle line:84% The second thing that people have tried to do, 00:59:33.430 --> 00:59:34.850 align:middle line:84% so people have spent a lot of time 00:59:34.850 --> 00:59:38.810 align:middle line:84% trying to build models or empirical models 00:59:38.810 --> 00:59:41.770 align:middle line:90% relating k0 to wind speed. 00:59:41.770 --> 00:59:45.050 align:middle line:84% The theory on this is somewhat weak. 00:59:45.050 --> 00:59:50.090 align:middle line:84% It's, how does wind speed then affect turbulence [INAUDIBLE]. 00:59:50.090 --> 00:59:51.830 align:middle line:84% But you can make empirical measurements. 00:59:51.830 --> 00:59:56.210 align:middle line:84% You could go out and make radon measurements, for example, 00:59:56.210 --> 00:59:58.090 align:middle line:84% in high wind speed conditions, and then 00:59:58.090 --> 01:00:00.290 align:middle line:84% go out a few weeks later or season later 01:00:00.290 --> 01:00:02.490 align:middle line:84% and make them under low wind conditions, 01:00:02.490 --> 01:00:04.250 align:middle line:84% and then look at the radon deficit 01:00:04.250 --> 01:00:07.750 align:middle line:84% and look at how k differs under those two conditions, 01:00:07.750 --> 01:00:11.250 align:middle line:84% and then try to basically map that out. 01:00:11.250 --> 01:00:13.690 align:middle line:90% You could look at bubbles. 01:00:13.690 --> 01:00:16.090 align:middle line:84% And the bubbles are usually approximated 01:00:16.090 --> 01:00:18.870 align:middle line:90% by white cap coverage. 01:00:18.870 --> 01:00:21.450 align:middle line:90% 01:00:21.450 --> 01:00:26.610 align:middle line:84% And it makes sense that bubbles should increase gas exchange. 01:00:26.610 --> 01:00:32.530 align:middle line:84% If you think about it, you're taking gases out of the air 01:00:32.530 --> 01:00:35.050 align:middle line:84% and you're sucking them down into the water. 01:00:35.050 --> 01:00:38.650 align:middle line:84% Some of that gas is dissolving before that bubble reaches back 01:00:38.650 --> 01:00:39.770 align:middle line:90% to the surface. 01:00:39.770 --> 01:00:43.130 align:middle line:84% And that would be a net flux into the water. 01:00:43.130 --> 01:00:45.450 align:middle line:84% Similarly, you can also think of bubbles 01:00:45.450 --> 01:00:51.690 align:middle line:84% as increasing the surface area between the water and the air. 01:00:51.690 --> 01:00:53.790 align:middle line:84% And by increasing the surface area, 01:00:53.790 --> 01:00:56.770 align:middle line:84% if you had something that was supersaturated in the water, 01:00:56.770 --> 01:00:58.773 align:middle line:84% you could diffuse gas into those bubbles, 01:00:58.773 --> 01:01:00.690 align:middle line:84% and some of those bubbles are going to make it 01:01:00.690 --> 01:01:02.170 align:middle line:90% back up to the surface. 01:01:02.170 --> 01:01:04.030 align:middle line:84% When they make it back up to the surface, 01:01:04.030 --> 01:01:05.610 align:middle line:84% they're going to lose gas to the atmosphere 01:01:05.610 --> 01:01:06.830 align:middle line:90% because they're going to pop. 01:01:06.830 --> 01:01:11.810 align:middle line:90% 01:01:11.810 --> 01:01:16.450 align:middle line:84% So those both would increase the-- 01:01:16.450 --> 01:01:22.480 align:middle line:84% those both would increase the transfer velocity. 01:01:22.480 --> 01:01:25.120 align:middle line:90% It should increase with fetch. 01:01:25.120 --> 01:01:28.920 align:middle line:84% Does everybody know what fetch is? 01:01:28.920 --> 01:01:35.260 align:middle line:84% Fetch is basically the distance the wind is blowing over. 01:01:35.260 --> 01:01:40.480 align:middle line:90% 01:01:40.480 --> 01:01:43.720 align:middle line:84% The fetch is basically, if the wind is blowing from one side 01:01:43.720 --> 01:01:46.640 align:middle line:84% to the other, the fetch is the distance across the lake. 01:01:46.640 --> 01:01:49.880 align:middle line:84% And if you looked at the lake, if you were on the-- if you were 01:01:49.880 --> 01:01:50.600 align:middle line:90% on the-- 01:01:50.600 --> 01:01:52.880 align:middle line:84% say the wind was blowing this side. 01:01:52.880 --> 01:01:56.200 align:middle line:84% If you looked at the waves, the waves 01:01:56.200 --> 01:01:59.360 align:middle line:84% would be really small on one side of the lake, 01:01:59.360 --> 01:02:00.840 align:middle line:84% and then they might be really big 01:02:00.840 --> 01:02:02.680 align:middle line:90% on the other side of the lake. 01:02:02.680 --> 01:02:04.560 align:middle line:84% And that's just because it takes a while 01:02:04.560 --> 01:02:07.600 align:middle line:84% for the wind-- for the momentum and the wind 01:02:07.600 --> 01:02:12.040 align:middle line:84% to be transferred into the water and to build up a wave state. 01:02:12.040 --> 01:02:15.440 align:middle line:84% And since turbulence, you think the same thing 01:02:15.440 --> 01:02:16.860 align:middle line:90% might be true for turbulence. 01:02:16.860 --> 01:02:19.440 align:middle line:84% It might depend upon the wave state 01:02:19.440 --> 01:02:22.640 align:middle line:84% and how long the wind has been acting on the water. 01:02:22.640 --> 01:02:26.200 align:middle line:84% Most of the time in the open ocean, fetch isn't into problem. 01:02:26.200 --> 01:02:29.920 align:middle line:84% But sometimes you'll also see it as wave state. 01:02:29.920 --> 01:02:36.040 align:middle line:84% So if the wind suddenly just kicked up in speed, 01:02:36.040 --> 01:02:38.760 align:middle line:84% the turbulence might not have caught up to it yet. 01:02:38.760 --> 01:02:41.620 align:middle line:84% And one way to do that would be to look at the wave states. 01:02:41.620 --> 01:02:44.440 align:middle line:90% 01:02:44.440 --> 01:02:46.120 align:middle line:84% If you go out and look at the gas 01:02:46.120 --> 01:02:51.480 align:middle line:84% exchange measurements-- and there's an example in the book. 01:02:51.480 --> 01:02:53.800 align:middle line:84% And this is where things get rather contentious 01:02:53.800 --> 01:02:55.480 align:middle line:90% in the literature. 01:02:55.480 --> 01:02:59.720 align:middle line:84% If you plot piston velocity or transfer velocity 01:02:59.720 --> 01:03:08.000 align:middle line:84% as a function of wind speed, the data kind of looks like this. 01:03:08.000 --> 01:03:11.960 align:middle line:84% And depending on how you interpret 01:03:11.960 --> 01:03:14.080 align:middle line:84% the data, whose data you decide to keep, 01:03:14.080 --> 01:03:18.440 align:middle line:84% whose data you decide to throw out, 01:03:18.440 --> 01:03:20.560 align:middle line:84% you can pass a number of different lines 01:03:20.560 --> 01:03:23.520 align:middle line:90% through that curve. 01:03:23.520 --> 01:03:28.200 align:middle line:84% Some of the curves, there's a classic curve 01:03:28.200 --> 01:03:30.320 align:middle line:90% by Liss and Merlivat. 01:03:30.320 --> 01:03:34.400 align:middle line:90% Liss and Merlivat. 01:03:34.400 --> 01:03:37.920 align:middle line:84% And you can tell that this field isn't as mature as other fields 01:03:37.920 --> 01:03:41.400 align:middle line:84% because the relationships are still-- we still 01:03:41.400 --> 01:03:45.360 align:middle line:84% talk about individual people's curves rather than saying, 01:03:45.360 --> 01:03:47.240 align:middle line:90% this is so-and-so's law. 01:03:47.240 --> 01:03:49.320 align:middle line:84% This is just somebody's estimate. 01:03:49.320 --> 01:03:52.560 align:middle line:84% So Liss and Merlivat said, well, we 01:03:52.560 --> 01:03:54.140 align:middle line:90% view it kind of goes like this. 01:03:54.140 --> 01:03:56.520 align:middle line:84% There's actually three broken lines. 01:03:56.520 --> 01:03:59.280 align:middle line:90% So it'd be three-- 01:03:59.280 --> 01:04:01.280 align:middle line:90% the right place for that-- 01:04:01.280 --> 01:04:07.950 align:middle line:84% three discrete lines that are joined together. 01:04:07.950 --> 01:04:09.630 align:middle line:90% There's a better word for that. 01:04:09.630 --> 01:04:10.778 align:middle line:90% STUDENT: Is U wind speed? 01:04:10.778 --> 01:04:11.570 align:middle line:90% PROFESSOR: Oh, yes. 01:04:11.570 --> 01:04:14.250 align:middle line:90% U is wind speed. 01:04:14.250 --> 01:04:14.750 align:middle line:90% Thanks. 01:04:14.750 --> 01:04:17.670 align:middle line:90% 01:04:17.670 --> 01:04:18.970 align:middle line:90% And it's usually referenced. 01:04:18.970 --> 01:04:21.070 align:middle line:84% You'll often see it as U10, which 01:04:21.070 --> 01:04:24.590 align:middle line:84% is the wind speed at 10 meters, because wind 01:04:24.590 --> 01:04:26.570 align:middle line:84% varies at the height above the surface. 01:04:26.570 --> 01:04:29.090 align:middle line:84% And so you try to reference it for a common height. 01:04:29.090 --> 01:04:32.270 align:middle line:90% 01:04:32.270 --> 01:04:35.750 align:middle line:84% Liss and Merlivat is basically three discrete lines, 01:04:35.750 --> 01:04:40.970 align:middle line:84% so they're basically linear in each region. 01:04:40.970 --> 01:04:43.290 align:middle line:90% And it's piecewise linear. 01:04:43.290 --> 01:04:44.350 align:middle line:90% That is important. 01:04:44.350 --> 01:04:49.790 align:middle line:90% Piecewise linear. 01:04:49.790 --> 01:04:53.830 align:middle line:84% Another famous one that goes through the same cloud 01:04:53.830 --> 01:05:03.470 align:middle line:84% is the Weinkauf relationship, which 01:05:03.470 --> 01:05:12.630 align:middle line:84% is k is proportional to the square of the wind speed. 01:05:12.630 --> 01:05:16.990 align:middle line:84% So it's a quadratic relationship. 01:05:16.990 --> 01:05:20.750 align:middle line:84% Now, from there, it gets really ugly. 01:05:20.750 --> 01:05:23.370 align:middle line:90% Weinkauf also now has a cubic. 01:05:23.370 --> 01:05:25.910 align:middle line:90% 01:05:25.910 --> 01:05:28.470 align:middle line:84% You have other people who are arguing it's actually 01:05:28.470 --> 01:05:30.990 align:middle line:90% linear with wind speed. 01:05:30.990 --> 01:05:35.070 align:middle line:84% And in some ways, the data isn't strong enough yet 01:05:35.070 --> 01:05:38.470 align:middle line:90% to partition between those. 01:05:38.470 --> 01:05:41.830 align:middle line:84% The problem is, obviously, the quadratic 01:05:41.830 --> 01:05:45.310 align:middle line:84% and the cubic, when you get to very, very high wind speed, 01:05:45.310 --> 01:05:47.830 align:middle line:84% the piston velocity keeps on shooting up. 01:05:47.830 --> 01:05:50.812 align:middle line:84% We don't have a lot of data at very high wind speed. 01:05:50.812 --> 01:05:53.270 align:middle line:84% It's very hard to go out and make gas exchange measurements 01:05:53.270 --> 01:05:56.375 align:middle line:84% in a hurricane, both technically, and also 01:05:56.375 --> 01:05:57.750 align:middle line:84% because you just don't know where 01:05:57.750 --> 01:05:59.470 align:middle line:90% the hurricane is going to be. 01:05:59.470 --> 01:06:03.660 align:middle line:84% You basically have to position yourself ahead of a hurricane, 01:06:03.660 --> 01:06:07.220 align:middle line:84% and know where it was in advance and all that. 01:06:07.220 --> 01:06:12.020 align:middle line:84% There are attempts to resolve that 01:06:12.020 --> 01:06:13.500 align:middle line:84% with some other measurements, which 01:06:13.500 --> 01:06:15.440 align:middle line:90% I'll talk about in a moment. 01:06:15.440 --> 01:06:17.900 align:middle line:84% But I do want to touch on one other thing that comes up 01:06:17.900 --> 01:06:20.640 align:middle line:84% a lot in exams and general exams, 01:06:20.640 --> 01:06:24.940 align:middle line:84% and things like that, which is the-- 01:06:24.940 --> 01:06:26.895 align:middle line:90% yeah, and, and, and-- 01:06:26.895 --> 01:06:30.700 align:middle line:90% 01:06:30.700 --> 01:06:34.500 align:middle line:84% which is the gas exchange residence time. 01:06:34.500 --> 01:06:37.620 align:middle line:84% So remember back we had that little model 01:06:37.620 --> 01:06:44.780 align:middle line:84% where we had some thickness h, which was the mixed layer. 01:06:44.780 --> 01:06:52.100 align:middle line:84% Well, you could think that gas exchange 01:06:52.100 --> 01:06:57.900 align:middle line:84% is going to try to push supersaturated waters 01:06:57.900 --> 01:06:59.500 align:middle line:90% towards equilibrium. 01:06:59.500 --> 01:07:02.180 align:middle line:84% Similarly, it's going to try to push undersaturated waters 01:07:02.180 --> 01:07:03.700 align:middle line:90% to equilibrium. 01:07:03.700 --> 01:07:07.460 align:middle line:84% And you can approximate that as a time scale. 01:07:07.460 --> 01:07:12.140 align:middle line:84% So this would be a time scale for equilibration that's 01:07:12.140 --> 01:07:16.460 align:middle line:90% going to be proportional to h. 01:07:16.460 --> 01:07:20.460 align:middle line:84% The deeper the mixed layer, the bigger volume you're looking at, 01:07:20.460 --> 01:07:23.740 align:middle line:84% the longer you would expect it to take 01:07:23.740 --> 01:07:27.180 align:middle line:84% to come into equilibrium, because your flux doesn't 01:07:27.180 --> 01:07:29.460 align:middle line:90% depend upon mixed layer depth. 01:07:29.460 --> 01:07:32.240 align:middle line:84% So your flux doesn't know how big the mixed layer is. 01:07:32.240 --> 01:07:34.328 align:middle line:84% So if you have a 10-meter mixed layer, 01:07:34.328 --> 01:07:36.120 align:middle line:84% the equilibration is going to go very fast. 01:07:36.120 --> 01:07:37.620 align:middle line:84% If you have 1,000-meter mixed layer, 01:07:37.620 --> 01:07:40.700 align:middle line:90% it's going to go very slow. 01:07:40.700 --> 01:07:45.020 align:middle line:84% And your piston velocity, your transfer velocity, 01:07:45.020 --> 01:07:47.600 align:middle line:84% if you think about that, that has units of meters. 01:07:47.600 --> 01:07:51.500 align:middle line:84% This has units of meters per second. 01:07:51.500 --> 01:07:54.400 align:middle line:84% And so you're left with something that is in time. 01:07:54.400 --> 01:07:56.940 align:middle line:90% 01:07:56.940 --> 01:08:08.890 align:middle line:84% And typically, typical values are tens of days for most gases. 01:08:08.890 --> 01:08:13.450 align:middle line:84% So it's going to take a few weeks to a month 01:08:13.450 --> 01:08:18.689 align:middle line:84% or so for other things to start equilibrating. 01:08:18.689 --> 01:08:21.430 align:middle line:84% And technically, it's the 1 over e. 01:08:21.430 --> 01:08:24.010 align:middle line:90% It's the 1 over e-folding time. 01:08:24.010 --> 01:08:27.970 align:middle line:84% So if you started with a concentration difference, 01:08:27.970 --> 01:08:31.850 align:middle line:84% after one e-folding time, you'd be down to 1 01:08:31.850 --> 01:08:33.870 align:middle line:84% over e the original perturbation, 01:08:33.870 --> 01:08:35.370 align:middle line:84% and then 2 e-folding times, you'd 01:08:35.370 --> 01:08:38.029 align:middle line:90% be 1 over e squared, et cetera. 01:08:38.029 --> 01:08:41.490 align:middle line:90% 01:08:41.490 --> 01:08:45.210 align:middle line:84% STUDENT: I don't understand the term folding time. 01:08:45.210 --> 01:08:47.410 align:middle line:90% PROFESSOR: So DC, Dts. 01:08:47.410 --> 01:08:49.210 align:middle line:84% Let's say you had some perturbation 01:08:49.210 --> 01:08:53.569 align:middle line:90% is equal to, say, minus kC. 01:08:53.569 --> 01:08:56.330 align:middle line:90% 01:08:56.330 --> 01:09:05.170 align:middle line:84% If you solve that, remember DC over C equals minus k Dt. 01:09:05.170 --> 01:09:08.850 align:middle line:84% And so it actually looks like radioactive decay. 01:09:08.850 --> 01:09:12.490 align:middle line:84% It's going to be C at any time is going 01:09:12.490 --> 01:09:17.569 align:middle line:90% to equal C0, e to the minus kt. 01:09:17.569 --> 01:09:19.710 align:middle line:90% And so when time-- 01:09:19.710 --> 01:09:24.330 align:middle line:90% 01:09:24.330 --> 01:09:27.109 align:middle line:84% when you get to 1 over e-folding depth, 01:09:27.109 --> 01:09:30.170 align:middle line:84% this is going to be-- this value would be 1, 01:09:30.170 --> 01:09:37.090 align:middle line:84% and so then it would be C equals C0 over 1 over e. 01:09:37.090 --> 01:09:41.090 align:middle line:84% And that's just called unfolding. 01:09:41.090 --> 01:09:43.430 align:middle line:90% It's just conventional notation. 01:09:43.430 --> 01:09:48.170 align:middle line:84% It's called 1 over e, but it equals the time. 01:09:48.170 --> 01:09:51.359 align:middle line:84% There are some caveats to the residence time. 01:09:51.359 --> 01:09:53.689 align:middle line:90% I went slow today. 01:09:53.689 --> 01:09:57.490 align:middle line:90% Oh, no, that clock's fast. 01:09:57.490 --> 01:09:58.670 align:middle line:90% It's 55. 01:09:58.670 --> 01:10:00.250 align:middle line:90% I went slow today. 01:10:00.250 --> 01:10:04.290 align:middle line:84% There's a couple of caveats to the residence time. 01:10:04.290 --> 01:10:11.330 align:middle line:84% For CO2, remember, most of the CO2 in water 01:10:11.330 --> 01:10:13.690 align:middle line:84% is in what-- most of the inorganic carbon in seawater 01:10:13.690 --> 01:10:14.870 align:middle line:90% is in what form? 01:10:14.870 --> 01:10:20.170 align:middle line:90% 01:10:20.170 --> 01:10:21.850 align:middle line:90% Bicarbonate. 01:10:21.850 --> 01:10:26.650 align:middle line:84% So most of the dissolved organic carbon is in bicarbonate. 01:10:26.650 --> 01:10:29.770 align:middle line:84% And so if you want to equilibrate the CO2 system, 01:10:29.770 --> 01:10:33.710 align:middle line:90% let's say you had 14 CO2. 01:10:33.710 --> 01:10:37.690 align:middle line:84% So you had radioisotope CO2 diffusing into the water. 01:10:37.690 --> 01:10:41.890 align:middle line:84% It's got to fill not only the dissolved CO2 gas. 01:10:41.890 --> 01:10:49.090 align:middle line:84% It's also got to fill H2CO3 star, bicarbonate, 01:10:49.090 --> 01:10:52.610 align:middle line:90% and carbonate ions. 01:10:52.610 --> 01:10:57.880 align:middle line:84% So there's actually a correction that t 01:10:57.880 --> 01:11:03.080 align:middle line:84% is going to equal h over k, just like what we wrote, 01:11:03.080 --> 01:11:10.840 align:middle line:84% times the total amount of CO2 in the water, the total DIC 01:11:10.840 --> 01:11:16.920 align:middle line:84% dissolved ionic carbon, over CO2 aqueous. 01:11:16.920 --> 01:11:23.160 align:middle line:84% And this latter factor is somewhere between 100 to 200. 01:11:23.160 --> 01:11:29.000 align:middle line:84% So the gas exchange timescale for C 14 01:11:29.000 --> 01:11:33.280 align:middle line:84% is going to be about 100 to 200 times longer than a normal gas, 01:11:33.280 --> 01:11:37.440 align:middle line:84% because CO2 has this huge reservoir of other compounds 01:11:37.440 --> 01:11:38.820 align:middle line:90% that aren't actually gases. 01:11:38.820 --> 01:11:44.240 align:middle line:84% Remember, the hydrated form the bicarbonate and the carbonate 01:11:44.240 --> 01:11:47.600 align:middle line:84% ion, they are not gases, so they cannot exchange across 01:11:47.600 --> 01:11:49.160 align:middle line:90% the air-sea interface. 01:11:49.160 --> 01:11:51.000 align:middle line:84% But in terms of a residence time, 01:11:51.000 --> 01:11:55.840 align:middle line:84% or in terms of equilibration time, you have to fill up. 01:11:55.840 --> 01:11:58.240 align:middle line:84% You have to put C14 and plug it into all 01:11:58.240 --> 01:12:00.920 align:middle line:84% of these other reservoirs, fill up all those other reservoirs 01:12:00.920 --> 01:12:02.960 align:middle line:90% before you came to equilibrium. 01:12:02.960 --> 01:12:06.660 align:middle line:84% So that means that t for C14 is about 10 years. 01:12:06.660 --> 01:12:10.320 align:middle line:90% 01:12:10.320 --> 01:12:14.200 align:middle line:84% Now, the last little tidbit I want to get to, there's 01:12:14.200 --> 01:12:17.200 align:middle line:90% a section in the notes on-- 01:12:17.200 --> 01:12:19.340 align:middle line:84% there's a long section in the notes on methods, 01:12:19.340 --> 01:12:23.000 align:middle line:90% and you can read that. 01:12:23.000 --> 01:12:24.640 align:middle line:84% And your problem set actually goes 01:12:24.640 --> 01:12:28.640 align:middle line:84% through one of the examples of one of the methods. 01:12:28.640 --> 01:12:30.440 align:middle line:84% But the last thing I want to touch on 01:12:30.440 --> 01:12:32.860 align:middle line:90% is what happens for CO2 gas. 01:12:32.860 --> 01:12:35.080 align:middle line:90% That's not C14. 01:12:35.080 --> 01:12:41.880 align:middle line:84% So you have regular gases [INAUDIBLE] 01:12:41.880 --> 01:12:45.700 align:middle line:90% approximately weeks to months. 01:12:45.700 --> 01:12:50.680 align:middle line:90% 01:12:50.680 --> 01:12:59.910 align:middle line:84% You have 14 CO2, which its t is approximately 10 years. 01:12:59.910 --> 01:13:06.450 align:middle line:84% It turns out for CO2 gas, t is intermediate between those two. 01:13:06.450 --> 01:13:09.550 align:middle line:90% It's about one year. 01:13:09.550 --> 01:13:14.550 align:middle line:84% And it has to do with the fact that as you add CO2 01:13:14.550 --> 01:13:19.790 align:middle line:84% to the water, what are you doing? 01:13:19.790 --> 01:13:20.790 align:middle line:90% What are you doing? 01:13:20.790 --> 01:13:27.870 align:middle line:84% You're increasing total CO2 or DIC. 01:13:27.870 --> 01:13:30.710 align:middle line:90% 01:13:30.710 --> 01:13:35.030 align:middle line:84% But what else are you doing as you add CO2 to water? 01:13:35.030 --> 01:13:37.230 align:middle line:90% You change it. 01:13:37.230 --> 01:13:39.230 align:middle line:90% You change its pH. 01:13:39.230 --> 01:13:44.330 align:middle line:84% So you are actually decreasing the pH. 01:13:44.330 --> 01:13:46.230 align:middle line:84% And one way of thinking about that is you're 01:13:46.230 --> 01:13:52.790 align:middle line:84% actually shifting the acid-base equilibrium 01:13:52.790 --> 01:14:01.390 align:middle line:84% from bicarbonate to CO2 aqueous, or H2CO3 star. 01:14:01.390 --> 01:14:05.150 align:middle line:84% And so that actually speeds up the equilibration 01:14:05.150 --> 01:14:11.410 align:middle line:84% because you're actually filling up more CO2 aqueous, 01:14:11.410 --> 01:14:12.830 align:middle line:84% so you're coming into equilibrium 01:14:12.830 --> 01:14:15.190 align:middle line:90% with the atmosphere faster. 01:14:15.190 --> 01:14:18.810 align:middle line:84% And so you get an intermediate time scale between the 10 years 01:14:18.810 --> 01:14:20.590 align:middle line:90% you would expect. 01:14:20.590 --> 01:14:24.830 align:middle line:84% If the pH didn't change in seawater, 01:14:24.830 --> 01:14:30.470 align:middle line:84% CO2 would have the same equilibration time as 14 CO2. 01:14:30.470 --> 01:14:35.050 align:middle line:90% This is because pH changes. 01:14:35.050 --> 01:14:39.830 align:middle line:90% 01:14:39.830 --> 01:14:41.882 align:middle line:90% We're out of time. 01:14:41.882 --> 01:14:43.590 align:middle line:84% There's some discussion in the notes that 01:14:43.590 --> 01:14:46.470 align:middle line:84% are on the web page about all sorts of fun, different ways 01:14:46.470 --> 01:14:49.820 align:middle line:84% that people have measured CO2, or excuse me, have measured 01:14:49.820 --> 01:14:51.540 align:middle line:90% gas exchange. 01:14:51.540 --> 01:14:52.720 align:middle line:90% Read those through. 01:14:52.720 --> 01:14:55.260 align:middle line:90% 01:14:55.260 --> 01:14:56.820 align:middle line:90% Oh, yeah. 01:14:56.820 --> 01:15:01.443 align:middle line:84% What I said was that the notes have discussion 01:15:01.443 --> 01:15:02.860 align:middle line:84% of the different methods that have 01:15:02.860 --> 01:15:05.400 align:middle line:84% been used to measure gas exchange, 01:15:05.400 --> 01:15:06.900 align:middle line:90% and you should read those. 01:15:06.900 --> 01:15:09.620 align:middle line:84% But for problem sets and stuff, I 01:15:09.620 --> 01:15:12.100 align:middle line:84% think some of these equations, the stagnant film 01:15:12.100 --> 01:15:15.620 align:middle line:84% model, the film replacement model, and the residence time 01:15:15.620 --> 01:15:21.700 align:middle line:84% are more useful and might be more amenable to being an exam 01:15:21.700 --> 01:15:23.120 align:middle line:90% question, for example. 01:15:23.120 --> 01:15:25.695 align:middle line:90% 01:15:25.695 --> 01:15:27.320 align:middle line:84% STUDENT: Yeah, I was just going to ask, 01:15:27.320 --> 01:15:33.660 align:middle line:84% does that mean in areas where surface water pH is lower than 01:15:33.660 --> 01:15:35.620 align:middle line:90% [INAUDIBLE] 01:15:35.620 --> 01:15:37.860 align:middle line:90% 01:15:37.860 --> 01:15:43.140 align:middle line:84% PROFESSOR: Well, but the pH isn't 01:15:43.140 --> 01:15:47.760 align:middle line:84% going to affect-- it's the change in pH as you equilibrate, 01:15:47.760 --> 01:15:50.468 align:middle line:84% because this is the time scale to reach equilibrium. 01:15:50.468 --> 01:15:52.760 align:middle line:84% STUDENT: But if you've already used up your alkalinity, 01:15:52.760 --> 01:15:54.627 align:middle line:90% [INAUDIBLE]. 01:15:54.627 --> 01:15:55.960 align:middle line:90% PROFESSOR: Well, it does change. 01:15:55.960 --> 01:15:57.580 align:middle line:90% There's something called the-- 01:15:57.580 --> 01:16:02.000 align:middle line:84% it's called the Revelle factor, and it actually changes. 01:16:02.000 --> 01:16:05.680 align:middle line:84% It actually changes slower in low-pH environments. 01:16:05.680 --> 01:16:10.660 align:middle line:90% 01:16:10.660 --> 01:16:16.100 align:middle line:84% Yeah, we will get to the Revelle factor later in the semester. 01:16:16.100 --> 01:16:17.430 align:middle line:90% Great. 01:16:17.430 --> 01:16:19.620 align:middle line:90% Good to see some of you in-- 01:16:19.620 --> 01:16:21.140 align:middle line:90% STUDENT: Question. 01:16:21.140 --> 01:16:21.980 align:middle line:90% PROFESSOR: Yeah. 01:16:21.980 --> 01:16:24.700 align:middle line:84% STUDENT: It has to do with [INAUDIBLE]. 01:16:24.700 --> 01:16:26.140 align:middle line:90% PROFESSOR: Oh, hang on. 01:16:26.140 --> 01:16:26.920 align:middle line:90% One more time. 01:16:26.920 --> 01:16:29.480 align:middle line:84% STUDENT: What does it have to do with it being carbon-14. 01:16:29.480 --> 01:16:31.020 align:middle line:90% And what do you-- 01:16:31.020 --> 01:16:32.500 align:middle line:90% why is it [INAUDIBLE]. 01:16:32.500 --> 01:16:35.420 align:middle line:84% I don't understand what that has to do with being carbon-14. 01:16:35.420 --> 01:16:36.540 align:middle line:90% PROFESSOR: Ah. 01:16:36.540 --> 01:16:42.340 align:middle line:84% The difference is, if you're just adding an isotope, 01:16:42.340 --> 01:16:46.610 align:middle line:84% this would be the equilibration time if the pH in seawater 01:16:46.610 --> 01:16:50.190 align:middle line:84% were fixed or buffered by something else, 01:16:50.190 --> 01:16:51.570 align:middle line:90% but that's not true. 01:16:51.570 --> 01:16:55.810 align:middle line:84% But it is true if you're adding an isotope of CO2 01:16:55.810 --> 01:16:57.630 align:middle line:84% because you're not actually changing-- 01:16:57.630 --> 01:17:00.610 align:middle line:84% you're adding so little of this that you're not actually 01:17:00.610 --> 01:17:06.370 align:middle line:84% changing the seawater pH of the seawater chemistry, Where 01:17:06.370 --> 01:17:09.810 align:middle line:84% if you add CO2 gas, you actually are changing the seawater 01:17:09.810 --> 01:17:11.250 align:middle line:90% chemistry. 01:17:11.250 --> 01:17:14.970 align:middle line:84% And then it speeds up because you're basically 01:17:14.970 --> 01:17:17.730 align:middle line:84% getting-- if you add CO2, you're making it more acidic 01:17:17.730 --> 01:17:22.490 align:middle line:84% and you're actually increasing the aqueous CO2 concentration 01:17:22.490 --> 01:17:23.490 align:middle line:90% faster. 01:17:23.490 --> 01:17:27.610 align:middle line:84% And so you're equilibrating with the atmosphere faster. 01:17:27.610 --> 01:17:28.470 align:middle line:90% Does that help? 01:17:28.470 --> 01:17:36.250 align:middle line:90% 01:17:36.250 --> 01:17:39.260 align:middle line:90% It is a tough concept. 01:17:39.260 --> 01:17:40.510 align:middle line:90% We should probably go over it. 01:17:40.510 --> 01:17:43.500 align:middle line:84% We'll go over this again in recitation on Monday. 01:17:43.500 --> 01:17:44.000 align:middle line:90%