WEBVTT 00:00:00.000 --> 00:00:01.940 align:middle line:90% [SQUEAKING] 00:00:01.940 --> 00:00:04.365 align:middle line:90% [RUSTLING] 00:00:04.365 --> 00:00:07.760 align:middle line:90% [CLICKING] 00:00:07.760 --> 00:00:09.607 align:middle line:90% 00:00:09.607 --> 00:00:11.190 align:middle line:84% GIAN PAOLO BERETTA: I'd like to start, 00:00:11.190 --> 00:00:16.320 align:middle line:90% since today it's March 8, 2024. 00:00:16.320 --> 00:00:18.460 align:middle line:84% I don't know if it is politically correct. 00:00:18.460 --> 00:00:23.530 align:middle line:84% So maybe MIT OpenCourseWare, will cut this part. 00:00:23.530 --> 00:00:29.430 align:middle line:84% But I'd like to dedicate this to one special woman, 00:00:29.430 --> 00:00:34.440 align:middle line:84% for me, who is my mother, who would have been 100 today. 00:00:34.440 --> 00:00:43.310 align:middle line:84% So that's kind of a dedication, personal dedication. 00:00:43.310 --> 00:00:49.210 align:middle line:84% Anyway, OK, so we are talking about exergies. 00:00:49.210 --> 00:00:52.560 align:middle line:84% And today, we will hopefully finish through this part. 00:00:52.560 --> 00:00:55.930 align:middle line:90% 00:00:55.930 --> 00:01:03.220 align:middle line:84% Remember, last time, we talked about what the exergies 00:01:03.220 --> 00:01:12.090 align:middle line:84% associated with a bulk flow state, which 00:01:12.090 --> 00:01:18.820 align:middle line:84% is this linear combination of enthalpy and entropy 00:01:18.820 --> 00:01:22.260 align:middle line:84% and which represents the maximum work 00:01:22.260 --> 00:01:28.260 align:middle line:84% you can extract from that bulk flow state in this situation. 00:01:28.260 --> 00:01:30.860 align:middle line:84% But it also represents the minimum work 00:01:30.860 --> 00:01:34.550 align:middle line:84% to produce from environmental condition 00:01:34.550 --> 00:01:37.180 align:middle line:90% that same bulk flow state. 00:01:37.180 --> 00:01:41.370 align:middle line:90% 00:01:41.370 --> 00:01:48.290 align:middle line:84% So that means that if you combine those two ideas, 00:01:48.290 --> 00:01:56.480 align:middle line:84% and you consider a flow that you want to change from a bulk flow 00:01:56.480 --> 00:02:02.990 align:middle line:84% state 1 to another state 2, depending 00:02:02.990 --> 00:02:11.190 align:middle line:84% on how these states are, how they compare, 00:02:11.190 --> 00:02:16.840 align:middle line:84% you may be able to do that while extracting some work, 00:02:16.840 --> 00:02:20.670 align:middle line:84% or you may be needing to spend some work 00:02:20.670 --> 00:02:24.760 align:middle line:90% to do that change of state. 00:02:24.760 --> 00:02:30.310 align:middle line:84% And the work involved always in a machine-- 00:02:30.310 --> 00:02:36.490 align:middle line:84% I mean, you can picture it in terms of a machinery that always 00:02:36.490 --> 00:02:38.150 align:middle line:84% has to interact with the environment, 00:02:38.150 --> 00:02:45.490 align:middle line:84% so as to perform the entropy exchanges that are needed so 00:02:45.490 --> 00:02:49.660 align:middle line:84% that the changes here are not accomplished 00:02:49.660 --> 00:02:53.110 align:middle line:84% by entropy production by reversibility, which 00:02:53.110 --> 00:02:57.310 align:middle line:90% would be a loss of efficiency. 00:02:57.310 --> 00:03:01.990 align:middle line:84% But the entropy changes are provided through the machinery 00:03:01.990 --> 00:03:05.790 align:middle line:90% by the environment. 00:03:05.790 --> 00:03:08.850 align:middle line:84% So the maximum work you can extract, 00:03:08.850 --> 00:03:12.780 align:middle line:84% or the minimum work you need to spend, 00:03:12.780 --> 00:03:16.650 align:middle line:84% is equal to the difference in the exergies 00:03:16.650 --> 00:03:23.015 align:middle line:84% between the input and the output or the output and the input. 00:03:23.015 --> 00:03:25.620 align:middle line:90% 00:03:25.620 --> 00:03:31.810 align:middle line:84% And as you see here, I've rearranged this expression 00:03:31.810 --> 00:03:37.600 align:middle line:84% collecting the m dot delta h outside. 00:03:37.600 --> 00:03:47.020 align:middle line:84% And so this represents the energy change of your bulk flow. 00:03:47.020 --> 00:03:50.955 align:middle line:84% And so you could even call it heat. 00:03:50.955 --> 00:03:54.170 align:middle line:90% 00:03:54.170 --> 00:03:55.910 align:middle line:84% It's not really a heat interaction 00:03:55.910 --> 00:03:58.730 align:middle line:84% because the bulk flow typically changes in temperature 00:03:58.730 --> 00:04:04.070 align:middle line:84% along the pipe or whatever pieces of equipment 00:04:04.070 --> 00:04:06.080 align:middle line:90% it flows through. 00:04:06.080 --> 00:04:10.790 align:middle line:84% So as it changes in temperature, if it experiences 00:04:10.790 --> 00:04:12.470 align:middle line:84% heat interactions, there are going 00:04:12.470 --> 00:04:14.420 align:middle line:84% to be many different heat interactions 00:04:14.420 --> 00:04:17.269 align:middle line:90% at different temperatures. 00:04:17.269 --> 00:04:22.280 align:middle line:84% But you could also represent this as an overall, 00:04:22.280 --> 00:04:24.350 align:middle line:84% or say, an equivalent heat interaction 00:04:24.350 --> 00:04:26.500 align:middle line:84% that would transfer the same amount of energy. 00:04:26.500 --> 00:04:29.220 align:middle line:90% 00:04:29.220 --> 00:04:32.670 align:middle line:84% And so you get this, quote, "heat" 00:04:32.670 --> 00:04:38.320 align:middle line:84% multiplied by something that looks like a Carnot coefficient. 00:04:38.320 --> 00:04:42.550 align:middle line:84% If you interpret delta h over delta 00:04:42.550 --> 00:04:47.920 align:middle line:84% s as an equivalent heat temperature, 00:04:47.920 --> 00:04:52.750 align:middle line:84% then this becomes a Carnot coefficient. 00:04:52.750 --> 00:04:54.940 align:middle line:84% I'm mentioning that because often people 00:04:54.940 --> 00:04:59.230 align:middle line:84% like to trace back to find Carnot 00:04:59.230 --> 00:05:01.340 align:middle line:90% coefficients in all situations. 00:05:01.340 --> 00:05:04.360 align:middle line:84% And all right, so this is the correct Carnot coefficient 00:05:04.360 --> 00:05:05.780 align:middle line:90% in this situation. 00:05:05.780 --> 00:05:12.880 align:middle line:90% 00:05:12.880 --> 00:05:19.080 align:middle line:84% So for example, this would be a heat pump setup. 00:05:19.080 --> 00:05:24.130 align:middle line:84% And then so you can define a first-law efficiency, 00:05:24.130 --> 00:05:31.610 align:middle line:84% which is the ratio of the heating of your flow 00:05:31.610 --> 00:05:33.910 align:middle line:90% to the work you spent. 00:05:33.910 --> 00:05:37.330 align:middle line:90% That's the COP. 00:05:37.330 --> 00:05:40.400 align:middle line:84% You can also call it first-law efficiency, 00:05:40.400 --> 00:05:45.130 align:middle line:90% but it can be greater than 1. 00:05:45.130 --> 00:05:50.050 align:middle line:84% And you can define a second-law efficiency 00:05:50.050 --> 00:05:55.970 align:middle line:84% as the ratio of the exergy associated 00:05:55.970 --> 00:05:58.790 align:middle line:84% with the useful effect, which in this case, 00:05:58.790 --> 00:06:02.400 align:middle line:90% is heating up this flow. 00:06:02.400 --> 00:06:08.610 align:middle line:84% So this is Ex2 minus Ex1 on the numerator divided 00:06:08.610 --> 00:06:11.130 align:middle line:84% by the exergy of the resource that you have 00:06:11.130 --> 00:06:16.450 align:middle line:90% used, in this case, the work. 00:06:16.450 --> 00:06:23.590 align:middle line:84% And again, you can represent these change in enthalpy 00:06:23.590 --> 00:06:25.010 align:middle line:90% as a heat. 00:06:25.010 --> 00:06:26.300 align:middle line:90% You can call it heat. 00:06:26.300 --> 00:06:30.040 align:middle line:84% And then that heat gets multiplied 00:06:30.040 --> 00:06:36.010 align:middle line:84% by its Carnot coefficient that transforms it to the associated 00:06:36.010 --> 00:06:39.720 align:middle line:90% exergy, as we have seen. 00:06:39.720 --> 00:06:42.670 align:middle line:84% Now, it turns out that this temperature-- 00:06:42.670 --> 00:06:48.480 align:middle line:84% so it's the equivalent temperature of a heat source 00:06:48.480 --> 00:06:52.380 align:middle line:84% that would provide the same amount of energy, 00:06:52.380 --> 00:06:55.590 align:middle line:84% the change in enthalpy, and the same amount of entropy 00:06:55.590 --> 00:06:57.570 align:middle line:90% to the flow. 00:06:57.570 --> 00:07:00.780 align:middle line:84% And the ratio of that energy over entropy 00:07:00.780 --> 00:07:05.160 align:middle line:84% provided to the flow has dimensions of temperature. 00:07:05.160 --> 00:07:08.610 align:middle line:84% And we will see in a moment, that it corresponds 00:07:08.610 --> 00:07:15.060 align:middle line:84% in several cases, to the logarithmic mean temperature 00:07:15.060 --> 00:07:18.155 align:middle line:90% between the inlet and outlet. 00:07:18.155 --> 00:07:22.240 align:middle line:90% 00:07:22.240 --> 00:07:30.210 align:middle line:84% Before I go to that, let me take up a very simple example, 00:07:30.210 --> 00:07:35.530 align:middle line:90% but which is anyway interesting. 00:07:35.530 --> 00:07:42.143 align:middle line:84% It's the exergy of a waterfall or of a hydraulic jump. 00:07:42.143 --> 00:07:45.250 align:middle line:90% 00:07:45.250 --> 00:07:49.640 align:middle line:84% Wherever there is such an opportunity, 00:07:49.640 --> 00:07:53.710 align:middle line:84% people have invested, and it's very hard 00:07:53.710 --> 00:08:02.320 align:middle line:84% to find a hydraulic jump that has not been transformed 00:08:02.320 --> 00:08:04.770 align:middle line:90% in a renewable energy source. 00:08:04.770 --> 00:08:08.340 align:middle line:90% 00:08:08.340 --> 00:08:16.270 align:middle line:84% This waterfall is the highest in Europe. 00:08:16.270 --> 00:08:18.330 align:middle line:84% It's not the highest waterfall, but it's 00:08:18.330 --> 00:08:19.780 align:middle line:90% the highest artificial one. 00:08:19.780 --> 00:08:26.080 align:middle line:84% It was made up by the Romans, not for energy reasons. 00:08:26.080 --> 00:08:29.350 align:middle line:84% I think they only needed to avoid some floods related 00:08:29.350 --> 00:08:34.070 align:middle line:90% to a lake that was above there. 00:08:34.070 --> 00:08:40.840 align:middle line:84% But as soon as it was possible, probably at the end of, I think, 00:08:40.840 --> 00:08:47.630 align:middle line:84% the 19th century, they started exploiting it. 00:08:47.630 --> 00:08:52.540 align:middle line:84% Now it is used almost every hour of the day, 00:08:52.540 --> 00:08:55.520 align:middle line:84% except when the groups of tourists are there. 00:08:55.520 --> 00:08:57.380 align:middle line:90% Then they stop. 00:08:57.380 --> 00:09:03.620 align:middle line:84% They let the water fall, so just to show it 00:09:03.620 --> 00:09:06.730 align:middle line:90% because it is an attraction. 00:09:06.730 --> 00:09:11.930 align:middle line:84% So how do you analyze something like that? 00:09:11.930 --> 00:09:15.910 align:middle line:84% In an example like that, the bulk flow state 00:09:15.910 --> 00:09:19.370 align:middle line:84% is characterized, not only by the thermal aspect. 00:09:19.370 --> 00:09:24.590 align:middle line:84% So it is not only a change in the enthalpy. 00:09:24.590 --> 00:09:28.760 align:middle line:84% But you also have to remember that the bulk flow state also 00:09:28.760 --> 00:09:31.920 align:middle line:84% has the kinetic energy and the potential energy. 00:09:31.920 --> 00:09:36.240 align:middle line:84% In this case, what's important is the potential energy, 00:09:36.240 --> 00:09:39.440 align:middle line:84% which of course, changes from this elevation 00:09:39.440 --> 00:09:43.345 align:middle line:84% to the elevation at the bottom where then the water goes away. 00:09:43.345 --> 00:09:45.910 align:middle line:90% 00:09:45.910 --> 00:09:51.350 align:middle line:84% You can neglect instead, the kinetic energy. 00:09:51.350 --> 00:09:54.410 align:middle line:84% So the energy balance reads like this. 00:09:54.410 --> 00:09:58.730 align:middle line:84% Presumably, this is when you don't just 00:09:58.730 --> 00:10:01.490 align:middle line:84% let it go as a waterfall, but you pass it 00:10:01.490 --> 00:10:05.720 align:middle line:84% through a proper turbine, hydraulic turbine 00:10:05.720 --> 00:10:16.270 align:middle line:84% to transform this energy into work, mechanical work. 00:10:16.270 --> 00:10:25.600 align:middle line:84% Also, if you recall our formulas for the ideal fluid, 00:10:25.600 --> 00:10:30.640 align:middle line:84% ideal incompressible fluid, the change in the enthalpy 00:10:30.640 --> 00:10:35.500 align:middle line:84% is equal to the specific heat times the change in temperature. 00:10:35.500 --> 00:10:37.690 align:middle line:84% There would be, also, an additional term, which 00:10:37.690 --> 00:10:42.740 align:middle line:84% is plus the specific volume times the change in pressure. 00:10:42.740 --> 00:10:46.540 align:middle line:84% But here, the water up and down is 00:10:46.540 --> 00:10:48.740 align:middle line:90% that same atmospheric pressure. 00:10:48.740 --> 00:10:52.220 align:middle line:90% So that doesn't contribute. 00:10:52.220 --> 00:10:53.920 align:middle line:84% So this is what we are left with. 00:10:53.920 --> 00:10:56.770 align:middle line:90% 00:10:56.770 --> 00:11:01.330 align:middle line:84% So the change in elevation, or the change in potential energy, 00:11:01.330 --> 00:11:04.810 align:middle line:84% can be transformed either in work if you're using it, 00:11:04.810 --> 00:11:09.230 align:middle line:84% or in an increase in temperature. 00:11:09.230 --> 00:11:18.930 align:middle line:84% So if you do not exploit this thing and these energy, 00:11:18.930 --> 00:11:24.100 align:middle line:84% and you just let it run as a waterfall, there is no work. 00:11:24.100 --> 00:11:26.670 align:middle line:90% So this and that become equal. 00:11:26.670 --> 00:11:29.160 align:middle line:84% And if you put them equal, you find 00:11:29.160 --> 00:11:37.790 align:middle line:84% that there is an increase in temperature of the water, which 00:11:37.790 --> 00:11:43.940 align:middle line:84% per unit of jump or change in elevation 00:11:43.940 --> 00:11:47.570 align:middle line:84% is given by g, the gravitational constant divided 00:11:47.570 --> 00:11:51.860 align:middle line:84% by c, the specific heat of water, 00:11:51.860 --> 00:11:54.630 align:middle line:84% which is 4.2 kilojoules per kilogram, K. 00:11:54.630 --> 00:12:04.510 align:middle line:84% And if you represent it in these fancy units like degrees Celsius 00:12:04.510 --> 00:12:10.030 align:middle line:84% per meter, it says that if you have a waterfall higher 00:12:10.030 --> 00:12:17.020 align:middle line:84% than this one, 430 meters, the temperature increase below 00:12:17.020 --> 00:12:24.050 align:middle line:84% will be 1 degree Celsius, not much. 00:12:24.050 --> 00:12:26.930 align:middle line:84% Then you can compute, of course, the entropy 00:12:26.930 --> 00:12:29.600 align:middle line:84% produced by irreversibility because that's 00:12:29.600 --> 00:12:32.640 align:middle line:90% the entropy balance. 00:12:32.640 --> 00:12:39.150 align:middle line:84% And again, you remember what for the compressible fluid model, 00:12:39.150 --> 00:12:44.950 align:middle line:84% the entropy goes as c times the logarithm of the temperatures. 00:12:44.950 --> 00:12:47.600 align:middle line:90% So you can rewrite it this way. 00:12:47.600 --> 00:12:50.570 align:middle line:84% And since the temperature increases is small, 00:12:50.570 --> 00:12:54.920 align:middle line:84% just one degree is small with respect to say, 00:12:54.920 --> 00:13:03.460 align:middle line:84% the absolute temperature which is 300 K. So 1 over 300 00:13:03.460 --> 00:13:05.440 align:middle line:84% is small with respect to 1, so you 00:13:05.440 --> 00:13:10.530 align:middle line:84% can approximate the logarithm of 1 plus x as x, all right. 00:13:10.530 --> 00:13:14.970 align:middle line:84% And so here is the approximation. 00:13:14.970 --> 00:13:17.220 align:middle line:84% And you can compute how much entropy 00:13:17.220 --> 00:13:23.170 align:middle line:84% is produced by irreversibility if this work is zero. 00:13:23.170 --> 00:13:24.680 align:middle line:84% This formula is also valid, also, 00:13:24.680 --> 00:13:30.230 align:middle line:84% if you get some work but not the entire maximum, the maximum you 00:13:30.230 --> 00:13:33.020 align:middle line:84% get, of course, when there is no entropy produced 00:13:33.020 --> 00:13:35.720 align:middle line:90% by irreversibility. 00:13:35.720 --> 00:13:42.010 align:middle line:84% So in as far as this is a good formula 00:13:42.010 --> 00:13:44.080 align:middle line:84% for the entropy production, it is 00:13:44.080 --> 00:13:48.220 align:middle line:84% set to zero when the work is equal to the potential energy 00:13:48.220 --> 00:13:48.720 align:middle line:90% change. 00:13:48.720 --> 00:13:51.950 align:middle line:90% 00:13:51.950 --> 00:13:58.920 align:middle line:84% And that is, it's like per unit-- 00:13:58.920 --> 00:14:10.010 align:middle line:84% so per unit mass of water that falls and per unit of height, 00:14:10.010 --> 00:14:13.380 align:middle line:90% it's equal to g. 00:14:13.380 --> 00:14:20.040 align:middle line:84% And g can be written as, of course, 9.8 meters per seconds 00:14:20.040 --> 00:14:22.620 align:middle line:84% squared, but it can also be written 00:14:22.620 --> 00:14:24.060 align:middle line:90% in these other fancy units. 00:14:24.060 --> 00:14:32.870 align:middle line:84% It's 42 megajoules per ton over 4.3 kilometers. 00:14:32.870 --> 00:14:39.710 align:middle line:84% Now 4.3 kilometers is about the height of the tallest 00:14:39.710 --> 00:14:43.500 align:middle line:90% mountain in Europe, Mont Blanc. 00:14:43.500 --> 00:14:47.190 align:middle line:84% So this means that if you take a ton of water 00:14:47.190 --> 00:14:56.090 align:middle line:84% and pull it down from the top of Mont Blanc to sea level, 00:14:56.090 --> 00:14:57.890 align:middle line:90% you get 42 megajoules. 00:14:57.890 --> 00:15:00.050 align:middle line:84% And 42 megajoules is an interesting number 00:15:00.050 --> 00:15:07.090 align:middle line:84% because it is the heating power of 1 kilogram of oil. 00:15:07.090 --> 00:15:10.480 align:middle line:84% So that gives you the order of magnitude 00:15:10.480 --> 00:15:15.390 align:middle line:90% of these kind of things. 00:15:15.390 --> 00:15:22.420 align:middle line:84% So you need one ton and the entire height of Mont Blanc, 00:15:22.420 --> 00:15:26.950 align:middle line:84% to match what you can do with 1 kilogram of oil. 00:15:26.950 --> 00:15:31.180 align:middle line:84% That shows you the density of available power that 00:15:31.180 --> 00:15:32.676 align:middle line:90% is in hydrocarbons. 00:15:32.676 --> 00:15:40.306 align:middle line:90% 00:15:40.306 --> 00:15:46.180 align:middle line:90% You can do the same in cooling. 00:15:46.180 --> 00:15:52.520 align:middle line:84% So I won't go much over the details of this slide. 00:15:52.520 --> 00:15:55.290 align:middle line:90% You find the same ratio here. 00:15:55.290 --> 00:15:58.790 align:middle line:90% 00:15:58.790 --> 00:16:10.260 align:middle line:84% And again, when you analyze problems like this, for example, 00:16:10.260 --> 00:16:15.870 align:middle line:84% you could have a situation in which your machinery, not only 00:16:15.870 --> 00:16:19.860 align:middle line:84% processes a flow of material, but maybe it 00:16:19.860 --> 00:16:26.130 align:middle line:84% also uses heat from some source at a given temperature 00:16:26.130 --> 00:16:30.100 align:middle line:84% and then uses work or produces work. 00:16:30.100 --> 00:16:33.490 align:middle line:84% So this would require that you make 00:16:33.490 --> 00:16:35.060 align:middle line:90% an energy balance like this. 00:16:35.060 --> 00:16:37.970 align:middle line:84% So you have two heat interactions. 00:16:37.970 --> 00:16:41.440 align:middle line:84% One with the heat source at temperature TQ, 00:16:41.440 --> 00:16:45.500 align:middle line:84% and the other with the heat source-- 00:16:45.500 --> 00:16:49.240 align:middle line:84% with the environment, which is always there 00:16:49.240 --> 00:16:54.420 align:middle line:84% to match, to balance the entropy. 00:16:54.420 --> 00:16:57.580 align:middle line:84% And then you have your entropy balance. 00:16:57.580 --> 00:17:00.030 align:middle line:84% And then as you see, we've seen it 00:17:00.030 --> 00:17:03.000 align:middle line:84% several times now, if you combine these two balances 00:17:03.000 --> 00:17:05.819 align:middle line:84% by taking the entropy balance multiplied 00:17:05.819 --> 00:17:08.670 align:middle line:84% by the environmental temperature and subtracting it 00:17:08.670 --> 00:17:13.950 align:middle line:84% from the energy balance, you get the so-called exergy balance, 00:17:13.950 --> 00:17:21.730 align:middle line:84% where you have the various heats multiplied by their own Carnot 00:17:21.730 --> 00:17:23.819 align:middle line:90% coefficient. 00:17:23.819 --> 00:17:27.560 align:middle line:84% In fact, the Carnot coefficient of the environmental temperature 00:17:27.560 --> 00:17:35.000 align:middle line:84% is zero here, so there is no exergy involved with this heat 00:17:35.000 --> 00:17:37.760 align:middle line:90% interaction. 00:17:37.760 --> 00:17:40.820 align:middle line:84% This is the Carnot coefficient that we just talked about 00:17:40.820 --> 00:17:42.710 align:middle line:84% associated with bulk flow changes 00:17:42.710 --> 00:17:47.240 align:middle line:84% and this is the exergy loss, or destroyed, 00:17:47.240 --> 00:17:51.675 align:middle line:84% due to the entropy production by irreversibility. 00:17:51.675 --> 00:17:56.630 align:middle line:90% 00:17:56.630 --> 00:18:05.480 align:middle line:84% Now, when you compute the change in exergy for a bulk flow, 00:18:05.480 --> 00:18:09.710 align:middle line:84% and you compute it for particular substances, 00:18:09.710 --> 00:18:12.680 align:middle line:84% then you have to substitute the constitutive relations 00:18:12.680 --> 00:18:15.230 align:middle line:84% for those substances, those relations that 00:18:15.230 --> 00:18:18.140 align:middle line:84% relate the enthalpy and the entropy 00:18:18.140 --> 00:18:20.210 align:middle line:84% to the temperature and the pressure. 00:18:20.210 --> 00:18:22.290 align:middle line:84% For example, if we are using a liquid, 00:18:22.290 --> 00:18:28.840 align:middle line:84% so this slide is for a liquid, as I said, 00:18:28.840 --> 00:18:32.360 align:middle line:84% the enthalpy change is equal to c 00:18:32.360 --> 00:18:34.610 align:middle line:84% specific heat times the temperature change 00:18:34.610 --> 00:18:36.740 align:middle line:90% times the specific volume. 00:18:36.740 --> 00:18:39.440 align:middle line:84% You can also write that as 1 over the density 00:18:39.440 --> 00:18:42.910 align:middle line:90% times the pressure change. 00:18:42.910 --> 00:18:47.860 align:middle line:84% And the entropy is c times the log of the ratio of the two 00:18:47.860 --> 00:18:50.870 align:middle line:90% temperatures. 00:18:50.870 --> 00:19:00.520 align:middle line:84% Now OK, so you can substitute, collect the heat part, 00:19:00.520 --> 00:19:06.850 align:middle line:84% so that you put in evidence this Carnot coefficient 00:19:06.850 --> 00:19:09.170 align:middle line:90% looking-like term. 00:19:09.170 --> 00:19:10.780 align:middle line:84% And then there is a term here, which 00:19:10.780 --> 00:19:19.200 align:middle line:84% is connected with the pressure drop as the flow goes there. 00:19:19.200 --> 00:19:24.690 align:middle line:84% Now, if you can neglect this pressure drop, at least neglect 00:19:24.690 --> 00:19:29.830 align:middle line:84% this with respect to the thermal part of this change in exergy, 00:19:29.830 --> 00:19:35.010 align:middle line:84% then you get that your change in exergy 00:19:35.010 --> 00:19:38.860 align:middle line:84% is equal to the heat times the Carnot coefficient. 00:19:38.860 --> 00:19:41.370 align:middle line:84% And this temperature equivalent to TQ 00:19:41.370 --> 00:19:45.060 align:middle line:84% is given by this logarithmic mean temperature 00:19:45.060 --> 00:19:49.360 align:middle line:84% of the inlet-outlet temperatures. 00:19:49.360 --> 00:19:51.585 align:middle line:90% I do the same for an ideal gas. 00:19:51.585 --> 00:19:54.280 align:middle line:90% 00:19:54.280 --> 00:19:58.520 align:middle line:84% So for the ideal gas, things change a bit 00:19:58.520 --> 00:20:04.470 align:middle line:84% because now the enthalpy is a function only of temperature, 00:20:04.470 --> 00:20:07.040 align:middle line:84% and the change in enthalpy is the specific heat 00:20:07.040 --> 00:20:10.640 align:middle line:84% at constant pressure times the change in temperature. 00:20:10.640 --> 00:20:13.280 align:middle line:84% And it's now the entropy that depends 00:20:13.280 --> 00:20:17.480 align:middle line:90% on pressure and temperature. 00:20:17.480 --> 00:20:21.200 align:middle line:84% So it's cp log of the ratio of the T's minus R log 00:20:21.200 --> 00:20:25.730 align:middle line:90% of the ratio of the pressures. 00:20:25.730 --> 00:20:31.050 align:middle line:84% So you can put it in exactly the same formal relation, 00:20:31.050 --> 00:20:34.040 align:middle line:84% except that here you have cp instead of c, 00:20:34.040 --> 00:20:38.640 align:middle line:84% and here you have the log of the ratio of the pressures. 00:20:38.640 --> 00:20:45.780 align:middle line:84% This is again, related to the pressure drop, 00:20:45.780 --> 00:20:49.560 align:middle line:84% namely, the work you need to spend in order 00:20:49.560 --> 00:20:53.850 align:middle line:84% to overcome the friction forces along the pipe in order 00:20:53.850 --> 00:21:01.290 align:middle line:90% to make the flow overcome those. 00:21:01.290 --> 00:21:03.900 align:middle line:84% But if you can neglect those, then we get, 00:21:03.900 --> 00:21:09.880 align:middle line:84% again, this formula and again, TQ is the log mean temperature. 00:21:09.880 --> 00:21:11.530 align:middle line:84% And there is a third case in which 00:21:11.530 --> 00:21:14.080 align:middle line:84% you have a similar situation, which 00:21:14.080 --> 00:21:17.530 align:middle line:84% is whenever you are changing phase, 00:21:17.530 --> 00:21:27.060 align:middle line:84% your flow is maybe boiling or condensing, 00:21:27.060 --> 00:21:31.130 align:middle line:84% then the change in enthalpy is equal to the change 00:21:31.130 --> 00:21:35.150 align:middle line:90% in the quality of the-- 00:21:35.150 --> 00:21:40.700 align:middle line:84% so the vapor fraction that we defined last time. 00:21:40.700 --> 00:21:42.950 align:middle line:84% So the change in quality times the enthalpy 00:21:42.950 --> 00:21:50.180 align:middle line:84% of vaporization for h2 minus h1, or the change in quality times 00:21:50.180 --> 00:21:53.380 align:middle line:84% the entropy of vaporization for the change in entropy. 00:21:53.380 --> 00:21:59.930 align:middle line:84% So you can also do the same thing, put outside the energy 00:21:59.930 --> 00:22:04.900 align:middle line:84% change of your flow, call it Q, and what's 00:22:04.900 --> 00:22:08.170 align:middle line:84% left as a form of a Carnot ratio where 00:22:08.170 --> 00:22:11.830 align:middle line:84% the TQ is the ratio between the enthalpy and the entropy 00:22:11.830 --> 00:22:14.080 align:middle line:84% of vaporization, which is exactly 00:22:14.080 --> 00:22:17.680 align:middle line:84% the temperature at which the boiling and/or 00:22:17.680 --> 00:22:19.530 align:middle line:90% condensation occurs. 00:22:19.530 --> 00:22:24.180 align:middle line:90% 00:22:24.180 --> 00:22:34.050 align:middle line:84% So for example, let's compute these number 00:22:34.050 --> 00:22:39.790 align:middle line:84% for the case of heating water, which is used for, for example, 00:22:39.790 --> 00:22:43.690 align:middle line:90% industrial applications. 00:22:43.690 --> 00:22:47.250 align:middle line:84% You often need steam or hot water 00:22:47.250 --> 00:22:52.320 align:middle line:84% for many processes or residential heating 00:22:52.320 --> 00:22:53.600 align:middle line:90% to heat up your homes. 00:22:53.600 --> 00:22:58.550 align:middle line:90% 00:22:58.550 --> 00:23:01.355 align:middle line:84% All right, so what I want to compute 00:23:01.355 --> 00:23:09.180 align:middle line:84% is this Carnot coefficient, which you see, 00:23:09.180 --> 00:23:13.140 align:middle line:84% is therefore, the ratio between the exergy 00:23:13.140 --> 00:23:16.415 align:middle line:90% over the heat that is provided. 00:23:16.415 --> 00:23:24.790 align:middle line:90% 00:23:24.790 --> 00:23:30.460 align:middle line:84% So it's the exergy content of your heated water 00:23:30.460 --> 00:23:31.910 align:middle line:90% after you heat it. 00:23:31.910 --> 00:23:33.370 align:middle line:90% That's the exergy. 00:23:33.370 --> 00:23:37.900 align:middle line:84% And the exergy, remember, is the minimum work 00:23:37.900 --> 00:23:41.990 align:middle line:90% required to do that job. 00:23:41.990 --> 00:23:47.120 align:middle line:84% So this ratio, exergy change over heat, 00:23:47.120 --> 00:23:53.695 align:middle line:84% represents the minimum work per unit energy of your heating. 00:23:53.695 --> 00:23:56.610 align:middle line:90% 00:23:56.610 --> 00:24:00.880 align:middle line:90% And so that is useful. 00:24:00.880 --> 00:24:02.570 align:middle line:90% So it's the best you can do. 00:24:02.570 --> 00:24:05.250 align:middle line:90% 00:24:05.250 --> 00:24:08.860 align:middle line:84% So if you compute it for these temperatures from, say, 00:24:08.860 --> 00:24:12.040 align:middle line:84% heating water from 60 degrees to 120, 00:24:12.040 --> 00:24:18.940 align:middle line:84% which corresponds to an industrial application 00:24:18.940 --> 00:24:30.080 align:middle line:84% and assume an environment at 300 K, that's 27 degrees C, 00:24:30.080 --> 00:24:32.120 align:middle line:90% here's the number. 00:24:32.120 --> 00:24:39.920 align:middle line:84% You compute that number, you get 17.2%. 00:24:39.920 --> 00:24:45.890 align:middle line:84% If instead you're heating water from 20 to 60 degrees Celsius, 00:24:45.890 --> 00:24:49.043 align:middle line:84% in the same environment, that would be 4%. 00:24:49.043 --> 00:24:54.604 align:middle line:90% 00:24:54.604 --> 00:24:59.600 align:middle line:84% So this is interesting because, for example, let me ask you, 00:24:59.600 --> 00:25:01.310 align:middle line:84% with this number, can you tell me 00:25:01.310 --> 00:25:05.600 align:middle line:84% what is the second-law efficiency 00:25:05.600 --> 00:25:16.780 align:middle line:84% of doing, for example, this heating with an electric boiler? 00:25:16.780 --> 00:25:19.840 align:middle line:84% An electric boiler uses electricity. 00:25:19.840 --> 00:25:23.440 align:middle line:90% Electricity is pure exergy. 00:25:23.440 --> 00:25:28.260 align:middle line:84% So how do you define the second-law efficiency. 00:25:28.260 --> 00:25:37.080 align:middle line:84% It's eta 2 is equal to the exergy 00:25:37.080 --> 00:25:51.160 align:middle line:84% of your result, useful effect, times the exergy consumed, 00:25:51.160 --> 00:25:51.660 align:middle line:90% all right. 00:25:51.660 --> 00:25:54.950 align:middle line:90% 00:25:54.950 --> 00:25:58.340 align:middle line:84% So in this case, you're using work. 00:25:58.340 --> 00:26:02.330 align:middle line:84% The exergy consumed is equal to the work 00:26:02.330 --> 00:26:04.540 align:middle line:84% that you're using in your electric boiler. 00:26:04.540 --> 00:26:08.870 align:middle line:90% 00:26:08.870 --> 00:26:21.810 align:middle line:84% And the exergy up there is Q times 1 minus Ta 00:26:21.810 --> 00:26:31.600 align:middle line:84% over TQ, where TQ is the logarithmic mean temperature. 00:26:31.600 --> 00:26:35.160 align:middle line:84% So it's precisely what we have computed here. 00:26:35.160 --> 00:26:37.910 align:middle line:90% 00:26:37.910 --> 00:26:42.320 align:middle line:84% Now, in an electric boiler, your work 00:26:42.320 --> 00:26:47.820 align:middle line:84% is completely transformed into heat by joule effect. 00:26:47.820 --> 00:26:53.050 align:middle line:84% So even if your boiler were 100% efficient, 00:26:53.050 --> 00:27:03.840 align:middle line:84% very well insulated you get that Q is equal to W, see. 00:27:03.840 --> 00:27:10.600 align:middle line:84% So we are left that the second-law efficiency is equal, 00:27:10.600 --> 00:27:13.113 align:middle line:90% in this case, to 4%. 00:27:13.113 --> 00:27:16.730 align:middle line:90% 00:27:16.730 --> 00:27:19.220 align:middle line:84% So 4%, and this is the kind of efficiency 00:27:19.220 --> 00:27:23.290 align:middle line:84% that signals how much room for improvement is there. 00:27:23.290 --> 00:27:26.340 align:middle line:84% So there is 96% room for improvement. 00:27:26.340 --> 00:27:29.800 align:middle line:90% 00:27:29.800 --> 00:27:34.540 align:middle line:84% Nevertheless, we do use electric boilers. 00:27:34.540 --> 00:27:37.780 align:middle line:90% But where? 00:27:37.780 --> 00:27:42.220 align:middle line:84% You use them where you don't need this-- 00:27:42.220 --> 00:27:45.890 align:middle line:90% to heat water all the time. 00:27:45.890 --> 00:27:49.400 align:middle line:84% For example, in the South of Italy, 00:27:49.400 --> 00:27:53.660 align:middle line:84% where I have a small house with olive trees, 00:27:53.660 --> 00:27:56.300 align:middle line:84% and I go there just for the summer, 00:27:56.300 --> 00:28:02.220 align:middle line:84% I have electric boilers because I use them, maybe, 00:28:02.220 --> 00:28:04.230 align:middle line:90% one month per year. 00:28:04.230 --> 00:28:12.610 align:middle line:84% So the investment cost wouldn't pay 00:28:12.610 --> 00:28:17.280 align:middle line:84% if I buy a more efficient equipment, like, would 00:28:17.280 --> 00:28:24.260 align:middle line:84% be a heat pump or even a gas, which is intermediate. 00:28:24.260 --> 00:28:27.720 align:middle line:84% Because the more efficient is the equipment, 00:28:27.720 --> 00:28:30.480 align:middle line:84% the more complicated is the machinery, 00:28:30.480 --> 00:28:31.830 align:middle line:90% so the higher the cost. 00:28:31.830 --> 00:28:39.500 align:middle line:84% And so if I use it for only a few months a year, 00:28:39.500 --> 00:28:44.300 align:middle line:84% it doesn't pay to invest that much. 00:28:44.300 --> 00:28:49.450 align:middle line:84% But still, you have to keep that in mind that this is the idea. 00:28:49.450 --> 00:29:00.340 align:middle line:84% And maybe I could have invested in solar thermal heating, which 00:29:00.340 --> 00:29:04.510 align:middle line:84% would even save me the cost of electricity 00:29:04.510 --> 00:29:12.600 align:middle line:84% at the expense of investment cost for the equipment. 00:29:12.600 --> 00:29:19.320 align:middle line:84% But also that has a problem in some countries 00:29:19.320 --> 00:29:23.100 align:middle line:84% and especially in the countryside where 00:29:23.100 --> 00:29:27.690 align:middle line:84% this equipment is left outside with nobody watching. 00:29:27.690 --> 00:29:37.540 align:middle line:84% It is easily stolen, so that's another issue, security. 00:29:37.540 --> 00:29:40.380 align:middle line:90% All right. 00:29:40.380 --> 00:29:46.650 align:middle line:84% So let me say a little more about fuels 00:29:46.650 --> 00:29:51.130 align:middle line:84% because we will in the second part of the course, 00:29:51.130 --> 00:29:59.340 align:middle line:84% we will do systems with chemical reactions. 00:29:59.340 --> 00:30:04.710 align:middle line:84% And so we will return to this in much more detail. 00:30:04.710 --> 00:30:07.250 align:middle line:84% But for the moment, let me just say 00:30:07.250 --> 00:30:15.380 align:middle line:84% that if I were to heat up something or water with a gas 00:30:15.380 --> 00:30:18.680 align:middle line:84% boiler, I would need to put here the exergy of the fuel 00:30:18.680 --> 00:30:20.240 align:middle line:90% that I have consumed. 00:30:20.240 --> 00:30:23.830 align:middle line:84% So how do you compute exergy for a fuel? 00:30:23.830 --> 00:30:26.190 align:middle line:90% The idea is the following. 00:30:26.190 --> 00:30:31.970 align:middle line:84% You take your fuel at environmental conditions, 00:30:31.970 --> 00:30:42.800 align:middle line:84% and you mix it, or keep it separate with just 00:30:42.800 --> 00:30:43.670 align:middle line:90% sufficient air. 00:30:43.670 --> 00:30:45.880 align:middle line:84% So the stoichiometric amount of air that is 00:30:45.880 --> 00:30:49.260 align:middle line:90% needed to oxidize that fuel. 00:30:49.260 --> 00:30:54.760 align:middle line:84% And then you have a piece of equipment, 00:30:54.760 --> 00:31:00.340 align:middle line:84% which you try to make as close to reversible as possible. 00:31:00.340 --> 00:31:03.290 align:middle line:90% 00:31:03.290 --> 00:31:08.630 align:middle line:84% And while this equipment produces the combustion 00:31:08.630 --> 00:31:11.030 align:middle line:84% or the oxidation of your fuels, and therefore produces 00:31:11.030 --> 00:31:19.700 align:middle line:84% products of combustion, it produces also work. 00:31:19.700 --> 00:31:23.090 align:middle line:84% It needs, as usual, an interaction 00:31:23.090 --> 00:31:26.210 align:middle line:84% with the environment, so as to exchange the entropy that 00:31:26.210 --> 00:31:34.070 align:middle line:84% is needed to balance the entropy without the need 00:31:34.070 --> 00:31:36.950 align:middle line:90% of irreversibility. 00:31:36.950 --> 00:31:40.740 align:middle line:84% And so this result is the exergy of your fuel, 00:31:40.740 --> 00:31:45.450 align:middle line:84% the maximum work you can extract while your products 00:31:45.450 --> 00:31:52.025 align:middle line:84% of combustion, notice, are down in mutual equilibrium 00:31:52.025 --> 00:31:52.900 align:middle line:90% with the environment. 00:31:52.900 --> 00:31:57.350 align:middle line:84% So are again, environmental conditions. 00:31:57.350 --> 00:32:08.160 align:middle line:84% Typically, we will see that the exergy of the fuel 00:32:08.160 --> 00:32:11.070 align:middle line:84% will be given by this expression. 00:32:11.070 --> 00:32:17.340 align:middle line:84% We will define an enthalpy of the combustion reaction 00:32:17.340 --> 00:32:22.470 align:middle line:90% and an entropy of combustion. 00:32:22.470 --> 00:32:28.330 align:middle line:84% So this combination is the Gibbs free energy 00:32:28.330 --> 00:32:31.930 align:middle line:84% of the combustion at standard conditions of pressure 00:32:31.930 --> 00:32:32.720 align:middle line:90% and temperature. 00:32:32.720 --> 00:32:36.940 align:middle line:84% That's the meaning of the naught up there, the superscript. 00:32:36.940 --> 00:32:39.010 align:middle line:84% And with a minus in front, that will 00:32:39.010 --> 00:32:46.270 align:middle line:84% be the most important contribution 00:32:46.270 --> 00:32:48.280 align:middle line:90% to the exergy of the fuel. 00:32:48.280 --> 00:32:50.920 align:middle line:84% There will be some term related to mixing 00:32:50.920 --> 00:32:53.200 align:middle line:90% that we will see later. 00:32:53.200 --> 00:32:57.270 align:middle line:90% Regarding the heat of-- 00:32:57.270 --> 00:32:58.930 align:middle line:84% the heating value, the heating value 00:32:58.930 --> 00:33:01.530 align:middle line:84% if I go back to this previous slide. 00:33:01.530 --> 00:33:10.670 align:middle line:84% Now, suppose I don't have any work extraction here, 00:33:10.670 --> 00:33:15.370 align:middle line:84% and all I have is an interaction with the environment. 00:33:15.370 --> 00:33:21.170 align:middle line:84% And so I burn my fuel and then exit the product, 00:33:21.170 --> 00:33:24.340 align:middle line:84% so cool down the products of combustion 00:33:24.340 --> 00:33:26.530 align:middle line:90% at environmental temperature. 00:33:26.530 --> 00:33:28.270 align:middle line:90% In order to cool-- 00:33:28.270 --> 00:33:31.760 align:middle line:84% doing that cooling down, I need to extract heat. 00:33:31.760 --> 00:33:36.190 align:middle line:84% That heat is the heating value of the fuel. 00:33:36.190 --> 00:33:38.940 align:middle line:90% Again, we'll return to those. 00:33:38.940 --> 00:33:45.170 align:middle line:84% The message here, for practical applications 00:33:45.170 --> 00:33:49.130 align:middle line:84% in which you need to compute the exergy of a fuel, 00:33:49.130 --> 00:33:54.710 align:middle line:84% the rule of thumb is that it turns out 00:33:54.710 --> 00:33:56.840 align:middle line:84% that for all hydrocarbons, we will 00:33:56.840 --> 00:34:02.690 align:middle line:84% see the detailed list, the ratio of this part 00:34:02.690 --> 00:34:11.590 align:middle line:84% of the contribution to that part is small, plus or minus 2.5%. 00:34:11.590 --> 00:34:14.199 align:middle line:84% So if you accept that kind of approximation, 00:34:14.199 --> 00:34:16.940 align:middle line:84% and typically in exergy computations, 00:34:16.940 --> 00:34:21.880 align:middle line:84% you can afford that kind of precision, 00:34:21.880 --> 00:34:26.330 align:middle line:84% you can simply see you can neglect this part. 00:34:26.330 --> 00:34:32.080 align:middle line:84% And so see that the exergy and the heating value 00:34:32.080 --> 00:34:33.929 align:middle line:90% are approximately equal. 00:34:33.929 --> 00:34:36.670 align:middle line:84% So you can say that the exergy of the fuel 00:34:36.670 --> 00:34:39.850 align:middle line:84% is approximately equal to the heating value-- 00:34:39.850 --> 00:34:46.030 align:middle line:84% to the yes, to the heating value of the fuel, 00:34:46.030 --> 00:34:48.730 align:middle line:84% which is, in turn, approximately equal 00:34:48.730 --> 00:34:50.610 align:middle line:90% to the lower heating value. 00:34:50.610 --> 00:34:58.060 align:middle line:90% 00:34:58.060 --> 00:35:00.640 align:middle line:84% As you know, there is a distinction 00:35:00.640 --> 00:35:04.360 align:middle line:84% between lower heating value and higher heating value, 00:35:04.360 --> 00:35:07.600 align:middle line:84% which has to do with the fact that in the products 00:35:07.600 --> 00:35:12.370 align:middle line:90% of combustion, there is water. 00:35:12.370 --> 00:35:16.960 align:middle line:84% And if you do the cooling of that water, 00:35:16.960 --> 00:35:20.530 align:middle line:84% of that stream of products of combustion, 00:35:20.530 --> 00:35:26.090 align:middle line:84% down to environmental conditions, some of the water 00:35:26.090 --> 00:35:26.770 align:middle line:90% will condense. 00:35:26.770 --> 00:35:30.220 align:middle line:90% 00:35:30.220 --> 00:35:36.790 align:middle line:84% And so the condensing of the water 00:35:36.790 --> 00:35:42.160 align:middle line:84% releases the enthalpy of vaporization. 00:35:42.160 --> 00:35:47.680 align:middle line:84% And that is additional energy that you can, in principle, 00:35:47.680 --> 00:35:48.180 align:middle line:90% extract. 00:35:48.180 --> 00:35:50.690 align:middle line:90% 00:35:50.690 --> 00:35:55.640 align:middle line:84% So you call lower heating value when 00:35:55.640 --> 00:36:01.880 align:middle line:84% you pretend that water doesn't condense even if you're 00:36:01.880 --> 00:36:05.220 align:middle line:90% going down to 25 Celsius. 00:36:05.220 --> 00:36:09.490 align:middle line:84% And the higher heating value is the opposite case. 00:36:09.490 --> 00:36:11.410 align:middle line:84% You pretend that it all condenses, 00:36:11.410 --> 00:36:15.750 align:middle line:84% even though, part of the water remains 00:36:15.750 --> 00:36:19.050 align:middle line:84% as a form of vapor mixed with the products of combustion. 00:36:19.050 --> 00:36:20.880 align:middle line:90% So these are two extremes. 00:36:20.880 --> 00:36:27.240 align:middle line:84% For example, methane, has a lower heating value 00:36:27.240 --> 00:36:31.830 align:middle line:84% of 50 megajoules per kilogram and a higher heating 00:36:31.830 --> 00:36:33.130 align:middle line:90% value of 55. 00:36:33.130 --> 00:36:36.610 align:middle line:84% So it's not an unimportant effect. 00:36:36.610 --> 00:36:40.680 align:middle line:84% It's like 10% the difference, so the contribution 00:36:40.680 --> 00:36:42.010 align:middle line:90% of condensation. 00:36:42.010 --> 00:36:48.119 align:middle line:90% 00:36:48.119 --> 00:36:54.710 align:middle line:84% In this table, I listed some heating values 00:36:54.710 --> 00:36:57.203 align:middle line:90% of some typical fuels. 00:36:57.203 --> 00:37:02.120 align:middle line:90% 00:37:02.120 --> 00:37:09.260 align:middle line:84% Yes, there are still technical units around. 00:37:09.260 --> 00:37:12.570 align:middle line:84% In Europe it's kilocalories per kilogram. 00:37:12.570 --> 00:37:16.353 align:middle line:84% Here, you get still BTUs per pound. 00:37:16.353 --> 00:37:22.050 align:middle line:90% 00:37:22.050 --> 00:37:25.870 align:middle line:84% International system of units is more like joules. 00:37:25.870 --> 00:37:29.190 align:middle line:84% And this is megajoules per kilogram. 00:37:29.190 --> 00:37:30.630 align:middle line:84% And you see that more or less when 00:37:30.630 --> 00:37:35.220 align:middle line:84% you present in terms of these units per kilogram, 00:37:35.220 --> 00:37:41.080 align:middle line:84% the fuels have different definitely heating values, 00:37:41.080 --> 00:37:44.840 align:middle line:84% but they are within a limited range. 00:37:44.840 --> 00:37:47.590 align:middle line:90% They're all around 40. 00:37:47.590 --> 00:37:49.545 align:middle line:90% 42 is crude oil. 00:37:49.545 --> 00:37:52.730 align:middle line:90% 00:37:52.730 --> 00:37:55.850 align:middle line:84% I mean, a typical value because crude oil varies 00:37:55.850 --> 00:37:57.150 align:middle line:90% a lot from place to place. 00:37:57.150 --> 00:38:04.160 align:middle line:84% But the canonical standard is 42 megajoules. 00:38:04.160 --> 00:38:08.090 align:middle line:84% That number that corresponds that we've 00:38:08.090 --> 00:38:14.300 align:middle line:84% seen, in this waterfall example, to lifting one ton of water 00:38:14.300 --> 00:38:17.305 align:middle line:84% up to the top of Mont Blanc from sea level. 00:38:17.305 --> 00:38:20.890 align:middle line:90% 00:38:20.890 --> 00:38:23.200 align:middle line:84% The same energy is what is needed 00:38:23.200 --> 00:38:32.580 align:middle line:84% to heat up one ton of water by 10 degrees Celsius 00:38:32.580 --> 00:38:38.460 align:middle line:84% or to evaporate, not one ton, but 18 kilograms of water 00:38:38.460 --> 00:38:39.545 align:middle line:90% at atmospheric pressure. 00:38:39.545 --> 00:38:43.250 align:middle line:90% 00:38:43.250 --> 00:38:47.330 align:middle line:84% So that's also oxidizing one kilogram of oil. 00:38:47.330 --> 00:38:50.780 align:middle line:84% So that's the heating value of one kilogram. 00:38:50.780 --> 00:38:55.746 align:middle line:84% If you compare it to the power density in some other-- 00:38:55.746 --> 00:38:56.246 align:middle line:90% natural-- 00:38:56.246 --> 00:39:03.410 align:middle line:90% I mean resource for-- 00:39:03.410 --> 00:39:08.290 align:middle line:84% primary energy, fission of uranium isotope 00:39:08.290 --> 00:39:14.720 align:middle line:84% 233, a half milligram of that will give you that same amount. 00:39:14.720 --> 00:39:19.880 align:middle line:84% So you see how different concentrations of energies 00:39:19.880 --> 00:39:20.770 align:middle line:90% we have. 00:39:20.770 --> 00:39:37.335 align:middle line:90% 00:39:37.335 --> 00:39:41.730 align:middle line:84% Now, for reasons that we will see later, but also 00:39:41.730 --> 00:39:48.060 align:middle line:84% just for fun, you can plot on this graph 00:39:48.060 --> 00:39:52.860 align:middle line:84% the history of efficiencies, second-law efficiencies, 00:39:52.860 --> 00:40:01.920 align:middle line:84% of technologies that mankind has developed over the years 00:40:01.920 --> 00:40:10.874 align:middle line:84% to convert fuel exergy into work, starting from the early-- 00:40:10.874 --> 00:40:20.200 align:middle line:84% the beginning of the Industrial Revolution in England, where 00:40:20.200 --> 00:40:30.970 align:middle line:84% you would use vapor to pump water out of the coal mines. 00:40:30.970 --> 00:40:34.130 align:middle line:84% And then you see, recognize here some names. 00:40:34.130 --> 00:40:40.330 align:middle line:84% See where efficiency of the order of these numbers-- 00:40:40.330 --> 00:40:41.050 align:middle line:90% OK, I'm sorry. 00:40:41.050 --> 00:40:46.020 align:middle line:84% The efficiency are on this side of the graph, so 1%. 00:40:46.020 --> 00:40:49.110 align:middle line:90% Today, you go up. 00:40:49.110 --> 00:40:55.780 align:middle line:84% We are of the order of 60%, 65%, almost 65%. 00:40:55.780 --> 00:41:06.520 align:middle line:84% The best available technology is reaching this much. 00:41:06.520 --> 00:41:12.670 align:middle line:84% The diagram is made a straight line 00:41:12.670 --> 00:41:17.500 align:middle line:90% by plotting, not the linear. 00:41:17.500 --> 00:41:19.960 align:middle line:84% This scale is not linear in the second-law efficiency. 00:41:19.960 --> 00:41:27.070 align:middle line:84% It's linear in the efficiency over the 1 minus the efficiency. 00:41:27.070 --> 00:41:30.790 align:middle line:84% So the efficiency divided by the room for improvement. 00:41:30.790 --> 00:41:35.060 align:middle line:84% This ratio is called the logistic scale. 00:41:35.060 --> 00:41:39.950 align:middle line:84% You could plot the same diagram on a linear scale, 00:41:39.950 --> 00:41:46.530 align:middle line:84% and you would get a typical S-shaped curve typical 00:41:46.530 --> 00:41:49.603 align:middle line:90% of any learning process. 00:41:49.603 --> 00:41:56.570 align:middle line:90% 00:41:56.570 --> 00:41:58.880 align:middle line:84% And in fact, you see, and I can even 00:41:58.880 --> 00:42:02.150 align:middle line:84% write the differential equation for this 00:42:02.150 --> 00:42:06.750 align:middle line:84% to obtain this formula, from which it is interesting, too, 00:42:06.750 --> 00:42:09.870 align:middle line:84% that you extract the time constant, 00:42:09.870 --> 00:42:13.080 align:middle line:84% the characteristic time of this learning. 00:42:13.080 --> 00:42:16.055 align:middle line:84% And this time constant is 60 years. 00:42:16.055 --> 00:42:21.226 align:middle line:90% 00:42:21.226 --> 00:42:28.690 align:middle line:84% I think you can prove that it's related to this slope 00:42:28.690 --> 00:42:31.270 align:middle line:90% here, the maximum height. 00:42:31.270 --> 00:42:39.910 align:middle line:84% So in other words, it took us 300 years to go from 1% to 65%, 00:42:39.910 --> 00:42:42.430 align:middle line:90% and we are not done yet. 00:42:42.430 --> 00:42:46.790 align:middle line:84% And because this is the second-law efficiency, 00:42:46.790 --> 00:42:50.320 align:middle line:90% the upper limit is 1. 00:42:50.320 --> 00:42:55.990 align:middle line:84% So that means that we will continue. 00:42:55.990 --> 00:43:03.470 align:middle line:84% So at the end of this century, if our learning process goes on, 00:43:03.470 --> 00:43:10.840 align:middle line:84% we will be at 85%, And still it will go. 00:43:10.840 --> 00:43:15.400 align:middle line:84% At least this is what history tells us. 00:43:15.400 --> 00:43:19.580 align:middle line:84% But since the correlation is very remarkable here, 00:43:19.580 --> 00:43:22.780 align:middle line:90% it's very likely that we do-- 00:43:22.780 --> 00:43:25.970 align:middle line:84% since this is typical of any human-- 00:43:25.970 --> 00:43:33.040 align:middle line:84% There is an entire section of the literature about the studies 00:43:33.040 --> 00:43:37.120 align:middle line:84% of the history of technologies that represent 00:43:37.120 --> 00:43:43.540 align:middle line:84% many other technologies on these logistic graphs, 00:43:43.540 --> 00:43:46.460 align:middle line:84% and they all show a similar behavior. 00:43:46.460 --> 00:43:52.870 align:middle line:84% You could also plot here the number of words 00:43:52.870 --> 00:43:58.660 align:middle line:84% that a child learns from when he doesn't 00:43:58.660 --> 00:44:01.490 align:middle line:84% speak to when he starts speaking, 00:44:01.490 --> 00:44:03.480 align:middle line:90% and it follows the same curve. 00:44:03.480 --> 00:44:08.590 align:middle line:90% 00:44:08.590 --> 00:44:19.960 align:middle line:84% And here, also, for fun, I just put the arrows on the timeline 00:44:19.960 --> 00:44:24.580 align:middle line:84% where the various names that are associated with thermodynamics, 00:44:24.580 --> 00:44:31.110 align:middle line:84% see Rankine, Boltzmann, and so on, 00:44:31.110 --> 00:44:34.505 align:middle line:84% are placed with respect to this graph. 00:44:34.505 --> 00:44:38.750 align:middle line:90% 00:44:38.750 --> 00:44:48.820 align:middle line:84% Somewhere, I think, somewhere here, or is it there? 00:44:48.820 --> 00:44:53.580 align:middle line:84% Yeah, no, probably here, that name. 00:44:53.580 --> 00:45:01.400 align:middle line:84% Mollier who gave the name of to the enthalpy 00:45:01.400 --> 00:45:07.110 align:middle line:84% versus entropy graph that I discussed the other day, 00:45:07.110 --> 00:45:14.770 align:middle line:84% is here and is also important because his student 00:45:14.770 --> 00:45:17.860 align:middle line:84% was Nusselt. Nusselt is another name you might 00:45:17.860 --> 00:45:20.380 align:middle line:90% have heard from heat transfer. 00:45:20.380 --> 00:45:23.050 align:middle line:90% So he was a student of Mollier. 00:45:23.050 --> 00:45:26.590 align:middle line:84% And actually, I think we pronounce it Mollier 00:45:26.590 --> 00:45:28.100 align:middle line:90% thinking that it is French. 00:45:28.100 --> 00:45:31.510 align:middle line:84% But he was German, so I don't know how the German pronounce 00:45:31.510 --> 00:45:34.740 align:middle line:84% Mollier, but I'll let you figure it out. 00:45:34.740 --> 00:45:37.260 align:middle line:90% 00:45:37.260 --> 00:45:40.320 align:middle line:84% In any case, I also put this slide 00:45:40.320 --> 00:45:43.590 align:middle line:90% because I wanted to advertise-- 00:45:43.590 --> 00:45:47.220 align:middle line:84% if you click here, you go to the proceedings of a conference 00:45:47.220 --> 00:45:54.540 align:middle line:84% that we held 2008 in memory of Professor Kenan. 00:45:54.540 --> 00:45:59.910 align:middle line:84% And so we edited this volume, and there 00:45:59.910 --> 00:46:06.150 align:middle line:84% are contributions about the state of thermodynamics 00:46:06.150 --> 00:46:10.020 align:middle line:84% at that time, which is not very different from the current one 00:46:10.020 --> 00:46:14.520 align:middle line:84% with big names, including Steven Chu, Max 00:46:14.520 --> 00:46:20.420 align:middle line:84% Tegmark, and many others that are 00:46:20.420 --> 00:46:24.320 align:middle line:84% considered big names in the field of thermodynamics 00:46:24.320 --> 00:46:26.840 align:middle line:90% and energy. 00:46:26.840 --> 00:46:31.390 align:middle line:84% All right, so, why am I talking about that? 00:46:31.390 --> 00:46:34.750 align:middle line:90% All right, well, because. 00:46:34.750 --> 00:46:36.730 align:middle line:84% we've seen that history tells us that we 00:46:36.730 --> 00:46:42.580 align:middle line:84% are going to go to 85% efficient by the end of the century. 00:46:42.580 --> 00:46:44.550 align:middle line:90% How can we do that? 00:46:44.550 --> 00:46:49.620 align:middle line:84% Because currently, the point of this slide is that we cannot do 00:46:49.620 --> 00:46:54.450 align:middle line:90% it with current technology. 00:46:54.450 --> 00:46:57.450 align:middle line:84% At least not with the current technology 00:46:57.450 --> 00:47:05.730 align:middle line:84% that uses the fuel to burn in a flame, in a combustion process. 00:47:05.730 --> 00:47:10.280 align:middle line:84% The reason is because this is the philosophy 00:47:10.280 --> 00:47:15.860 align:middle line:84% of our traditional power plants, flame-based, is 00:47:15.860 --> 00:47:18.050 align:middle line:90% that you burn the fuel. 00:47:18.050 --> 00:47:20.220 align:middle line:84% And with the hot products of combustion, 00:47:20.220 --> 00:47:24.740 align:middle line:84% you heat some working fluid, and you make 00:47:24.740 --> 00:47:28.363 align:middle line:90% it work in a thermal cycle. 00:47:28.363 --> 00:47:32.810 align:middle line:90% 00:47:32.810 --> 00:47:39.180 align:middle line:84% The thermal cycle, for example, in a combined gas 00:47:39.180 --> 00:47:49.520 align:middle line:84% turbine and steam thermal cycle, has an efficiency of about 85%. 00:47:49.520 --> 00:47:53.350 align:middle line:84% So it means that your irreversibility in your power 00:47:53.350 --> 00:47:57.100 align:middle line:84% plant wastes only 15% of the exergy 00:47:57.100 --> 00:47:59.890 align:middle line:84% that thermal part of your power plant 00:47:59.890 --> 00:48:02.480 align:middle line:84% receives from the hot products of combustion. 00:48:02.480 --> 00:48:05.380 align:middle line:90% 00:48:05.380 --> 00:48:07.970 align:middle line:90% And then you have the flame. 00:48:07.970 --> 00:48:13.070 align:middle line:84% The flame per se, by itself, without losing one 00:48:13.070 --> 00:48:19.870 align:middle line:84% BTU of energy wastes, because it's an irreversible process, 00:48:19.870 --> 00:48:23.980 align:middle line:90% wastes 25% of the exergy. 00:48:23.980 --> 00:48:30.640 align:middle line:84% So if you multiply the two efficiencies here, 75 times 85, 00:48:30.640 --> 00:48:34.240 align:middle line:90% you get about 64. 00:48:34.240 --> 00:48:37.580 align:middle line:84% And that's the explanation of why. 00:48:37.580 --> 00:48:46.330 align:middle line:84% So 64, it means that we are wasting 36% of the exergy. 00:48:46.330 --> 00:48:48.730 align:middle line:90% And where is that wasted? 00:48:48.730 --> 00:48:55.170 align:middle line:84% OK, 25 here, and another 15, or more or less, here. 00:48:55.170 --> 00:49:04.160 align:middle line:90% 00:49:04.160 --> 00:49:09.750 align:middle line:84% So you see, in order to get to 85%, we must 00:49:09.750 --> 00:49:14.910 align:middle line:84% we must get rid of the waste that we have in combustion. 00:49:14.910 --> 00:49:19.270 align:middle line:84% We must use the fuel, not by burning it 00:49:19.270 --> 00:49:21.200 align:middle line:90% but in some other way. 00:49:21.200 --> 00:49:27.410 align:middle line:90% 00:49:27.410 --> 00:49:32.030 align:middle line:84% And as we will treat combustion in a few weeks, 00:49:32.030 --> 00:49:37.160 align:middle line:84% we will end up drawing this diagram in which you have 00:49:37.160 --> 00:49:39.090 align:middle line:90% the enthalpy versus entropy. 00:49:39.090 --> 00:49:41.930 align:middle line:84% It looks like an energy versus entropy diagram. 00:49:41.930 --> 00:49:45.450 align:middle line:84% You have the fuel-air mixture here, 00:49:45.450 --> 00:49:47.420 align:middle line:84% and the products of combustion there. 00:49:47.420 --> 00:49:55.000 align:middle line:84% And it turns out that, when you burn your fuel in a flame, what 00:49:55.000 --> 00:49:58.480 align:middle line:84% you do is to move from this to that, 00:49:58.480 --> 00:50:04.620 align:middle line:84% and you produce entropy by irreversibility. 00:50:04.620 --> 00:50:09.690 align:middle line:84% Whereas, before burning it, your fuel 00:50:09.690 --> 00:50:13.085 align:middle line:84% has an exergy which is represented by this much. 00:50:13.085 --> 00:50:17.010 align:middle line:90% 00:50:17.010 --> 00:50:22.660 align:middle line:84% And you have now here, it as an exergy that 00:50:22.660 --> 00:50:24.230 align:middle line:90% is represented by this much. 00:50:24.230 --> 00:50:27.340 align:middle line:84% So you've wasted this much exergy because 00:50:27.340 --> 00:50:28.810 align:middle line:90% of this irreversibility. 00:50:28.810 --> 00:50:33.580 align:middle line:90% 00:50:33.580 --> 00:50:46.470 align:middle line:84% So the flames are the bottleneck of efficiency in fuel usage 00:50:46.470 --> 00:50:47.860 align:middle line:90% to power conversion. 00:50:47.860 --> 00:50:50.740 align:middle line:90% 00:50:50.740 --> 00:50:52.480 align:middle line:90% And this is why-- 00:50:52.480 --> 00:50:55.180 align:middle line:84% people realize that, of course, and they 00:50:55.180 --> 00:51:00.640 align:middle line:84% are working on developing alternatives 00:51:00.640 --> 00:51:07.060 align:middle line:84% to this way of burning instead of the flame. 00:51:07.060 --> 00:51:10.110 align:middle line:84% For example, with the fuel cells, 00:51:10.110 --> 00:51:16.880 align:middle line:84% you oxidize your fuel while you are also 00:51:16.880 --> 00:51:21.870 align:middle line:90% extracting electrical energy. 00:51:21.870 --> 00:51:26.760 align:middle line:84% Because you see, in order to avoid the irreversibilities, 00:51:26.760 --> 00:51:30.090 align:middle line:90% you need to be quick. 00:51:30.090 --> 00:51:33.600 align:middle line:84% For example, in an internal combustion engine, 00:51:33.600 --> 00:51:38.650 align:middle line:84% when you light the spark at the top dead center, 00:51:38.650 --> 00:51:43.440 align:middle line:84% and the fuel air mixture starts to burn, 00:51:43.440 --> 00:51:45.520 align:middle line:84% there is a flame which propagates. 00:51:45.520 --> 00:51:48.580 align:middle line:84% So you can view it in slow motion. 00:51:48.580 --> 00:51:56.020 align:middle line:84% It takes a while to entrain the entire combustion chamber. 00:51:56.020 --> 00:52:00.230 align:middle line:84% But in reality, that happens in milliseconds. 00:52:00.230 --> 00:52:06.240 align:middle line:84% So you have to be quicker than that 00:52:06.240 --> 00:52:10.830 align:middle line:84% if you want to do it at that level, 00:52:10.830 --> 00:52:19.510 align:middle line:84% or you have to develop alternatives to flame. 00:52:19.510 --> 00:52:25.300 align:middle line:84% For example, you can determine a different path 00:52:25.300 --> 00:52:28.760 align:middle line:84% to oxidize the fuel with intermediate steps 00:52:28.760 --> 00:52:31.810 align:middle line:84% so that you can control the intermediate steps 00:52:31.810 --> 00:52:38.930 align:middle line:84% and use them to avoid the irreversibilities. 00:52:38.930 --> 00:52:41.290 align:middle line:84% Or you can use the fuel cell, which does it 00:52:41.290 --> 00:52:48.070 align:middle line:84% with electrochemistry, and then you can integrate your fuel cell 00:52:48.070 --> 00:52:54.590 align:middle line:84% in a thermal cycle that uses the thermal energy that is released. 00:52:54.590 --> 00:52:59.320 align:middle line:84% So the entropy that needs to be taken away from the fuel cell, 00:52:59.320 --> 00:53:05.030 align:middle line:84% is going to be used by a bottoming thermal cycle. 00:53:05.030 --> 00:53:12.530 align:middle line:84% And just doing that, on paper, I list here some efficiencies 00:53:12.530 --> 00:53:18.280 align:middle line:84% that can already be reached, which 00:53:18.280 --> 00:53:22.440 align:middle line:90% go beyond the limit of flames. 00:53:22.440 --> 00:53:35.590 align:middle line:90% 00:53:35.590 --> 00:53:43.060 align:middle line:84% And this takes me to this last topic of the first part, which 00:53:43.060 --> 00:53:47.500 align:middle line:84% is also going to be the topic of the homework 00:53:47.500 --> 00:53:50.680 align:middle line:90% that I will put out today. 00:53:50.680 --> 00:53:58.300 align:middle line:84% Regarding that, I'm going to put a deadline, which is just 00:53:58.300 --> 00:54:01.750 align:middle line:90% before the spring break. 00:54:01.750 --> 00:54:06.580 align:middle line:84% But I did that because I want you to be 00:54:06.580 --> 00:54:08.300 align:middle line:90% free for the spring break. 00:54:08.300 --> 00:54:12.850 align:middle line:84% But if you need to take more time, feel free to do it. 00:54:12.850 --> 00:54:16.340 align:middle line:84% I don't want to spoil your spring break. 00:54:16.340 --> 00:54:20.500 align:middle line:84% But even if you want an extra 10 days, do take them. 00:54:20.500 --> 00:54:23.110 align:middle line:90% I don't really care. 00:54:23.110 --> 00:54:24.470 align:middle line:90% It's your choice. 00:54:24.470 --> 00:54:27.260 align:middle line:84% So there is an official deadline, but it's not. 00:54:27.260 --> 00:54:28.335 align:middle line:90% It can be broken. 00:54:28.335 --> 00:54:32.870 align:middle line:90% 00:54:32.870 --> 00:54:40.506 align:middle line:84% All right, so allocation, why is this problem interesting? 00:54:40.506 --> 00:54:44.260 align:middle line:90% 00:54:44.260 --> 00:54:47.590 align:middle line:84% OK, what's the question that it answers? 00:54:47.590 --> 00:54:51.700 align:middle line:84% What fraction of the fuel consumed 00:54:51.700 --> 00:54:56.600 align:middle line:84% in a co-generation facility should be 00:54:56.600 --> 00:54:58.375 align:middle line:90% allocated to the heat produced? 00:54:58.375 --> 00:55:01.195 align:middle line:90% 00:55:01.195 --> 00:55:07.570 align:middle line:84% Now, in a co-generation facility, we use a fuel. 00:55:07.570 --> 00:55:10.440 align:middle line:90% 00:55:10.440 --> 00:55:14.410 align:middle line:84% And it produces, not only electricity, 00:55:14.410 --> 00:55:18.780 align:middle line:84% but it also produces heat, which can 00:55:18.780 --> 00:55:23.153 align:middle line:84% be used for industrial or for residential uses. 00:55:23.153 --> 00:55:30.430 align:middle line:90% 00:55:30.430 --> 00:55:36.580 align:middle line:84% That heat that is produced this way, goes into the homes. 00:55:36.580 --> 00:55:42.580 align:middle line:84% And it is important to know how much primary energy was 00:55:42.580 --> 00:55:44.710 align:middle line:90% used to produce it. 00:55:44.710 --> 00:55:47.260 align:middle line:90% Why is it important? 00:55:47.260 --> 00:55:54.290 align:middle line:84% Because of real estate and efficiency regulations. 00:55:54.290 --> 00:55:56.980 align:middle line:84% Now, almost all countries, and I listed here 00:55:56.980 --> 00:56:05.140 align:middle line:84% the names of these regulations in various countries, 00:56:05.140 --> 00:56:13.070 align:middle line:84% see, it goes from Europe almost anywhere, including, of course, 00:56:13.070 --> 00:56:14.330 align:middle line:90% the US. 00:56:14.330 --> 00:56:17.930 align:middle line:84% Energy performance certificate of a building or energy 00:56:17.930 --> 00:56:21.110 align:middle line:90% score, home energy score. 00:56:21.110 --> 00:56:25.590 align:middle line:84% It essentially tells you, of your house, 00:56:25.590 --> 00:56:28.280 align:middle line:90% what's the level of efficiency. 00:56:28.280 --> 00:56:31.520 align:middle line:84% And that level of efficiency determines 00:56:31.520 --> 00:56:33.240 align:middle line:90% the value of your house. 00:56:33.240 --> 00:56:36.920 align:middle line:84% So if I go buy a house, I care about how much 00:56:36.920 --> 00:56:40.040 align:middle line:84% it consumes because that's the bills I 00:56:40.040 --> 00:56:43.460 align:middle line:90% will receive to heat it up. 00:56:43.460 --> 00:56:52.070 align:middle line:84% And so if it is an efficient house, 00:56:52.070 --> 00:56:54.840 align:middle line:84% it has more value than an inefficient. 00:56:54.840 --> 00:56:58.410 align:middle line:90% 00:56:58.410 --> 00:57:04.530 align:middle line:84% So this problem, in fact, since in order 00:57:04.530 --> 00:57:06.690 align:middle line:84% to compute this energy score, you 00:57:06.690 --> 00:57:10.180 align:middle line:84% need to know, among the various parameters, 00:57:10.180 --> 00:57:15.930 align:middle line:84% it's not only how good are the windows and the walls and so on, 00:57:15.930 --> 00:57:16.870 align:middle line:90% and the roof. 00:57:16.870 --> 00:57:22.740 align:middle line:84% But it's also how efficient is the equipment 00:57:22.740 --> 00:57:26.830 align:middle line:84% that you're using in order to produce the heating? 00:57:26.830 --> 00:57:31.810 align:middle line:84% And if you live in a city like Brescia, 00:57:31.810 --> 00:57:35.770 align:middle line:84% or if you live at MIT now, I know that also here we 00:57:35.770 --> 00:57:40.810 align:middle line:84% have the same problem, that you have a co-generation facility 00:57:40.810 --> 00:57:44.540 align:middle line:84% which is not in your house, but it's somewhere else in town. 00:57:44.540 --> 00:57:49.660 align:middle line:84% And then through pipes, they send heat to you. 00:57:49.660 --> 00:57:53.750 align:middle line:84% In order to do that calculation of the home energy score, 00:57:53.750 --> 00:57:58.060 align:middle line:84% you need to know how much energy was consumed, 00:57:58.060 --> 00:58:04.510 align:middle line:84% or what is behind that heat that you are using, which substitutes 00:58:04.510 --> 00:58:12.460 align:middle line:84% your local boiler or gas boiler that you 00:58:12.460 --> 00:58:13.640 align:middle line:90% have in a standard house. 00:58:13.640 --> 00:58:18.380 align:middle line:84% So in my condominium, I still have the gas boiler, 00:58:18.380 --> 00:58:21.260 align:middle line:84% so the question is easily answered. 00:58:21.260 --> 00:58:24.340 align:middle line:84% I look up how much heat has been produced 00:58:24.340 --> 00:58:27.460 align:middle line:84% over one year, how much gas I paid, 00:58:27.460 --> 00:58:30.460 align:middle line:84% and that tells me how much energy is 00:58:30.460 --> 00:58:34.340 align:middle line:90% behind my BTU of heat produced. 00:58:34.340 --> 00:58:43.270 align:middle line:84% But if it is co-produced, co-generated in a heat and power 00:58:43.270 --> 00:58:48.910 align:middle line:84% facility, Combined Heat and Power, CHP facility, then 00:58:48.910 --> 00:58:52.320 align:middle line:90% the question is not that simple. 00:58:52.320 --> 00:58:55.680 align:middle line:90% 00:58:55.680 --> 00:58:57.930 align:middle line:90% So here is a scheme. 00:58:57.930 --> 00:59:02.610 align:middle line:84% Here is the facility which produces work and heat 00:59:02.610 --> 00:59:04.145 align:middle line:90% and uses fuel. 00:59:04.145 --> 00:59:08.260 align:middle line:90% 00:59:08.260 --> 00:59:12.790 align:middle line:84% Now, normally, that work would be 00:59:12.790 --> 00:59:15.220 align:middle line:84% produced in a separate production 00:59:15.220 --> 00:59:21.550 align:middle line:84% facility that uses just some fuel and produces only work. 00:59:21.550 --> 00:59:25.240 align:middle line:84% And that heat would be produced, like in my gas burner, 00:59:25.240 --> 00:59:30.550 align:middle line:84% by a separate production equipment that uses some fuel 00:59:30.550 --> 00:59:33.640 align:middle line:90% and produces that. 00:59:33.640 --> 00:59:37.090 align:middle line:84% So the question is, how do we compare 00:59:37.090 --> 00:59:42.510 align:middle line:84% these separate production scenario 00:59:42.510 --> 00:59:45.460 align:middle line:90% with a co-generation facility? 00:59:45.460 --> 00:59:54.400 align:middle line:84% And you see, the reason is that we know before we start, 00:59:54.400 --> 00:59:58.480 align:middle line:84% I mean, without any additional discussion, 00:59:58.480 --> 01:00:04.830 align:middle line:84% we can compute how much fuel we saved with respect 01:00:04.830 --> 01:00:06.350 align:middle line:90% to the separate production. 01:00:06.350 --> 01:00:08.960 align:middle line:84% That is called primary energy savings. 01:00:08.960 --> 01:00:12.330 align:middle line:90% 01:00:12.330 --> 01:00:20.340 align:middle line:84% It is defined as the ratio of the difference between what 01:00:20.340 --> 01:00:25.560 align:middle line:84% I would consume in a separate production, what I actually 01:00:25.560 --> 01:00:33.380 align:middle line:84% consume in my co-generation facility, divided 01:00:33.380 --> 01:00:37.050 align:middle line:84% by what I consumed with the reference production. 01:00:37.050 --> 01:00:39.590 align:middle line:90% So this is the ratio. 01:00:39.590 --> 01:00:44.640 align:middle line:84% And we know that typical co-generation facilities 01:00:44.640 --> 01:00:49.900 align:middle line:84% allow you to save between 20% and 40%. 01:00:49.900 --> 01:00:51.640 align:middle line:84% So we're talking about large amounts. 01:00:51.640 --> 01:00:57.840 align:middle line:84% That's why it is pursued and done. 01:00:57.840 --> 01:01:09.010 align:middle line:84% So we know how much that's the overall savings. 01:01:09.010 --> 01:01:14.790 align:middle line:84% But the problem is that in order to do 01:01:14.790 --> 01:01:25.820 align:middle line:84% that calculation for the home energy parameter, 01:01:25.820 --> 01:01:29.350 align:middle line:90% you need another number. 01:01:29.350 --> 01:01:34.770 align:middle line:84% You need, essentially, the COP for the heat. 01:01:34.770 --> 01:01:38.940 align:middle line:90% It's how much the efficiency. 01:01:38.940 --> 01:01:44.160 align:middle line:84% It says, you see, you need to know this denominator. 01:01:44.160 --> 01:01:46.560 align:middle line:84% How much of the fuel, which has been 01:01:46.560 --> 01:01:49.560 align:middle line:84% used in the co-generation facility 01:01:49.560 --> 01:01:54.650 align:middle line:84% has to be assigned to the production of heat. 01:01:54.650 --> 01:01:57.510 align:middle line:90% 01:01:57.510 --> 01:02:02.280 align:middle line:84% And there is some arbitrariness into how we define this. 01:02:02.280 --> 01:02:03.850 align:middle line:90% It is no-- 01:02:03.850 --> 01:02:05.990 align:middle line:84% Yeah, some people claim there is a thermodynamic-- 01:02:05.990 --> 01:02:07.300 align:middle line:90% we'll see that exergy-- 01:02:07.300 --> 01:02:10.750 align:middle line:84% The exergy people will claim that that's 01:02:10.750 --> 01:02:13.030 align:middle line:90% the method that you should use. 01:02:13.030 --> 01:02:16.420 align:middle line:84% But in our discussion, we will show that that's 01:02:16.420 --> 01:02:19.250 align:middle line:90% not appropriate, not yet. 01:02:19.250 --> 01:02:22.180 align:middle line:90% 01:02:22.180 --> 01:02:27.320 align:middle line:84% So we need to define allocation factors. 01:02:27.320 --> 01:02:31.200 align:middle line:84% So suppose we have these allocation factors, alpha, 01:02:31.200 --> 01:02:32.710 align:middle line:90% they add up to 1. 01:02:32.710 --> 01:02:35.880 align:middle line:84% So essentially, it's the percentage of fuel 01:02:35.880 --> 01:02:45.020 align:middle line:84% that we think is being used for, say, alpha W 01:02:45.020 --> 01:02:50.370 align:middle line:84% for the work production line and for the heat production line. 01:02:50.370 --> 01:02:53.540 align:middle line:84% So you think of your co-generation facility 01:02:53.540 --> 01:02:58.040 align:middle line:84% as an equivalent separate production facility in which-- 01:02:58.040 --> 01:03:00.265 align:middle line:90% or as having two internal lines. 01:03:00.265 --> 01:03:03.700 align:middle line:90% 01:03:03.700 --> 01:03:07.930 align:middle line:84% If in fact, if your combined production was simply 01:03:07.930 --> 01:03:10.640 align:middle line:84% that you have two separate lines, 01:03:10.640 --> 01:03:14.750 align:middle line:84% then you would easily find what the alpha is. 01:03:14.750 --> 01:03:18.130 align:middle line:84% You just use whatever it goes on one line 01:03:18.130 --> 01:03:20.890 align:middle line:84% and whatever fuel goes on the other line. 01:03:20.890 --> 01:03:30.790 align:middle line:84% But combined heat and power is best 01:03:30.790 --> 01:03:35.950 align:middle line:84% when you don't have separate, but you're 01:03:35.950 --> 01:03:40.450 align:middle line:84% using the various levels of temperature 01:03:40.450 --> 01:03:43.660 align:middle line:84% at which your working fluids are, 01:03:43.660 --> 01:03:47.270 align:middle line:84% to do what is appropriate to reduce the irreversibilities. 01:03:47.270 --> 01:03:49.150 align:middle line:84% And so you have a lot of equipment here 01:03:49.150 --> 01:03:56.240 align:middle line:90% which play the game of both-- 01:03:56.240 --> 01:03:58.990 align:middle line:84% They are both on the side of the work production 01:03:58.990 --> 01:04:02.140 align:middle line:90% and of the heat production. 01:04:02.140 --> 01:04:04.450 align:middle line:84% But in any case, suppose we have these alphas, 01:04:04.450 --> 01:04:13.250 align:middle line:84% and then, for example, we could define the separate efficiency, 01:04:13.250 --> 01:04:15.130 align:middle line:90% so the partial efficiencies. 01:04:15.130 --> 01:04:17.200 align:middle line:84% Partial efficiency of work production 01:04:17.200 --> 01:04:21.740 align:middle line:84% would be the work, divided by the amount of fuel 01:04:21.740 --> 01:04:25.300 align:middle line:84% only the part that I have associated with that production. 01:04:25.300 --> 01:04:32.420 align:middle line:84% And the COP for heat is the heat divided by the complement 01:04:32.420 --> 01:04:40.070 align:middle line:84% to that, so that's the fuel energy associated with the heat 01:04:40.070 --> 01:04:41.680 align:middle line:90% production. 01:04:41.680 --> 01:04:48.040 align:middle line:84% And of course, you can also compute partial primary energy 01:04:48.040 --> 01:04:54.630 align:middle line:90% savings by comparing what-- 01:04:54.630 --> 01:04:59.105 align:middle line:90% the amount of fuel that is-- 01:04:59.105 --> 01:05:02.240 align:middle line:90% 01:05:02.240 --> 01:05:07.350 align:middle line:84% the amount of fuel that is used in separate production, 01:05:07.350 --> 01:05:10.640 align:middle line:84% you subtract what you actually consume 01:05:10.640 --> 01:05:14.180 align:middle line:84% in your co-generation facility, so that's the numerator 01:05:14.180 --> 01:05:16.080 align:middle line:84% and compare it to the separate production. 01:05:16.080 --> 01:05:21.860 align:middle line:84% So that gives you the savings of the co-generation with respect 01:05:21.860 --> 01:05:26.240 align:middle line:84% to-- partial to the production of electricity 01:05:26.240 --> 01:05:27.925 align:middle line:90% and the same for heat. 01:05:27.925 --> 01:05:30.750 align:middle line:90% 01:05:30.750 --> 01:05:32.840 align:middle line:84% And if you have that number, alpha 01:05:32.840 --> 01:05:37.760 align:middle line:84% Q that number alpha Q is what is needed for the home 01:05:37.760 --> 01:05:42.680 align:middle line:90% index, efficiency index. 01:05:42.680 --> 01:05:44.910 align:middle line:84% So in the beginning of co-generation, 01:05:44.910 --> 01:05:54.845 align:middle line:84% people reasoned and defined allocation factors in this way. 01:05:54.845 --> 01:05:57.510 align:middle line:90% 01:05:57.510 --> 01:06:03.930 align:middle line:84% We call this method the incremental electricity-centered 01:06:03.930 --> 01:06:04.636 align:middle line:90% allocation. 01:06:04.636 --> 01:06:08.620 align:middle line:90% 01:06:08.620 --> 01:06:14.720 align:middle line:84% It basically says, all right, I, in my co-generation facility, 01:06:14.720 --> 01:06:18.470 align:middle line:90% I produce this much work. 01:06:18.470 --> 01:06:24.270 align:middle line:84% If I produced it in the reference separate production 01:06:24.270 --> 01:06:28.660 align:middle line:84% facility with this reference efficiency, 01:06:28.660 --> 01:06:33.180 align:middle line:84% I would have consumed this much fuel, W over the reference 01:06:33.180 --> 01:06:33.970 align:middle line:90% efficiency. 01:06:33.970 --> 01:06:36.890 align:middle line:90% 01:06:36.890 --> 01:06:42.900 align:middle line:84% So that in my co-generation plant, I produce more than-- 01:06:42.900 --> 01:06:45.230 align:middle line:84% I'm sorry, I consume more than that fuel. 01:06:45.230 --> 01:06:47.760 align:middle line:90% I consume F. 01:06:47.760 --> 01:06:51.720 align:middle line:84% So if I subtract what I would have consumed 01:06:51.720 --> 01:06:53.970 align:middle line:84% for the production of that work, it 01:06:53.970 --> 01:06:57.720 align:middle line:84% means that the extra fuel I'm consuming 01:06:57.720 --> 01:07:03.660 align:middle line:84% is attributed to the heat that I'm producing. 01:07:03.660 --> 01:07:07.330 align:middle line:90% 01:07:07.330 --> 01:07:13.870 align:middle line:84% And therefore, you would put at the denominator here. 01:07:13.870 --> 01:07:18.760 align:middle line:84% You would assign to that heat, this extra fuel with respect 01:07:18.760 --> 01:07:20.770 align:middle line:84% to the separate production of the electricity 01:07:20.770 --> 01:07:23.960 align:middle line:90% that you have done. 01:07:23.960 --> 01:07:31.770 align:middle line:84% But this, of course, is unfair because it 01:07:31.770 --> 01:07:37.890 align:middle line:84% assigns all the primary energy savings to the heat 01:07:37.890 --> 01:07:41.230 align:middle line:90% and zero to the work. 01:07:41.230 --> 01:07:44.410 align:middle line:84% If it is true that my co-generation facility saves 01:07:44.410 --> 01:07:50.030 align:middle line:84% 40% of the fuel, it means that there 01:07:50.030 --> 01:07:51.660 align:middle line:90% is a benefit of co-generation. 01:07:51.660 --> 01:07:54.920 align:middle line:84% And that benefit, is it really all 01:07:54.920 --> 01:07:57.410 align:middle line:84% due to the production of heat, or is 01:07:57.410 --> 01:08:01.135 align:middle line:84% it should be distributed between the two products? 01:08:01.135 --> 01:08:06.360 align:middle line:90% 01:08:06.360 --> 01:08:14.280 align:middle line:84% So another more balanced way of reasoning, which 01:08:14.280 --> 01:08:21.220 align:middle line:90% took over later, is to define-- 01:08:21.220 --> 01:08:28.000 align:middle line:84% maybe some local or state authority, energy authority, 01:08:28.000 --> 01:08:34.319 align:middle line:84% defines or states in some standards-- 01:08:34.319 --> 01:08:37.200 align:middle line:84% reference values for the efficiencies 01:08:37.200 --> 01:08:45.510 align:middle line:84% of separate production of heat and work. 01:08:45.510 --> 01:08:49.710 align:middle line:84% So they define some reference values. 01:08:49.710 --> 01:08:55.470 align:middle line:84% And then they say, all right, use 01:08:55.470 --> 01:09:03.979 align:middle line:84% as allocation factors, the weighted fraction of what 01:09:03.979 --> 01:09:09.529 align:middle line:84% you would have consumed by producing the same W and same Q 01:09:09.529 --> 01:09:13.149 align:middle line:90% in separate facilities. 01:09:13.149 --> 01:09:17.350 align:middle line:84% So this defines-- because this W over eta reference 01:09:17.350 --> 01:09:20.740 align:middle line:84% is the fuel you would have consumed if you produced 01:09:20.740 --> 01:09:23.710 align:middle line:84% this amount of electricity in separate production, 01:09:23.710 --> 01:09:28.240 align:middle line:84% and Q over COP reference is the fuel 01:09:28.240 --> 01:09:32.470 align:middle line:84% that you would have consumed if you have produced 01:09:32.470 --> 01:09:36.340 align:middle line:84% that amount of Q, the same as your co-generation facility 01:09:36.340 --> 01:09:40.078 align:middle line:90% in a separate production. 01:09:40.078 --> 01:09:43.790 align:middle line:84% The good thing about these allocation factors 01:09:43.790 --> 01:09:51.350 align:middle line:84% is that it distributes equally the primary energy 01:09:51.350 --> 01:09:55.610 align:middle line:84% savings to the heat and the work, 01:09:55.610 --> 01:10:03.500 align:middle line:84% so that the partial primary energy savings for work 01:10:03.500 --> 01:10:07.100 align:middle line:84% is equal to the partial energy savings for heat, 01:10:07.100 --> 01:10:10.270 align:middle line:84% and it's equal to the overall partial energy savings. 01:10:10.270 --> 01:10:13.750 align:middle line:90% 01:10:13.750 --> 01:10:18.160 align:middle line:84% The question is, what reference values 01:10:18.160 --> 01:10:23.110 align:middle line:90% should the authority select? 01:10:23.110 --> 01:10:28.630 align:middle line:84% OK, one method is to simply do it arbitrarily, or maybe 01:10:28.630 --> 01:10:30.440 align:middle line:90% do it by some logic. 01:10:30.440 --> 01:10:34.070 align:middle line:84% You publish it, and it stays there for some years. 01:10:34.070 --> 01:10:40.310 align:middle line:84% Then maybe you update those reference values. 01:10:40.310 --> 01:10:53.370 align:middle line:84% The other extreme is you select the exergy reasoning. 01:10:53.370 --> 01:10:56.790 align:middle line:84% So you say, well, that's used as reference 01:10:56.790 --> 01:11:01.110 align:middle line:90% values, the best you could do. 01:11:01.110 --> 01:11:05.430 align:middle line:90% Namely the reversible processes. 01:11:05.430 --> 01:11:07.173 align:middle line:90% Yes. 01:11:07.173 --> 01:11:09.090 align:middle line:84% AUDIENCE: If I'm understanding this correctly, 01:11:09.090 --> 01:11:12.910 align:middle line:84% so the first method was used earlier 01:11:12.910 --> 01:11:15.580 align:middle line:84% because it didn't require these select reference 01:11:15.580 --> 01:11:17.240 align:middle line:90% values to be calculated. 01:11:17.240 --> 01:11:24.020 align:middle line:84% It just used the efficiency of the work producing 01:11:24.020 --> 01:11:27.470 align:middle line:84% part of the co-generation plant itself. 01:11:27.470 --> 01:11:30.710 align:middle line:84% GIAN PAOLO BERETTA: Yes, at the beginning, 01:11:30.710 --> 01:11:34.070 align:middle line:84% certainly, it was an easy way of reasoning. 01:11:34.070 --> 01:11:36.860 align:middle line:84% It didn't require an authority to define. 01:11:36.860 --> 01:11:41.630 align:middle line:84% And also you didn't have the motivation. 01:11:41.630 --> 01:11:47.070 align:middle line:84% The motivation came, and this is how we came with this question, 01:11:47.070 --> 01:11:49.640 align:middle line:90% and this is how-- 01:11:49.640 --> 01:11:53.430 align:middle line:84% I'll give you the reference to a paper with your advisor, 01:11:53.430 --> 01:11:54.260 align:middle line:90% Professor Ghoneim. 01:11:54.260 --> 01:11:56.210 align:middle line:84% We worked together on this problem 01:11:56.210 --> 01:12:01.340 align:middle line:84% because the utility which produces 01:12:01.340 --> 01:12:04.070 align:middle line:84% district heating in Brescia came to us 01:12:04.070 --> 01:12:06.740 align:middle line:84% and asked, OK, we have a problem now. 01:12:06.740 --> 01:12:13.370 align:middle line:84% Because we are giving these numbers, but with these numbers, 01:12:13.370 --> 01:12:18.210 align:middle line:84% every apartment goes into the top class. 01:12:18.210 --> 01:12:24.560 align:middle line:84% So we are assigning so low consumption of fuel to the heat 01:12:24.560 --> 01:12:28.910 align:middle line:84% that we are providing them that they are so happy they are 01:12:28.910 --> 01:12:32.000 align:middle line:84% in class A+, even with the windows open. 01:12:32.000 --> 01:12:33.570 align:middle line:90% So it doesn't make sense. 01:12:33.570 --> 01:12:36.470 align:middle line:84% That's why they came, and so I said, we need something more. 01:12:36.470 --> 01:12:39.990 align:middle line:84% And so they also, after these discussions, 01:12:39.990 --> 01:12:41.970 align:middle line:84% they also went to the European community 01:12:41.970 --> 01:12:45.970 align:middle line:84% and had them change the regulations. 01:12:45.970 --> 01:12:46.710 align:middle line:90% AUDIENCE: Thanks 01:12:46.710 --> 01:12:47.752 align:middle line:90% GIAN PAOLO BERETTA: Yeah. 01:12:47.752 --> 01:12:50.580 align:middle line:90% 01:12:50.580 --> 01:12:56.820 align:middle line:84% And so the exergy idea is, let's take as reference 01:12:56.820 --> 01:12:59.100 align:middle line:90% the best we could do. 01:12:59.100 --> 01:13:04.170 align:middle line:84% And the best we could do is the reversible case. 01:13:04.170 --> 01:13:16.430 align:middle line:84% So what is the best we could do in terms of efficiency 01:13:16.430 --> 01:13:19.960 align:middle line:90% for work production? 01:13:19.960 --> 01:13:25.470 align:middle line:84% If I have to produce this much work, 01:13:25.470 --> 01:13:33.940 align:middle line:84% and I'm using a fuel, with an exergy that is this much, 01:13:33.940 --> 01:13:42.150 align:middle line:84% Ex, well, if there are no irreversibilities 01:13:42.150 --> 01:13:44.310 align:middle line:84% in my machinery, so it's reversible, 01:13:44.310 --> 01:13:47.100 align:middle line:90% the exergy gets all transformed. 01:13:47.100 --> 01:13:49.500 align:middle line:84% There is no loss of exergy, so the exergy of the fuel 01:13:49.500 --> 01:13:53.500 align:middle line:84% goes all into exergy of the product, so it's 1 to 1, 01:13:53.500 --> 01:14:01.650 align:middle line:84% so W max, or let's say rev, is equal to the exergy of the fuel. 01:14:01.650 --> 01:14:03.660 align:middle line:84% But the exergy of the fuel, we said, 01:14:03.660 --> 01:14:06.520 align:middle line:84% is approximately equal to the heating value. 01:14:06.520 --> 01:14:08.255 align:middle line:90% Let's call it QF to simplify. 01:14:08.255 --> 01:14:11.220 align:middle line:90% 01:14:11.220 --> 01:14:16.080 align:middle line:84% So that means that this machinery, reversible machinery, 01:14:16.080 --> 01:14:19.530 align:middle line:84% that could do that, has a first-law efficiency, which 01:14:19.530 --> 01:14:29.175 align:middle line:84% is what we call eta W ref, which is the work produced. 01:14:29.175 --> 01:14:32.930 align:middle line:90% 01:14:32.930 --> 01:14:34.190 align:middle line:90% First law. 01:14:34.190 --> 01:14:44.600 align:middle line:84% So it's divided by the heating value of the fuel, the energy 01:14:44.600 --> 01:14:45.960 align:middle line:90% that has been consumed. 01:14:45.960 --> 01:14:52.710 align:middle line:84% But this is also approximately equal to the exergy of the fuel. 01:14:52.710 --> 01:14:55.705 align:middle line:84% And as you see here, this is approximately 1. 01:14:55.705 --> 01:15:02.760 align:middle line:90% 01:15:02.760 --> 01:15:10.380 align:middle line:84% Whereas, the same story, if I use my fuel, 01:15:10.380 --> 01:15:21.710 align:middle line:84% and I want to produce heat at the temperature TQ, 01:15:21.710 --> 01:15:26.210 align:middle line:90% the exergy of that heat is this. 01:15:26.210 --> 01:15:33.380 align:middle line:84% And if I have no irreversibility all that goes into this. 01:15:33.380 --> 01:15:45.120 align:middle line:84% So the eta, let's call it COP, would 01:15:45.120 --> 01:15:54.430 align:middle line:84% be the Q divided by the energy of the fuel 01:15:54.430 --> 01:16:01.090 align:middle line:84% because COP is a first-law idea, so the energy of the fuel. 01:16:01.090 --> 01:16:06.105 align:middle line:84% And the energy of the fuel is QF. 01:16:06.105 --> 01:16:14.150 align:middle line:90% 01:16:14.150 --> 01:16:19.280 align:middle line:84% But QF, again, is approximately ExF. 01:16:19.280 --> 01:16:24.930 align:middle line:90% 01:16:24.930 --> 01:16:29.250 align:middle line:84% So this is Q divided by the exergy. 01:16:29.250 --> 01:16:31.290 align:middle line:84% The exergy gets all transformed in that. 01:16:31.290 --> 01:16:35.270 align:middle line:84% So here in the denominator, I put Q 1 minus Ta over TQ. 01:16:35.270 --> 01:16:39.020 align:middle line:90% 01:16:39.020 --> 01:16:49.990 align:middle line:84% OK, so the COP is one over the Carnot coefficient calculated 01:16:49.990 --> 01:16:54.680 align:middle line:84% at the temperature of our production, heat production. 01:16:54.680 --> 01:16:57.680 align:middle line:90% 01:16:57.680 --> 01:16:59.510 align:middle line:90% So you certainly can do that. 01:16:59.510 --> 01:17:02.515 align:middle line:84% So I'll give you a numerical example for this in a moment. 01:17:02.515 --> 01:17:06.710 align:middle line:90% 01:17:06.710 --> 01:17:16.020 align:middle line:84% So here's a paper with Professor Ghoneim and another colleague 01:17:16.020 --> 01:17:24.970 align:middle line:84% of mine in Brescia, Paolo Iora, which we addressed the issue 01:17:24.970 --> 01:17:30.380 align:middle line:84% and acknowledged that there is no correct way to do it. 01:17:30.380 --> 01:17:34.450 align:middle line:90% 01:17:34.450 --> 01:17:40.130 align:middle line:84% It's hand waving, and it's arbitrary in some sense. 01:17:40.130 --> 01:17:48.900 align:middle line:84% But the idea that we introduced was this. 01:17:48.900 --> 01:17:58.850 align:middle line:84% OK, suppose this local authority has 01:17:58.850 --> 01:18:06.590 align:middle line:84% to decide what efficiencies, reference efficiencies to set. 01:18:06.590 --> 01:18:09.590 align:middle line:90% What criterion should they use? 01:18:09.590 --> 01:18:14.120 align:middle line:84% Well, they would look at their local area. 01:18:14.120 --> 01:18:17.580 align:middle line:84% And by local area, it could be a small district, 01:18:17.580 --> 01:18:23.010 align:middle line:84% it could be a town, it could be a state, it could be a nation, 01:18:23.010 --> 01:18:26.930 align:middle line:90% It could be Europe. 01:18:26.930 --> 01:18:30.110 align:middle line:84% It could do this at various levels 01:18:30.110 --> 01:18:34.830 align:middle line:84% because there are standards, local standards, and so on. 01:18:34.830 --> 01:18:37.620 align:middle line:84% In the homework, I'll give you reference 01:18:37.620 --> 01:18:48.780 align:middle line:84% to a European standard, which was 2007, which had the issue. 01:18:48.780 --> 01:18:51.120 align:middle line:84% Frankly, I didn't follow up, but I'm 01:18:51.120 --> 01:18:56.230 align:middle line:84% sure that they've improved a lot with more recent standards. 01:18:56.230 --> 01:18:58.790 align:middle line:90% 01:18:58.790 --> 01:19:01.340 align:middle line:84% So that means that the problem is of interest 01:19:01.340 --> 01:19:03.410 align:middle line:84% also at the European level, which 01:19:03.410 --> 01:19:08.973 align:middle line:84% is a congregation or a community of several nations. 01:19:08.973 --> 01:19:12.770 align:middle line:90% 01:19:12.770 --> 01:19:19.910 align:middle line:84% OK, So you do take the data that come from various facilities 01:19:19.910 --> 01:19:21.530 align:middle line:90% in your local area. 01:19:21.530 --> 01:19:29.060 align:middle line:84% Every facility is always obliged to communicate to some energy 01:19:29.060 --> 01:19:33.030 align:middle line:84% authority, their consumptions and their productions yearly, 01:19:33.030 --> 01:19:36.350 align:middle line:90% at least yearly. 01:19:36.350 --> 01:19:46.400 align:middle line:84% And so take those data and look at your overall system 01:19:46.400 --> 01:19:49.430 align:middle line:84% as a co-generation system because after all, it 01:19:49.430 --> 01:19:51.070 align:middle line:90% produces work and heat. 01:19:51.070 --> 01:19:56.070 align:middle line:90% 01:19:56.070 --> 01:20:06.280 align:middle line:84% And you know how much fuel has been used for each of them. 01:20:06.280 --> 01:20:11.650 align:middle line:90% 01:20:11.650 --> 01:20:30.100 align:middle line:84% So if I have assigned a value for the allocation factors, 01:20:30.100 --> 01:20:33.200 align:middle line:84% like alpha W and alpha Q. So if I'm the authority. 01:20:33.200 --> 01:20:35.140 align:middle line:90% I decided these numbers. 01:20:35.140 --> 01:20:40.780 align:middle line:84% With these numbers, those who have combined heat and power 01:20:40.780 --> 01:20:42.490 align:middle line:84% facilities have used them in order 01:20:42.490 --> 01:20:47.090 align:middle line:84% to compute their own partial efficiencies. 01:20:47.090 --> 01:20:51.590 align:middle line:84% So they will tell me how much fuel they 01:20:51.590 --> 01:20:56.650 align:middle line:84% have used or is behind this work and how much is behind the heat. 01:20:56.650 --> 01:20:59.310 align:middle line:90% 01:20:59.310 --> 01:21:03.450 align:middle line:84% So I compute the overall efficiency 01:21:03.450 --> 01:21:05.760 align:middle line:84% for the heat production and for the work production 01:21:05.760 --> 01:21:08.920 align:middle line:90% for the local facility. 01:21:08.920 --> 01:21:10.065 align:middle line:90% I mean, for the local area. 01:21:10.065 --> 01:21:14.340 align:middle line:90% 01:21:14.340 --> 01:21:21.340 align:middle line:84% But then I can also apply my same rules or allocation 01:21:21.340 --> 01:21:23.710 align:middle line:84% coefficients or allocation fractions 01:21:23.710 --> 01:21:32.420 align:middle line:84% to the local area viewed overall, as an overall combined 01:21:32.420 --> 01:21:35.440 align:middle line:90% heat and power facility. 01:21:35.440 --> 01:21:44.370 align:middle line:84% And if I have given the correct values of alpha, 01:21:44.370 --> 01:21:50.030 align:middle line:84% I should get the same number, whether I 01:21:50.030 --> 01:21:55.130 align:middle line:84% look at it locally with small facilities 01:21:55.130 --> 01:22:02.316 align:middle line:84% or the overall local area system. 01:22:02.316 --> 01:22:13.370 align:middle line:84% So that was the method that we have provided, and here 01:22:13.370 --> 01:22:16.330 align:middle line:90% is an example with some numbers. 01:22:16.330 --> 01:22:18.990 align:middle line:90% 01:22:18.990 --> 01:22:22.260 align:middle line:84% So suppose we have a local area and suppose 01:22:22.260 --> 01:22:28.220 align:middle line:84% that we have separate production facilities that 01:22:28.220 --> 01:22:38.050 align:middle line:84% have 52% efficiency for energy, for electricity, and 90%, 01:22:38.050 --> 01:22:44.260 align:middle line:84% so a 0.9 COP for the production of heat, 01:22:44.260 --> 01:22:45.853 align:middle line:90% like industrial boilers. 01:22:45.853 --> 01:22:50.560 align:middle line:90% 01:22:50.560 --> 01:22:57.550 align:middle line:84% And here, the combined heat and power plant is a combined cycle. 01:22:57.550 --> 01:23:02.420 align:middle line:84% This is also a back pressure steam turbine data. 01:23:02.420 --> 01:23:05.560 align:middle line:84% But I'm going to discuss only this one. 01:23:05.560 --> 01:23:07.210 align:middle line:84% And these are two parameters that 01:23:07.210 --> 01:23:08.840 align:middle line:90% characterize a combined cycle. 01:23:08.840 --> 01:23:12.450 align:middle line:84% So it's the ratio of the work to the heat that is produced. 01:23:12.450 --> 01:23:24.680 align:middle line:84% And the first-law efficiency, so 78. 01:23:24.680 --> 01:23:29.880 align:middle line:84% So suppose that the reference values 01:23:29.880 --> 01:23:38.340 align:middle line:84% are taken as the values of the separate productions 01:23:38.340 --> 01:23:41.390 align:middle line:90% in my local area, 52 and 90. 01:23:41.390 --> 01:23:43.970 align:middle line:90% 01:23:43.970 --> 01:23:46.010 align:middle line:90% So look at just the first line. 01:23:46.010 --> 01:23:50.120 align:middle line:84% Here are the numbers that come out with the three methods 01:23:50.120 --> 01:23:52.120 align:middle line:90% that we discussed so far. 01:23:52.120 --> 01:24:01.790 align:middle line:84% So the electricity centered keeps, essentially, 01:24:01.790 --> 01:24:04.070 align:middle line:84% the same efficiency for the electricity 01:24:04.070 --> 01:24:07.910 align:middle line:84% as separate production because it gives all the advantage 01:24:07.910 --> 01:24:08.520 align:middle line:90% to the heat. 01:24:08.520 --> 01:24:12.410 align:middle line:84% So it would make it appear that you are producing heat 01:24:12.410 --> 01:24:15.960 align:middle line:90% with a COP of 354. 01:24:15.960 --> 01:24:21.180 align:middle line:84% That created that problem that I told you 01:24:21.180 --> 01:24:32.865 align:middle line:84% of unfair and unacceptable, too much advantage to the heat. 01:24:32.865 --> 01:24:37.890 align:middle line:90% 01:24:37.890 --> 01:24:39.720 align:middle line:84% In a sense, if you kept that, everybody 01:24:39.720 --> 01:24:41.290 align:middle line:90% would want the district heating. 01:24:41.290 --> 01:24:46.200 align:middle line:84% So it would be a fight to have your houses 01:24:46.200 --> 01:24:47.480 align:middle line:90% to be district heated. 01:24:47.480 --> 01:24:50.050 align:middle line:90% 01:24:50.050 --> 01:24:57.940 align:middle line:84% If you do the exergy, which is the other extreme method, 01:24:57.940 --> 01:25:03.140 align:middle line:84% the electricity efficiency goes down. 01:25:03.140 --> 01:25:06.480 align:middle line:90% And the COP is still very high. 01:25:06.480 --> 01:25:09.090 align:middle line:84% If you use the separate production method 01:25:09.090 --> 01:25:16.680 align:middle line:84% with these references, this gets more reasonable. 01:25:16.680 --> 01:25:20.970 align:middle line:84% What's reasonable is that there is an increment 01:25:20.970 --> 01:25:23.730 align:middle line:90% in the separate production-- 01:25:23.730 --> 01:25:26.700 align:middle line:84% I mean, in the partial efficiency for work 01:25:26.700 --> 01:25:32.890 align:middle line:84% and also the same increment for heat. 01:25:32.890 --> 01:25:45.540 align:middle line:84% So going from 52 to 63 is an increment of maybe, what, 20%, 01:25:45.540 --> 01:25:52.330 align:middle line:84% well also going from 90 to 109 is 20%. 01:25:52.330 --> 01:25:58.350 align:middle line:84% So you have evenly distributed, you have treated equally, 01:25:58.350 --> 01:25:59.410 align:middle line:90% work and heat. 01:25:59.410 --> 01:26:02.370 align:middle line:84% So you gave to both work and heat 01:26:02.370 --> 01:26:12.330 align:middle line:84% the same weight or the same advantage of the co-generation. 01:26:12.330 --> 01:26:19.260 align:middle line:84% But a problem is, that when you now 01:26:19.260 --> 01:26:28.210 align:middle line:84% compute for your local area, the local average 01:26:28.210 --> 01:26:38.735 align:middle line:84% of the efficiencies, you don't find the same values. 01:26:38.735 --> 01:26:42.170 align:middle line:90% 01:26:42.170 --> 01:26:45.590 align:middle line:84% For in this example here, so you have 01:26:45.590 --> 01:26:49.490 align:middle line:84% to define how important co-generation 01:26:49.490 --> 01:26:52.350 align:middle line:90% is in your local area. 01:26:52.350 --> 01:26:58.630 align:middle line:84% And so you have to define an electric index, which is 50% 01:26:58.630 --> 01:27:00.510 align:middle line:90% In this case. 01:27:00.510 --> 01:27:09.820 align:middle line:84% That means that heat is twice the work 01:27:09.820 --> 01:27:15.040 align:middle line:84% and also that your co-generation facilities cover 40% of the heat 01:27:15.040 --> 01:27:16.810 align:middle line:90% production in the local area. 01:27:16.810 --> 01:27:21.820 align:middle line:84% With these numbers, you can compute the local averages. 01:27:21.820 --> 01:27:32.470 align:middle line:84% And these local averages are 62 for work and 96.8 for heat. 01:27:32.470 --> 01:27:37.160 align:middle line:84% For work it's not too far, but for heat, it's 01:27:37.160 --> 01:27:41.930 align:middle line:84% far because 109 is very far from 96. 01:27:41.930 --> 01:27:46.650 align:middle line:84% So what we propose is simply to say, 01:27:46.650 --> 01:27:50.630 align:middle line:84% all right, let's use the local area's numbers 01:27:50.630 --> 01:27:54.260 align:middle line:90% and use them as reference. 01:27:54.260 --> 01:28:05.630 align:middle line:84% So if I use them as reference, of course, numbers change, 01:28:05.630 --> 01:28:09.780 align:middle line:84% and the local numbers get closer. 01:28:09.780 --> 01:28:12.260 align:middle line:84% But not yet, I have to keep doing. 01:28:12.260 --> 01:28:12.760 align:middle line:90% So. 01:28:12.760 --> 01:28:16.290 align:middle line:84% If I iterate at a certain stage, I 01:28:16.290 --> 01:28:28.820 align:middle line:84% get to a place in which, yeah, in principle, I 01:28:28.820 --> 01:28:39.250 align:middle line:84% should get that these two numbers become equal and also, 01:28:39.250 --> 01:28:40.910 align:middle line:90% so there's no more improvement. 01:28:40.910 --> 01:28:44.680 align:middle line:90% And so the local area, so the-- 01:28:44.680 --> 01:28:46.570 align:middle line:90% yeah, the local area Is-- 01:28:46.570 --> 01:28:48.910 align:middle line:84% I'm not sure these numbers are really 01:28:48.910 --> 01:28:51.320 align:middle line:90% correct because this is 90.8. 01:28:51.320 --> 01:28:53.440 align:middle line:90% This is 92. 01:28:53.440 --> 01:28:57.010 align:middle line:84% So there may be something wrong in these numbers. 01:28:57.010 --> 01:29:02.870 align:middle line:84% Because the idea was, I believe, but I may be wrong now, 01:29:02.870 --> 01:29:07.060 align:middle line:84% so you check on me because that this should become 01:29:07.060 --> 01:29:12.020 align:middle line:90% almost equal in the long run. 01:29:12.020 --> 01:29:15.850 align:middle line:90% All right, so that's the idea. 01:29:15.850 --> 01:29:18.850 align:middle line:90% 01:29:18.850 --> 01:29:26.560 align:middle line:84% But the story is not finished because now this same issue 01:29:26.560 --> 01:29:35.580 align:middle line:84% of allocation comes up, also, when you have hybrid facilities, 01:29:35.580 --> 01:29:38.040 align:middle line:90% hybrid power plants. 01:29:38.040 --> 01:29:39.733 align:middle line:90% For example. 01:29:39.733 --> 01:29:54.900 align:middle line:84% you know that we could use solar energy for heating water. 01:29:54.900 --> 01:29:59.420 align:middle line:84% And one way, of course, so you have solar energy. 01:29:59.420 --> 01:30:10.720 align:middle line:84% And suppose you have one of those parabolic mirrors that 01:30:10.720 --> 01:30:15.405 align:middle line:84% focus the solar energy onto a pipe. 01:30:15.405 --> 01:30:18.180 align:middle line:90% 01:30:18.180 --> 01:30:23.880 align:middle line:84% And in this pipe, you run water or you 01:30:23.880 --> 01:30:28.350 align:middle line:84% run a mixture of molten salts so that you 01:30:28.350 --> 01:30:29.830 align:middle line:90% can go a higher temperature. 01:30:29.830 --> 01:30:34.770 align:middle line:84% So you run diathermal oil so that it doesn't boil. 01:30:34.770 --> 01:30:41.130 align:middle line:84% So you run a fluid that takes up that heat. 01:30:41.130 --> 01:30:43.430 align:middle line:84% Depending on what fluid you use, you 01:30:43.430 --> 01:30:45.040 align:middle line:84% can reach different temperatures. 01:30:45.040 --> 01:30:48.430 align:middle line:90% 01:30:48.430 --> 01:30:59.850 align:middle line:84% For example, with air and water, if you pressurize it, 01:30:59.850 --> 01:31:06.290 align:middle line:84% you can go 120 degrees C, maybe higher, 01:31:06.290 --> 01:31:08.720 align:middle line:84% but you have to go higher pressures. 01:31:08.720 --> 01:31:13.220 align:middle line:84% With diathermal oils, you can go up to 300, 01:31:13.220 --> 01:31:17.840 align:middle line:84% 350 because then at higher temperatures, the oil 01:31:17.840 --> 01:31:18.870 align:middle line:90% disgregates. 01:31:18.870 --> 01:31:22.840 align:middle line:84% And so you reach some technological limits there. 01:31:22.840 --> 01:31:28.530 align:middle line:84% Molten salts, you can reach maybe 500, 550. 01:31:28.530 --> 01:31:33.420 align:middle line:84% So people have built power plants 01:31:33.420 --> 01:31:36.390 align:middle line:84% with this idea of concentrating solar energy. 01:31:36.390 --> 01:31:46.060 align:middle line:84% These mirrors follow the Sun so that you use it efficiently. 01:31:46.060 --> 01:31:50.050 align:middle line:84% There are other architectures of similar ideas, 01:31:50.050 --> 01:31:57.260 align:middle line:84% like, you have lots of mirrors on your field, 01:31:57.260 --> 01:32:02.190 align:middle line:84% and there is a tower, and your pipe is there. 01:32:02.190 --> 01:32:08.060 align:middle line:84% So the sunlight, with the mirrors, 01:32:08.060 --> 01:32:16.700 align:middle line:84% heats up this pipe that is up there. 01:32:16.700 --> 01:32:22.480 align:middle line:84% And that way you concentrate, and you get high temperatures. 01:32:22.480 --> 01:32:25.130 align:middle line:84% And then the rest, once you have these high temperatures, 01:32:25.130 --> 01:32:27.580 align:middle line:84% you can use your standard thermal cycle 01:32:27.580 --> 01:32:32.925 align:middle line:84% and convert thermal energy into mechanical and electrical work. 01:32:32.925 --> 01:32:36.000 align:middle line:90% 01:32:36.000 --> 01:32:38.610 align:middle line:90% So no problem about that. 01:32:38.610 --> 01:32:44.410 align:middle line:84% This belongs to the realm of renewable facilities 01:32:44.410 --> 01:32:49.750 align:middle line:84% that obtain important incentives from state, governments, and-- 01:32:49.750 --> 01:32:57.130 align:middle line:84% And so those are very important because they allow 01:32:57.130 --> 01:33:05.110 align:middle line:84% you to pay for the equipment and some of these helps 01:33:05.110 --> 01:33:07.810 align:middle line:84% are, for example, here I gave examples 01:33:07.810 --> 01:33:13.370 align:middle line:84% of tax credits, cash grants, loan programs, 01:33:13.370 --> 01:33:15.530 align:middle line:90% all sorts of different things. 01:33:15.530 --> 01:33:19.720 align:middle line:84% And this is just only something in the United States. 01:33:19.720 --> 01:33:21.980 align:middle line:84% Every country has its own way of doing this. 01:33:21.980 --> 01:33:25.530 align:middle line:90% 01:33:25.530 --> 01:33:33.820 align:middle line:84% It's similar to what you do for photovoltaic. 01:33:33.820 --> 01:33:37.570 align:middle line:84% So photovoltaic is a direct conversion 01:33:37.570 --> 01:33:40.100 align:middle line:84% of solar energy into electricity. 01:33:40.100 --> 01:33:42.070 align:middle line:90% This is less direct. 01:33:42.070 --> 01:33:47.600 align:middle line:84% It goes through heat and then you have a power plant. 01:33:47.600 --> 01:33:50.150 align:middle line:84% And in the end, you also produce electricity. 01:33:50.150 --> 01:33:54.255 align:middle line:90% 01:33:54.255 --> 01:33:58.260 align:middle line:90% So what is the problem? 01:33:58.260 --> 01:34:05.500 align:middle line:84% The problem is that sometimes when you do these power plants, 01:34:05.500 --> 01:34:11.380 align:middle line:84% it is also useful to hybridize it. 01:34:11.380 --> 01:34:17.210 align:middle line:84% In other words, use this heat, yes, in your facility, 01:34:17.210 --> 01:34:21.210 align:middle line:90% but use also some fuel. 01:34:21.210 --> 01:34:23.690 align:middle line:84% Use that heat, but use also some fuel. 01:34:23.690 --> 01:34:26.510 align:middle line:90% 01:34:26.510 --> 01:34:30.050 align:middle line:84% Because that allows you to use the facility more 01:34:30.050 --> 01:34:33.020 align:middle line:84% hours per year, for example, or maybe 01:34:33.020 --> 01:34:36.170 align:middle line:84% it allows you to increment the temperatures 01:34:36.170 --> 01:34:41.690 align:middle line:84% and improve on the overall efficiency. 01:34:41.690 --> 01:34:47.540 align:middle line:84% And so it's either that you start from a solar facility 01:34:47.540 --> 01:34:52.610 align:middle line:84% and hybridize it using fuel, or sometimes, 01:34:52.610 --> 01:34:56.810 align:middle line:84% which also happens very often, you 01:34:56.810 --> 01:35:00.330 align:middle line:84% start from a traditional facility, fuel based, 01:35:00.330 --> 01:35:04.460 align:middle line:84% and you hybridize it by putting a solar field on the side 01:35:04.460 --> 01:35:07.970 align:middle line:84% to, for example, provide the low-temperature heating 01:35:07.970 --> 01:35:10.430 align:middle line:84% that the fuel does in a less efficient way 01:35:10.430 --> 01:35:13.130 align:middle line:84% or do some other kind of integration. 01:35:13.130 --> 01:35:26.530 align:middle line:84% So in all these hybrid problems, the important aspect is that-- 01:35:26.530 --> 01:35:28.420 align:middle line:84% the important question is, all right, 01:35:28.420 --> 01:35:32.940 align:middle line:90% I produce work, electricity. 01:35:32.940 --> 01:35:36.630 align:middle line:84% The question is, how much of that electricity that I produce 01:35:36.630 --> 01:35:41.700 align:middle line:84% can be said to be renewable, and how much is not? 01:35:41.700 --> 01:35:45.960 align:middle line:84% Because the renewable fraction gets the incentives. 01:35:45.960 --> 01:35:47.880 align:middle line:90% The other doesn't. 01:35:47.880 --> 01:35:52.110 align:middle line:84% So even here, we have a problem, which 01:35:52.110 --> 01:35:57.520 align:middle line:84% is entirely dual to the one that we have discussed. 01:35:57.520 --> 01:36:01.860 align:middle line:84% And that's why I'm going to go fast on this. 01:36:01.860 --> 01:36:10.110 align:middle line:84% But I will ask you, in your homework, which, by the way, 01:36:10.110 --> 01:36:11.730 align:middle line:90% this is a heavier homework. 01:36:11.730 --> 01:36:13.400 align:middle line:90% So it's also more work. 01:36:13.400 --> 01:36:17.960 align:middle line:90% 01:36:17.960 --> 01:36:21.860 align:middle line:84% So it will have two parts, two videos. 01:36:21.860 --> 01:36:25.310 align:middle line:84% One with a problem on co-generation, and the other 01:36:25.310 --> 01:36:31.640 align:middle line:84% is put words in these slides about this part 01:36:31.640 --> 01:36:33.950 align:middle line:90% of the hybrid facilities. 01:36:33.950 --> 01:36:40.550 align:middle line:84% So in any case, the duality stands on the fact 01:36:40.550 --> 01:36:43.430 align:middle line:84% that in the previous problem, we had the alphas 01:36:43.430 --> 01:36:44.580 align:middle line:90% on the left-hand side. 01:36:44.580 --> 01:36:49.500 align:middle line:84% Here, we have the betas on the right-hand side. 01:36:49.500 --> 01:36:53.370 align:middle line:84% So beta R is the renewable fraction of electricity. 01:36:53.370 --> 01:36:55.250 align:middle line:90% So beta R is the key. 01:36:55.250 --> 01:36:57.650 align:middle line:84% It's the number that will give you access 01:36:57.650 --> 01:37:01.920 align:middle line:90% to these economic incentives. 01:37:01.920 --> 01:37:06.360 align:middle line:84% Also, here, you can talk about primary energy savings 01:37:06.360 --> 01:37:11.790 align:middle line:84% and also talk about partial efficiencies, where 01:37:11.790 --> 01:37:13.040 align:middle line:90% you put up there-- 01:37:13.040 --> 01:37:16.130 align:middle line:90% 01:37:16.130 --> 01:37:18.290 align:middle line:90% you see, F is the fuel. 01:37:18.290 --> 01:37:21.320 align:middle line:84% It's the hydrocarbon that you're using, 01:37:21.320 --> 01:37:24.740 align:middle line:90% and R is the solar energy. 01:37:24.740 --> 01:37:31.980 align:middle line:84% So again, once you have these betas, 01:37:31.980 --> 01:37:36.660 align:middle line:84% you can think that your hybrid facility has two lines. 01:37:36.660 --> 01:37:40.190 align:middle line:84% One is the one that produces electricity 01:37:40.190 --> 01:37:43.250 align:middle line:84% starting from the fuel and the other that 01:37:43.250 --> 01:37:48.510 align:middle line:84% produces other electricity starting from solar, 01:37:48.510 --> 01:37:51.300 align:middle line:84% and you want to do this splitting. 01:37:51.300 --> 01:37:57.940 align:middle line:84% So you can define the primary energy savings with respect 01:37:57.940 --> 01:37:59.330 align:middle line:90% to separate production. 01:37:59.330 --> 01:38:01.435 align:middle line:84% So separate production will be, I only 01:38:01.435 --> 01:38:08.050 align:middle line:84% have one solar facility and one fossil fuel facility, separate. 01:38:08.050 --> 01:38:11.060 align:middle line:84% Apparently, it is better if you combine them. 01:38:11.060 --> 01:38:14.050 align:middle line:90% You get higher efficiencies. 01:38:14.050 --> 01:38:16.000 align:middle line:84% I don't have experience, so I don't 01:38:16.000 --> 01:38:19.190 align:middle line:84% have the numbers of if it is of the same order, 01:38:19.190 --> 01:38:21.950 align:middle line:90% maybe 40% is too much. 01:38:21.950 --> 01:38:25.510 align:middle line:84% But for sure, there is some improvement 01:38:25.510 --> 01:38:29.290 align:middle line:90% in the overall efficiency. 01:38:29.290 --> 01:38:35.590 align:middle line:84% Also here, again, at the beginning and perhaps even still 01:38:35.590 --> 01:38:43.470 align:middle line:84% now, because I don't know if this problem has evolved enough, 01:38:43.470 --> 01:38:52.060 align:middle line:84% there is one way, that we call an incremental fossil-centered, 01:38:52.060 --> 01:38:55.850 align:middle line:84% where you give priority to the renewable. 01:38:55.850 --> 01:38:59.200 align:middle line:84% And so you say, all right, I use that fuel. 01:38:59.200 --> 01:39:03.490 align:middle line:84% With that fuel, I usually produce this much electricity. 01:39:03.490 --> 01:39:08.190 align:middle line:84% Fine, so the extra electricity is attributed to the solar. 01:39:08.190 --> 01:39:11.520 align:middle line:90% 01:39:11.520 --> 01:39:18.030 align:middle line:84% But that's unfair because it doesn't distribute evenly 01:39:18.030 --> 01:39:19.990 align:middle line:90% the primary energy savings. 01:39:19.990 --> 01:39:25.170 align:middle line:84% So again, you can use a separate production method 01:39:25.170 --> 01:39:29.190 align:middle line:90% like we did for the other case. 01:39:29.190 --> 01:39:31.520 align:middle line:90% And again, you could use exergy. 01:39:31.520 --> 01:39:34.310 align:middle line:90% 01:39:34.310 --> 01:39:38.780 align:middle line:84% Here are only one point I need to explain, 01:39:38.780 --> 01:39:47.690 align:middle line:84% is that, what's the exergy of solar energy? 01:39:47.690 --> 01:39:50.870 align:middle line:90% That's a chapter in itself. 01:39:50.870 --> 01:39:55.810 align:middle line:84% But you could argue that there are some papers, 01:39:55.810 --> 01:39:57.830 align:middle line:84% I can give you references to those papers. 01:39:57.830 --> 01:40:00.370 align:middle line:90% 01:40:00.370 --> 01:40:02.070 align:middle line:90% We also contributed some. 01:40:02.070 --> 01:40:04.840 align:middle line:90% 01:40:04.840 --> 01:40:07.000 align:middle line:90% A good number is this. 01:40:07.000 --> 01:40:14.760 align:middle line:84% Of course, there are formulas that get you to this one, 01:40:14.760 --> 01:40:18.810 align:middle line:84% meaning that energy coming from the Sun 01:40:18.810 --> 01:40:22.590 align:middle line:84% comes from a very high temperature source, the order 01:40:22.590 --> 01:40:28.880 align:middle line:90% of these many K, Kelvin. 01:40:28.880 --> 01:40:34.830 align:middle line:84% So the photons that come from the Sun carry not only energy, 01:40:34.830 --> 01:40:35.695 align:middle line:90% but also entropy. 01:40:35.695 --> 01:40:41.260 align:middle line:90% 01:40:41.260 --> 01:40:47.230 align:middle line:84% But then there is a problem that as it gets to the atmosphere, 01:40:47.230 --> 01:40:50.060 align:middle line:84% and you get to the surface of the Earth, 01:40:50.060 --> 01:40:55.060 align:middle line:84% you get some direct lights and some rays 01:40:55.060 --> 01:41:00.350 align:middle line:84% and some indirect through refraction, 01:41:00.350 --> 01:41:10.720 align:middle line:84% and yeah, so from the sky, the sky has a certain temperature. 01:41:10.720 --> 01:41:13.710 align:middle line:84% So there are lots of reasoning that 01:41:13.710 --> 01:41:16.330 align:middle line:90% go behind a number like this. 01:41:16.330 --> 01:41:20.140 align:middle line:84% And so, again, this is a chapter in itself. 01:41:20.140 --> 01:41:23.130 align:middle line:84% But in any case, the problem here 01:41:23.130 --> 01:41:39.370 align:middle line:84% is that with the exergy method, you're using the reversible heat 01:41:39.370 --> 01:41:42.290 align:middle line:90% engine as a reference. 01:41:42.290 --> 01:41:46.090 align:middle line:90% And that is not feasible. 01:41:46.090 --> 01:41:48.020 align:middle line:84% Actually, I see that the time is over, 01:41:48.020 --> 01:41:51.460 align:middle line:84% so maybe we'll return just with few words at the beginning 01:41:51.460 --> 01:41:55.210 align:middle line:84% of next lecture about this because there's still something 01:41:55.210 --> 01:41:56.840 align:middle line:90% I want to say that I didn't. 01:41:56.840 --> 01:41:58.940 align:middle line:90% And it is important also. 01:41:58.940 --> 01:42:03.000 align:middle line:84% So hold on, don't do the homework yet, OK. 01:42:03.000 --> 01:42:03.500 align:middle line:90% All right. 01:42:03.500 --> 01:42:04.583 align:middle line:90% So I'll see you next time. 01:42:04.583 --> 01:42:06.270 align:middle line:90% See you Tuesday. 01:42:06.270 --> 01:42:14.000 align:middle line:90%