 Today, we want to look at the long assignment which I had given you earlier. Now, this assignment is really about understanding some chemical reactions that occur in the natural environment. So, I have just listed some of the things that happen photosynthesis, respiration, nitrogen fixation, nitrification, denitrification, methanogenesis. This is what typically would happen in the natural environment. And the context is of course, we might want to purify water using a natural process or we might want to grow a crop during a natural process. Whatever might be the case, we have to deal with these many chemical reactions. So, what I have tried to do is to give you some data, so that we can understand how to model a very complicated reaction system. So, this is the object of the exercise. So, the problem that we want to solve, let me illustrate is the following. We have a natural environment in a chemical reaction equipment. Now, I the natural environment can as an example I have taken is soil. Now, you can use this to purify water. You can use soil to make produce various crops. In this experiment, what has been done is, we have acetate in the form of sodium acetate, ammonium source as ammonium chloride, nitrite source as sodium nitrite and nitrate source. In this particular experiment, we have not used any nitrate. So, that is 0. So, what goes into the reaction equipment is a carbon source. It is nitrogen source in the form of ammonium chloride and sodium nitrite. So, the experiment is that, you measure all the compositions of acetate, which is measured as COD and then of ammonium is measured as NH 4 plus nitrogen. Nitrite, which is also measured and this is also measured NO 3 minus plus. So, you have essentially 4 measurements on what is going on in the reaction equipment. And the postulate is that, this is what happens in the natural environment, that there is a change in COD because of the chemical reaction. There is a change in all these numbers and therefore, we should be able to measure what happens in the reaction equipment. Based on this, we want to say something about what happens in the reaction equipment. This is the object of the exercise. Now, I have with me some data. This I have taken from what I have already given you. So, I have written down. I have just taken some of the data run number 3, 6, 12, 21, 30 and 36, where input COD is given, output COD is given, input nitrogen as ammonium is given, output is given. So, this is in. Let me write it here. In, out, in, out, in, out, in, out. So, this is what is given. Now, we want to understand what goes on. To understand what goes on, I suggest the following model. The suggestion is the following. I will come back to this in a minute. So, what we are searching is that in the reaction environment that we have nitrite gets converted to ammonium. That means it is a reduction reaction for which energy is required. But this reaction could go the opposite way as well. We do not know. The data will tell us what will happen to the reaction. NO 2 minus can get oxidized to form NO 3 minus. Then NH 4 plus and NO 2 minus can, can react to form nitrogen and water. So, these are the 3 reactions which is postulated to take place in this soil environment. Of course, so many things may happen. But what is suggested is only these 3 reactions. And the acetate, which is in the form of acetic, acetic acid. I have written as acetic acid. It gets oxidized to carbon dioxide and water. And of course, we expect that because of all these reactions, some amount of cell synthesis will occur. And therefore, the cell synthesis reaction we are not able to tell. The stoichiometry is not very easy to represent. I have just represented as cell synthesis. So, we expect that ammonium which is formed in reaction 1 is what is going to be used for protein synthesis to make the cells. So, it is well known that if ammonium is produced in a reaction, then that will be used for cell synthesis. This is one important result that comes out of experiments in biology. That nitrogen that is fixed because of biological reaction goes to form cell. That means whatever ammonium is produced will form cells. So, let us try and look at this data in some detail. So, what you want to say is that, if I say this is reaction 1, this is the x 1. If I call this as x 2, if I call this as x 3, if I call this as x 4, call this as x 5. So, there are 5 reactions that are taking place. And how many experimental data do you have? We have experimental data. We are able to measure, what are we able to measure? We are able to measure ammonium. We are able to measure NO 2 minus. We are able to measure NO 3 minus. So, we have 3 reactions, data. There are 3 reactions. So, we should be able to find out what happens. 3 independent reactions, 3 measurements. Therefore, we should be able to tell what happens to nitrogen. And then we are measuring this as well in the form of COD. Therefore, we know what is happening to carbon. At least we know what is the change that is happening. Now, what I am saying is that, if we postulate that whatever ammonium that is fixed in the reaction. See, this reaction is called fixation in organic nitrogen getting converted to organic nitrogen. It is called fixation reaction. Therefore, if this actually happens, then we can say that all these ammonium nitrogen goes into cell synthesis. In other words, what I am saying is that, if x 1 is known, then x 4 is simply alpha times x 1. This is the assumption that we make. What is alpha? Alpha is the number of grams of cell per gram of nitrogen. Is this clear? If there is nitrogen fixation in the environment, that biological nitrogen goes into form cells. And the amount of cell formed is simply alpha times x 1, where x 1 is the biologically produced nitrogen. Now, this is not a bad assumption, because there is a lot of data which suggests that if ammonium is produced biologically, it goes to form cells. Now, you notice here that we have 4 reactions and there are 4 measurements. Therefore, if indeed our postulate is right, we have a complete description of what is happening. Therefore, we should be able to tell what is the amount of cell mass that is produced and how production of cell mass depends upon the process variables. What are your process variables? Your process variables are as you can see from here, may be your feed rate, the rate at which you feed or may be the carbon to nitrogen that you provide in the feed or may be the composition of the feed itself. So, we know the composition of the feed, we know the C by N that we have chosen. Therefore, in principle if our postulate is right, we must be able to tell how much cells are formed and therefore, we should be able to predict how the process is running. Now, it is the context is let us say we are trying to clean water. This is an obvious example that all of us might be interested in. What are we interested in? We are trying to get rid of the pollution in water and that pollution is measured in terms of COD in terms of nitrogen, in terms of nitrate, in terms of nitrate. So, it is a complete description of what is the quality of water that you start with and what is the quality of water you end up with. Therefore, we must be able to tell how to clean this water to the extent that you desire. So, since what we are trying to say is that this formulation that we have provides a way of telling how to design equipments to be able to produce what we want. If that production is clearly specified, we must be able to tell from this model if it is correct, what will happen to the process and what we can do to design such processes. So, this is the exercise that we want to do. Now, let us just look at this data and ask you a few questions. We have 1, 2, 3, 4, 5, 6, 7 sets of data out of 7 large numbers that I have given you. Let us look at what happens to ammonium, what happens to nitrite. Just look at the data. You started with 90, it went to 15.4. We start with 90, it goes to 15.4. You start with 107, it becomes almost 0. That means, in this process nitrite is almost fully consumed and you can see amount of nitrate is not very large. Now, how much nitrogen we putting in? How much nitrogen is in the output? We starting with how much nitrogen? 107 plus 90 about 197 and then what is we end up with how much? 15.4 and almost 1.1 about 16. So, we put in 197 units of nitrogen and what we get out is only 16. So, huge amount of nitrogen is lost, a huge amount of nitrogen is lost. So, I wanted to appreciate this in agriculture huge amount of nitrogen is lost. In fact, this huge amount of data which says that 85 percent of nitrogen is lost. Now, this tells you clearly, it is lost. We want to know why, we do not know. Now, you look at carbon measured as COD, this 385 it becomes 90. So, you can see carbon is lost, nitrogen is also lost. Now, whether this nitrogen which is lost, is it fixed as cells or is it going up into the atmosphere? We do not know. As per this model that we have written, the model we have written, we have only accounted for nitrogen that is going into the atmosphere. We accounted for the oxides of nitrogen NO 2 minus and NO 3 minus. So, our postulate is a nothing else happens. Suppose, N 2 O is formed, we do not know, we do not know. That also go out. So, we do not know, whether it is N 2 or N 2 O, we are in some doubt as of now. But, what is important is that, the huge amount of nitrogen is lost. In the experiment also, we find huge amount of nitrogen is lost. Now, if you look at, let us quickly see the correlation. How much ammonia is lost? How much nitrite is lost? Do a quick calculation. See that ratio. Do a mental calculation. Do a mental calculation. Ideally, you should plot. You can do a mental calculation. This is 75 and this is 107. 107 to 75. 107 divided by 75 is what? 1.3. How much is it? 1.3, 1.4. Look at the next data. 51 and then 6.3 which is about 45 and this is about 60. 45 to 60, that ratio would be 60 by 45. About 1.3, 1.35. Please look at. It is important to recognize that this data suggests this ratio, the loss of ammonium to loss of nitrate. Look at that ratio. See, soil, huge number of reactions occur in soil. We all understand that. We are modeling it in terms of simply 4 reactions, not thousands of reactions. And look at the kind of order that you can see in the data. So, if you look at each of the data and tell me what is this ratio please quickly. What is the ratio of loss of ammonium to loss of nitrogen, loss of nitrate to loss of ammonium or calculate this ratio? Just calculate loss NO 2 minus divided by NH 4 plus. Roughly you tell me some numbers. What is that ratio? Find that ratio quickly please. Let me write here. See, this is what we want to find out. NO 2 minus divided by NH 4 plus. Please tell me this ratio. Run number I am just writing down. 3, 6, 12, 21, 30 and 36. Please tell me this ratio. Have you all got this data? You have taken down this data. Give me this number please. No, I want the ratio. NO 2 minus 1.3, 1.4. What was that number? 1.4 across reasonably constant. Run number 3, 1.42 and then run number 12, 1.42, run number 21, 1.42, run number 30, 1.42, 4.3 and run number 36. What I want to draw your attention is even though many many reactions might be taking place, when we look upon this equipment in terms of this ratio NO 2 minus NH 4 plus, it seems to suggest this ratio is reasonably constant. What meaning can you attach to an experiment in which this ratio remains reasonably constant? How do we understand? What can we say might be happening? What can we say might be happening? Look at these reactions. NH 4 plus, NO 2 minus giving you N 2. What do we expect if this reaction is taking place? What do we expect? It should be 1 to 1. The ratio should be 1 is to 1. It is not 1 is to 1. So, this is the reaction that is responsible for the loss. This would not be able to explain the difference between NO 2 minus and NH 4 plus. So, something more is happening. Let us see how to understand this? Reaction 1 and reaction 2. So, that could explain this. So, from the data it appears that there is not much of NO 2, NO 3 minus. That is true. But, this reaction may not be as important. But, what extend is reaction 1? We do not know whether it explains all that. So, what we have to now do is to be able to model this and tell how much in the data, how much is x 1? How much is x 2? How much is x 3? How much is x 1? Is this clear? From the data, it is a multiple reaction. We know how to handle multiple reactions. So, given this data, what is x 1? What is x 2? What is x 3? What is x 4? Can we find out? That is what we should do. How to do that? So, let me write it here. Please remember this reaction. I am going to write. I will write this stoichiometry. Let me write this stoichiometry. So, I will write a balance for NO 2 minus. NO 2 minus, what is equal to what? How much is coming in? Let us say this A naught is coming in and its reaction, NO 2 minus is consumed in reaction 1, reaction 2 and reaction 3. So, I say it is A naught minus of x 1, minus of x 2, minus of x 3. x 1, x 2 and x 3 are the units of, let us say, milligrams per liter or some appropriate units. Is it alright? And then NH 4 plus, notice here, NH 4 plus is in reaction 1. It is formed in reaction 3 and it is consumed. So, it is B naught, B naught plus x 1, minus of x 3. Is it alright? NO 2 minus, NO 3 minus, sorry, C naught and it is, what happens to N? So, I call this as equal to A equal to B equal to C. A, B and C are measured quantities. Now, can you tell me what is x 1, what is x 2 and what is x 3? I will write the answers. Please tell me whether it is. So, this is equal to C minus C naught. Is it alright? Yes or no? x 3, can you just solve this algebraic equation and tell me? I will write the answer here, but you please tell me whether this is okay. I am just writing the answers. So, you have to tell me whether it is. Please solve the algebraic equation and tell me whether this is okay. So, can we now say, now that the data, see the data is given, can we now find out what is x 1, x 2 and x 3? Is this clear? What is x 1? What is x 2? What is x 3? I want to tabulate that. You have these equations with you, all of you. What is x 1? What is x 2? What is x 3? So, I want to make a table of the answers for these 6 data. So, this is run number 3, 6, 12, 21, 30 and 36, x 1, x 2, x 3. I want to write x 4, I want to write x 5 also. I want to get all the numbers from you. Run 3, 6, 12, 21 and 36. x 2, you can read out. x 3, you have to calculate. But anyway, please tell me the answers. I want the answers. So, we can go 1 by 1. Run 3, what is x 1? Let us do 1 by 1, please. Run 3, what is x 1? So, there all of you can get the answers. x 1 for run 3, please. 15.7. It is in milligrams per liter. Run 3 is 15 and x 3. 90.7. Similarly, for run 6, do x 1 for run 6, please. So, run 3, this is what the answers have been given. Do you all agree? Tell me for run 6, please. 7.5 and 46 is what I have got. Anybody else? Run 6. Run 6. How much? 50.6 and x 1. 5.8 is it. Anybody, why I have not? I have got a slightly different answer. Run 6.7, run 6, 59, 40. Please, would you please recalculate? Is this correct? 5.8? Everybody gets it. And, 50.6 is correct? Yes. Alright. Then, I have made a mistake. Run 12. What is the answer? x 1. 15. And, x 3. 89.3. Very good. Run 21. 14. And, x 3. 87. Then, comes run 30. Run 30. Run 30 is how much? Run 30. 204 is about 140. So, what is the answer? 204 plus 140 is 340. 170, it should be. Run 30. x 1. 29. That is what I am getting. And, then, x 3. I am getting that also. Run 36. Everybody is done. x 1, x 3. x 1 to x 3. Tell me run 36. Run 36, please. 28.5. 28.3. And, the other one. I have got 168. Anyway, this is. I hope all of you have the data. So, I can put this on top. So, this is how the experiments look. x 1 and x 3. What is the ratio? x 1 to x 3? x 3 to x 1? Around 6. Around 6. Where is 10? If you plot all these 54 sets of data, you will find. Actually, it is a reasonably correlation around 6.6 or so. Around 6.6 or so. Around 6.6 is what I expect based on the data. So, what we are saying is that x 3 to x 1. See, this reaction is taking place in the soil environment. As per the model, the ratio of x 3 to x 1 seems to be reasonably constant. Now, how do we explain this? What does it mean? I mean, what meaning can we attach? These are the reactions that we are postulating. Of course, what happens is hundreds of reactions may be happening. But, we are postulating that only these 5 reactions are sufficient to understand what is going on. We find that x 3 to x 1 is about 6.6. I like the number 7. There are 7 electrons in the outermost shell of nitrogen. Therefore, I like that number 7. The ratio is 7. This is what I like. It does not mean that I am right. So, I like to think that it is 7. 1 by 7 is 0.14. For last 50 years, the data on agriculture says that 85 percent of nitrogen is lost. What is x 3? x 3 is nitrogen lost. And what are we getting? 85 percent of nitrogen is lost. On other words, there is a very simple experiment which is nothing to do with agriculture. And these experiments are done with equipment, very ordinary kind of equipment, titrations and all that. Nothing very sophisticated. But, it is able to give you insights into reactions which are extremely complicated. There are just too many things happening. On other words, if you have the right model, you can handle extremely complex reactions. That is the message of the experiment like this. What we are saying is that what is x 1? x 1 as per this reaction is the nitrogen that is fixed n o 2 minus going to n h 4 plus. Which means that biologically, the nitrogen gets fixed. That is why this reaction. So, what is being said is that this ammonia would get fixed in the cells. So, that means, if I tell you the alpha, the grams of cells per gram of nitrogen. Suppose, let us say if you look at bacteria, typical soil bacteria is about 12. Alpha is about 12. If you look at ground net, alpha would be around 20. If you look at wheat, alpha would be 60. If you look at sugar cane, alpha would be 300. If you look at wood, alpha would be 200. Now, these are all well known numbers. How much nitrogen is there in the cell is a well documented kind of information. We can get it from the literature. So, if you know x 1, you should be able to tell how much cells are produced. And therefore, if you are doing a waste treatment for example, you know how much cells are formed and therefore, how much sludge is produced. Waste treatment sludge is a nuisance. People do not want sludge. So, you can tell from here how much sludge will be produced in your process. Once you have made these measurements, you can tell you have to handle so much sludge. So, much of cell mass will have to be handled. Now, in these 6 sets of data that I have given you, I have chosen these sets so that the x 1's are always positive. There are many sets of data where x 1 is negative. What does x 1 negative mean? It goes the reverse way. And therefore, no cells are produced and therefore, no sludge is formed. Therefore, you do not have to deal with problem of sludge in waste treatment. You understand? See, the insights that it can give you is enormous. So, by appropriately choosing your process, you can produce cells or you may not produce cells. The cells are essentially respiring. You know, there are cells in the system which respire. They do not grow. They grow, but they do not reproduce. Is this clear? What we are saying? All right. Now, x 1, x 2, x 3, x 4, x 5 are in the units of milligrams per liter. Now, clearly if you want to look at a reaction equipment, this milligrams per liter does not make sense. Does it? Where is the data? See, you can look at this data here. The flow is very different. So, actual production will be whatever x's you have calculated multiplied by the flow divided by the reactor volume. So, if you want to express what is happening in your process, you have to multiply this by f divided by volume of the equipment. Then only you can say what is the productivity per unit volume per unit time. Is this clear? So, we should multiply this x's by f divided by reactor volume, which is 20, which is given. v is 20. v is 20 liters. It is given. So, you can express all the numbers so that, you know, when you are operating at 12, the productivities will be f multiplied by this and all that. So, you can calculate and find out the productivity. Clear? So, be careful to ensure, understand that, you know, productivity is very different because the flow rates are very different. So, what is x5? Quickly tell me. You can read out from your table. x5, where is x5? This difference. I just want to write down those differences. Tell me the numbers, please. Run 3. What is COD lost? How much? Run 3. 6. 614. Second one? 564. 564. Third? 608. Fourth? 600. Fifth? 625. Is it? 655. 655 and then 636. These are the numbers. So, if you multiply by f, f is not mentioned here. I will put f here. So, it is 33612312. These are the flow rates in liters per hour. These are the flow rates in liters per hour. So, we can calculate productivity. Now, looking at x5 and x3. So, first, this is c by n is one point. I have to put this c by n here. c by n, this is 1.86, 1.86, 1.86, 1.86, 0.93, 0.93. Now, generally biological process have a very strong dependence on c by n. So, you find out what is this ratio? c by n is 1.86. This ratio, you have to find this ratio. f multiplied by productivity wise. Otherwise, you cannot compare. Please find out this number, which is f multiplied by x5 divided by volume. That is how you have to calculate. When you do that, there are some calculations involved. Do not worry about that. What you will see? Some of you have done this already. What you see is something interesting. We will not do this now. I will just tell you the result. You can do it at home. If you make a plot of, let us say, x5, the units are say, milligrams per litre per hour. Say, x3, also in the same units of milligrams per litre per hour. If you make these plots, you will find there are straight lines and it will be like this as c by n changes. Some of you have done this. I understand. Many of you may not have done this. What it says is the loss of nitrogen. This is the loss of nitrogen per unit volume per unit time. This is the loss of carbon measured as COD per unit volume per unit time. All biological processes, you have this kind of relationship. That loss of nitrogen to loss of carbon are correlated. In soil, they seem to be highly correlated as we find in this kind of data. What I had asked you to do is to find out that kind of correlation, so that we can use it for various purposes, including design. I have done that. I will show you those numbers. See, I have done this. Your answers look something like this. That means, when you make a plot of loss of nitrogen to loss of carbon measured as COD, I find I was very surprised to see such good straight lines, but they seem to be extremely good straight lines showing the correlations extremely high. Then, production of nitrogen to loss of nitrogen. That ratio appears to be 1 by 6, 1 by 7. I like to say it is 1 by 7. It is not 1 by 6.6. So, it is 1 by 7. So, that you get a correlation like this. See, this correlation is important. What does it say? It says in biological process. So, this comes out of curve fitting. You would have to do this at your home. When you do this fitting, I get something like this. Loss of carbon measured as COD, which is x 5 and then I will do loss of carbon divided by loss of nitrogen. This ratio is 2.84 times C by N. This is what comes out of the data. Now, if you assume that whatever x 1 is formed, it goes to form cells. Therefore, alpha times x 1 is x 4. If you make this assumption, then the cell produced to carbon lost looks something like this. That means, loss of carbon measured as COD to production of cells on the right hand side is the ratio of x 3 to x 1, which I say is 7. C by N is of the reaction environment. That is something that we will choose. Alpha is the product you are producing. If it is cell, alpha may be 12. If it is ground net, alpha may be 16, 20. If it is wood, it might be 200, whatever. So, we want to test this particular equation, whether it explains what happens around the world. Let us do a small experiment, test how it predicts what happens around the world. See, one data that we know is that in the US, lot of data is there. In the US, this, the carbon to nitrogen in soil is about say 20 or something like that. Some say 15, some say say 20. Let us take this 20. You are growing corn, but alpha is 75. So, what is right hand side? 2.84, it is 7 close to 20. This is 20 is 400. Alpha is 75. 400 divided by 75 is how much? 5.3, correct? 5.3. Now, 5.3. So, left hand side also, we should get 5.3. That means, this cell production, what is x 5? What is the carbon lost from soil? Now, there is lot of data which is around available around the world, where about 20 tons per hectare per year is the kind of carbon lost from soils. So, x 5 is about 20. So, what is x 4? Around 4. So, if you look at the US, you will find that the production of corn will be around 4 tons per hectare if it is an unfertilized soil. But moment you put fertilizer, it improves. So, for unfertilized soils in the US, we will have corn production of about 4 tons per hectare. Plenty of data is there. Moment you put nitrogen, what will happen to c by n? It will come down. So, once c by n comes down, your x 4 will increase. On other words, what we are trying to say here is x 5 represents energy and that energy you can harvest and get it in the form of food by appropriately adjusting c by n. So, what is being said is soil has energy in the form of x 5, which is soil organic carbon. Soil has carbon. Now, you have to harvest that in the form of food. If you do not do anything, the natural c by n will give you let us say 4 tons per hectare. Now, if you put external nitrogen in the form of urea, reduce the c by n, appropriately the production will increase. So, what has this c by n given you? It is only ensured that you are able to harvest more of the soil carbon as food. Is that clear? We are harvesting more of carbon in soil as food. This is what this whole equation is saying. So, by adjusting the carbon to nitrogen ratio of soil, you are essentially ensuring that more carbon of soil can be returned to us food. If you look at India for example, c by n in India is quite high. The reason is that the respiration rates are very high in India and things like that. So, c by n of about 30, 35 is not uncommon. Suppose you say let us say we are trying to grow corn in India. Instead of 20, c by n is 35. So, what will be our production? The x 5 still people take it as 20, but the case in India is not the case. It is not as high as 20. So, assume it as 20. What is x 4? c by n is 35, 2.15. So, what we are saying if there is enough carbon in soil, you can still get a production of 2 tons per hectare of corn. But what seems to happen is that carbon in soil is also very low, particularly in our regions because of respiration. So, carbon is very low in soil means what? There is not enough carbon in soil to be returned as food. So, even if you put fertilizer, you cannot get much food out of soil because there is not enough carbon in soil. So, what is being said is that if you are trying to grow bakers east, you have to provide glucose. Then only bakers east will grow. If you do not provide glucose, carbon source is not there means it cannot produce. In the same way, if you want to grow food, you need carbon in soil. Simply pruning fertilizer in soil is not going to give you food. This is the point I am trying to put across to you. Whether it is growing bakers east or making alcohol in a fermenter or growing food, the fundamentals are not very different. Essentially, it is trying to harvest the energy of carbon which has to return to you. That is what we are saying. So, this equation essentially tells you that if you have carbon in the environment, you can harvest it provided your C by N is appropriate. Now, you can explain why you can produce 600 tons of tomato in Israel because alpha, tomato is what 98 percent water and the alpha value is something like 600 or so. There is practically no nitrogen. So, when you are producing a crop which does not have much nitrogen, your production will be very high. It is nothing to be said and surprised about. Somebody comes and says, I will produce some so many 100 tons, 400 tons of tomato per hectare. It is to be understood. The moment you understand this, you can understand it is possible. It is not that. It is not. So, these are the important issues that you must recognize that in whether it is producing alcohol in a fermenter, producing bakers east in a fermenter, producing penicillin in a fermenter or producing in soil, the fundamentals are known that you need a carbon source, you need a nitrogen source and an appropriate environment for your organism to work. This is all it says. See, the example I took, carbon C by N of Indian soils are quite high. The reason it is high, there are number of reasons for this. Returning organics to soil has somehow been discontinued for some reason after synthetic fertilizers have come. That means, waste organics which was previously going back to soil very effectively because it was a farm environment even in a village. But nowadays, it is all urbanized and therefore, the waste is accumulating in the urban area. It is not returning to the farm. So, C by N is very high and therefore, your productivity is very low. X 4 is very low. Second reason is that since respirations are very high in our environment, the carbon in soil itself is quite low. If you go to the US, the carbon is very high because it is a temperate environment. So, the carbon is extremely large and that is not the case in our environment. So, this is two difficult situations which we have to handle part of the reason why our production is not as high. C by N of a natural environment if you go to a forest, C by N is fixed because it is evolved over millions of years. So, C by N of soil would not change. See if you go to northeast, source of your northeast slash and burn and then they grow. See they slash the forest and they grow for a number of years and then they abandon it. The reason is that forest comes with high good value of C by N, C by N around 14 to 15. So, you give very good crop. Crop yields are very high and after 4, 5 years it collapses and then you leave it, come back after may be 10, 12 years. That is what the tribals have done in the northeast and by and large this practice has kept the forest in reasonably good shape. It is not that the forest have disappeared, they are in pretty good shape. On other words, C by N seems to be an important parameter for productivity of biology. So, this is in our hand, C by N is in our hand, but what is important to recognize is that when you decrease C by N, you are harvesting the carbon of soil. So, higher the C by, lower the C by N, higher is the rate at which you are harvesting. If what you harvest, if you do not return your waste, that soil is going to deplete rapidly. See, we are producing by agriculture, we are producing more, but our waste are not return into soil. It is going into Ganga, Yamuna, whatever it is not going back to the farm and that is the problem which is responsible for lower productivity. X 5 is low, C by N is high. Both seem to be working against us. Is this clear? This is the point, the most important point as far as biology is concerned that there is an inverse relation, alpha is high means you will get very high production. You will get huge amount of tomato, understandably because nitrogen is low. See, what happens is that people would like to calculate what is the energy that is required to do whatever you are doing. Whether it is producing penicillin, it is producing baker's yeast or alcohol or producing in soil, whatever is the biological environment, how much energy is required to do what you want. Now, we have said that these 5 reactions is what is taking place, correct? Reaction 1, 2, 3, 4, 5. So, there is an energy delta H, delta free energy of formation, free energy for change for each of these reactions. Similarly, I mean standard heats of formations and all that. So, that you can calculate what are the delta H for all these reactions. What is the energy that is required for this reaction? How much energy is released by these reactions? So, if you assume in soil, there is no loss of energy in the sense that this completely synergized, fully synergized. So, all the energy is fully utilized. Suppose we assume, which means I say that this applies. I say that this equality applies, which means x 1 delta H 1, x 2 delta H 2, x 3 delta H 3 equal to 0. This is an assumption. We do not know whether it is right or wrong. Now, we are saying that the x 3 and x 1 are related by this, x 3 to x 1 we are saying is 6.6. I am saying it is 7. We can quarrel, but let us say it is lambda. So, x 3 to x 1 based on our experiment, it is saying it is lambda, correct? And then I am saying that whatever ammonia is produced biologically, it is fixed in cell. Therefore, the x 4 that are cells you will produce is simply whatever is x 1 that is produced, multiplied by alpha. Alpha is known. If it is bacteria of soil is 12, if it is whatever, plenty of data is there. So, on other words, this sigma x i delta H i equal to 0, then it give you this kind of relationship. This relationship, if you just look carefully, it is an interesting relationship. X 3 is known and inside here, the only unknown is delta H 4. What is the energy required to make the cell? Energy required to make the cell. All these are well. In principle, we can plot x 3 versus x 5, correct? X 3 versus x 5, we can plot. The data is there. X 3 data you have, x 5 data you have, yes or no? Therefore, if it turns out that it is a good straight line, if it turns out and it is often the case, because this term is not very large. This term is not very large. Therefore, it turns out to be a good straight line. Your data will tell you it is a reasonably good straight line you will get. So, that from the slope, you can find out what is the value for delta H 4. Is that clear? What I am saying? So, we have done these experiments for each c. You can do this for every c by n. This can be done for every c by n. So, what are we saying? We are saying that we conduct experiments at different c by n and find out what is the energy that is required for growing this, for making the cell. This cell can be paddy, wheat, wood, tomato, whatever, baker's yeast, whatever is your organism of interest. What is this delta H 4? It is the energy that is required to grow that cell. I mean cell synthesis. How much energy is required for cell synthesis? Now, then once you have the data, you can plot the data. In fact, that is the exercise that I have asked you all to do. I do not have a good answer. The answer I like to give is that life has evolved over millions and billions of years. Clearly, it would have made good use of the energy. Therefore, energy is in short supply always. Therefore, it would make the best use of whatever energy it has. This assumption it may not be righted, but it appears from whatever number that emerges from very simple lab experiments that it is not wrong. What we are saying is not wrong. In the sense that there appears to be the great effort to maximize or utilize energy available most efficiently and not allow it to be dissipated. This is the kind of answer that is coming out of the data. You should look at the data carefully. What we are saying now a little bit more that the energy that is required to make the cell depends on c by n. That is the kind of relationship that emerges from the fitting. When you fit the data, the energy for cell synthesis kilo joules per gram multiplied by alpha equal to this. Suppose, you are growing a crop which is alpha is 200, then clearly the energy for cell synthesis is low. If you are growing a crop where the alpha is 10, the energy for cell synthesis is high. There is one result. Second result is that c by n, higher the c by n, higher is the energy that is required to grow the cell. On other words, it is saying exactly what farmers will tell you that if there is not enough, if your c by n is high in soil as it is in Indian, the energy required to grow crops are very large. Same crop if you grow in the US, the energy required is much lower because c by n is much lower. On other words, the US environment gives you a far more congenial c by n. The forest environment of northeast gives you a far more congenial c by n for you to have much higher productivity. On other words, if you can maintain forest everywhere, we have the highest productivity. If we can afford to live on forest by enlarge, the productivity is extremely large. That is the kind of message that comes out of ecology. So, what I have tried to do is that project what we call as ecology, natural processes and all that. In terms of numbers thermodynamically, we can understand that energy is most efficiently used in a very wholesome forest environment. In agricultural environment, energy is not used so efficiently and therefore, the energy consumption is much larger. For example, in typical agricultural land in the world, would have a production of about 6 tons per hectare. If it is a forest, it will be 22 tons per hectare. But, forest will produce wood where the nitrogen is only 0.5 percent, while agriculture will produce food where the nitrogen may be about 2.5-3 percent. So, as seen in that terms, you cannot say it as inefficient because energy wise, it may be just as good. Quantity wise, it may be different. So, we have to look at all these things not only in terms of quantity, but in terms of energy as well. So, what I have tried to do here is to project both quantitative numbers and energy numbers. So, that you can see how the natural systems perform. So, that is the exercise problem sheet, whatever the number is. So, there is enough that you can now finish off it. I will stop there.