 So we have been discussing about this mixed flow reactor and of course this is the diagram which we have given and then we just want to know what is the concept of mixed flow and if you do not want to use your brain like you have done in your b-tech you know simply saying that perfect mixing is one where everywhere inside you have same concentration and temperature, okay. So that will create some cobwebs, some you know not properly understanding things like for example. So the moment we say that perfect mixing most of us feel that you know it is instantaneous reaction it is not, right instantaneous mixing that is correct instantaneous the moment you have a concentration of C A not just entering it should be instantaneously mixed to a concentration of C A f or conversion wise X A f C A f is safe because C A not is coming in C A f is is the concentration due to perfect mixing but when I looked at that concentration has come that concentration in the reactor is prevailing please listen to this one carefully that concentration C A f is prevailing due to elements of various residence times inside the reactor and you know that because it is a perfect mixer by definition of perfect mixing itself the outlet residence time distribution and also the inside residence time distribution is exactly same here also you will have 0 to infinity residence time distribution that means okay I will take a small sample outside here and then I will look into what are the residence times I may see there molecules or packets entered infinite time back that means very long time back infinite means not really infinity okay then it also would have average residence time is 10 minutes just for easy discussion so all those molecules will not be exactly at 10 minutes so we will have 100 minutes even 1000 minutes 1 or 2 molecules, right 500, 150, 10, 1 almost 1 second also why all this is happening again because of perfect mixing when you are continuously sending this C A not there may be one molecule which may be very quickly coming out of the reactor and then joining this string so practically that molecule is not able to react but on the average when I look because of the mixing there are molecules now spent you know at 10 minutes 100 minutes 20 minutes 1 minute and 500 minutes all that combination and that will give you the average concentration inside the reactor which is also reflecting in the outside you know the outlet so that is the concentration what we see here C A F is the concentration because of mixing of various elements of various residence times just extend your imagination from here to plug flow so the moment you have plug flow I think this is a tubular reactor like this and we are only talking about exit here also exit concentration is C A F but what about inside concentrations very seldom yeah so if I draw this this may be C A not this may be C A F and of course here I have F A not F A and all that right so we are talking about here the concentration C A F at the exit but the moment I go inside the C A F is different than the higher than the next one then you move somewhere inside that will be higher like that if you come back here then you will have C A not concentration that means here what do I have I have the concentration decreasing slowly right and this is C A not this is C A F okay now it is the same thing if I plot here C A not yeah how do I plot this this is C A not okay this is C A this is C A not because it is instantaneous mixing concentration will decrease to C A F which is this there is no slow decrease here this is C A F okay sorry this is only spatial okay no problem this is C A not this is C A F but now the difference why even writing without writing equation why plug flow reactor should give you more conversion for a given volume for a given volume in this and here you will get less conversion for a given volume is here the concentration is changing slowly and then what about rate here here here do I have different rates why I have different rates concentration are different we know that at any point we have K into C A if it is first order reaction or correspondingly whatever reaction we have so that means what I see at the outlet is the accumulation of all that I do not say not accumulation or not material accumulation we are talking the changes in reaction and the concentration slowly that means number of rates I have inside the thing and what I see here at the outlet is some kind of average of all those rates whereas here how many rates I have only one because throughout the system I have only one one concentration so that is and that rate corresponding to C A F outlet concentration so is it more than or less than inlet concentration definitely much lesser right so if I I mean example if I say that C A not equal to 10 moles entering 10 moles per liter and outlet is 1 mole C A equal to 1 mole per liter okay what is the conversion now we are talking about constant density system conversion equal to 90 percent you know the definition C A not minus C A by C A not so I think for some people I think also better right C A not minus C A F by C A not this will be point nine that is the concentration okay that is the conversion which I get here in the outlet and which is same throughout right so corresponding to this C A C A F the rate if I calculate minus R A equal to K into C A F only one rate which is very low that means that is almost the exit rate right so now in our design expressions we will have always this rate in the denominator by R A okay by something by R A it will come now here I have only one rate and the rate is very less okay I mean very less means it is not I mean it is corresponding to exactly this rate only okay here also if I have 90 percent conversion here also I will have 1 mole 1 mole per liter only right I mean for comparison sake please remember that so here also I have 1 mole coming out okay here also we have 1 mole per liter and here also I have 1 mole per liter only but before coming here as 1 mole per liter it would have gone through so many rates so rate means already some conversion would have occurred whereas here there is only one rate and one conversion and one concentration so this rate is because the average of that is only one only one rate whereas here there are so many rates and then all of them giving me more conversion when compared to this because I have only one rate here and I have here theoretically how many rates you can put inside imagine infinite because that is the reason why at every cross section again we are thinking that we have infinite mixing that means each cross section now depends on one I mean sorry is equivalent to one tank so infinite number of tanks you can put there so that is why you have here more conversion for given volume and here you have less conversion for a given volume because the rate is only one that r a is small now but only one rate and that is the reason why you have you know larger volume for a given conversion larger volume for a given conversion or for given volume higher conversion right so that is what you have to remember I think you know this should go out now I think after this course definitely at least the basic definitions must be very clear in the mind right why plug flow is efficient what is the definition of plug flow what is definition of mixing I could have completed this long time back if I do not discuss much about you know simply saying that assume complete mixing but still you will have many many doubts in your mind that what is this perfect mixing and instantaneous reaction you feel there is no instantaneous reaction there is still an average rate right average rate due to various residence times inside the reactor whereas here I have all the residence times of all the molecules are exactly same here we are talking about outlet here it is also outlet only but outlet and inlet exactly same here right whatever is happening also reflect in this one if you have doubts you have to raise and ask me right okay so that is how it happens that P f r is definitely you know having more conversion for a given volume if someone is asking you in the interviews or in some examinations this question probably you know you have to definitely imagine that this residence time distribution that is coming into picture that is why by definition of plug flow we say that each individual molecule should spend exactly same time and there we can prove that that is not so in a mixed system where the residence times are varying from 0 to infinity right that means the molecules are packets which are spending 1 minute less conversion 2 minutes slightly more conversion 1,000 minutes 100% conversion but there is no use of that being inside because it is like it is already converted there is nothing will happen but still that is occupying some volume right so that is why to compensate that volume if you want to get the same conversion as plug flow what you do here you increase the total volume that is why for a given conversion the volume of plug flow will be smaller and the volume of the mixed plug flow will be larger because you want to compensate the rate lost due to residence times so see here every particle is spending exactly same means the conversion is same in each and every packet right so even if I take the average of that definitely I will have same conversion whereas here I have 100 packets I mean here also 100 packets but equal concentration here also 100 packets but starting from CA0 to CAF that I am again averaging right so that will definitely give me yes less conversion but what I am trying to do is I am now trying to provide more volume so that some more time all these packets will be on the average okay all these packets again are going to spend time so that is why that will compensate this conversion yeah higher conversion here by increasing the volume anyway even if you derive the equations and then able to calculate you will definitely see there are many graphs I think Levenspiel book has given that you know for given conversion what is the volume for first order reaction second order reaction third order reaction you will just go take 90 percent line and then read this side then you will know what is the ratio of volume of CSTR single CSTR and volume of PFR that ratios are given right so directly some people may give always in chemical engineering we use lot of dimension less numbers the volume of mixed flow by volume of plug flow also is a kind of dimension less number okay yeah and conversion is anyway dimension less number but it will be depending on again what is the order of reaction so you have one line for one order of reaction then you just read and then okay for first order so much difference second order so much difference okay so that is why one can also easily prove it so if you have still further any doubts about mixed flow and plug flow now I think we are going to stop that now right so please tell me please ask me please do not keep those cobwebs again okay how do you operate CSTR okay to see we are talking about only steady state system now but how do you come to that level where you have zero to infinite residence time under steady state condition so that means you can slowly fill up the entire empty take empty and then slowly fill up so level raises and then after that it comes out okay so then what is the concentration when it is about to come out because our steady state starts only at time t equal to zero yeah but I think you know we have to be specific here so means how slow you are talking 20 hours also we can down here 20 hours but we are talking about average residence time right yeah see very slow reaction means it may take more time for the reaction to happen and may be much more time the moment you want to go to 99 percent conversion see these are all vague things in our mind that is what exactly I am asking you know that cobwebs so why should I use a reflex in this reactor that is boiling of the reactor what should I do under what conditions yeah there is perfect mixing in the system when you are talking why should I boil and why why should I replace there are some the extent that doesn't take place in a normal temperature like what I mean we should also be clear there like what it has to be taken up to the boiling point of the mixture okay then body flux will come back we have to put a what for you are doing the question is that I have a liquid way the boiling point is only 60 example but the reaction is taking place may be around 100 degree centigrade okay it will not happen normally but you know you can conduct in gas phase problem comes when you have two reactants where once one boiling point is higher another boiling point is you know lower and if the reaction is somewhere above or in between then the low boiling point one will be boiling you have to keep the number of moles same that is why what you do is either you yeah either you put a condenser so that it evaporates immediately gets cool and then falls there but that is not the reaction problem okay it is only just it is only disting there and then falling there so then no question of taking out okay that is the easiest one otherwise you can also put a outside condenser and then again feedback under steady state conditions the number of moles will be kept same okay so that is only you are only trying to see that the concentration are not changing due to evaporation that is all you know that is only the physical thing it is not the actual reaction because if I allow that to go out then you will have one reactant yeah you lose one reactant right so that is why just close it perfectly otherwise you know I told you in our villages when they are cooking rice I told you know they put water just above and then cook because that is also same thing water should not get evaporated yes here will not change you know I think you have perfect mixing there and I close this okay here I have and then you have the outlet somewhere here right so put a condenser and again send it back that is only the engineering problem as a mechanical engineering problem where how do you put that whole where the vapor is escaping where it has to condense and it has to come down that is all okay and for that condenser again you should have some coolant entering coolant coming out and all that that is just only engineering problem it is not really CRI problem there CRI problem means that you should maintain number of moles yeah not uniformly the way it has to be in normal reactor so that is all but you know other than that there is nothing special in that kind of thing you know not only that there I think this question is good now because he is asking only reflex but I can extend this question to heat transfer if the reaction is highly exothermic right simply putting a external jacket may not give me that kind of area where I can control the temperature highly exothermic I want to control around may be 75 degrees but with providing only that jacket and also whatever is available you know coolant right still I may be getting around 90 what will do so people take out a stream there put an external heat exchanger again send it back that is one way other way is directly put the coils inside there are many ways or again inside also you have all the time instead of wall you have only coils these are all again mechanical engineering problems how do you remove the heat I mean heat if the area is not sufficient even for batch it is same it is not only for C S T even in batch reactor if only jacket is not providing sufficient area for removal then you have to go to various means various means of removing putting internal coils because sometimes internal coils you cannot put because they may be highly corrosive liquids okay so then you have to take out and then you know effective volume will be good effective volume will also decrease and mixing may not be proper because inside coils if you put near the coils again mixing these are all general engineering problem that is what exactly the difference between science and engineering a scientist will not bother about all these things you somehow remove the heat okay so that is what I have been telling you the difference between science engineering and technology technology is the one where it is ultimate telling you that use this temperature use these flow rates use this volume you will get this much product and this technology doesn't need any brain at all if you want to just copy one technology that is all that is why I don't know you may not anyone has worked in pharmaceuticals oh you work it now which pharmaceutical is that here yes okay good so earlier when when we were doing also our b-tech and m tech వారధిందింద్టి మారం పూడికెత్ కందేలిడికటారికిసందికంది. totally that was destroyed by the people who are working there inside. You know the employers, the, sorry, employees. What they did was, they just you know duplicated the technology, there was some software drags, this, I also took training at the time. In REC Varangal was one place where we had what is called chemical plant engineering, in BITEC. So one semester we have to go for industrial training. One semester, it is not in between the semesters where you have three weeks, four weeks like that. So one week, I mean one semester we were there in Hyderabad, some people went to fact Kerala FACT, FACT and some people went to Bombay, Noseal and because at that time our strength was only 30, now also maybe I do not know 30, 45 they increased, okay in REC Varangal I am telling, now NIT Varangal. So when we went there, at that time it was running okay. But after 10 years later when we saw, then in the news and all that, that entire company was totally destroyed. What happened was the people who are working there, they simply copied the technology because we know only temperature, pressure, what is the size of the vessel, simply duplicated, outside, very near to I D Pell only. You know that Balanagar area, I do not know what, you are familiar with thing? Yeah, there were many, many pharmaceutical companies that have come there. All of them, you know normally we have a partner called wife, so wife's name, that company because this fellow cannot start on his name. He is working still there, he is getting salary here but he is producing the same thing in some other unit and then he was trying to send it to other, not export but other companies where most of the pharmaceutical companies if they are producing headache tablet, they collect material here and there and then only mix and then tablet and then give it to you. Putting Navaljan name or Disprin name, okay. Now I do not know, now Chinese are dumping I think, lot of those things here, right. So but unfortunately what has happened, or fortunately we do not know, what has happened there was that if there is some problem there, they were not able to solve because they know only that temperature, that pressure, that volume of the vessel and that is all, that kind of studying. And many units have been closed may be after 5, 6, 7, 8 years because the product was not coming the way they expected, most of the time the colour is changing because you do not know how to control that. There are no fundamentals, that is what you know, technology state but even then few companies have survived because now they used, they started using their brain, that means they went to technology to engineering how to solve that colour removal for example. And then from there to science if it is required, right, that is one way. So technology, engineering and science, in the beginning itself you understand all the science in the lab with the help of chemists, right. And then try to find out under what conditions you will get very purest form of product when you do not get the colours, all that you understand and then start. And you know engineering principles are heat transfer and heat removal for example or heat addition or stirring or you know collecting the filtration, tabulating, all these are engineering applications, I mean engineering principles. So then finally Navaljan tablet will have this condition, this condition, this condition, this condition if you want to produce Navaljan that is what is technology because again you know I am just giving you, many people lifelong we may not remember what is the difference between or we may not know what is the difference between science, engineering and technology. This Saturday I was there in Guntur one college, RVR, JC college or so and because my friend is a vice chancellor now in Vigyan, we both did PhD here in IIT Madras, so one V0, Professor V0, so he was also there in Vigyan, Vignan University, he also just asked me just to come there because I had morning afternoon there was lecture, lecture is not for students but for faculty only, they are faculty, not chemical engineering, all faculty about research that is why I went there, what is research because there are many, they have 240 faculty members, out of that may be I think around 30 or 35 or may be around 30 have the PhDs, okay. You may think that so what, I think there are many people with PhDs who do not know anything still, okay but I think in academic institution that gradient must be as much as possible, gradient means PhD to B Tech teaching, now if you go to many private engineering colleges B Tech teaching to B Tech, okay he would have just finished it now finally here and would have got the result and immediately he is asked to teach again B Tech people may be third year, second year or whatever, so where is the gradient that delta C concentration gradient because I think this fellow is in equilibrium that fellow also may be how much time may be one year before or six months before, so that accumulation of knowledge is not that easy to do, so that is why I just went and told them that you know unless at least for your self-confidence even if you do not teach well that confidence you will have at least, okay I can teach if you do PhD and when you are doing PhD a good PhD make you think, that is all. So wonderful quotations are there, Arbindo told that no one can teach anyone, really no one can be taught, when you are listening to me that means your mind is already thinking about that, that is why you are listening, so but only thing is as a teacher I can only make you think, that is what all my classes last 15, 20 years, before that I do not remember what I have done, okay, first 5 years so, right, so that is why so many questions I raise even if you do not raise because those questions are supposed to make you think, that is all, why I was telling was that I asked the same question, in Vignan college I asked the same question what is the difference between science engineering and you know technology and I also asked them, I do not know whether I told you this particular thing, okay, in the last class, I mean in the beginning, I asked them I think there are chemical engineering students only I met in Vignan and I told them that you know you have written your examination that M-set entrance examination in Andhra, okay, they call M-set, still they call M-set or yeah, so that examination and your subjects were maths physics chemistry, correct no, only maths physics chemistry, then you join here in R-V-R J-C college in chemical engineering and do you know what is the degree you are getting, that is what I asked them, some people kept quiet, they do not even know poor fellows you know, nice, nice guys, they do not want to know what is the degree also, so some people said that sir we get technology, yeah that is what precisely I wanted to ask you, you started with basic sciences courses and then you passed them, then suddenly you came to R-V-R J-C and then depending on your rank and all that, then you are given chemical engineering, chemical engineering, okay, it is not chemical technology what they got and at the end of 4 years you are going to get chemical technology, have you any time thought what is the connection between these three, I tell the same thing everywhere, okay, did I ask this question, okay I also told you, yeah, so not even one could not and I saw there was some 6, 7 faculty and the faculty members, at least I observed some 3 that their face also has shrunk a little bit, that means they also do not know, that is not their fault, I am not finding any blame, okay, because I was interested in that so I first question myself, I also do not know when I first joined here what is the difference between science, engineering and technology, later I have to see many things because no book you find this, I tell you and some journal papers are you know about technology, you have to go to humanities journals and all that finding out what is the definition of technology, so when I am doing it only finally I thought that this is the logical explanation for and now I think many people say that you know this is the same thing what we are discussing, so that is why the technology is totally different but always you can start from technology to science or science to that is only left to you but there are some things where you cannot start with trial and error, for example aeroplane design, okay or racket design, these are all highly sophisticated, okay, they have to solve all the fluid mechanics equations, there are only two three forces, right buoyancy, lift and drag, that is all, you can make I think even 100 tons object to fly using only three forces but you should have the feel for that three forces, okay, then only you can solve that otherwise you caught and you do not have to worry drag, lift and what is the other one, buoyancy when you are designing a bullock cart, correct, no, in villages who is using computer to design bullock carts, no one, no, very happily they will do it, I think this is by experience, family, family wise it will come, one family in the village will be experts only in making bullock carts, so they know what is the size of the wheel but if you go to science again there is tremendous science and the science through technology those people have perfected and you know by wrongly designing the length wise and where you keep those, I am talking about bullock cart, where you keep those big wheels, why should there be first of all so big, there is beautiful theory in that and where in between you put, is it in between or somewhere slightly behind or slightly front, if you change wrongly the bull will die, then you have to pull it, okay, because you know its neck will be strained, that design also is there in that but by experience they got it, okay, so that is what is technology, for example brick I told you, another example, brick technology, try to make scientific bricks, then you have to go to materials, you know what is that, material science course what you have taken and you have to find out strength of this each grain and strength of multi grains, how do you put them, what should be the amount of mud, what should be the amount of you know the solids, what is the particle size, how do you orientation, what is the temperature to centre, all those things will, that is science, how many people are using that, still many houses are safe you know, I think many many houses are safe, so that is why I think all these things are also important but you have to think about this, you have to discuss in your mind, you know finally there also I told all faculty most important thing is they, for all of us is that, this brain, okay, unless you have that good brain you can never deliver either in teaching or even in research and 3 hours I have taken continuously, okay, they have not slept, I can see that, okay, they have not slept, I think in between jokes and all that were there so I think I thought they have enjoyed, that to when Saturday evening 3, 2, 2, 5, very difficult to, as I told them, very difficult to keep you here but still try, that is all, I think except some 4, 5 where they have to go, I think all, there are almost around 150 people, only 4, 5 people went after last half an hour, that is all, maybe they have some work there, okay anyway, so this is the one, that is why I was trying to encourage you to take you know, to think and then ask me questions, if you do not get that any doubt now, when you are preparing for the exam you will get definitely doubts, so at that time you can ask me, okay, yeah, good, so this is the one. Now once we understand this, here we have developed an equation, right, so that equation was V by F not equal to these things you have to remember, whoever it is, DXA by minus r A, now let us also derive an equation for this which is very, very, very simple, okay, so for this mixture flow reactor also when you are writing an equation, it is isothermal, so we have to write only mass balance equation and mass balance equation M B for A, this is M F for design equation, yeah, M B for A will be universal equation tells me it is input of A equal to output plus, yeah, plus reaction plus accumulation, okay and as I told you that we are steady state people, so that will be zero and the, this mass balance you can write mass means mass only, no K G, right, I have to write K G entered, K G leaving and all that, right, but we can also convert that into moles, but why do you do that in chemical engineering, particularly in reaction engineering, see the moment you go for distillation column, do you use moles, how many entering moles coming, what do you use there, okay, no, you are not, you are Bala, no, okay, input I am talking about, input distillation column, mass only, normally standard question is 100 K G Bala, right, okay, yeah, so like that only we do not use and for example heat transfer, you know these are simple things where you would have not thought I say, that is what only I am trying to give those connections, right and I think I also found in some interviews when I asked, okay why are you using moles in the reaction engineering and in heat transfer and mass transfer when you are using only you know the actual mass K G in terms of K Gs, I do not get answers easily and the same problem even in mechanical engineering when you go, even for chemical reaction they use mass, they also use combustion for combustion reactions, they simply write you know 12 K Gs of carbon reacting with the easy to relate, easiest one is 1 mole, 1 mole, 1 mole depending on the stoichiometry, otherwise 1 mole needs 2 moles to give 5 moles, otherwise you just now see that you know maybe 100 grams here, 100 K Gs here, another 500 K Gs here giving me 600 K Gs, mass cannot be produced suddenly anyway, so that balance, so that is why instead of that, this is what exactly what you have also done in your that batch reactor design problem, if you convert everything into moles that is easy, what you calculated you know that 769 divided by number of batches, no no, that 10, 10 tons divided by number of batches is only mass, but if you convert that into moles, then so many moles have been produced, acetic acid no, ethyl acetate, to produce that how many moles of acetic acid is required, I think acetic acid is the key component there, so many moles, but you can calculate maybe 6 moles, 6 moles, but this 6 moles equivalent to only 30 percent because your conversion is only 30 percent, so that is why you have to know compensate that, you have to take that divided by 0.3 will give you more number of moles that should be in the reactor, what you have assumed is 100 percent conversion, with the first time when you made that mistake, so that is why very simple balance only, that is the reason why all the time we will go for moles, that is why here also we will have moles per second because it is flow reactor, so and I know here our units f A naught is moles, volume is volumetric flow rate, meter cube per second, C A naught either you can use kg moles or gram moles per unit, for later and X n naught equal to 0 anyway that does not have any units, so here I will simply write f A 0 number of moles that are entering per unit time and output is f A, f very simple here, then reaction is minus R A into V, V is the total volume, earlier we have taken only, yeah only differential element, that is all what the volume, this is d V, why? Again I am telling you, yeah, so this is the distributed parameter system, that means there is distribution of concentration along the line, it is not one concentration, it is not lumped, lumped means everything together, right, so that is the reason why whenever you have changes within the system, either temperature or concentration because you know we are talking about either energy balance or mass balance or momentum balance, these three, right, so there you have to assume a small element and finally when you write input, output and then expand that with boundary conditions, you will get a differential equation, whereas in lumped parameters, that means everything together, there is no change at all here, you do not get a differential equation, you simply get an algebraic equation, so that is why here minus R A, change is only in this V, total V, there is no change, if I take a small element here what do you write, I cannot write anything because concentration is same, yeah, yeah, concentration is same throughout that element, R A is also same throughout that element, not only that element, entire system R A is same, so I cannot write anything, you know it changes, so that is the reason why you take the whole volume R V, anyway that is equal to zero, right, so this if I write this, this will be F A naught minus F A f equal to minus R A into V, so in our normal terms, you know in conversions if you are able to express this, what is the conversion equation we have given for flow system, F A naught minus F A by F A naught, F A f here is, otherwise I have to put X A f here, okay, good, anyway we will put that one here, so now yeah, this F A naught and F A f, if I convert this into F A f, this is general definition of X, right, so then what do I get here, this is equation 1, equation 2, equation 3, equation 4, then replacing equation 4 in 3, please write there, replacing equation 4 in 3, that will be F A naught X A f because we are talking about, this is general expression, okay, or if you are getting confused, but I think, no, not required, that should be general expression and you should be able to extend that, okay, yeah, so X A f equal to minus R A into V, right, so in this format when I want to compare, this will be V by F A naught equal to X A f by minus R A, so this is the equation what you get, this equation is, right, what is the difference between this equation and this equation, what does they tell you physically? yeah, within that integral you have that R A, so what does that mean? different rates, there are so many different rates, where you are having some kind of average of rates all right, whereas here there is no average, there is average but only one, okay, so that is why you will get here simple algebraic equation, there it is an integral expression because all these rates at various points I have also average and that comes through mathematics under that integral, so that is the reason why if I plot this integral, I mean this equation I will get here, yeah, 1 by minus R A versus X A you will get this and this is the area under the curve, this equal to V by F A naught, same thing I also draw here, this is also 1 by minus R A versus X A, I get exactly, you know, rate will not, 1 by R will not change, it is same right, for a given conversion same X A f, it is X A f, here also X A f, what volume I have to take now? Not area under the curve because there is no integral there, so I have to have this integral, sorry that rectangle area, okay, so then this entire thing now will be V by F A naught and you see this is the area in terms of volume, what you have to spend or what you have to provide more to compensate all that residence time distribution, that is why you know again I can tell you that, yeah, because this volume, this is the extra volume where why this is happening, this is happening because I have more and more, okay, more and more pockets, spending less and less time inside the reactor, so to compensate that I should have this much area more and why should I take rectangle, this is another question which I ask many students may not answer, why should I take, sorry, tell me Anupriya, no idea, yeah, who else can say for only, why should I take here rectangle, there of course area under the curve is that integral what you are talking, so many people may not know, Devayan you have the right hand side tells us X A if I am plotting 1 by minus R A to X A X into Y that will give you the rectangle yeah, I think you know most of us may not get that because this is 1 by minus R A just assume 1 by minus R A equal to Y okay, simply 1 by minus R A equal to Y now this is Y into X A F so Y is 1, X into Y area of a rectangle that is all, I think but many people do not know that, many people in my experience I talk to many students they are not able to answer that, why that is coming, because simply instead of writing Y we write 1 by minus R A so that is what we are doing, wonderful things in mathematics, because mathematics course is mathematics totally segregated, we do not know how to bring that information to our engineering, that is why we started talking mathematics of chemical engineering, so that once more can we combine I think d Y by d X you know how to solve, d Y by d X C as a function of some X and Y, but the moment I write d C A by d T, no idea d C A by d T also is a first time differential equation, is a function of some concentration, so then you do not know how to do that, so that is why I think those mathematics are taught only for you to make comfortable in these subjects wherever these mathematics come so that is why this is simply, I think follow know all of you see whenever I have a graph like this this is Y, this is X and this is Y, this is X so what is the area of this X and Y okay, so that is what we are doing, instead of writing 1 by Y we have written 1 by minus R A which is a parameter like Y, Y into X will give me the total area which is coming from this equation I have not done something else it is coming from this equation whereas here this will tell me from calculus that this is the area which I have taken a small strip calculate what is the area what is the area there it is delta X multiplied by Y, what is Y there again 1 by minus R A so Y d X and then Y not Y d X Y this is what is this where we are averaging all this in this equation so you will get the average rate definitely more than the average rate of this okay, you understood know this average rate is more than the average rate of this so that is why this is more more means you are dividing this volume will be less for a given conversion that always you have to tell okay so because it is minus R A is small there that is why when you are dividing with smaller number this volume will be larger good so now when you compare this equation and this equation where is tau coming there why do we worry about tau there in fact tau is not correct know by writing the natural material balance material balance means moles you automatically get only V why should I calculate tau and tau equal to again volume by volume volume rate another subroutine in the mind so many things I have to remember so simply that is why straight away go for V by F A not but why that tau has come can you just think why that tau would have come by 0 which is molar flow rate so V by V A not and I know also you can calculate or concentrations also you can calculate because these two are known volumetric flow rate also you can calculate but why why this another headache or you know in Tamil why this colovary what is that colovary only correct pronouns I am here 35 years but I do not know how to speak Tamil I understand so why that colovary it is not required can you think why that that should be what time of operation it is steady state no is a steady state reactor why do you need time do you need time for steady state steady state means once you start it goes to how many years if there is no problem correct now time will not come here if you are batch reactor then I have to tell time was in was in direct I am getting was in direct I am getting was in direct I am getting was in direct I am getting but why do I want to know that because I do not mean for producing that much conversion I need that much volume it is steady state reactor and volume let us say 2 meter cubed I got why do I want to know again time I am not saying whatever you are telling right or wrong I am just only making you think I cannot teach you anything so I am just making you think flow rate MBA first I think management market market survey that is one thing which you know before starting the calculations correct now you should know what is the capacity of the plant what do you do either you do market survey or you will hire MBA guy and then you fellow you go and get all the data how many times how much time we are going to get this much it is a steady state one why do you want to know how much time continuously it is coming once it is once it attained that conversion under great conditions where is the time coming there answer is very simple because unfortunately we started derivation batch reactor because batch reactor has T by C not equal to now whatever we studied in LKG only that is strongly printed here correct know you do not forget alpha beta when LKG so that but this is LKG for us batch reactor was the first so there it is in terms of time now we thought always we should have other reactors also in terms of time which is not required so this time this time is the batch time batch reaction time so because I have this T by C A not I would also like to write this equation as tau by C A not so that you know I do not have to remember that is all only for that reason otherwise if you want to really calculate volume of the reactor you do not need that expression is sufficient I mean it is not a great thing what I am trying to tell here but you know some things which are not useful not required for us right you understood know only for similarity because that is tau right this is T by C A not which we started our B take you know the first reactor so that is why now our mind goes okay now let me also write in that same term so that same format so that I will remember what is uniform format you can convert as tau by C A not and write for mixed flow that also you can convert as tau by C A not and write because V by F A not equal to tau by C A not you know how that comes where tau equal to tau is defined as volume by volumetric flow rate