 1.5? How are you able to manage different answers for the same question? All the data exactly same. So great I say, even science is not exact. We thought only, you know God is not exact because it can be described by anyone in any form, Ok. But science at least I thought we thought, you know, exactly one can define, right. Newton's law whether you do IET it is same it should not change so, but i think here our problem with the correct answer is 7 minutes. Period wise is 7 m cube it is anyway 2 m cube inhibition range for which we can get anenced blink. collapse with alipening okay check again so, i think that correct answer will be around that it is of course slightly complicated problem it is reversible reaction and also it is of course the other timing and all that you have to add. I think you will get the reaction time, how much reaction time you got by the way? Yeah I think around 5000 seconds is the correct answer, yeah around 5000, 4920, 4920 seconds, yeah still you manage so low value, if the reaction time is right, is only reaction time plus another 1800 you have to add, 5000 around 5000 is okay, yeah that may be I think when you are taking you know that other value slightly this way that way, yeah and then you have to add that 30 minutes means 1800 seconds or you can convert that into minutes and then add so then divide with total production rate number of batches and per batch that is all correct you know, how many number of batches, what do you mean by too much, around 13 batches, no no you have again the 30 minutes going and all that no, yeah so but I think that is the one 7 meter cube, around 7 meter cube you will get may be 6.9, 6.8 like that, try again but the reaction time is right, I do not know how you have calculated other things, okay reaction mixture density also is given, where do you go wrong? It is you know probably you would have gone wrong where you have C A not equal to, is not equal to C B not in this case, okay 0.74, 0.74 I got but anyway others I think others also you try I think many people I think I know only 10 people would have done, the remaining other people would be only watching, okay I think you also do and then let us discuss later, okay so I got around 7, may be wrong sometimes, okay around 7 meters, 7 meter cube, okay good yeah I think now come to the class, now present class, plug flow reactor, right we have been discussing about the concept of plug flow reactor and you know I asked you can you write two concepts in C R E, right that is one of the that is the last question in that 0th test, the first day when I give that test, okay there was no answer, this is one of the concepts, concept means something you imagine in your mind and then based on that you develop all the equations and now try to find out whether you have your original I mean assumption and the actual calculations whether both are same or not, if both are same then your concept is right, right so this is one of the concepts in chemical engineering and this is a beautiful concept plug flow why it is beautiful I will tell you a little bit later and we told that the basic definition of plug flow is tell, time spent by each and every molecule must be same, so then automatically you should have flat velocity profile, now I think you have a feel what is what do you mean by axial mixing, axial missing is pushing people in the queue backward and forward, okay like that even in reactors because of the turbulence and you should not confuse with the turbulence and mixing, the turbulence in pipe is very very limited in the sense that it is only velocity fluctuations where we take them as turbulence whereas mixing also told that there is turbulence but mixing is a big chaos, mixing occurs throughout the equipment whereas in the turbulence when you have a pipe and then when you are talking about pipe flow, okay very clearly we have to distinguish that because we have two extremes, one is mixture flow reactor other one is plug flow reactor, so in our plug flow reactor when there is a pipe and then through which the flow is going then the turbulence what we are talking is velocity fluctuations, now you can go and see macabre smith book or some other fluid mechanics book where they nicely show only small variations in the fluctuations of the velocity, that fluctuations are not allowed now for plug flow even that fluctuations are not allowed, right so that means molecules enter exactly like flat velocity profile without any fluctuations it will move and now the reaction depends on how far it has moved and you know the total length we are providing for the reaction to take place, you let us imagine that you have provided 30 seconds for 99 percent conversion example, right so around 10 seconds you will be in one third then the reaction I mean the conversion will be not exactly one third here it is not linear, okay conversion cannot be linear I mean depending on what kind of reaction you are talking so that is why here you will have some conversion then afterwards again you will have some conversion afterwards again you will have some conversion but when I look at the cross section you will have the same concentration at that cross section that is why we say we have infinite sorry yeah infinite mixing radially and all of you would have assumed you know definitely or yeah I think for your gate examination also you would have you would have prepared that infinite number of tanks giving you plug flow, okay really did you understand that concept mathematically you can prove it, okay but really has it gone to your blood when once it goes to blood only the concepts will be with you all the time, okay yeah what is our assumption in the assumption itself if you have that definition of infinite number of tanks giving you plug flow just in the assumption itself but we never go deeper into that assumption correct no so what is the assumption at any cross section you have infinite mixing when do you get infinite mixing when you have one perfect mixer, okay how many cross sections we have in this that is all that is why infinite number of tanks also when you calculate you know for 90 percent conversion plug flow is this much okay sorry for 90 percent conversion plug flow is okay for 90 percent conversion mixed flow reactor is giving some volume, right now you want to use number of tanks in series, okay you calculate for one tank volume for 90 percent conversion it will be much larger than plug flow then you take two tanks what will happen to the volume decreases okay to some that also we will do one example later then you take three further decreases you take ten it becomes very small when you go to infinity that will be equal volume size will be equivalent to almost zero where you are defining what is radial length yeah transverse direction radial length I mean that radial dimension see how simple it is I do not need any mathematics for that, okay this is a favorite I mean topic for many examiner also to be given prove that infinite number of tanks give you the plug flow equation you take first order and then write you know some equations and then try to prove it you do not have to prove it really if you of course mathematically there are still some people who will not believe words so that is why for them mathematics are required so then you go for mathematical proof and say that yes what I imagine and what I also mathematically proved both are same you see how simple it is to remember now very very simple to remember why infinite number of tanks should give you plug flow it is in the definition itself normally we do not think beyond assumption of flat velocity profile some more things if you a little bit you think a little bit more then it will be radial direction mixing equal to infinity and axial direction mixing equal to zero, okay so but I think I may give in the examination prove mathematically that infinite number of tanks will give you plug flow that is different okay that is mathematically examination but the concept wise very simple to do that because I am taking sufficient time because the entire reaction is reaction engineering is based on only two reactors out of that the second assumption you know that mixed flow assumption is very simple for easy imagination that is very simple whereas this one is not that simple like parity we repeat because my teacher repeated that it must be flat velocity profile I will also go and tell that it is flat velocity profile fortunate or unfortunately if you become teacher and then you also tell the same thing flat velocity profile so like that generations it goes as flat velocity profile without trying to understand what is the real concept why why this flat velocity profile should be for plug flow because idea is that each and every particle must spend exactly same time for that all these definitions are required flat velocity profile at axial mixing equal to zero radial mixing equal to infinity all these things are required right and then we also have other extreme g e devis is grandfather of chemical engineering okay another he is cousin he is cousin was this are the deal at him so that is why you have to do that I may know that is only your interest I told you there is no description of real pleasure in learning we cannot tell in words I told you know there are few things which you cannot tell in words yeah so that is why this joy of learning is totally different I mean you cannot express in words joy of learning and the moment you have that kind of learning in you you should not get arrogant but I think you will be happy with yourself others may not be happy that much but you yourself are very very happy if you know many things but that should not go to you into your head and then you should not be little others there is cold others and all that okay but still I think that gives you you know that is why I mean every god must be like that but we see you know this lot of movies and many movies are there in Krishna on Krishna okay I told you I am not particularly religious on anything I do not all are equal for me but example I am telling so he knows what is going to happen I mean at least in the books what is going to happen what has happened what is happening so that means he has got all the knowledge and you can see him how he will smile also very carefully you can see that you know that smile will not be laughing like me ha ha ha he will never Krishna will never okay because other people will laugh like that Duryodhana may laugh like that so like that you know every time you look at him you know you look at him as if he is very very pacified person very calm like that I think any any gods I mean at least we imagine gods yeah any gods history if you read all of them must be like that because all of them understood what is going to happen all the knowledge what they have okay we are only trying to draw some fraction of it one millionth of it one billionth of it from that source if you imagine I mean if you really truly believe God I believe in nature I think so that is why what we are learning is all from the nature and the entire research is only to crack nature just to find a small thing of what is happening how clouds are forming big problem I know big research problem how they move why that shapes they are not beautiful circles or beautiful triangle triangles or rectangles you know all different kinds of shape and you look at a cloud and then just imagine that it must be a beautiful girl it looks it looks like beautiful girl or again you know you look at that and then say that it might it must be a beautiful bird then it looks like a beautiful bird because by the way we always say beauty with girls we never say with boys you know the reason I think it is on this planet it is totally different human beings are totally different if you take any animal male is very beautiful only in humans rivers happen no really see peacock for example male peacock is very beautiful lion that male lion is really wonderful to see you know that the magnanimity and that kind of you know that the moment you look at that oh my god lion but if you see again female lion you do not feel that every day you may be seeing you know any animal which cannot see without the aid of light in the night they will happily sleep after 6 o clock the moment dark comes but that is the only time you start working and we are also same on this planet the life is same life cannot be different because all these species have come on this planet there are some I think 90 percent of the species daytime sunlight only they take food and then they do not do any job anyway they search for the food throughout and once they have sufficient food then they want to propagate their own species and then that is all I think male female will join and then they simply propagate their species that is all you are chosen on this planet only to propagate your species if you allow the humans I think you know they will really pollute very fast okay so that is why I think all other restrictions are there in China only one child and India it may come off child or something like that sometime because we are crossing China okay so but I think you know naturally they will control on their own in other species right I do not know whether you heard the name Aries Rutherford Rutherford Rutherford Aries okay as anyone read his book you read that I will give you noble price if you really understand that okay really I think you know very very complicated he has written same Levenspiel information in terms of mathematics but if you understand these concepts and go to Rutherford I mean Aries book wonderfully you understand but his mathematical knowledge is fantastic I think even for conversion he uses the term Xi where it for most of us we do not even know how to write this I see like this that is Xi Xi is the conversion for him we write simply XA like this what do you call that Xi you know it is not epsilon epsilon is only this epsilon does not have tail Zeta is again different it goes like this you know they also have that capital form and also they also have small form okay yeah so they have I think you know this is Xi so that kind of complicated but I think he is very stable very good and he writes poetry poetry comes when your mind is stable please remember that anyway so coming back to that that is why I told you know all these started because of the pleasure in learning that you have to test the moment you test yourself you cannot come back we will say that you have that nectar no amruth yeah this will taste much more than amruth this this passion for knowledge once you start enjoying the happiness of learning really I am telling you you just try that I don't know if even one price I think I will be very very happy so that is why you know our time is limited during our education right so we will have only in the school you will learn something but you don't understand okay when the university you learn also but with understanding you have to do that then we when that understanding comes automatically fantastic really very very happy so for that only thing is you have to read read read and then try to understand that's all if you are not able to understand ask friends ask people ask teachers all that and you should not feel bad that you know to ask anyone if you don't know something if I don't know how to add to at 2 plus 2 equal to 4 that means really I don't know that so that means why should I feel bad I can happily go and ask that's why each in each each and every individual is different my learning capacity is different so you would have understood 2 plus 2 equal to 4 I would have not but because I should not compare with you and then go and say that no no no I think I can't ask because people will laugh at me and all that you should not because each individual is different who will say that okay after 1st class you should remember this after 2nd class you should remember that after chemical engineering you should remember that or mechanical you should remember that these are all our own limitations what we put but brain will not accept that that depends on only your capacity of learning so for that and also one beautiful thing with brain is anytime you can learn I think even a person about to die 90 years if he is interested in chemical engineering he can still come and start with what is chemical engineering and all questions and then you can learn brain accepts that it's not that beyond certain time you cannot learn so that is the beauty with brain that is beauty with nature anytime you want to learn you can learn not only we any species otherwise you do not survive if that learning capacity is not there learning capacity doesn't mean that getting degrees yeah learning capacity is you know trying to observe with the nature and also go along with the nature and try to escape nature if there is like for example there is a tsunami or there may be explosions or there may be what is the law and all that comes you know well knows yeah all this because all species are all the moment they see lot of lightning and also thunder right yeah so that's why I mean that's also a learning no no no I don't want to learn I will just stay there even if thunder comes means you will be charred that's all you will become carbon element 12 with see yeah I don't know periodic table what is position okay anyway so okay I will give you one more concept here to remember so that you know you will not forget what is plug flow definitely most of you would have done the resonance time distribution okay so now we say that each and every particle should spend exactly same time okay so now if if I introduce here some color so that I will also see how this color is spreading throughout the reactor plug flow reactor so what I do is I have you know various various ways of putting this color one way is just imagine I have a tube 4 inches tube and then I take a disc disc of color disc we only remember our CD discs I am not talking about the hot disc okay hot disc has got another meaning okay CD type very small thickness red colored one this is white color this is water which is flowing and suddenly I would like to introduce that red disc inside this which is totally soluble it is soluble it is not hot disc that is what I was telling you okay so then and I know that the total time is 10 seconds how this disc moves inside the disc it is you know water is continuously flowing by some it is only imagine the experiment by some imagination I will just assume that okay the disc suddenly entered into the cross section exactly fitting there exactly fitting there it is uniform cross section even though I have written slightly bulked here bulked there I think you know it is exactly same cross section how does that move moves as not able to imagine able to imagine know because this is water flowing just imagine that small thickness of that flow has become suddenly red how does that move yeah Sushmita you are telling something moves like what exactly as a disc because that is the reason why when you have this equivalent to your direct delta function okay that is what is called pulse input pulse input suddenly introduce the pulse and then observe at the end how how do we get this pulse right so even at 50 percent of the time if you look at the midway then exactly you will see that red disc and here it comes that is why we normally show that the pulse enters like this and then comes out exactly not reversed but same thing this is what is direct delta function this is what I also asked another question in for ideal reactors plug flow and zero test yeah plug flow and mixture flow what is the ET this is the concentration we are talking but a concentration can be converted into more useful function called exitage distribution function okay why useful I think we will discuss when you come to RTD why that is useful why we should define like that but this is simple concentration now pulse input sorry this pulse input we discussed now let us say that I have step input step input is water is entering continuously right the color of water we know then I will also have another stream of red fluid red okay so then a time t equal to zero I will switch off this there is a wall here and there is another wall connected the moment I switch off this wall another wall will open exactly same flow same flow no disturbances not allowed disturbances not in reality you will have not no disturbances allowed then I will allow these red fluid to enter and then come out what do you see at the end after time equal to 10 seconds you see only red fluid that is step input you know you have the step entering here something like this and also coming out exactly yeah something like that exactly like that so RTD also is very easy know for imagination once you have this but in reality what happens in reality when I have this you know we are talking about turbulence turbulence in pipes so that means turbulence in pipes is small fluctuations over the velocities so then what will happen to this disc when you have small fluctuations over this velocities like what how does that because you have uniform concentration in this disc right so it is a yes uniformity yeah it is center center of what center of the pipe at center of the disc there is no pipe here I think pipe it is just yeah if I look that okay I think let me draw this you know this is the disc I am introducing it should be it should be in fact infinitesimally thin but if I write infinitesimally thin you cannot see so that is why I am drawing it a little bit thickness okay so imagination is this one yeah this is the disc which I have just entered right and this is uniform concentration throughout when it is moving there is velocity fluctuations over this around this right so how does that spread somewhere here somewhere here how does that spread see there what happens is the concentrations at this point at this point because this side water this side water correct know imagine somewhere inside here this side water have this side water water we have but now it is moving with the velocity fluctuations so from here to here when it comes then the concentration here is less and concentration here also is less so you will have like this concentration no this is concentration I am plotting this is the concentration okay this is the concentration and this is the distance this is the thickness of the thing now that pulse is slightly getting widened yeah so at this point it may go like this that is what is residence time that how you see this is concentration only what we are talking if I now see this is time at this end if I see so that means the the molecules which are here the front portion when it is moving those things will come first and then later at the centre and later at the back so that is the disturbance what we have there that is the spread in residence time so I also gave you some example that you know when you have this kind of fluctuations and if the average time is 10 seconds some molecules may come in 8 seconds itself because of the fluctuations I think I do not know whether I gave you this example when you are talking about that Tirupati Q okay so when you are about to see the God I think maybe you are just entering that main temple main portion so then when someone pushes you you are very happy because you will just go and jump before the God okay that means he is able to see at least maybe few seconds before then the person who is just in his line okay he was in that line but because of the forward backward movement someone pushed him so he felt forward so that is for him that that is exit I am telling that is why so then that means he will come slightly earlier so that is why the molecules here if I have 10 seconds mean residence time some will come in 8 seconds or 9 seconds and someone will come in 11 or 12 seconds but that is small disturbance that is small disturbance and in plug flow you will have only small disturbances because your velocity fluctuations are not large if you have infinity velocity fluctuations excellent mixed flow reactor why a molecule here is about to leave okay then because of infinite fluctuations you have there may be one fluctuation which will suddenly take this one here okay it cannot go out anyway because continuously it is pushed all the material so then again suddenly it may be pushed somewhere here okay so if you have that infinite fluctuations that is mixing what you are telling so then you will have throughout the reactor you have the same concentration that is the other extreme that is the other extreme okay that is all how simple it is to remember these concepts you know but entire reaction engineering is based on this again I am repeating that is why I am spending so much time because you should not forget no one words at least that is all very simple and the residence time distribution wise also you will have very small distributions when you have plug flow when mixed flow comes I will tell you how much distributions you will have there very small distributions only normally that is why that distributions to take care of these small distributions we use what is called axial dispersion model axial dispersion model actually this is the correct model for you know when you assume plug flow the correct model is axial dispersion model because definitely there will be some dispersion you can never avoid that okay you can only avoid if you are using infinite velocities if you need if you are putting infinite velocities then across the entire universe you will have the length of the pipe correct velocity equal to infinity so whatever length you put 0 0 time only you can provide I am exaggerating okay so so that is why the correct model for any any plug flow model is ideal plug flow model is the correct one real realistic model is only axial dispersion model but we take that and then we will first derive the equations ideal plug flow to see what kind of equations we get and how far we can deviate from that unit processes by Sriv every day you are using his book Sriv was the person who has really pushed unit operation unit processes name after looking at unit operations name we also should have for reactors you know all chemical processes are imagined as unit process that is why the name of the book also beautiful book what is that book that is the book you know straight away like Levenspiel used chemical reaction engineering after that Gragins used unit processes in organic synthesis all reactions you know nitration alkylation tell some more ester esterification it's not organic organic process alkylation yeah okay I mean all that yeah all that they are sony nitration binge not binge in alkylation there are so many things all those processes have been divided into unit processes okay and for chemical reaction engineering who has put this name for plug flow and mixed flow at least just guess someone told Levenspiel but is not not Levenspiel Levenspiel beautifully used all these concepts denby kg yeah kg not grams kgs kg denby he is the person I think you know the name is given to him that he was the person who has given his writings are fantastic he is from UK I think he was in Cambridge Cambridge University or Cambridge only I think but wonderful really the way he writes he won't use much mathematics but he will tell all beautiful things about the subject in terms of words only conceptually is excellent chemical equilibrium name of the book this book book may be I think 500 pages around that chemical equilibrium wonderful book again I think you know you know thermodynamics is most of the time abstract and then nice concepts nice words only we have to use so that is why this book is called one of the Bibles for thermodynamics for chemical engineering so that is why denby books wonderful book even if you don't understand read it ten times if you understand you will automatically ten times if you read automatically you will understand but you will not have time to read ten times because all of us only are focusing okay tomorrow exam today night preparation over that is the problem with all of us you know our education system is like that okay that is chemical equilibrium is one book another book is chemical reactor theory and introduction very simple introduction that is another name another book chemical reactor theory in fact this course chemical reactor theory was named after that book it is coming for a long time almost 20 to 25 years this course chemical reactor theory okay last 30 years I think this course this course is there in 18 madras and that course is named only after that book came small book you can read like a novel not much mathematics but wonderful explanations even for plug flow also you will not mention directly time as the basic definition of plug flow but you will give two assumptions and then say that one assumption automatically requires this condition the time of each and every particle is exactly same like flat velocity profile that is one assumption one point he gives so that one point flat velocity profile should automatically will satisfy only when all particles are exactly spending same time okay