 please take this plug flow assumption you write plug flow assumption this I have taken from dinby book the original person in his own words we will write that and then you know you can just I think whatever you have discussed it is here but nothing like you know you have a para on that so that anytime you can refer, okay plug flow assumptions one over any cross section normal to the fluid motion over any cross section normal to the fluid motion the mass flow rate the mass flow rate and the fluid properties in the bracket fluid properties in the bracket pressure, temperature and composition pressure, temperature and composition close the bracket or uniform or uniform per two there is negligible there is negligible diffusion relative to the bulk flow good right next para that is point one and point two next para is under assumption one the residence time of all the fluid elements in the reactor is same and all these fluid elements pass through the same sequence of pressure temperature and concentration changes, okay right next para under assumption two the molecules of reactants and products do not diffuse from one element to another element of fluid, okay then write another para the above two restrictions allow the conversion in each element same what is assumption one in your normal terminology what is assumption one is it flat velocity profile any proposition infinite mixing in the radial direction is assumption one because you are having pressure temperature and composition same at any cross section no so that means you have infinite mixing in the that is what our assumption is most of the time we will tell that what is second assumption actually mixing equal to zero, okay so under assumption two what I try to tell was that first assume that all particles have uniform residence time then the other two automatically come he has given the other way he first defined those two then said that under assumption one all residence times must be same, okay under assumption two there is no diffusion that means there is no actual mixing on that but actual mixing only radial mixing must be there otherwise you know you do not get uniform concentration and temperature very good yeah so now I will just give you one exercise very simple exercise for you to do and then keep in your notebooks and when I ask separate test probably you have to derive this so for unsteady state plug flow reactor minus dow f by dow v equal to minus r a plus dow c a by dow t that is equation which you have to derive, okay that means you have to write the material balance it is only isothermal condition, okay so what is entering what is leaving what is accumulation what is reaction all four terms, right earlier we have taken only yeah all three except accumulation now you have to also put accumulation and then you will get dow c a by dow t but you have to write clearly what is the element you have taken what is entering in the element leaving in the element accumulating in the element reacting in the element put all four cancel out whatever is there and arrange that equation in that format, okay good now we will go for mixed flow reactor, okay so this name mixed flow reactor leaven sphere uses very widely so that is why we also use that but there are also other names for this, okay mixed flow reactor you should have heard of CSTR, yeah back mixed reactor so this is CSTR what is the meaning of CSTR, okay so what is the difference between this and then batch reactor where you are also continuously stirring that is also a reactor that is also a tank, okay so how do we know that because for batch reactor also it is same continuous stirred tank reactor there is continuous stirring correct no and it is a tank reactor it is a tank and reactor so yeah so what we have to remember here is that continuous with respect to what so they are right there continuous flow stirred tank reactor they have put f here CSTR continuous flow stirred tank reactor to specify but I think you know so many words we do not have patience to use so that is why we say CSTR that continuous is with respect to yes good so I think other reactor also BMR back mixed reactor continuous stirred tank is straight forward that is what is happening flow is continuous there is stirring it is a tank and it is a reactor so continuous stirred tank reactor good then why what do you call it as back mixed reactor you see all these things you have to think you should have asked 2 years 4 years back no no I think 3rd year only it comes no B Tech 3rd year only reaction engineering you should have asked the teacher in that class sir why are you for example this C C refers to what is it a continuous stirring or continuous flow continuous stirring means it is equivalent to batch reactor they are also continuous stirring here also continuous stirring so BMR means if you would have told BMR then you could have asked what is this BMR back mixed what do you mean back mixed so that means it is mixing back okay I think this name has also come from the 2 origins okay one is that with respect to plug flow reactor itself axial mixing is also called back mixing correct no it is going forward again coming back going forward again coming back okay so that means you know that is what some kind of back mixing is happening but that is limited to only small axial direction but small region right but in CSTR when you say back mixing the yeah let me also draw now the figure normally what we draw for CSTR okay so this is the one we will show that it is continuously entering continuously leaving and if it is non isothermal reactor you will also put okay so here may be anywhere you can introduce so I will introduce here coolant in entering coolant leaving that is the coolant okay so here you will have same thing FA0, V0, CA0, XA0 so here you have FAF, CAF, VF, XAF okay so we are talking about back mixing so the idea here is that you are continuously feeding this you know reactants and then they come they mix here and then some of these molecules which are which have just entered because of mixing some of them may about to leave so this is the outlet about to leave but when they are about to leave because of mixing because mixing means chaos okay the definition of mixing is that any particle yeah will stay in the reactor and the probability of okay the probability of leaving a molecule okay the probability is same for all the molecules when they are about to leave the probability I think it is a confusing definition mixing okay so you know some of these things we do not have real meanings like I told you again love okay mixing we say mixing we say perfect mixing what do you mean by perfect mixing when do you say that you have perfect mixing yeah when do you say that you have complete mixing she is saying when I say perfect mixing complete mixing okay so now tell me when do you say you have complete mixing what level see every concentration may be at what level we are talking huh the desired level of homogeneity yeah what is that level homogeneity how do you define again really because you should think all this no see you know even if you do not have perfect mixing also some molecules you will collide with some molecule okay so that is why how can you expect that one molecule collide all molecules my god it is a kabadi kabadi versus you know thousand people versus one guy they will pull him out I say so one molecule we cannot know yeah see the the the definition there is probability for this molecule is maximum when it is colliding with any other molecule you know that is what the probability of this molecule colliding with any other molecule not all molecules so any other molecule means what are what are you trying to say that molecule may be here or here or here or here or here or here the colliding molecule may be coming here okay so the probability of that molecule colliding any molecule is same like that for every molecule the probability is same any one molecule you take so the probability of that molecule colliding with any molecule inside the system is same, right and we are talking about the homogeneity when you said homogeneity you know homogeneity at molecular level that is the real definition what is the size of molecule you cannot even measure you cannot you cannot see it and you need very very sophisticated instrumentation to look at the particular molecule now we have beautiful instruments, okay so that is what is the definition of perfect mixing and back mixing is that molecule which is about to leave because of that chaos again it may be brought back even to the feed that is what is back mixing the fellow who is about to go out okay like you know you joined 4 years back for B Tech and then you now about to leave okay in the final year you are now asked again to go and join 1st year 1st year 1st semester 1st class okay that can happen in perfect mixing okay that is why in all academic system that 4 years if every one of you pass what is the system you describe P f r plug flow all of you really all of you are spending exactly same time 4 years all of you join on 1 day all of you leave on the convocation day over exactly in between what you do is not matter does not matter but you know the leaving entry and leaving is exactly same that is what is plug flow but in reality what kind of flow you expect axial mixing why some people may take 6 years some people may take 4 years only because you do not have that system but in IIT our system credit system theoretically one can go in 3 and a half years also because it is electives you know core cores are compulsory for everyone and if you allow them now I think we put a maximum of 6 courses here right if you allow them if you are very good you can take even 8 courses in a semester so that means you are able to complete some more courses before others so you can go earlier I think that in USA many universities they have that credit system there it is axial dispersion the average time is 4 right so some people may go in 3 and a half years okay 3 years may be 2 I mean ambitious but I think 3 and a half years they may go then some people may go we do not know that time infinite time also they take because that means they never got the degree that is what it happens so that means it has got long tail we say correct no time the infinite also still is not coming out so you still in the we take classes so that is why that back mixing is that example where you have completed almost everything and now you are brought back and then put again first year so that is what happens in the mixing when the molecule is about to leave it can back mix with the molecules which are just entering that is what that is the meaning no when you are asked to sit down in again first year you are now joining the molecules which you have which have just now entered those students would have just then joined you are also joining them that is what is the meaning of back mixing you see how much meaning is there in each and everything I mean as students you have to start questioning I say even now we can start questioning you should make the teachers life hell really if all of you are asking questions my god we will become very sharp I say really we will become very sharp I know those those people who hands off then we cannot do anything with them you ask and I will say something and then we will go we will forget but many people are not like that when a student ask it is also a challenge to the faculty member to learn if he does not know immediately and to request others to explain and also he will learn and come and teach you so that he is also learning that is why teachers are lifelong learners you will stop if you go for job but we never stop learning really so but I think you can aid them to learn more with your questions any question and there is no stupid question only there is stupid answer okay question is not at all stupid anytime I tell you because I told you know simply okay how many noses a person has human being has okay it is not a stupid question because you have never seen a human being so you do not know whether there is one nose or ten noses okay or legs how many legs a human being has you would have never seen a person like there is a horse in you know that author movie right yeah that horse what is the specialty of that horse unicorn I do not think it breathes with nose it breathes something here I think there are some two holes here I think if I remember correctly yeah so some change okay so that kind of horse okay where is the nose for that horse means you cannot tell because nose is here I mean that is what I remember vaguely now I do not remember whether it is but here these flaps will move up and down that is what I have seen here some flaps are there so that is why I am just giving an example that you know the question you should not be afraid in asking any question so at the maximum what will happen if you ask a wrong question there is no wrong question I am telling but in the in the in the heads of your own classmates okay so you may be afraid that you know if I ask this question my classmates will laugh at me so when someone laughs what will happen nothing will happen only his teeth will be seen correct no you see who is your laugh and the teeth I can see it is very difficult to laugh without showing the teeth though how can you laugh I say try it is very difficult to laugh without yeah so what will happen maximum some white material will come more more light is reflected the room will become more brighter that is all so nothing will happen to you okay nothing will really happen that is why I encourage you to ask any question in the moment you have any doubt any doubt I tell you but you are not doing that I think every class I tell but I think because they are not asking then I will ask the questions and I will also answer the question so that is what is happening in most of the classes I think you should do that okay good so in the perfect mixing you know that simplest assumption is that we have perfect mixing now the question is how do you define perfect mixing so we are trying to say that this mixing is at molecular level if at molecular level if you can see the homogeneity homogeneity means you take a small amount and then see all the molecules are uniformly present there and you take in another corner another small lump and then see again there you will also get the same composition like any other place in the reactor okay it is very simple to just only keep in your mind that is the meaning of perfect mixing okay good so now we can also tell something connected with this what is called residence time distribution by the way what is the residence time distribution plug flow reactor residence time distribution the moment we say distribution our minds 50 percent will be closed distribution I am simply asking what is the residence time distribution in plug flow so then what do you say straight line is not distribution I am just asking what is the residence time distribution in words you can tell okay so then what do you say residence time distribution is 0 same you cannot say distribution is not same distribution means there is a distribution you know 10 seconds means exactly everything is 10 seconds what is the distribution distribution means you should have 5 6 7 8 9 10 11 12 13 14 15 that is the distribution like you have here distribution of ages all of you are not exactly 21 correct no all of you if you have exactly 21 in this world also this group has plug flow that means 21 years back exactly your bond if the date of birth also is same for all the people but in this room we have distribution from almost 21 to 65 because I am also in this room I say I cannot eliminate myself okay yeah you see that is the distribution one guy with 65 years and many people with 20 there are some people with 30 years there are some people you know maybe external registration people would have been around 32 33 and I do not expect 50 40 like that generally so I think you know it goes peak around 30 35 I am not 35 around 30 or maybe 28 and then long tail this fellow here 65 okay that is the distribution okay so that kind of distribution is 0 for P of r so that is why sometimes we also ask tell me a reactor where R T D equal to 0 P of r okay now we see this because of this thing what is happening to R T D here residence time distribution oh R T D means I think this is R T D we use residence time distribution that means when you look at the outlet how the particles are coming whether some particles are coming slightly earlier if the mean residence time is 10 minutes in this case or some particles are coming so 20 minutes 30 minutes or all the particles are coming at 10 minutes only okay if you say that all particles are coming only exactly at 10th minute then I have the plug flow that that all that over 4 classes we have taken now we are talking about mixture flow in this case how the molecules come out because molecules are very easy very difficult to imagine so now let us imagine that these molecules are you know group together some packets of molecules and now it is a continuous reactor and I am now imagining that I have these packets continuously entering and also these packets are continuously leaving just for the sake now okay just imagine that these packets are continuously entering continuously leaving okay good then we can also imagine afterwards molecules then when the let us focus on some 100 molecules these are R 100 packets and at time T equal to 0 it is continuously feeding continuously coming out right so at one time I would like to find out what is happening to these 100 packets now I just imagine you know jadu you know magic so through magic I will say that let these 100 particles will be red color so all of them will be suddenly red right now I will try to follow that red color here according to perfect mixing definition all these 100 there are many others also many other packets these 100 packets only I am concentrating these 100 packets will be uniformly distributed throughout instantaneously because that is the meaning of perfect mixing okay so then when you have that immediately uniformly distributed when they are distributing because of mixing only they are distributing one packet may come here and that may suddenly come out right there may be another packet which may go to this corner but still it is mixing well but it is not able to come but it is moving here moving here moving here moving here there that can happen because of again mixing yeah mixing right so that is why you have the molecules moving inside but some of them will very quickly come out and some of them may not come out for long time that means you have the residence time distribution if I choose that 100 100 packets one packet will come in one second another packet may come in 5 seconds another packet may come in 50 seconds okay the mean mean residence time is let us say 100 seconds for easy imagination right and some other packets may come thousand seconds after thousand seconds so that means if I plot that concentration of particles because you know concentration means that more moles per unit volume okay if I am able to plot that then what kind of graph you get good okay so now before that we can also these are the packets with red color and all that now imagine that I have water so that I can ask you how to plot that graph concentration versus time okay so I have water and continuously water is entering water is going out then what I did here is that I took my pen that is red color I have okay so that red color one maybe 10 drops or one drop suddenly I added I have a small reactor you know maybe 50 ml yeah jar okay the baker so continuously I am putting water continuously water is coming out so in this there is stirring good stirring then at one point of time I just put my ink red ink one drop what will happen it is a perfect mixture what will happen to this ink instantaneously completely mixed okay so then onwards how the color changes inside the reactor or at the outlet just before adding what is the color colorless okay at time t equal to 0 I have added that color so my time t equal to 0 will start here this is concentration okay right at time t this is 0 at time t equal to 0 I added the previously it is only white instantaneously it is distributed mixed very well so then what is the definition of perfect mixing other extension of perfect mixing also is when you have this assumption the contents inside and also contents in the outlet both are must be same right the moment you mix it this color also will immediately reflect in the outlet okay yeah this is where I am measuring now that concentration in the outlet not somewhere inside in the outlet so now tell me how the concentration whether the concentration increases or decreases first of all concentration why why it should decrease yeah Abdul has another idea concentration decreases or increases there are only two options but Abdul says it is increasing yeah why it is increasing and decreasing yeah when more and more what is there more and more it is diluted why I mean at time when it will be high after one second why one second I think Sushmita will say two seconds can you contradict her then I will say five seconds why do you choose one second we can shoot even zero because instantaneously so yeah it is only at zero at the time you have the maximum concentration because you are not adding concentration later you are voting you are adding the concentration only at time t equal to zero onwards you are stopping the one drop I have added that is all what is continuously flowing at that time it is uniformly mixed so instead of drop if I say I added 10 grams of color 10 grams weight wise what is the concentration if I have one liter one liter reactor I have 10 gram per liter that is the maximum okay then continuously what is entering under this will also going out yeah it continuously decreases okay continuously decreasing means you can draw that lines in infinite number of ways correct no there is no unique way of decreasing I can draw like this like this like this like this I can draw like this like this like this oh no no increasing so like this anyway no no increase so that is why all that is not valid for mixed flow in mixed flow it is only valid mathematical also we can show that if it is exponentially decreasing so this one and then exponentially decreasing exponential okay simple right exponential exponential okay right okay good now I know that at time t equal to zero I have the maximum concentration in our example it may be 10 grams per liter okay that at that instant afterwards it may be nine eight six seven like that go on not six seven six five four two three till what time it will come why infinity yeah until all the particles come out that is a logical answer but what is the time taken for all the particles to come out why you do not know yeah it depends on actually what is the system you are using for measurement of that concentration if the color if you are not able to see beyond certain concentration eyesight okay that means it does not mean that everything has come still there may be one or two molecules where you cannot see the color but still it comes out so that is why we say theoretically it is infinity so that means now what is the residence time distribution zero to yeah that is what zero to mathematically we can put no when with perfect mixing you will get a differential equation where you have exponential e power minus one by e t okay so e power minus t by t bar it will come right that we can prove I mean when r t comes it comes but I think why I am telling this now at this point of time is that we have a system where residence time distribution equal to zero you have another system where residence time distribution equal to zero to infinity as far as reaction is concerned which system you think more efficient for a given volume more efficient means more conversion example I gave adding this color and all that which we say trace and all that so that example I gave to show that there is residence time distribution in mixed flow whereas there is no residence time distribution in plug flow how did we prove there there is no residence time distribution there you added one disc in the pipe correct no color disc without any disturbance to this disc exactly it comes out at the end after yeah whatever time you provide 10 seconds or whatever so that means if there is a distribution that disc should have spread like this same things or why do you say that one drop can I put this you know disc here you can also put that disc there you know I show just just arrow here but actually only if I have one arrow no fluid can enter correct no it should be a pipe so that pipe is something like this right so in this pipe now I will suddenly introduce my disc correct no I can do that then that comes here I will count my time t equal to zero when it comes here and assumption is this fellow is not dispersed in the in that pipe it is still maintaining as exactly disc only when it comes here so here I have the disc the moment it touches you know it enters there what will happen to this disc pieces into pieces what is the piece size molecule molecule because it is perfect mixing we are assuming right so that way it is now made into pieces into pieces and now one piece it will throw out very quickly out of the reactor so that may be somewhere here okay because concentration you are calling that piece weight divided by volume of the reactor so may be one gram would have come you know not one gram all that ideal mixing that will be maximum ten ten eight nine you know that will slowly decrease but in an exponential way you know if I say ten eight nine and all sorry ten nine eight seven it is not linear again time I am not telling at what time it is coming so that is why yeah so this timings are all of them will fall on this exponentially and okay that that disc is into I mean destroyed into pieces and pieces and then that will also come exponential way whereas the same disc there in a plug flow without any disturbance it will come exactly same time I think without any same time means yeah exactly same time the entire disc will come so that will be t equal to may be ten seconds if you t bar equal to ten seconds if you take at the end of ten seconds right here I told you for comparison sake volume of the plug flow reactor volume of back mix reactor both are same one later one later so volumetric flow rate is same what is t bar in these two t bar is defined as or t bar or tau the constant density system you are talking volume by volumetric flow rate okay yeah I think aria this is I do not know whether you could get this this is a meter cube divided by meter cubed per second okay so meter cubed meter cubed will get cancelled then you will get seconds that is why this time is taken as volume by volumetric flow even though there is a derivation actually for that also there is a derivation in r t d I think I can show you that okay that is why we call this one t bar as volume by volumetric flow rate right yeah based on volumetric flow rate what do you mean by hydraulic residence I said constant density system okay so t bar right even even in volume expansion how do you define that tau even if it is mixture flow even if it is plug flow even if there is change in the moles right still we define tau based on initial volume there both are entering same at the same temperature same pressure so that is why tau will not change t bar will change actual flow okay that will come when we are talking about later okay good so this is what is t bar see t bar is same in both here right so here t bar this is going to 0 to infinity right infinity I cannot show that is why I think I just only draw something there so my t bar will be somewhere here t bar equal to tau so that means you see now if I take this is the average residence time so now beyond average residence time also there is there are molecules coming till infinity right now I asked you the question that what will happen during reaction path you know I asked you a question know that given the same volume okay so where do you get more conversion I said efficiency more conversion plug flow you said why because in terms of residence time distribution you can beautifully explain that that is why I am asking this question residence time distribution initially where is conversion very high you see all these cobs you have to remove totally right because I tell you see here we have written XIF right what is XIF inside the reactor same thing and is it same thing throughout the reactor yes because it is mixture flow then where is the more conversion or less conversion here it is only one conversion steady state conversion even CIF is same this we are talking about isothermal okay yeah I have to write here isothermal yeah isothermal right so that is why temperature is same throughout anyway good yeah so that is why why do you say that for in a in a mixture flow you will have you said less conversion or or you are not of the opinion to have less conversion because many students will think that mixing is good for reaction it is not good for reaction why mixing always dilutes the concentrations when you have dilution of concentration except negative order reactions and we do not find them many in the nature so negative order means okay first order if I take negative order minus 1 minus r i equal to k by c a you put zero concentration you get infinite rate excellent how do you maintain zero concentration yeah I mean theoretically that is very good no but negative order reactions you do not see in nature okay this is greater than zero only zero plus okay so that is why I mean most of the things but in under some conditions you get also negative order but that negative order comes only when you have the you know you asked also question how can Watson models right how can Watson models I also asked a question what is the information you get from how can and Watson models how can and Watson models will give you only rate expression for heterogeneous catalytic reactions so under certain conditions of that complicated equation when you are simplifying terms when you are removing terms some terms how are you removing some terms when I have 100 may be partial pressure of a and 1 partial pressure of b and the denominator again you may have another 20 partial pressure of c so like that when you have this one we can remove some people may remove even 10 because okay it is okay I mean it is not when I put 90 the 10 also I can remove so when you are simplifying under some conditions you will get some constant divided by yeah partial pressure or concentration of some component that becomes negative we do not have many so that is why we only have positive orders greater than zero then under those conditions you will have definitely a mixture flow reactor giving low conversions because now you come to packets one packet has come here immediately you added that 100 packets continuously you are adding so one packet has come here very quickly what is the conversion in that packet very quickly instantaneously it came out very less so that means are we using that concentration are we using that concentration we are not able to right so quickly it comes out so that means in that there is no conversion and I may have another particle coming the meanest time is only 10 minutes let us say and the particle is coming the packet is coming after 100 minutes what will be the conversion there okay 100 percent but after 100 percent is converted what is this fellow doing inside you know it is waste no see it is a dead space in fact there that fellow has to come out and fresh fellow has to come for the reaction to take place what you see here is instantaneous mixing and when I look at this reactor I will see the concentration you know the packets which have stayed 1 second 2 seconds 5 seconds 100 seconds 200 seconds imagine packets no okay so now that means in in the packet where 1 minute back it entered conversion may be only 1 percent the packet which has entered 100 minutes back because it may be there still because still infinity it has to come the conversion is 100 percent the average of that now remove the packets and then just imagine molecules so what you see is the average composition of all these packets and these pockets are there because of mixing with various times different times what you see at the outlet is which you cannot see with naked eye is a composition average of all these packets with different times you look at the reactor you will have again 0 to infinite distribution why that is the definition of perfect mixing I measured here 0 to infinity but even if I look at inside because this is true reflection of inside inside also I will find out packets with 0 to infinite residence time distribution so then in the particle which has entered just 1 minute back conversion may be 10 percent in another 150 percent another 140 percent another 160 percent average of all that is coming here that is what what you see on the other hand one second as you will come on the other hand you have the plug flow in plug flow okay all these yeah all these packets again 100 I just introduced all these packets are coming absolutely we are not allowing any actual mixing or any you know disturbance all of them will be coming here what is the conversion of all the packets here if you define 100 percent that is 100 percent conversion or if it is 90 percent the I mean it is 90 percent conversion in each and every packet so now I break all the packets and then mix them it is same whereas here if I break them and then see I have 20 percent 30 percent 50 percent 40 percent 100 percent average of that is definitely smaller than this now doubt this itself is ideal residence time distribution because we are mixing ideal perfect mixing perfect mixing an ideal reactor not assuming we can mathematically prove we are not assuming here mathematically we can prove precise it is exponential decay that is why we said packets because one molecule you cannot say conversion so there should be a group of molecules that is why we are saying it is conversion right yeah this is number of them as 100 and when we let us after some time let us check the outlet if we packet our 1 comes then 2 comes then 3 comes then 4 comes it is not possible no no no see when it is not possible we do not have to discuss that no when it is not possible because you know here I collect let us say small amount of liquid right so now when I look into that if my packets are able to identify if when I am identifying I will see packet with 1 minute residence time 2 minutes 5 minutes 6 minutes 100 minutes all that now 100 minutes 100 percent conversion 5 minutes 1 40 percent conversion another 60 percent conversion all that average only I am seeing at the outlet no no you are imagining that these packets are coming one is coming first afterwards another one is coming afterwards no when I take a sample of you know some amount of liquid in that liquid itself I will see all my packets with different ages and average of that you know and now different ages means different conversions all those conversions I then mix them and then see that that is what what you are seeing when you are measuring it at molecular level okay so then what you see here is a low conversion because you are now mixing the packets with 100 percent conversion that means zero concentration zero concentration of reactant okay with with 1 minute packet where the concentration is you know if I have 10 moles per litre that may be 9 moles per litre that means 1 percent conversion sorry 10 percent conversion right so these things I am mixing right Abdul what I see at any time here is a mosaic of all residence times theoretically speaking zero to infinite residence time and when I have these packets with zero to infinite residence time the conversions or concentrations in each packet is different I am now putting all of them together and then trying to get an average concentration that concentration will be differently yeah I mean if you are talking about product it is more than the concentration of concentration of product okay conversion is let us take that conversion is definitely less than the conversion in plug flow that is the reason why without even equations we can say that why the concentration or the conversion in a plug flow reactor is higher than conversion in a mixing flow what you have to remember is that it is not instantaneous reaction when the continuously when you are putting some fresh reactant that goes here it is already having some concentration CAF outside because of perfect mixing and the CAF also is coming because of average of all those packets you are talking about steady state that means steady state has reached somewhere already earlier we are talking about steady state only if it is unsteady state then we have to also see how concentration one can find out that is not a problem okay we are talking about steady state where CAF is already established here by the combination of packets with different concentrations right so then when this is continuously entering when and that distribution of packets because you know no accumulation there some one liter is entering let us say in one second in that one second this one liter is coming out in this one liter if I see I have zero to infinite residence time distribution so in that various conversions various concentrations so the average concentrations will be less same thing here plug flow I have here one liter entering one liter coming out so when I take one liter here when I see it and then because of our ideal definition that one liter only exactly comes here so what is the conversion in that one liter a one liter contains 100 packets exactly same now I am mixing them I destroyed them and then mixing in terms of molecules what is the concentration there or conversion there exactly same so you are not diluting whereas in that case it is diluting please remember I think Merit also was asking me sir it is instantaneous reaction in mixed flow no okay that average you are perfectly mixing but that perfect mixing creates zero to infinite residence time distribution which comes at the outlet and by definition outlet equal to outlet conditions must reflect inside the reactor the distribution here also exactly zero to 100 percent I am sorry zero to infinite distribution so then the conversion here and conversion here is exactly same Pooja you are asking some quick question doubt very good now how can it be equal to inside cf because one packet is coming out so it have a distribution okay 10 percent 20 percent 30 percent and one packet is residing in that container for more time period so it have 30 percent 40 percent so there is difference in shape in outside and outside no what is the definition I think you have to do this experiment in your room you have taps there inside no maybe I think you have the bathroom taps you know take a glass okay allow the water to flow into the you know tap water into that and then you know let it overflow you call Danya or someone and then ask take a pencil stirring okay then add one drop of ink right just see whether you are getting same color inside and same color outside when it is overflowing yeah so then why do you say that cf is different here cf is different here it is exactly that is what is perfect mixing definition no the combination of all that because of mixing that zero to infinite residence term distribution which gives you some average concentration that is reflecting here because this this is a continuous reactor where whatever is coming here it has to overflow it has come out right so whatever is happening you will have immediately coming out because of perfect mixing you just imagine you have the tank and then you know glass tank where you have a very high stirring I think if you go to our lab I think maybe Nagarajan or Rahul will show you we have a star tank there you know in that RTD experiment you put one drop of ink and then show them I think you know beautifully you can understand that the moment you put that one drop of ink if you allow good mixing there the same concentration is reflected in the overflow pipe outlet okay then onwards the color is decreasing in the tank and also the color is decreasing in the outlet that is why this concentration decreasing continuously okay so beautifully we can imagine it is not a problem at all for us