 Okay, yah, this is what what we have been discussing and I think you have to again forcefully come to the class, that means you know till now this particular non-azothermal reactor you could have deleted before the examination. Right, so again anyway you do not reload, so that is why, I think again I have tell you what we have done and as far as graphical design is concerned, what we have generated was xa verses t this is one way of easy way of doing you know the graphical design because I have three parameters x, t and r the way whatever way I want I can plot it right I can also plot here r verses t I can also plot here t verses x I mean t verses x is there are the r verses t and r verses x okay all these things possible the other one will be constant but easiest way to use this graphical method is by plotting x verses t that is most convenient way you can also do the other way you know like eating you can also eat food like this right you can also do like this like this like this and then also eat I mean otherwise you too you can try to eat also with leg so all possibilities are there so that is the reason why what is the simplest way as engineers this is the simplest way and you also seen that if we have irreversible reactions what kind of graph you get yeah what is this this is r values r equal to 1, 10, 100, 1000 like that right and we have also shown graphs for reversible exothermic reaction and also reversible endothermic reaction right those graphs also we have plotted this is x A verses t okay so this is what this is irreversible yeah what Abdul this is exothermic endothermic this is endothermic and the other one is again x A verses t like this yeah I mean actually these are the peaks and this is exothermic these are the graphs and as far as design is concerned we have to now find out temperature as a function of x A or vice versa ahh I think it is spoiling okay this is x A as a function of temperature this you get from E B I hope you remember E B E B is energy balance not electricity board or something because I think most of the time you may be you may be remembering daily things but here it is energy balance okay good so this is yeah so now this can be any shape you know that means it need not be straight line it can be any shape okay that functionality so you may have curve so when the curve is drawn like this then you have to see the corresponding points and then list out x verses r A where they intersect now you have a field x t r A right if I take okay so now if I take some way of drawing okay my line is something like this that means conversion is ahh temperature is decreasing as conversion is increasing correct correct no this is t not and conversion is increasing but temperature is decreasing where is it possible is it possible at all Swami endothermic irreversible reaction okay good so now I can take these points like this point at this point I have temperature this is the temperature conversion and r next point again I have conversion temperature and r okay again like that so when I take all these values like ahh x A temperature temperature r and 1 by minus r okay r A also we can write 1 by minus r good right I think ahh ahh x A I have written there so now this one yeah if I plot x verses these two that is normal way how do we plot when you want to get the volume okay or given conversion you can also get volume or given volume you can also get conversion that is how our equations are that is what what we have plotted 1 by minus r A verses x A then area under the curve will give you yeah the volume okay so now when I plot this particular graph what kind of thing I can get yeah that day I gave you really crazy thing like this like this it went up and down and all that so now I do not want to give that kind of crazy thing but now this one so what do I get now how what kind of graph I will get simple analytically because here approximate values are given there what kind of 1 minus r A x A graph I get yeah like what Abdul switch it off then tell thinking what means seriously thinking yeah now tell me what kind of graph I get ahh like this yeah he says like this is it right we are plotting 1 by minus r A yeah merit says straight like this sir okay what else all kinds of shapes you can tell them what is the correct shape I am asking okay yeah why so much time see this is where you have to use your brain I say this is where I am very happy to tell you all the time use your brain you should have that kind of imagination in your brain otherwise I tell you you cannot do anything you cannot do anything Gopi decreasing from where it decreases tell me how it decreases yeah from where here here here so he is decreasing like this or like this how it is decreasing oh my god yeah so Ram krishna comes see why do not you approximately put those values and then see I say you support Abdullah it is not election I say you support I support Abdul I support Swami I support Arya what is this decreases how it increases normal rates yeah normal is it goes like this okay yeah I think you know that imagination is very much required unfortunately in your schools you have never used brain afterwards I am probably you may not even know that there is a brain called a thing called brain because everything is told there no you have to do this you have to do this you have to do this per day at 10 kg books and I think 20 kgs homework and out of that 19 kg is done by your mother and 1 kg by your father over that is all I think some marks they will give and then you pass and come here you know that really that imagination is very very important and it is not difficult even now you can try that see all the brains are not that bad you know they are definitely trainable okay we have not lost hope yet so that is the reason why now at least you start thinking I have been telling you know instead of sitting and then seeing google 4 of you or 5 of you can sit in your room and then okay now Abdul can ask Maharshan Khar you plot concentration profiles in distillation column yeah why not or you know counter current heat exchanger okay temperature profile okay and how many crystallizer the concentration gradient within the cake what is this useless thing you go and click google and that fellow will give 0.3 seconds 1.5 billion you know topics what you do with that so instead of that I think you can ask that okay now I have a plug flow reactor exothermic reaction plot what plot conversion temperature along the length wonderful but you are not doing that I think you know just plotting is is not that easy you have to imagine a lot first of all you should know what is a plug flow reactor and you also should know what is you know conversion in that and you also should know whether it is exothermic or endothermic so much thinking is required for plotting those values I mean plotting those graphs and you try that you will do very well in your life later I tell you that imagination that is why I appreciate movie people tremendous innovation and tremendous imagination is the only there in movies arts and music in engineering no imagination all those imaginations have gone long time back absolutely we are training I say you know how many people are getting b-tech degrees in India now 7 lakhs or so per year what all of them are doing I say without any imagination and all that what do they do what do they do supports TCS that is true TCS they may go but I think all 7 lakhs cannot go to TCS I think some more people can go you know this is what is happening there is your imagination at least after coming here are going to higher studies okay b-tech forget over and time is irreversible you cannot go back and get that so that is why at least now the present time use it more usefully effectively so that you will be happy with yourself I say finally you are not making me happy okay you will be happy with yourself if you do very well in any subject and that comes only through imagination imagination for everything this imagination is required okay I told you know sometime back mental screen that mental screen should be very very sharp okay so that means the moment you close your eyes if I tell you okay I think same example I gave you okay Bombay what do you remember India get get off India India get a get away of India okay that is what Gopi has seen so that is what he remembers right I think anyone Harishankar what you remember you did not go to Bombay okay you need not go but still you can see some pictures Karinakapur or someone your favorite I don't know you know that is also Bombay know okay yeah movies also that is what what you remember most of the time very easily so but that that means still your mental screen is screen is working the moment you are able to imagine some favorite actors for some favorite actor all that so otherwise you know if mental screen is not I mean active you cannot see them also you are able to see you know some people some people your favorite people okay now which city you have seen what do you what do you remember out of all the places you remember railway station anyway that is his mind so it you know that image is fixed there so I think he knows railway station so like that all of us have that image so similarly the moment I say plug flow reactor that should be in your mind that screen that should flash yes plug flow reactor really it is correct I think you know if it is if I say that tanks in series number of tanks inside this all that should flash in your mind then only you can draw that otherwise it is not that easy and those things must be in the mind I thought I will do lots of things but I like this I am wasting my time you know all the time to tell you to make that brain active but is the brain dead I say all the time I think you know I am not able to make that brain active huh Swami what should we do injections are no injection also you need imagination you know what kind of injection how do you put it so I think so many people how can I inject all that in my mind I am telling so I have to imagine all that so that is why imagination is very very important so this is one of the simplest things so what I thought I will ask you know for continuity sake but I think you know you took a lot of my time now okay so now this is x i f if it is volume to be fine so now this area will give me v by f a not okay so what you are indirectly doing is by doing this is that you are solving material and energy balance equations that is all what you have done correct no this graphical design at this point I have a solution for you know this rate right and corresponding temperature and corresponding conversion that is what what we are doing instead of solving them on the paper we are now solving them on the pay on the still on the paper only but graphically you are doing that right so that is why even though this is easy to imagine this line need not be linear it can be any shape and procedure is same whatever intersections you have to you know the line goes through then those intersections that x values r values t values you have to have and then in fact I can also because it is okay by the by it is which reactor I have not told you any reactor here so now you have all the information for plug flow even this one I if I ask you what is the temperature profile and conversion profile can you plot there from the same data you can concentration versus temperature and all that you know conversion temperature along the length right all that information is there on that that is why this graphical design is a beautiful design okay good so this is one part this is what what we have done now let me tell you the adiabatic design adiabatic design also we have done adiabatic design means there is no heat yeah in or eat out right okay that q equal to 0 so only thing is we will have a nice insulation so that you know the heat will not escape and then we are trying to find out what is the relationship between temperature and conversion and we did it for mixed flow reactor to easily understand that what is the relationship you got for adiabatic system adiabatic reactors for adiabatic reactors for all three reactors I think that I will prove later but all three reactors you will get the similar equation t equal to t0 beta xa where beta equal to C A not del h area by rho C P right C P is the specific heat okay good so this is the kind of equation you get and in fact this is what also I have drawn and a general graph is available for us this again very nice information if I plot if I plot xa versus temperature okay so I will draw the lines and then ask you what is the meaning of all these lines okay I may get one line like this or I may get these are all adiabatic lines okay what is that central line called excellent isothermal line okay so this is isothermal yeah then left is endothermic excellent left is endothermic yeah the other one is exothermic all these three good right so now this also gives you a lot of information for example you know sometimes when you have a highly exothermic reaction and you want to limit that temperature increase you know what do you do sometimes and what are the various ways what we can do and it is not external thing I am asking now it is not external cooling without external cooling also to some extent we can control the temperature what do you do question is clear or just something I am asking yeah question is that I have an exothermic reaction and I do not have any means of removing heat or adding heat okay here removing heat exothermic reaction now but still I can reduce the temperature to some extent by some other means various possibilities are there yeah recycle is one thing but recycle I think other than recycle in fact recycle is what Sahu is telling exactly same thing okay it is now adding almost like innards correct no because product once it is already formed and it is not again nothing is happening it is not again going to reactants it is it is not reversible reaction okay so that is why either recycle reactor or most of the time we also use inert gases particularly for gas phase reaction where catalytic reaction particularly and the catalyst is very sensitive to temperatures so you would not you would not like to anywhere in the reactor reach high temperatures and if they reach high temperatures then the catalyst will be spoiled so that is why deliberately you add like nitrogen okay so that means how this how this line moves by the addition of innards so that means yeah what is becoming I think assuming that I have added lots of innards in which direction it moves Abdul think I say yeah not this side no it has to go this side because idea of adding innards is to reduce the temperature or to make almost isothermal so that is why by adding innards you can bring it here this is adding innards okay so like that all possibilities are there I think you know this is a very nice graph how do you get is just by material just by energy balance only this is the equation now depending on your slope negative or positive then you will have either this side or this side right and last time you know you are getting confused at all that so for that exothermic reaction and endothermic reaction for endothermic reaction E1 is both are positive only E1 and E2 there are 2 E1 is yes please make a note of that E1 greater than E2 endo and E1 less than E2 exo okay and always delta HR defined as E1 minus E2 the other day I think you are trying to say so many things right so that is what I think that also let me write delta HR is written as E1 minus E2 depending on this and sometimes you know the convention is minus delta HR equal to a positive quantity is exothermic our convention the way we write the data okay good so this is the one which is very nice information now taking these things if I have an endothermic reaction adiabatic system okay or an exothermic reaction how do you actually design the reactor so this already this is what this is in fact is endothermic irreversible is there already endothermic reaction okay if it is exothermic reaction and reversible for example so then what do I do reversible exothermic reaction reversible exothermic reaction and I have an adiabatic reactor okay yeah first of all we have to go to this one is reversible exothermic reaction good yeah so reversible exothermic this is endothermic already we have given reversible exothermic okay so let me draw those lines this is x t versus xa so then we will have like this then yeah so those are the rate lines and this is r equal to 0 equilibrium line this is what I have asked that 0 at the test also is yeah so this is r equal to 1 may be 10 say etc okay tell me now what what what I have to do here what is the procedure adiabatic reactor I just want to design adiabatic reactors yeah t0 t0 I know t0 is somewhere here straight line means like this this one okay I have done straight line so what is the meaning of that exothermic adiabatic is it straight line vertical oh my god I think you have here I say you have just here exothermic endothermic I have not even removed this okay but you deleted this graph from your brain and you are not even able to see this when it is there I am very clearly telling that reversible exothermic reaction for all exothermic reactions temperature should increase with yeah with conversion right with conversion temperature should increase so I have to draw a line something like this okay can I touch this line imagine imagine no idea what is no idea sitting and just think I say when what is that r r equal to last line 0 line yeah if I go to 0 line what will happen to me why I can't go it is a reversible reaction but in design what will happen now okay what is the precision now okay assuming that I have drawn this line oh my god okay yeah there is a new line now okay so this is the line now now what is the procedure what is the procedure yeah again I have to find out now for each yeah there are many like this right so yeah I should now list out as as shown here x t and then rate and then take 1 by minus r a and then finally plot 1 by minus r a verses x a okay so is there any limit for me or I can take this value this value this value this value this value there are no other values further otherwise I also could have yeah I cannot draw this I cannot draw beyond that I cannot even touch it the moment you touch what will happen you go to infinity okay if you go to infinity you cannot come back that's all I think you know that is infinity okay so that is the reason why somewhere we have to stop that is a wonderful point I want to tell you okay somewhere you have to stop where actually no this line goes through many many interesting points many things we can discuss here okay now this is the highest rate this is the lowest rate this is 0 okay so now when you are moving like this what is happening it is first seeing anyway this side also you will have like this right so at this point it is cutting like this and then next and then next and then how it is going now yeah in fact if I move this line for easy explanation okay from here if I draw the line it is first going through because here is not that easy to explain because the way I have drawn but now when I draw this line here okay let me draw with the reading yeah so t not normally we will have low temperatures no okay to start with whatever possible reaction temperature we will have then it is now crossing the rates lower rates is it logical not logical why not logical why logical at lower temperatures the rate will be less so that is why you start with lower rates and now there are two things now concentration as well as temperature both it is exothermic reaction so then what happens concentration falls a little bit but temperature increases because of exothermic nature area following exothermic that means heat is released and that heat increases the temperature of the bulk fluid right the fluid which is moving so then you will have increase in temperature this temperature increases now rate of reaction correct no minus r equal to k e4 minus e by RT into CA right temperature increases rate of reaction even though concentration is a little bit less but the functionality of this temperature is exponential whereas that is only first order or second order okay CA or CA square right normally CA cubed maximum otherwise you cannot go beyond that right so then temperature yeah okay that heat again increases the temperature now this temperature you have some rate sorry some concentration now concentration is falling a little bit but temperature is trying to compensate so like that this combination of initially small temperature and high concentration after sometime both concentration concentration decreasing anyway the combination of concentration and temperature may reach the highest rate and then afterwards what is happening even though the temperature is high concentration is falling okay so you will not have again more rate of reaction temperature is there but concentration is not there for reaction to take place that is why this line goes through all that history initially you have some low rates then slowly the rates are increasing and may be this is the highest rate for this line this one this one is the highest rate for this line and afterwards it is now going to this is low rate this is low rate this is low rate the other side it is crossing for the lower rates okay so now initially increase reached maximum and then going to again lower rates and then finally touches zero that means if you are using that zero value for design you cannot design because now tell me if I plot x a verses 1 by minus r a verses x a if I plot what kind of line I get that plot this is the imagination I say imagination imagination I think my explanation you could follow no Swami initially when reactants are introduced at time t equal to 0 t0 is not very high t0 is not very high concentration is high reaction is taking place right so when reaction is taking place heat is released because it is exothermic heat okay so that heat increases the temperature even though concentration falls here little bit now the combination of this temperature and concentration rate will be more so similarly you go on you know temperature increases and concentration falls here little bit but that combination is still more rate more rate it reaches a maximum so beyond some point that concentration falls so much right so then you will not have high rate then it has to go to in fact lower rates and that highest rate line is okay blue highest rate line is this you know this maximum that is the highest rate okay you have all the rates but these are the highest points in fact this is the locus of maximum rates that you have to cross so once you cross once you are here it is increasing once you cross this you are decreasing I mean the rates are decreasing so now tell me if I plot 1 by minus r a versus x a what kind of graph I get like autocatalytic you shape you get okay so now is it a mixed flow reactor or a plug flow reactor no no no I am not talking about this this line it cannot be combination what do you mean it is plug flow reactor what we have discussed all this is for plug flow reactor right in plug flow reactor only when it enters you have a position where temperature and concentration okay gives a rate yeah change then afterwards another position another position another position okay how many positions you have in mixed flow there are no position straight away you have to go to one point but that will be on this line same line but at one point that point corresponding to what conversion you are trying to find I mean I am not trying to find you are fixing to find out the volume anyway that will come a little bit later so now what area I have to take conversion is one yeah yeah but that is true that is why that you shape that is why simply parabola okay so this is yeah now what area I have to take are you convinced that this is a plug flow reactor why because this line traces each and every position where there is a concentration and temperature in a plug flow reactor yeah both along the length of the reactor actually you can now get more and more Gopi more and more visualization what is happening in a plug flow reactor so at every cross section you have we say that different rates and all that now we are also adding temperatures and what you are showing here is the average of all the trades so now yeah this is the final conversion which I have fixed so what is the area I have to get that is all area under the curve so it must be something like this yeah this is V by F and R okay so now exothermic reaction we have discussed and also endothermic reaction we have discussed okay for plug flow even recycle also it is very easy now for me right so recycle means I will have here only it is not starting from X equal to 0 it is only starting from X equal to some value how do I find at that value you have an equation for recycle reactor X A 1 equal to you should know recycle ratio definitely so that recycle ratio R R R you can substitute and then X AF is given because you are now trying to find out volume that means X AF you know right so you can know X A 1 and from that point this line is valid from that point to X AF value right now one thing what you have you can notice in this graph is that if you start with high temperatures T0 if T0 is high is it advantage or disadvantage rate will be high okay yeah then that is immediately seen but when you move along is it advantage or disadvantage why disadvantage yeah so the conversion which you can attain is only this much that means only this much so maybe 40 percent whereas if I go here and then draw the line advantages or disadvantage yeah why it takes time I think it is not taking time it is take volume because now here I am in the presence of very very small rates not high rates so naturally 1 by R will be very large correct no so then I will have large volume of reactor so that is why this is a beautiful optimization program where you will start is it 1 reactor or is it 10 reactors how do you really use this information to design the most optimal reactor you see how much information on that simple innocent looking graph it is looking really innocent no but you should know what is innocent first of all okay yeah so so much information on that okay now let me ask you a question about mixed flow reactor I have the same thing mixed flow let me draw separately again this is reversible PFR okay all right if I have mixed flow MFR yeah so this is no not like this yeah is almost constantly this is XA this is T then I have like this like this yeah because I need only one point where because mixed flow there is no positional change okay right at the moment it enters you will have only one concentration one temperature or one conversion and which is equivalent to XA so how do I now calculate my volume for this and don't immediately conclude here someone was telling that recycle reactor we have not drawn this for recycle reactor we have only drawn for adiabatic PFR we are talking about all adiabatic okay right because you saw the shape and then you try to put one reactor another reactor you will never get that right in this case because it is the rate information which we got after imagining that we have plug flow reactor then only I will get this line and it is starting from here to here going through all kinds of rates initially low afterwards again low in between high so that is why you get that shape because I think autocatalytic reaction probably you liked so much anything you see that shape autocatalytic reaction and immediately draw first PFR first MFR and next PFR do not do that okay so all these histories as come only because of this particular line okay good now mixed flow quickly I thought of doing so many things how do how do I draw here my line so that I will get the volume again here like V by F A not I had also find out V by F A so Smitha what is known to us conversion yeah okay so now now tell me excellent you have to first draw the straight line okay good then now I draw this straight line then yeah T not excellent I know T not is here now what we should do how do you look at that point straighter straight means like this again we are discussing about this is what first of all which reaction exothermic or endothermic exothermic yeah so that means that line so I know this flow I have to plot simply with that slope that line so now how do I calculate volume so actually yeah you know even though I draw this line but I do not have this point this point this point this point here I have only one point because it is mixed flow so now show me how do I calculate now volume yeah what I have to plot here this is 1 by minus r A versus yeah how do I get it very simple now this is X I F for me right right because X I F is fixed point 8 for example so that is the line I have here point 8 then this one this this line this line is cutting this line at this point so if r equal to 1 there 1 by minus r A equal to also 1 that is the point which I have to locate and then simply simply multiply what merit set is 110 percent right simply locate that minus r A 1 by minus r A multiplied by X I F because that is nothing but rectangle area correct no this is 1 by minus r A that is what is the point okay r A and 1 by minus r A this is X I F point simply do that so this is how we will design our reactors using graphs what are we anything no but which line cuts how do I know which are cuts which point this point how do I know unless I plot this how do I know oh after that yeah that is fine after that this graph you are talking that is fine that is no problem but I am thrilled with graphical design I dog grabs one okay yeah so that is why this is the yeah this is this is again V by F enough okay so now you can see that we have this one design blindly saying that okay I will just go T 0 I know and also I will I know the slope slope is nothing but you know the properties of CNR and Rho CP delta HR and all that so I know the slope I draw the line and if it is plug flow I will know the history of all the rates I will note down all the rates and 1 by minus r A versus X A graph I will give me the volume if it is mixed flow only one point I will locate and then get all these but most of the time if you want to because always we have we will try to optimize in our life whether it is a reactor or your own life I think we optimize okay so now one question what we can ask is that this T 0 which you have chosen or someone given is it really good one so if it is not that means what is meant by good one for that T 0 volume should be minimum volume should be minimum can I locate that with the same information can I locate that so again I will draw this graph here so this is X A versus T reversible exothermic okay the endothermic and all that we will discuss later and you have okay I will also now simply drawing this line where this is this is r equal to 0 equilibrium line and this one is locus of maximum rates max okay so that line I have and of course in between I have all this you know for example this will go like this next one will go like this somewhere here will go not much like this so all the lines are here they won't cross these don't take that so that is what I have now how do I locate I think maybe it is difficult for you to tell this particular part and even now what I know is conversion right we are only trying to find out volume and reverse problem is simply finding out conversion if volume is known so now I know conversion so then I will just draw the line okay and now what I have to do I have to know locate my T not so what I do is I randomly choose okay one line here another line here another line this is T not 1, T not 2, T not 3 etc but there are parallel lines because Delta H R is constant and C P and all that is not changing with temperature so what I do now is I will do the same exercise for all those lines I will take all the rates which are intersecting corresponding conversions then I will have a graph like this I know one V by F A not right now I will come here again do the same thing now I will have another V by F A not and then I will go here and then do the same thing again so I will have this trial and error basis which will give me the minimum area or the volume minimum area understood know so that means probably this will be the correct one right and all the time you get for reversible exothermic reaction this kind of parabola type curve so this area so this is 1 by minus area versus X A so you will get like this so the area V by F A not minimum out of all three possibilities minimum out of all three T nots all three all three T nots okay so actually with the experience you can really start either here or here or here you can automatically start that okay because first of all you have to fix the conversion right we know that definitely if I go this side volume will be minimum why rate is high but your conversion will be only 10 percent so that is why draw the line first conversion line okay okay then you choose T not values and then draw the lines right so then you will find out the minimum V by F A not minimum for this for this for this which one is the minimum then that is the correct T not so that means you can even fix now T not okay yeah and normally this cannot give you T not because okay will you here as per this graph is concerned what kind of graph you get for this possibility would you get this kind of graph yeah because you have not crossed the maximum that means you are only increasing rates the other side decreasing has not come okay so I think you know definitely the T not may not be valid so by trial and error one can fix this okay I mean as you are asking something forgotten because now I also asked a question how do I find out now optimal T not optimal T not which gives me minimum value so that is why again I started PFR now I have to start again next one is MFR what do I do for MFR I have the same graph X A versus X A versus T okay same thing again reversible so this is the maximum root locus maximum yeah so like this you have now I have fixed the X A okay how do I find out Avinash now I have to look at my T not which is optimal T not T not and this is for mixture flow how do I do it equation is same different temperature you have to draw the line but where does that cut here you have the nice thing from your mind can you tell where does that cut which line it cuts maximum yeah excellent where is that yeah here so the point which is passing through this must be giving me optimal T not because this is the maximum root this is the one right so if you don't know that then you can draw a line here you can draw a line here and then try to find out which one will be you know this will be the maximum rate for this T not this will be the maximum rate so and that depends on the slope that slope you have parallelly you just move like this like this so it cuts this line this line at this point in fact Rahul may say that sir you don't have to do all that correct because the moment you draw the line horizontal line it cuts this line and you know what is the point you don't have to do trial and error okay I am telling trial and error because you know we started with trial and error so same kind of procedure I am trying to tell you okay so if you are smart enough you can easily find out that is the maximum root maximum rate locus so it must be on that because that is 1 by r must be minimum so correct no for v by f not so then you will get I think now now I am afraid to draw the graph okay so there also I can take correspondingly that r 1 by minus r versus xa rectangular area will give me minimum only okay excellent we will stop here tomorrow class what we do is is there an optimal temperature progression for exothermic reversible exothermic endothermic or reversible sorry irreversible endothermic exothermic reversible endothermic reversible exothermic is there an optimal progression of temperature that means we are not talking about one reactor we may be talking about a series of reactors you know that gives you very clear picture I asked you one question why a multi bed reactor is used for you know that 0th for SO2 SO2 to SO3 3 reactors are used in series okay now you will know under this discussion why that is used there you heard of that SO2 to SO3 reaction okay it is adiabatic reactor and adiabatic multi bed reactor for sulphur dioxide production in the step SO2 to SO3 okay so when you discuss tomorrow you will know what is that reason exactly why people use that okay