 yesterday we were about to derive the formulas and then left them in graphical design also we need this formula, Ok some equations we have to derive and then we will go for graphical design, Ok but I have drawn now some graphs, Ok so in the last class we have given some graphs where we have to plot you know there are 3 variables in whatever way you want you can always try to plot them changing x, y, y, x and all that but logically there is only one way to draw logically where we are convenient with that kind of drawing so that only we plot but before doing that how do you get those graphs which I have given there, right someone going like this someone increasing decreasing and all kinds of things are there but how do you get those actual lines there that is what first we will decide and for this we will take irreversible reactions first and in this case it really does not matter whether you have first order reaction or second order sorry whether you have exothermic reaction or endothermic reaction, Ok irreversible only temperature decreases with endothermic temperature increases with exothermic, Ok and but the rate lines will be increasing only all the time so for irreversible reactions let us first take that I have a very simple thing like it is going to products it is irreversible so products will not affect anything there so then minus r A for this one is k C A to the power of n and of course as usual we are going to get k C A for n equal to 1, right so now it is a non-isothermal reactor where I can write this equation minus r A equal to k 0 e power minus e by r T C A not 1 minus x A and we are also telling that you know there is no volume change, Ok this is the equation 1 and equation 2, Yeah so this equation I would like to arrange in terms of x A not in terms of x A x A and as a function of the other two then you will get that by re-adjusting this equation you will get minus r A e power minus e by r T whole thing divided by k not C A not this is equation 3 so this is one equation, right so now I have 3 variables that is x A as a function of now minus r A and T all other things are constant what is k not I think I do not have to derive that equation you know very simply you can write this equation so k not is the frequency factor which I know and C A not initially I know and e and r activation energy you have to measure before you start this, Ok it is a first order reaction and for second order reaction also you can write this but only thing is that will be more complicated so that is why we are writing in the simplest form first order you are taking and now how can I draw this graph which minus no no no I think that is plus only that is plus only yeah you check it yeah that is plus only right yeah so now yeah like the graphs which I have shown you the other day yesterday now I can plot x verses T or x verses r or r verses x all combinations are possible but most convenient way of drawing this one is in terms of x and T so when I say when I have x A and T in x axis and x as in y axis conversion is in y axis Ok so now what is the parameter for us now r is a parameter Ok and anyway the maximum conversion because I am plotting conversion it cannot be more than 1 so that line can be shown something like this so now I have to calculate this x every time I have to substitute for a T that means I should know the range of temperature and that is the reason why thermodynamics you know when we are talking about Gibbs free energy and all that you know so at that time I know definitely what is the corresponding temperature and then equilibrium conversions right equilibrium conversions so then I will know the range of temperatures where I will get this that means equilibrium conversion is if it is 60 percent that itself is x A equal to 1 for us because beyond that it cannot go Ok yeah unless otherwise of course you have very very large k values right so but anyway now I can assume minus r A as let us say 0 of A 0 of A put nothing will happen you know we should not use that then a small value for minus r A then calculate for various T's then I will get x verses T so I will have lines like this going this is the kind of lines this is for each one r so how r is increasing or decreasing this way or increasing this way or is this is r 1 r 2 r 3 r 4 so from the graph can you tell I mean because you have the idea as temperature increasing rate must so this will be in this increasing order Ok so this is minus r A 1 minus r A 2 etc Ok yeah or maybe I think you know this will be 1 r A equal to 1 this may be 10 this may be 100 this may be 1000 just give you some physical feeling exothermic endothermic does not matter yeah even endothermic as the temperature is increasing irreversible what will happen to rate even endothermic you are increasing the temperature so it should increase so that is why it is irreversible exo r endo does not matter Ok only irreversible you will have problem sorry reversible you will have problem Ok good so this is very simple then we will see later how do we use this for our graphical design but this is the first one then the second case is I have uhh yeah reversible endothermic reversible Ok first I will write exo r endo because the equation is same only sign changes endothermic exo r endothermic now it is irreversible simplest scheme which we can uhh write without getting confused with mathematics is this scheme where C r not equal to 0 much simpler Ok only C r not is there and uhh for exothermic endothermic you also know that you know E 1 E 2 depending on those two values you can find out which is endo which is exo r endo that I will tell you a little bit later right yeah so now what is the rate equation here minus r A equal to K 1 C A minus K 2 C r so this is equation number 4 yeah so this equation I can write in terms of uhh it is activation as a R Heine's equation this is K 1 0 yeah E power minus E 1 by R T into C A not 1 minus X A correct for the first part second part K 2 0 that is the frequency factor E power minus am I crossing my boundaries Ok E power minus E 2 by R T into C A not X A so this is equation 5 Ok yeah this is minus R A so this also I would like to write in terms of X A this algebra you have to do on your own very simple it is L K J algebra separating X A and writing in terms of you know minus R A and temperature that is all Ok so if I do that you know all these things can be again I have to blackmail you saying that this may come in the surprise test otherwise you do not do it know that is the problem so but anyway this X A can be written as K 1 0 E power minus E 1 by R T minus minus R A not by R A not by C A not again whole thing divided by K 1 not E power minus E by E 1 by R T plus K 2 0 E 2 by R T Ok so this is just separation and I can also write that in a much nicer way where X A yeah 1 minus minus R A E power E 1 by R T E 1 by R T this divided by K 1 0 C A not again this whole thing divided by 1 plus K 2 0 K 1 0 yeah E power minus E 1 minus E 2 by R T yeah so this is a nice form equation 6 thank you oh yeah yesterday I made a mistake in writing uhh that Vantop's equation Vantop's equation you remember no yeah that K 1 K 2 I have written small small K 1 K 2 actually both of them are capital K 1 K actually it should be K K by K not but both are capital the other side we have T and T not know so that is corresponding to that K not and K I am sorry capital K right yeah so that is please correct that Vantop's equation I think raise me or someone where is raise me oh there yeah I think they found out that sir it must be K 1 that is right capital K capital K 0 and capital K then only that limits will be satisfied otherwise no because normally our convention is small case are for rate constants and capital K are for equilibrium constants so that is why yeah Ok good so this is the one and now right you are right E 2 minus E 1 yeah otherwise I should have removed minus there that is all E 1 minus E 2 yeah so now uhh actually this E 1 minus E 2 is is what E 1 minus E 2 E 2 of reaction do you remember that reaction coordinate diagram I think which I have told you sometime back also Ok yeah so I think may be I have to draw for some other people who do not want to remember so that is why I just again I write once more so that they will remember I think may be I will draw here as a small one yeah what are the coordinates energy and it is not reaction rate actually yeah it is actually reaction path reaction path Ok yeah so when you have this kind of may be this is activated yeah this is one same thing reaction path verses E then I may have another one not so much correct no so what is this one yeah this is E 1 E 2 please remember this is a nice problem to be asked a nice question to be asked in the interviews Ok yeah so then this one will be E E 1 E 2 so which is endothermic which is exothermic here this is this means E 1 minus E 2 this will be negative value so this is exo Ok I have also write here delta H yeah Ok I write here itself in general delta H R equal delta H R equal to E 1 minus E 2 right so if E 2 is greater then this becomes negative then it is exothermic reaction and yeah the other one is endo so this is exo yeah this is the one no E 1 minus is E 2 the top one is endo yeah you are right where is my yeah Ok sorry yeah this is endo this is exo no no E 1 greater than E 2 oh yeah yeah what I wrote is right is this one you are telling yeah yeah no sir E 1 minus E 2 what is this you are playing with me no I think I do not want to listen to you so I think I have written E 1 minus E 2 does not matter yeah that is right yeah do not play because I started listening to you that is very bad I think I have to take my own decision I have everything here Ok good yeah so this is the one Ok so now this one will be now accordingly the values of E 1 and E 2 this will be either exothermic or endothermic that is why as far as derivation is concerned I have written here exothermic or endothermic right if delta H R is negative then we have exothermic and if delta H R is positive we have endothermic Ok so now let us plot those graphs so now I will take endothermic case this is 2 delta H R is yeah positive good yeah so what kind of graph I will get if I want to plot again same thing X A versus T this is what the question which I asked you long time back in 0th exam yeah tell me how do I draw that so how do I draw it tell me ok first what you have to do it is a reversible reaction that means R equal to 0 also possible right R equal to 0 so that means I can substitute here R equal to 0 for reversible reaction then I will worry about delta H R equal to positive or negative thus so this term will be there for R equal to 0 this will vanish so this will be 1 by all these Ok so now R equal to 0 it is a function of only T I mean R equal to 0 now calculate for different T is what will be the X straight forward so then you will get what line equilibrium line or some other line you will get equilibrium line how the equilibrium goes there you are telling increase like this you said decrease or decrease you are telling increases like this as T goes on 10 kilometers like this and 1 micrometer like this so as T increases X decreases Ok tell me of the Decrease the Temperature huh recently also I have plotted I say even yesterday I plotted it is there Abdul see yesterday's notes yeah I saw that where where where is it increasing or decreasing increase see I can happily draw there without asking you but by asking you I thought some of you will think that is the reason why I am again asking many many times same thing yeah Abdul now you tell decrease increasing and decreasing Ok now you tell you draw you tell me now I will draw I will draw do not be operated I say all of us can make mistakes I also made many mistakes you played with me also Ok tell me very good so it goes no no you have shown me as it goes like that is enough correct what is that is right so this is and finally anyway this one will be yeah that maximum you know equilibrium yeah I mean on the extreme conditions it can go to 1 also Ok good so this is the 1 this is R equal to 0 not below that is right only yeah so then if I take R equal to 1 for example R equal to 1 see as temperature is increasing what will happen to the rate it is increasing here but I know you can actually calculate anyway I am going to give you an exercise also which you have to do on XL and then you will know yourself Ok so depending on delta HR value you have to calculate X versus T and then plot Ok you take this this value delta HR once positive once negative so then you will know actually you feel it when you do it so that is the reason yeah this is ok I mean you can write the way you want it can be there it can be there the absolute value only I have to find out whether positive or negative that is all once you subtract one from the other Ok yeah the total is negative total is positive I say yeah delta HR right so that is why I think that is no problem yeah you tell me the other one R equal to 1 below that how it goes same shape yeah it is not exactly same shape it goes something like this something like this trying to reach so this minus R A here equal to 1 10 100,000 like this Ok this is for endothermic Ok good so exothermic here also I have to write a reaction Ok same again X A versus T Ok so this one first R equal to 0 same equation but I think depending on this values you will get yeah so it starts from almost to the top like this it goes Ok good this is R equal to R A minus R A equal to 0 now for very smaller R equal to 1 for example yeah it increases and decreases because for exothermic reaction forward reaction till some point it will increase then backward reaction starts dominating so it will come back again so that is why it reaches a maximum and then goes like this not touching that if it touches then again 0 it cannot because this is a value for R so you also have another line like this another line like this another line like this so this is minus R A equal to 1 10 100 good so actual optimization problem is only with exothermic reaction that optimization thing we will talk later little bit later yeah Ok so now how do I use this information for the graphical design Ok so we will take the simplest one for graphical design that is yeah we will take some general curves for graphical design Ok so this is the information we will discuss again later for as far as optimization concern how do you use this this this and all that but now you take any one of those general figures like this figure I will take first right so that figure I will just exaggerate and then try to draw here X A versus T so then we have something like maximum is 1 there like this this is rate minus R A equal to 1 10 100 1000 like this Ok so what I have here is I just used only now the material balance equation I think you know without talking about any reactor but this is the equation what I have used and now I have generated that information now to get this volume of the reactor now I have to use pot another minus R A why various minus R A is there you have not no one told you this one in your B Tech or M Tech this design around Krishna no really I mean this pot is really wonderful pot in Levenspiel and most of you would have used only Levenspiel book you also yeah you avoid because you know if you learn you have to write in the exam so that is why I think what do you mean by reaction path yeah it is not reaction path from energy balance you should now get the relationship between conversion and temperature if you have no I told you that for simplest case adiabatic you will get a straight line assuming that delta H R equal to constant so if you plot that then that line will intersect all those rates Ok if you take for example adiabatic right but it need not be adiabatic all the time that means you may have sometime the non adiabatic case where if you are talking about reactor you know plug flow reactor along the length you have various temperatures and also you have various rates are conversions various rates and also various conversions but energy balance gives this conversion versus temperature so and the way I remove heat any shape of line I can get it is not straight line the way I get adiabatic case adiabatic is a special case right adiabatic is a special case so the conversion versus temperature line or you know that relationship Ok I think I will also tell you here energy balance will give me energy balance gives X A as a function of temperature Ok and of course we are taking here for simplicity delta H R is constant and all that over that way range Ok so this relationship if I have adiabatic case and also delta H is not varying with temperature not only delta H R there is another thing also which varies with temperature in energy balance C P C P can also vary with temperature right because in that relationship you get definitely delta H R and also definitely C P when I also derive one equation just to give you a sample but this one as just simple analysis so this relationship I can plot whatever way I can plot whatever way I want it right so for example I may say that I have a relationship something like this this is crazy you will scold me but still it is okay like this it is really crazy Ok but I can have that kind of crazy also because it is only depends on how I am removing heat along the length of P F R this is P F R this line is for P F R Ok so now I have drawn this now I have entire design information on that graph can you identify that information I have the entire design information on that graph now Krishna have you thought about this this is very beautiful one I said that is what indirectly you are solving that minus R A temperature and corresponding rate that is what no when you are plotting that each intersection will give you only that information so that is why I may take for example here this is X A right and correspondingly this is R A so this is X A this is R A means 10 Ok this X A this X A may be I mean just let me say that this is 0 to 1 so this may be point 2 point 2 and this may be not this may be exactly 10 correct no it is cutting here then it is going here no there are many many lines in between you can draw any number of lines you can take any number of R's and any number of X's Ok but here from this graph only I have few so I am just trying to draw that in fact there is another line also which goes here R equal to 5 for example so then again you have to take this line and this line and of course when you are going systematically with conversion right so Ok now just ignoring that now you have this point where I may say that Ok that is equal to point 5 what is the value 1 R equal to 1 and again it is coming to this point where this may be point 6 X equal to point 6 and what is this value 10 Ok yeah so then next value somewhere here so somewhere here it should increase then it should go yeah like that so this one may be point 7 point 8 point 9 Ok I think approximately I can say that this is touching here yeah touching here that may be point 7 5 Ok so then what is the value 100 and finally this may be around point 9 right point 9 and what is the value again 1 so now I have to I have to I will remove this one function Ok this is 1 by minus R A so if I simply plot point 2 equal to point 1 this is 1 this is again point 1 this is again point 0 1 and this is 1 how do I plot that I think very Savita Savita is there Ok yeah so Savita what you asked yesterday I just want to give this one that is why I have drawn that crazy line so now I can plot 1 by minus R A versus X A I have that information right it is a plug flow reactor so it is starting with point 1 minus R A equal to point 1 somewhere here what is the maximum value 1 Ok so this may be point 2 point 4 point 6 point 8 and then 1 Ok so now point 1 point 2 X A this also point 2 point 4 point 6 Ok this is point 2 point 4 point 6 point 8 this is 1 Ok so just approximately trying to draw that so then for point 2 it is point 1 so somewhere here the point Ok good so then what value next one is point 5 point 5 is somewhere here and 1 ah jumped here this is the one afterwards point 6 point 6 point 1 point 1 means again point 6 this is 1 so it has come to this point Ok then point 7 5 point 7 5 is somewhere here so this is again point 0 1 still less Ok then point 1 again increase it to point 9 here this is 1 how do I draw now of course here to start with may be somewhere here that means corresponding to X equal to 0 also I have to calculate that value Ok or I had X equal to 0 how do I get from here X equal to 0 is this line no X equal to that means there is another line which is also going through like that right so that value also I know understood no or last hope Ok last hope because I started putting values there if I have not put values generally probably you could have been in the class Ok yeah but anyway corresponding points we have to take and then print out and then plot then you will have some value here definitely so you will have like this like this like this yeah so now what is the volume of the reactor because we have plotted for plug flow so area under the curve all this area is really crazy place and you know if I take this is my conversion is point 9 Ok so this one equal to P of r so area under the curve will be V by F A not Ok I mean this is really crazy as I told you Ok this is really crazy but I just want to tell you but it can be really crazy also depending on the way you remove heat that depends on what is the functionality between X and T but nice guy will be adiabatic reactor where you will get a nice way of that 1 by minus r A versus X A you will get some other very nice way for this kind of increase in the rates because again if you go to this kind of increase in rates then you will have a different kind of I mean graph that means I am talking about X A versus 1 minus 1 by r A versus X A graph but what you have learnt here is that the extra thing is that even with non isothermal reactors the final area under the curve only will give me the that cannot go wrong right but instead of calculating I mean integrating now I can find out those points correspondingly the intersection point and then corresponding X right and I have drawn here how many points 1, 2, 3, 4, 5 only but you can draw any number of lines in between so that you will know again another point here may be another point here another point here all that right because between this and this Abdul how many lines I can draw infinity so that is why you can draw whatever you want and then get that for smooth curve so that you can join nicely right so that is the procedure graphical procedure and now if I just want to know that for adiabatic case what kind of okay this is for PFR none of you are asking me what do I do for CSTR okay that is what I told you know I have to question I have to answer but you do not answer I think now it is beautiful PFR now you tell me how do you do MFR okay Anupriya ask like that okay so now how do I do it for MFR how do I do it for MFR I think may be these equations you have noted down I will remove these let me say that I have the same minus no no XA versus T graph yeah so R is increasing anyway in this fashion this is R A equal to 1 10 100000 like that okay 1000 like that okay tell me you have a yeah how do I find out what is the what is the problem I am asking is it volume of the reactor you have to find out volume of the reactor no area under the curve so that means what you should know how many times I repeat this if you know the volume what you can find out conversion if you know conversion what you can find out volume so that means what I am asking here volume okay that means you should know conversion definitely you should know conversion let us say I have 80 percent conversion so that means I can draw that line 80 percent conversion line there okay yeah right so it is exactly same thing you know even if this graph graph is crazy so it going like this you know this is XA as a function of T now you see this graph is cutting at only one point which is yeah this point able to see that point right yeah so this line of course there is I mean I put 10 there but it may be 8 line 8 this is also of course this 10 is also continuing like this okay I think I will also plot nicely we have different colors here so my X verses T graph is okay and I have another nice color this is XA equal to so now you see this line this line that means you know this R this is okay this red line this is minus r i equal to 8 8 8 8 okay that is 8 minus r a line and this is XA line equal to 0.8 and this line it is going and cutting here so that means this is the point another color that is the point okay because in a mixture flow reactor there will be only one point I think you know one rate corresponding to one conversion conversion we fixed already now you can also get correspondingly what is the temperature from this graph so all the outlet conditions you have now right you know XA that is the line which you have drawn and you know minus r a now where it is cutting right and also you know corresponding temperature so that is how you do even for recycle reactor also so recycle reactor what you have to do is you will draw a line something in between like this I mean if it is a straight line need not be straight line so it can be like this but you know that conversion is not 0 in a recycle reactor when it is entering reactor that part you have to remember but whereas there and here X equal to 0 right I mean the entry X equal to 0 right so that is why you can now also extend this one for recycle reactor right even batch reactor I mean all reactors whenever you have temperature versus conversion relationship and you have this information this kind of graph we have done it for simplest case like you know a going to minus r first order reaction right but you can plot these graphs and also those all those graphs for any kind of rate but only thing is you have to separate XA and then you have to write that in terms of minus r a and T temperature so plot this way because this is the most convenient convenient way of getting the information for the design okay understood no I think not that happy you know I do not know why because you lost somewhere please tell me if you not understood why lost somewhere that is any car that is that means any kind of heat exchange I have see I told you that this XA versus XA as a function of temperature that relationship you get only from the energy balance right so that energy balance when you are writing may be probably I have to write that and then tell you okay I will write it and then tell it may be that still there may be some people who may not be understanding that okay so now I will write for exothermic reaction sorry not exothermic yeah adiabatic reaction okay I think this is equation not required okay I will just may not be following but any other people also not able to follow how do you get that line you are you are also not able to follow okay so then what did I tell I mean what is the meaning of writing there energy balance gives XA as a function of temperature what is the meaning of that no meaning yeah may be you tell that if there is no meaning sir you can write sir there is no meaning that is all and what kind of relationship you can expect tell me what kind of relation you can expect you cannot expect any kind of you know specific kind of relationship okay but only for adiabatic case you can expect a straight line so that is why I just want to give you know that adiabatic you know the energy balance and for the simplest reactor mixture flow then you will know that energy balance for MFR okay so let me give you this we this is the one and here I have volume volumetric flow rate volumetric flow rate constant density and all that we are assuming and also I have here the density is rho that also is required in one way of writing and I have CP and T not here also I have rho is in a way constant and then CP T but okay XA this is 0 XA not equal to 0 and of course I can also get a CA not and all that also yeah CA not I can write here CA also I can write there so if I want to write this equation you can also write in terms of FA not or FA FA means molar flow rate okay but now we are writing in terms of volumetric flow rate V is the volumetric flow rate okay good so now energy balance what is the time energy balance what we have is input input equal to output plus energy generated or consumed due to reaction okay if it is exothermic reaction it is generated if it is exothermic reaction absorbed okay yeah plus it is unsteady state it is steady state only it is not unsteady state yeah plus we have heat removed by external means so that means I may have here jacket and some amount of heat is this is T okay TC also TC that means you have the heat capacity of this fluid so high the temperature increase in that I am practically not seeing assumption it is simply an assumption okay it may be there may be one degree increase okay but as an engineering as an engineer first I want to simplify the problem understand and then the remaining things I can follow later okay so that is what this is what then this is when I am writing this I can write here this heat input is okay first of all heat input should be what are the units I have to balance it is kilo joules per time okay that is what is the heat all right right so this is V rho Cp T not that is what is entering here equal to V rho Cp T right that is coming out and reaction if I take I have exothermic reaction then this becomes negative so that means you know I should have written input because that also becomes input inside so that is why okay I write here plus R minus minus RA into delta HR what are the units of that into into volume and what are the units of this this is kg this is a meter cubed per second and this one is kg per meter cubed and Cp is okay joules okay kilo joules per yeah this is where you make the mistake you know that depends on this flow rate okay if it is kg per meter cube this will be expressed per kg no Cp you can express based on your molecular weight either and based on mole or kg so that is why please be careful in the examination we will make that mistake that is why better write that but in this case it is kg per degree Kelvin or may be degree centigrade I will put here okay that does not matter okay so then I have degree centigrade so now what is this is cancelled this is cancelled this is cancelled I have kg per second correct no kg per second so that is the balance what we are making plus I have this external means as simply q where q a q equal to ua delta T what is a all this heat transfer area okay u what is u the heat transfer coefficient between this liquid and overall heat transfer okay that ua and delta T is this because everywhere you have the same temperature T because here you have T right everywhere you have temperature so T minus TC T minus TC everywhere and that is why we assumed that we have a fluid where it can absorb any amount of heat without increasing its temperature that means Cp must be Cp must be very very high yeah that means you know I have to write here negative this entire quantity as negative if I have exothermic that means that will become input here okay yeah I think that is fine no problem yeah that is fine depending on delta HR value I thought you will write that okay so now this is the equation now what we are saying is if I take that this is 0 what I have adiabatic system there is no heat removal right or adiabatic no rho and Cp we are assuming that is they are not changing with temperature because I think all these are assumption otherwise unnecessarily the equation will be so complicated I told you you will forget about actually what we are discussing and worried about the big equations that is the reason why we are simplifying to understand the concepts okay good so now if I separate this and yeah I have another equation here this is delta HR and what is that what we need we need a relationship between conversion and temperature but is it this is the material balance equation but is it relating conversion versus temperature yeah so I have now the material balance equation where minus R A into V equal to F A naught X A or F A naught I can also write in terms of V by C A naught correct no yeah V into C A naught because I have not used to the F A so that is why I am writing that okay so now I can substitute that here so what we get here V rho Cp T naught equal to V rho Cp T then I have here for minus R A delta V I have V minus V C A naught yeah V C A naught X A delta HR into X A right so this equation I can now write T minus T okay here I will write T minus T naught equal to see the writing I am creating correctly or not C A naught delta HR by rho Cp into X A check this you will get it no good very good so now this is what this is what we are what we are calling as beta so T minus T naught equal to beta into X A okay okay T minus T equal to beta X A now how do I plot this information on this graph or shall I draw a fresh graph X A versus T yeah I mean what is the slope do I know the slope 1 by X A right it is 1 by beta right because X A is Y this is T so I can write this equation only as X A equal to 1 by beta okay this is T by 1 by beta minus T naught by beta not 1 by beta so that means this is Y this is MX and this is C okay plus here okay that depends on that okay good so now this is the one what is slope now for me 1 by beta so when I plot that here if it is exothermic reaction the temperature must increase right right so okay good so this now it goes something like this right so this is minus r A equal to may be 1 10 100,000 like this sorry 1000 like this so this is energy balance right so then I can also draw number of lines here for exothermic for exothermic it is positive in fact for endothermic it is negative it comes like this it goes like this it goes like this for endothermic okay yeah you know how can you say that because for exothermic as temperature is increased I mean as conversion is increasing temperature must increase or as temperature is increasing conversion must increase okay good so so this one yeah now here this is a point this is a point this is a point this is a point and in between another line here this is a point so now you can see this point X A versus minus r A X A versus minus r A X A minus r A X A minus r A list out like that exactly and then plot 1 by minus r A versus X A then area under the curve that will give you the diagram how is it okay yeah because this is the functionality what you are telling this we say now T you know X A this one this one this one as X A as a function of T this is what what you are telling now if I add this Q and then solve that equation because there is another T also here because that is T minus T C in this Q okay did I write that okay this Q is U A delta T which is nothing but T minus T C that I have to substitute there yeah yeah in this one now then depending on my Q values how I am operating sometimes you know I may operate sometime only with some Q afterwards some other Q afterwards some other Q then it may take any other part crazily yeah so that is the one what you are talking that energy balance gives X A as a function of energy balance giving you know the functionality the relationship between conversion and temperature this is what is the simplest case what you have taken and I will draw for each reactor and we will derive for each reactor the energy balance equations material balance equations and then we will try to find out how do you solve the those equations for finding out the actual volume of the okay so that is what we will do in the next class and I know you will be unhappy if I include this in examination Monday right yeah so I think Monday all this will not be included and shall I include very simple no third test you will have a okay good so then I think till multiple reactions you will have you know it doesn't mean that I am giving only multiple reactions multiple reactors and multiple reactors also only we have done so portion for the second quiz is from zero to multiple reaction from beginning to what is the other thing once you understand multiple reactors and multiple reactions the other one is LKG single reactors is single reactors are LKG only so that you should not crib okay yeah