 So this is what we have been discussing and the other day we had the data one problem and what we discussed in the last class was about the integral rate and if you want to try the integral rate the first step is assuming you have first order reaction then you have to assume you have second order reaction for second order reaction suppose that means first order reaction you assume and the test try to arrange as far as possible in terms of straight lines. So that is why in yesterday class what we have plotted was minus ln 1 minus xa equal to k t or t versus t so k will be the slope automatically if it is second order then you know if it is not fitting that means the data okay if the data falls something like this experimental points are something like this it is not a straight line please do not draw straight line like this okay this is the problem if you go to excel definitely excel will draw you know you have options you know polynomial straight line and all that right so that is why if you ask that first option without knowing when you click that it will draw a straight line there okay if you draw a straight line there okay it is going through origin no so that means of course some points here 2 point this side 2 point that side you may think that beautiful fit okay but actually if you look carefully it is occur this is where you make the mistakes okay so take the data as accurately as possible I think that we have discussed you know how to take data there are many methods we have to use either conductivity method or simple titration method for analyzing the concentrations always in this rate equation finding the you have to first conduct experiment and then you should have data concentration versus time concentration of the key reactant versus time okay so then you can convert that data into first order reaction data or second order reaction equivalent data and if it is second order what is the equation you are going to use again it is a batch reactor what you have used so you have t by C A not equal to because this is constant that equation for any rate that equation is same so dx A by minus r A now it is second order it will be K C A square right so this K C A square again you will convert that into yeah so this is 0 to x A and you can also convert this you know it need not be in terms of x A if you are comfortable with C A also you can use yeah C A also one can use that it is not always only you know this format and provided it is constant density system that is very important this is a general expression so that is why concentration we are not writing but if you know exactly that it is a constant density system or there is no mole change between the right hand side and left hand side then you can use constant density system and then the algebra will be a little bit simpler that is all I mean it is not going to change entire thing but it is a little bit simpler so then you have dx A by K C A not 1 minus square C A square also then you have to integrate this expression I am not giving the integral expression right the reason is I am giving particularly when you have you know other people who have not been exposed to this I am just trying to draw 1 or 2 trying to explain 1 or 2 equations and this is how you have to now find out again what is the relationship between concentration and time or conversion and time and then you have to arrange that equation in the form of a straight line and then you have to plot check again if again that is not exactly falling on the straight line because you know straight lines are very easy to observe whether it is really falling or not okay curves are very dangerous you do not know how it turns right so that is why you have to be more careful right so that is why try to write the equations as much as possible in terms of straight lines if you now go back to Levenspiel and then see entire third chapter you would like to plot only in terms of straight lines I am just trying to making you recall what has happened there and I am sure most of you would have done that third chapter atleast in C R E right so that is why I have given also many questions on this third chapter again so that once more it is review for you and then you can quickly finish that right okay good so like this we have to always try to find out for homogeneous reaction what is the rate of reaction so this is assuming that we have integral method if you have differential method earlier I think I have written their integral method now you have the differential method and for differential method what is the starting point you have concentration versus time and what do you do by differential method because we know that ya the rate d C A by d D is equivalent to minus r A but it is not again correct for most of the things if you have a constant variable density system it is not true you will have some more things there okay so that is why if you have a constant density system liquid phase then straight away minus r A equal to minus d C A by d T this is the one constant density system right so by measuring this d C A by d T from a slope where you have concentration versus time this is C A not and because we are plotting for reactant it decreases maybe first I have to put the points okay so now ya this is the rate this is the concentration how it is decreasing okay concentration versus time ya so now slope at any point will give me a rate but again it is not that easy the way I am telling you atleast I do not know how many of you really done one problem using by drawing slopes and then solving the problem anyone has done that frankly in your bidding you have done it how did you draw the slopes how do you draw this how do you how do you draw the tangent what do you do with capillary capillary what do you do with capillary how what is capillary I mean glossed yes is available in the market for drawing this because I have first time I am I am listening to this capillary all of you are from the same university or what ya okay what is this capillary what do you do you have the tube then you have the curve where do you put what point like this a like this inside that we can see the curve sir if that coincides with that few inside then we get we point point we plot points on it we will get normal and with that we will draw tangent because I think you know it is good because I think capillary may again distorts also because it has kind of curvature and all that and if you look the old book by Wallace W A L A S Stanley Wallace I think a kinetics for chemical engineers also that is the title he has also written a book on equipment design there he gives an appendix how do you measure exact otherwise you know differential method is one of the most difficult methods you should not touch that method at all unless it is inevitable you do not have any other choice because we make easily mistakes when you draw the slopes I mean the tangents easy mistakes and you will get tremendous you know error that is why what he says I tried also I think it beautiful I mean when I read that in the book he takes a mirror he is using capillary but again capillary has curvature it is a round tube no ya so that may also distort a little thing it is not straight so what he does is he puts that like this this is mirror he puts like this okay and then he sees this image as a continuous image inside the mirror it should look as continuous then draw the line normal so once you have the normal tangent is very easy to drawn because I think 90 degrees you can measure and then draw it that is one of the very foolproof method okay did I give any problem with this technique no not no but it is real experience it is very good if you are able to draw that so like that and also you do not have to take the draw these so I mean the tangents on each and every experimental point you can choose for example you can choose your own because it is a continuous line so you can take convenient maybe 9 moles per hour 8 moles per hour 7 moles per hour 6 moles per hour like that you can choose and then because you may not get that exactly C verses time it may not be exactly 1 mole or 1 mole per later 2 moles per later 3 moles per later 5 moles per later because whatever you take the sample whatever you measure that only you plot there so for convenience you can also do that so once you have that slopes you are now going to list out all the slopes right which is nothing but minus r a minus r a 1 r a 2 minus r a 3 etc and corresponding to these concentrations these concentrations right so then you have C a 1 C a 2 C a 3 etc okay so what is the assumption here we assume now that we have minus r a equal to now I think I converted dc by d 2 minus r a equal to k into C a to the power of n now take logarithms so lawn lawn minus of r a because minus of r a is not a negative number okay minus is only indication that it is for reactant that's all yeah so then this is equal to lawn k plus n into lawn c now you plot this on log log graph minus r a verses lawn c yeah what do you expect from this now first of all you should expect no straight line you should go to straight line m n a and it has to go through origin no why lawn k is there first of all there is no origin for logarithm okay zero is not there okay point not not one point not not not one like that only it goes so so like this if you put okay don't do this first don't draw the line and then put the points first first to put the points and then draw draw the line because I am simply drawing there so the slope will give me what slope is again and this one okay I made something like this okay so this intercept will give me lawn k right so if you want to find out again activation energy with k that functionality also then now you do the experiment with various temperatures then you will get various slopes then you have to plot again yeah lawn k verses 1 by T and you know lawn k verses 1 by T slope is a disaster I think most of the students will make errors there because it is semi log in fact it is not log log graph and fogular explains how do you find out you know for semi log graphs and all that in appendix I think he gives at least on latest volume I don't know I think it must be there okay what book you followed Gopi lawn sphere okay lawn sphere somehow don't tell all these things I think in the appendix okay good so that is all this is the method what you follow for differential method yeah mirror which angle that is what I am telling you know this is the line wherever you put I put here for example and then if I put wrongly like this then this this curve will go like this it is not continuous so you have to turn the mirror such that you have this line continuously going you know you know mirror no because this side you cannot see only this side you see the image I know it may be people thinking that glass okay so that is why inside inside this mirror from this side we can see that that side you cannot see I think you better try that okay yeah you can see I say this is the reflection you know here I have the mirror where I can see my face okay yeah then you put that here right and then look at this you know from here you just see whether this line this line is distorted because this reflection comes no in the mirror this reflection comes this this entire curve you can see that but you have to turn such way that this entire curve looks a continuous curve okay so then only that is the normal to that point it is a very nice method no you do not get you try I think you know the other way if you put again why you should put always this way that way you try you won't that point is same no at that point you will have the continuity you are not checking the entire curve at that point it distorts that you have to turn such that you will have I think it is a good experience I say you have to do that it is a very nice experience I think some data problems also I gave no yeah if you do not have I will send another 10 with only data points where you can plot and then see it is a good experience and you will never forget once you do that is why I think it is really very good if you are able to try and other than that I do not know any other method which is very very accurate even this capillary tube also is not I mean in my view it cannot give accurate because that curvature again distorts a little bit whereas this is flat mirror so where you will get the continuous curve the very accurately you get and before that what you have to draw is a smooth curve through all the points as far as possible all the points if you take very bad data you cannot draw so that is why experimentalist should be first an experimentalist who guarantees that the data is reproducible and also very accurate data and I tell you it is humans who behave very erratically every second every minute every day because I think you know all things with life behave like that fortunately experimental setup does not have life so once it is acting in one way it acts always in that way for the same conditions that is why my students also come and tell me sorry it is not reproducible I will scold them first okay because that fellow does not have life equipment so that is why it will not behave differently you should get exactly the same readings and if you are not getting exactly the same readings means it is not the that fault it is your fault okay I am not talking about some heat transfer experiments where you know heat may dissipate depending on you have some more winter or rainy season and all that we are not talking about that kind of things for example kinetics if you are able to reproduce today tomorrow day of tomorrow every time same equipment same stirring okay same temperature you should exactly reproduce the data and we are imagining first we have that kind of data and then only we are talking about all this if you have the wrong data that is why my student will have help with me okay first I will suspect that these people have not taken data correctly if it is not logically can if they have logical errors I also don't know how to find out okay logically and the curve seems to be logical because we have this phenomena in our mind no so if something is happening inside something should come that is why all I think now I don't have to tell about research scholars because all of you also research scholars because you are also doing a project all m tech students are supposed to do the projects so when you are doing this expectation is very very important when guide gives the problem to you okay to find something okay he may say that again my simple example is okay you find out friction factor impacted back okay so now you definitely you are not that dumb where you don't know what is friction what is factor and what is packet bad and all that because you have sufficient knowledge know to understand what is a packet bad how the friction is acting in packet bad and what is happening when the fluid is moving through the packet bad all that phenomena must be in your mind that is why in fluid mechanics that is what what you learn then you draw the graph just analytical graph putting x and y coordinates okay friction factor versus packet back you draw the line how it should be whether it is straight line or increase or decrease or increase and decrease both now if you have that good imagination now you go and then do the experiment if you are able to get at least the shape I am not telling that you know exact values okay you have to get you cannot get exact values because you don't know what is the flow rate you don't know what is the you know particle size and what is the porosity and all that you don't know when you are imagining all these in any packet bad when the fluid is moving it will definitely experience drag that is friction and now the material the flow cannot simply enter unless I pump that is why you call pressure drop so that much pressure drop unless I overcome that material cannot go I mean the liquid cannot go or gas cannot go that is why all packet beds we use Ergun's equation to calculate pressure drop because if there is less than that pressure drop for example blower we also use sometimes blower without knowing the difference between compressor and blower blower whenever it sees some resistance it stops correct no blower it doesn't have sufficient energy to rotate but whenever it experiences some drag inside some resistance inside then the speed of the motor will decrease here where in in the blower but whereas compressor it has got very high because it compresses compresses and stores in a tank and from there you are drawing in the tank also you have 8 atmospheres 10 atmospheres whatever you set there and whereas blower is working at slightly above atmosphere that's all just atmospheres pressure so that is why even if you put your hand there it will not turn you try your hairdryers hairdryer is a blower very people may be using that dryer you put your hand the speed of the you know that fan will decrease sound also changes the moment you just put there okay so that is why it cannot have sufficient pressure drop to push the liquid if you are using a blower through a packet right so that is the expectation okay pressure drop should increase or decrease when you plot pressure drop versus velocity in a packet you see decrease increase remains constant why see the what is actually happening for the pressure drop it is a phenomena something is happening there some physics is going on there right so he says you know it increases and then state constant you explain to me why it increases why it says constant it is a packet bit no not only packet bed even if you take a mt tube also same thing happens increases yeah why you are telling increasing or decreasing increasing yeah what about increasing how it increases and now at this point of time instead of asking reaction easiest thing for me is to ask a known thing to you and fluid mechanics and pressure drop you know generally known to us because that is the first course of thermodynamics fluid mechanics that is the reason why I started this okay and earlier batch also it did not get and because our department changed some structure now so that is why many people are not taking you know these two courses first course anyway you don't have a choice this is compulsory for most of you know except for MS Phd okay so that is why I am trying to tell not for you to get the jobs but if you come probably you will have you know more knowledge in all these things that is the reason I am telling and particularly mtech is a course based program whatever course you want you can take you don't have to even listen to the guides the project is partial fulfilment for the courses for the degree it is not the main but still you have to do that some part you have to do that whereas Phd and MS research is the courses are the partial fulfilment of the entire degree you know the research so that is why I think you know whatever courses you like you have to come and learn whenever you have feeling that you learn something in that course if the second course of that person is coming I think you better take that course once you have this course I know my own experience I think in 2000 I was HOD but I also went to IOCL for recruitment chemical engineers totally we have reviewed almost around 120 130 students so every day that 120 by 5 you know 5 days around 2020 morning to evening and also I think they were very good not only just one or two questions and throwing them out sufficient time is given to that is why 5 days for 120 people and there are universities and companies also 125 are interviewed in one day also okay yeah so then from 80 made us 7 people have come 3 M tech and 4 MS IT and committee committee one professor from Kanpur one professor from Delhi and another 2-3 people from IOCL itself so totally some 61 people were there so then normally in any interview those who have gone for interview you also should have experience they will ask what is your favorite subject many people because probably we don't know how to ask questions in all subjects so that is why probably we will say that what is your favorite subject and out of 7 there will be one person now you ask that is what normally we will say but anyway I think you know general questions also should be asked then I think all these IIT guys or IIT Madras guys told only reaction really they have taken my 2 courses so then believe me all 7 got the jobs I have not asked any question and they have they were only discussing among the other I was I just kept quiet I did not say anything okay they were thinking I know there was my friend afterwards he became very close friend one gosh now he retired he was the R&D head he was the chairman of that committee he was telling that why IIT Madras is very good in reaction hearing everyone is very good here all that he was talking I did not tell him only last day I told he was asking me who is the teacher and when I told him oh you have taught them but I think that has become a favorite subject not only that batch afterwards even here when students go when they ask you know what is your favorite subject many students used to tell theory okay but it happened only when they took 2 courses not one course because this course is only general things you know the concepts and theories that is why chemical reactor theory what we say but actual applications for heterogeneous systems and all that will come in the next close packet beds fluidized beds moving beds moving beds I am not covering and you know slurry reactors all that we cover there so with that knowledge again some of the things will be repeating repeating there also the same question why asked you pressure drop increases decreases I may again ask in that course also that is why you have that information going to your blood that is why you feel that you have more confidence when someone asked the question yeah you know which subject you are so that is the reason why I mean if it is possible I think better take any course whatever you like okay and then spend time on that and this is very important I am not talking about only my course and I am talking about a research where you have to plot that graph when pressure drop increases if someone tells I will give you example because that thinking thinking thinking is very important I think at least most of you would have gone by bike through wheeler not cycle cycle you may not have that kind of effect okay bike if you are going when you are going at 30 40 50 60 whether drag on you is increasing or decreasing increasing you do not feel that you actually feel that if you have something loosely tied and all that may fly out correct no and beyond certain velocity you may also fly out correct I think that also happens okay actually that is the training they give for this paratroopers where they have a big blower I have seen that in discovery channel so this fellow jumps from the top and the velocity is so much he is floating he is fluidizing and the velocity they said if you remember correctly 127 kilometers per hour or maybe 1207 miles or kilometers I do not remember you know per hour that is where they are floating they are practicing because that is what they experience when they jump from the flight okay so that is why theoretically that is possible you know for your afterwards if the blower is having much more capacity than what they are floating if the blower speed is increasing then they will be pneumatically conveyed yeah really they will go away from the building or otherwise hit the ceiling okay all these things may happen that is why now if I ask you to drop you know all this drag is only measured in terms of drag you can never measure directly you can never measure how do you measure drag you feel that you feel that you know your body like that even particles feel but how do you measure it it measured always as far as I know it is measured always in terms of pressure pressure drop okay that is why you put a manometer and then try to measure that so now if you plot that because now you know the phenomena as the velocity increasing this should increase now if I ask you to plot friction factor friction factor versus velocity how do you plot it also increases increases increases okay how do you define friction factor I think you know you know just recall the friction factor graphs do you remember friction factor graphs of the pipe flow huh you remember no are they increasing or decreasing you do not remember decreasing for lamina lamina for its degree see equation wise is correct but I am I am you see equations may be difficult to remember I think at least diagram when you see you may remember more time so much discussion on the first course what we have taken in your beating okay and also you have done the experiment you have done the experiment in the lab also fluid mechanics even packet bed also it decreases why first of all increase or decrease so you said increasing or increasing yeah ramesh you have any idea according to the equation friction factor is okay but in friction factor what is the difference increases or decreases the definition the definition of friction factor ah by funda shear stress by velocity it is delta p by half rho u square kinetic energy it is delta p by kinetic energy half rho u square and into you have again h by dp or dp by h and all length length will come if you have a packet bed okay otherwise you know d by l of the tube or something will come there now can tell me why it decreases u square you have in the denominator as velocity is increasing u square again tremendously increases so that is why friction factor decreases normally our logic is our intuition is friction also should increase correct no like drag friction also that is why we make the mistake that is in fact one of my favorite questions in interviews okay yeah because i think many people think that okay friction factor increases right but i think you know by definition by definition it it has to decrease because you have rho u square u square tremendously increases and that 16 by n re also we know use this derivation only you will get that you know both sides when you put properly the units and all that then only you will get 16 by n re for laminar flow okay and for this one for stokes law you know for single particle and all that 20 by 24 by 24 yeah that they are cd also defined again using the same thing of rho u square in the denominator so that is the reason okay good so that is why this when you are doing experiment because i started all this because of the experiments when you are doing these experiments or any research you should have this kind of it need not be experiment even theoretically also if problem is given to write the theoretical equations or to solve the problem theoretically you should have this expectation what is happening inside that is why you know lost 15 20 years my teaching is only explaining phenomena phenomena phenomena inside what is happening if you are able to think mathematics will be automatic okay good so that is the reason why we should have you know expect that because now i am plotting only concentration versus time for a reactant then automatically it should decrease if you are increasing if someone plot that is increasing there is something wrong you may be measuring only product okay so that you have to be careful good so like this now you have to repeat the you know all integral expressions that is why i request all of you where you lose in the examination because examination is also important for you is in the mathematics conceptually now onwards you do not have to learn anything new except when you put two reactors what happens three reactors they are not so big conceptual things they are all simple now you know what are kinetics how do you find out kinetics right differential method and as well as integral method i prefer always integral method because that gives you very very accurate fitting whereas if you are able to do this kind of you know some very accurate technique to go for this slope measurement and tangent measurement then you will have also good there right so this n will give you the order of reaction and then k will give you the rate constant okay so when you go to actually the heterogeneous systems how do you find kinetics we will also discuss there right that is also not easy because there it is mass transfer most of the time you know in slightly reactor there are four mass transfer steps and one reaction step in every heterogeneous system there is only one reaction step we will close here