 సిమరమని సిక్ర ͡°ర్ మునాడి ఆదారాidor పౌకకేవాలీ బిమువాయాయ NICK విముదౄదా చ చీసి ఌవూడికదలి చ౔సడివా. for a certain conversion, right. So if I know if it is the two steps controlling that is mass transfer through the film and also reaction on the surface if both are controlling then this is the equation. So as usual we can also now simplify this for individual cases if it is film control we know that K s goes to infinity that means the rate of reaction is very very large. So then this term will not be there because this is 1 by K this K s is very large so this term will vanish. Then we have T film equal to rho b b K g not C A g plus 1 by 3 n plus 1 this is the equation equation 15. Then if I have reaction control then we know that K g is very large value. Then the equation is T equal to R rho b K g not C A g into only this term will be there so this will be 1 minus X b to the power of 1 by 3 by oh sorry this will be simply K s yeah this will be simply K s yeah so this is equation number 16. So if you look at particularly equation number 16 I do not know I think in your notes can you check what is the reaction control equation which we got for the other model where product also is present on the surface yeah it is exactly same no it is same do you know why it is same yeah so the other steps do not you know even if they are there you do not feel at all so it is only the reaction control yeah so the other two mass transfer steps are faster so then this is equivalent to your reaction control where you know the other mass transfer steps are not you are not seeing the mass transfer steps at all it is only the reaction control okay whereas here it is not exactly the same and you can depending on this K g value again this K g changes with diameter right this is what yesterday we have seen K g changes with diameter and you know that for large particles it is inversely proportional right and for large particles no for small particles it is inversely proportional and for large particles it is 1 by square root of yeah DP these two cases right so if you substitute that in this and then try to simplify then you will get this T is proportional to R to the power this depends on small particles and large particles 1.5 it changes the exponent changes to 1.5 to 2 okay of course we can also calculate now what is tau tau is conversion for yeah 100 percent conversion time required for 100 percent conversion then we can calculate tau and we can also write this is called as T by tau right for example if I write this one as T by tau yeah what do you get only this will disappear yeah but n plus 1 will be there correct no this will not go to 0 X B equal to 1 yeah and here yeah it will be there simply X B equal to 0 X B equal to 1 it will be there now this n plus 1 depends whether you have small particle or large particle for small particle it is half 1 for large particle it is half that will come there that coefficient will come there but that will be there okay and this tau if I take here this is straight forward only this much will be there okay so then in terms of T by tau also one can write these equations good so you please just think about these things and with this the two models which I wanted to do we have completed and they are not very difficult models they are simple models and we wanted to make the entire process as a simple process without much complications and it is said that shrinking core model in most of the time most of the time it is valid for gas solid reaction non catalytic reactions but what can be the deviations in this model when can you say that this may not be acceptable because no model is acceptable in all the situations right yeah 100 percent that is why we have some assumptions and all that yeah which assumption may not be valid the first assumption what we made was that you know isothermal isothermal I think it is a valid assumption because the particle conductivity is very very large so generally when the particle unless otherwise you have highly exothermic reaction if you have exothermic reaction that is not valid because reaction is going on temperature changes yeah but one thing which is not mainly valid is the sharpness of the shrinking core model we have nicely drawn one particle and this at center after sometime T we are just saying that that is the shrinking core that actually will be diffusive that actually will be diffusive so that means exactly your CAC is not there and RC you can never identify exactly that is the sharp boundary that is one of the things but anyway I think you know people have done experiments and then finally found that this is one of the very well represented model for gas solid non-catalytic reactions okay good afterwards a few more things about this one some more information about this if I have the shrinking core model and as I have been telling you that we do not know which one may be rate controlling there are various ways you know tau can be used for example if you want to plot the whole rate versus temperature all these things again analytically some information must be in our mind so I am simply trying to plot my rate of reaction versus may be with respect to A okay or with respect to B right so because the other one is nothing but minus dna by dt right equal to minus 1 by b dn by b dt so that is only the relationship okay so if I am able to plot either one of them how does that look like rate of reaction during reaction during the entire reaction you do not know which one is rate controlling okay so if you have only one rate controlling at least we can easily visualize but here what is that what we can normally expect is something like this so this is rate of reaction and here let me plot with temperature that will give us an idea which one which may be rate controlling right so you know I mean logically you can also get the answer for this at low temperatures generally which will be rate controlling reaction right at very high temperatures mass transfer so at low temperatures the rate may slowly increase like this okay and after sometime it may go like this this is one logical way of representing the rate of reaction with increase in temperature so I can say here that I have this one is reaction control okay yeah here what is controlling yeah which mass transfer I have to yeah ash is controlling so this may be ash controlling and in between somewhere you may have film control okay and we know at very high temperatures even the mass transfer through the film may be higher when compared to diffusion through the pores yeah ash through pores through pores so that is the reason why this is the kind of curve we may expect and as a check if you do not have which one is controlling right so let me say that you do not know and you did like this and you got only this portion that means you got all the time a straight line till the temperature you have conducted so then what is the idea you get rate of reaction and it is only going like this but it is not going you know taking this turn and then becoming almost horizontal no it is not happening it is only just almost a straight line okay so then we can conclude that this may be reaction control and then you yeah here you do not get all this portion when you start at high temperature because the temperature range anyway it is not theoretically 0 okay yeah so at high temperatures and you do not know which one is controlling you are somewhere here okay so at that time when you are getting almost there is not much change even though you are increasing the temperature it must be mass transfer control and generally in this sinking curve model it is diffusion control because diffusion through the pores is generally difficult when compared to diffusion through the film because in the film what do you have in the film what do you have Shekhar yeah it is only gas gas diffusion so it is not that difficult right so whereas in the pores depending on the pore size if you have very large pores again that is a different matter that is what next we would like to try to do okay for truly homogeneous model what kind of equations we have to derive but let me finish this whole thing about sinking curve model then we will go for that homogeneous model okay so this is one and based on this this first paper on combustion you know where systematic studies were done on coal combustion was done by some Agi and Kuni in the Japan and they have very beautifully systematically done even in most of you are not even born at that time 1955 okay yeah so how beautifully they have done the experimental so systematically coal combustion Agi and Kuni 1955 so he plotted or they plotted rate constants yeah I think because it is actual data they have input you know centimeters per second and here it is temperature Kelvin and how many rate constants will be there for coal combustion here how many rate constants will be there rate constants in this sense may be you know all process including mass transfer as well as yeah here only two but whereas in normal sinking curve model it will be three you know diffusion also comes there okay and here we will have only two but you see how beautifully you know the data has been collected this is 1000 Kelvin yeah 1400 1800 2200 Kelvin yeah this side the rate changes as a 100000 okay this is 100 this is 1 okay 100000 it is a log log scale sorry it is semi log yeah this is normal and this is semi log graph and then just draw the lines okay so then yeah at 100 1000 slightly away from that it starts and this goes to almost like this that is one line and then you have for if the diameter of the particle is 1 centimeter so then you will have approximately I want to draw this okay maximum is somewhere here okay so goes like this all this is for dp equal to 1 centimeter and this one is u equal to velocity right yeah also we have seen the term velocity there when you are there having 1 centimeter per second this one is 10 centimeters this is 100 centimeters no no no 1000 yeah so this is 1 meter per second and this is 10 meters per second yeah so then it is reduced to 1 mm 1 centimeter to 1 mm so that will be again approximately I would like to draw this this is for dp equal to 1 mm again here we have 1 centimeter u 1 centimeter per second 10 centimeters 100 centimeters this is 1 meter and this is 10 meters per second per second so finally you also have for dp equal to 0.1 mm here the velocities are 1 and 10 both are same here 1 u equal to this is 1 also 10 centimeters per second and the next one is 1 meter per second this is 1 meter and this is 10 meters per second yeah all that I have patiently drawn just to ask you how do you interpret the data okay and the examination I am very dangerous man you know in the examination I will give that graph and then ask you okay write about that what do you predict but that is very good training I say because that is what what you do in your PhD or whatever you do research okay you draw the graph collect the data and then try to interpret what is happening okay so this regime is which controlling low temperatures this is reaction control and here if I draw this line something like this this something like this something like this all all these lines yeah so this line okay this line will give me the k value ks value this one okay and this line will give me kg value right from here to here now of course these values are actually given by them these are all k values okay these are all kg values but you see it is increasing like this increasing like this and here the asymptote where truly I have the mass transfer control. So the simple reaction rate for this is minus rea equal to cag by 1 by kg plus 1 by ks that is the one okay so low temperatures this is infinity this is controlling high temperatures this is kg is controlling okay so there are many things it is not simply I have drawn and then you know we will just close here there are many things what you can predict so what is happening with increase in dp or decrease in dp the rates are increasing yeah why these are the questions generally take dp dp equal to 1 centimeter 1 mm and 0.1 mm so the rate of reaction we say that it is increasing yeah rate of reaction is increasing kg increasing why kg should increase as dp is yeah very good yeah that is the kind of interpretation okay we know that as you know dp is increasing or the kg is inversely proportional to yeah kg yeah diameter so smaller the one more mass transfer so more rate of reaction okay so within the velocities now you take one particle and now you see 1 centimeter 10 centimeters 1 meter 10 meters so now again it is increasing is it logical yeah yeah so this is how one has to really present the experimental data so beautiful that is why even though it is one of the oldest one still it is very highly respected data okay and I mean presently we do not have that kind of patience to collect the data we will take one point and write 100 models for that earlier it was reverse you take 100 points and then write one model because modeling is you know because you have computers you have everything so okay and your packages so one data point and then 100 models but world and style is that 100 data points and one model which is staying all through because that is solid model okay so this is how one has to find out really which one is rate controlling and how do you get the data all that information you can get from these graphs okay and still the way I am explaining it is not that simple okay you have now asked me how they have collected the rate of reaction data okay for rate of reaction first and then only all these things are analyzed or even here all that one has to really think before starting the experiment how do you analyze my data okay I conducted the experiment but how do you analyze for example coal combustion data how do you find out you see we do not have thinking at all absolutely particularly with experiments we imagine that we have one particle and then I asked you to find out rate of reaction how do you do that how do you find correct I mean that is right you can find the weight loss how do you find out so all these things you have to imagine no I mean no one is going to tell you if you get the job shaker so that is one thing I thought I will ask you you asked me before that you know you you just told on your own not asked you know first of all you have two phases there okay gas and solid which one you are concentrating what androg was telling was that okay solid solid also can be followed gas also can be followed right if it is gas oxygen concentration has to be monitored in the outlet but normally in the combustion process you send lot of oxygen and you do not worry so you may not have yeah that is another indirect way of finding out okay then you can convert into you know how much oxygen has been okay so then what are the methods you use for analyzing gas I am just trying to think you know I will make you think yeah if you do not have GC because people I think 100 years back or 70 years back I do not know they do not have GCs how they could have done it gas you have totally forgotten about this one no titrations totally forgotten no one is doing titrations nowadays I think yeah that is like bullock cart technology you know that is solid all the time if nothing is working you know bullock cart will work because nothing happens to bullock cart normally because there is no high fund or mechanism there nothing to get spoiled there okay so that is why this titration thing analysis is always valid but because we do not have patience that is why we are running after fast analysis yeah GC is one I think it is fair to accept that GC is one anything else otherwise actually you have to do you have to collect the samples took that take the samples and then dissolve in something else if you are following CO2 take the sample or allow the outlet gas itself through go through some other chemical where all CO2 is absorbed and then indirectly you will find out how much CO2 is absorbed then you calculate what is O2 would have reacted all that okay and okay as Andhraag said I think if you want to find out the weight what is the technique use you heard of TGA I mean you heard of TGA no you said TGA you did not say anything weighing scale of course the principle of TGA is weighing scale only yeah originally people have done that they constructed very very sensitive balance and one side they used to put coal particle may be you know 10 grams or 20 grams or 50 grams and then the other side it is balancing the weight and you have I think in your I do not know whether you have done the drying experiments that is one of the principles we also constructed that long time back okay so then you can find out what is the weight change and you know that weight can be converted into moles and of course moles per unit time and then you can find out what is the weight okay so all these things we do not normally tell all these things we do not normally tell it is exactly like our movies you know where I think I have been telling this I think last class also I have told this all our movies how does the movie start with the young boy and young girl coming and then first either fighting or I mean first side they never fall in love even though they fall in love I think egoism they do not accept so that is why a boy has to pay in the girl girl has to pay in the boy and then till interval it will go over after interval I mean in between we have some songs and all that I think over all that so after that only villain comes villain may be in the form of mother mother in law for you know both sides or father father in law so like that you know brother brother in law sister sister in law so you have in India so many relationships so you can that is the variation in all our movies one movie we will have brother another movie we will have sister another movie we will have you know Chettapa also okay so all kinds of people we will have so then anyway after that I think everyone will accept and then the movie ends with marriage that is all what we show all the problems actually start after marriage how many of us I think really seeing those movies this is also exactly like that we know we think that you know we are not telling you all that simply I plot rate versus concentration rate versus temperature right but if you do not think properly in your life you never understand what is that rate how do I get this rate that is why I told you even after PhD can you design a pump because we would have never told you how to design a pump you could have solved problems absolutely no problem right you should have solved problems you could have got yes out of that you know in that subject but finally when someone asks that okay I think I have a problem I do not know how to calculate my HP for my pump means I do not know how to calculate that is why I made a point that you know every time I will repeat these examples okay so that at least you will be aware you may forget the moment you cross the door you might forget okay like that matrix movie where he tells that okay you do not remember anything the moment you cross the door so I am not cursing like that but I think at least you know most of you do that you will forget and you remember only just before one day before the examination and the next day you will again everything will go good anyway so that is why there are so many things when you are teaching a course which is not directly told like our movies only I am telling right there are so many so many things which you have to really remember whichever you have to understand and for every course general thumb rule of professor Anand is if I am teaching one hour you have to work four hours at least in your role for that course that is why we have 24 hours per and a maximum six subject so 24 hours that is the idea okay per semester so otherwise you do not get anything you may come and sit till I look at me very skeptically this fellow talk something I think you know I just listen and then otherwise I will coming I will drill hole from this side to this side so that there is no retention there straight away it comes out okay why wasting time so that kind of attitude if you come and then you just stare at me that is all otherwise I think at the end you do not get anything at the end I do not get anything that I have satisfaction that okay I taught them where they have understood something and then retained something retained retaining is very important for teacher otherwise I think next semester also if I teach all these things you come and sit here as if you never heard of this okay yeah so that is the kind of teaching what we have and also your response anyway we will close here Monday Monday will you know Monday we will meet and Monday again I can give for example derivation of this okay