 I am going to discuss the four chemical engineers actually the discussion will be quite general but let me to put the subject in perspective what you have are processes which are divided into rate controlled processes and mere say near equilibrium process under rate controlled processes you will have several courses you will have heat transfer your mass transfer your momentum transfer which is your fluid mechanics here you have thermodynamics the stage cascades is characteristic of classical chemical engineering operations it is still chemical engineering itself I must give you some history basically it started about 100 years ago started as an offshoot of industrial chemistry and there have been some paradigm shifts in chemical engineering started actually with I think Arthur little first initial 25 years of chemical engineering in MIT in Cambridge and so on but simply descriptive industrial chemistry they simply describe the industrial process and you if you had had a good description of paper making then you went there the placement they also had a placement in those days you would go there and you would answer all questions about paper and you would be taken immediately as a chemical engineer the paper industry then Arthur little in 1925 I think surround that time he suggested why are you guys doing this in the university you have to be more general than this there are common processes in all the chemical industries you teach that in props loved it because all of a sudden they did not have to know the details of the paper industry because it is a damn nuisance knowing all the details because they will keep changing every other day and all the changes appear very vital for the industry but for you it is like noise unless you have invested money in it unless you are getting some returns from it the changes are inconsequential the conceptual changes are very few so that is when they start they started this era of unit operations and you still have good books like McCabe and Smith and it is a classical books Badger and Banker all these but in any case reactor theory became part of it in educational institutions in India only in the late 60s or early 70s but that was the age of unit to processes and unit operations 1962 birds to attend Lightfoot wrote this book on transport phenomena what really happened was in the mid 50s suddenly chemical engineers were in getting jobs the nuclear industry became very important and all of a sudden nuclear industry found the chemical engineers were fairly ignorant of molecules of atoms in that there was energy in it and so on so there was no point in hiring them if you have to explain to them that the whole industry is based on production of energy from the atom and all of a sudden there was a shift from engineering from technology to what is called engineering science and that is when birds to attend Lightfoot wrote their book and Amundsen and Arras came to Minnesota they were both PhDs in mathematics so this came about so this was called the period of you might say chemical engineering science earlier it was called the period of the age of the handbook you might say I do not know if any of you have a chemical engineering handbook and you had to buy this book it a very fat you carried it under your arm exactly like doctors carry a set the scope I mean the proof of being an engineer was to carry a slide rule in one hand in the handbook and the other but even now the handbooks are the source of all design eventual design because in practice design a synthesis and you want to put things together you finally have to bridge a gap in ignorance let me explain philosophically what we do in courses in the university and this is not a derogatory description this is an actual description you take a large problem this is true in science this is true in engineering you find that there are conceptual difficulties that are very hard to solve so what you do is divide the large problem to two parts one of which contains the conceptual difficulty you put it aside and then you solve all the problems concerned with the other half where there is no conceptual difficulty those also require a lot of intelligence and cleverness once you have solved all that you you then you know a lucky generation gets away with five years of research on that all those problems are solved then you go back to the other half you do the same clever thing you divide that into two halves keep away the conceptual difficulty unless there is an Einstein who comes along and solves this meanwhile you solve all the problems in the other half this is how analysis proceeds until the last conceptual bit is solved you can't synthesize it for design for design you have to use empiricism and empiricism is still used partly because we don't understand turbulence so coming back you have this age of unit operations the age of the handbook the age of unit operations and then you have the age of chemical engineering science we really don't have a paradigm shift afterwards although after about for 20 years of great enthusiasm about mathematical modeling and chemical engineering science people discovered you are not wise enough to advise the industry very often so you go back and ask what can we do and one of the paradigm suggested by James way was head of MIT chemical engineering department he said back to industry but it's not a good paradigm it's not been universally accepted because unfortunately industry is very focused on the bottom line so you can't use the industry as a guide for education education has to be general and then when you you will find applications you are sufficiently intelligent you will find applications in the industry so as far as this the curriculum here is concerned we have all these courses you have all these these processes have been combined into transport phenomena is transport phenomena is really based on phenomenological theory phenomenological theory is simply conservation laws all laws in nature are conservation laws the conservation laws that your view will be concerned about as chemical engineers are primarily conservation of mass conservation of energy and conservation of momentum in all when you write the conservation laws they simply general laws that says input minus output is equal to accumulation so in a sense it's only common sense but the biggest problem in phenomenological theory is that your experiments are done by a stationary observer you can only do experiments by sitting in the lab sticking a pressure gauge may be on a on one location in the pipe the fluid that's flowing through is changing constantly the way the laws are written conservation of mass is for example written simply by looking at the same mass of elements all the time that means if you had to do the experiment on the same massive elements you let sit on it and move with it so the Lagrangian observer is the observer the Lagrangian observer is the observer who moves with the mass with the center of mass that observer is the one for whom the laws are written in order to convert this from the Lagrangian observer to the Eulerian observer observer who is standing in the laboratory you use what's called the Reynolds transport theorem it's a simple theorem that relates what happens what an observer moving observer sees to what a stationary observer sees this transformation gives you the phenomenological laws in a way in which you can solve them but it's not yet the full story because when you write the phenomenological laws you have talked about what comes in through the surface or what comes in from a distance like four body forces gravity and so on if you're talking of fluid flow or surface forces like pressure or shear stress and so on you have to write symbols for these those are not included in the original description the original description transport phenomena assumes that if you know temperature as a function of position and time if you know density of each species as a function of position and time and if you know temperature this is for energy this is for mass and for momentum V as a function of position if you know these three independent these n plus 4 this is n components 1 and 3 components of the velocity if you know n plus 4 variables as a function of position and time completely then you have a complete engineering description you can derive any quantity you want you can do all the calculations in order to calculate these you have to use the conservation of energy you have to use the conservation of mass you have to use the conservation of momentum but when you use these you introduce new variables when you write the phenomenological theory for these you introduce new variables as I said the first step in phenomenological theory is what does the observer see you have to look at what the Lagrangian observer sees and related to what the Eulerian observer sees that you do the next step is to write fluxes motion of energy across a boundary Q the heat flux or motion of mass which is the diffusion flux or you look at because if you are a center of mass observer the relative moment is the diffusion flux similarly for momentum you look at the shear stresses but for all these you use new symbols so in writing the phenomenological theory in sense it is a tautology that is you write it in terms of new variables that you have to then connect back to here connecting these variables the fluxes again as functions of T ? I V and R and T writing this this is called constitutive relation this tells you how the matter that you are dealing with is constituted so you need the phenomenological theory this is the laws the universal laws that you believe in at least that have been so far not contradicted because there is nothing proved in science you only have uncontradicted experience so far you combine these with boundary conditions because you have to define a system write the phenomenological law for it write the constitutive relation for it finally substitute boundary conditions and of course there is faith in calculus the variables are continuous you can differentiate them so on so this is your all of this comes under what is called continuum mechanics you assume that the systems you are dealing with a large enough to contain a very large number of molecules so if the molecule number of the change in the number of molecules is always discrete you may go from 10 to the power 23 to 10 to the power 23 plus 1 but this one in 10 to the power 23 is so small you can construct a differential change so if you are dealing with very small systems you have problems in this case so this is your transport phenomena this is what you will deal with effectively very often you will not write differential equations because these equations are very hard to solve the whole theory of mathematics that has developed in order to solve these equations especially when they these relationships get nonlinear and also even here even in the phenomenological theory what the moving observer sees becomes a nonlinear term so all of these are nonlinear equations they are not easy to solve the ones you can solve are linear equations of course you can hit the idiot box on the head and get answers I mean if you hit it hard enough now with different software you will get numbers but you do not know whether the numbers are right you have problems of convergence very often you have a PhD thesis in which you spend 3 years proving that the result is in fact correct the number is finally right so this is what you do in all the other courses and if you can't solve the differential equation they get very complex you have empirical equations relating variables of interest to the variables in the that you can measure so empirical equations are very very important part of design in fact this is empirical in itself the flux itself if you write Newton's law saying the shear stresses minus mu times the gradient of the velocity you are writing an equation that you observed from experiment all constitutive relations come from experiment although in continuum mechanics they tell you what the structure is thermodynamics here itself has an constitutive relation you call it an equation of state what you do here is define a certain number of variables there is one relation between variables that comes from experiment that's the equation of state so in thermodynamics you have the two laws which are equivalent of the phenomenological theory actually three if you like but the third law is only simply defines for you the so-called third law of thermodynamics simply tells you a state in which the entropy is 0 so that you can calculate absolute entropy but you have essentially you deal with two laws and constitutive relations only you don't call them constitutive relations here you the nomenclature is that you call it equation of state what stage cascades does is use mass balance again and thermodynamics coming back here you will find the thermodynamic input in stage cascades is in the form of an equilibrium curve an equilibrium relationship that will be given to you they will say analyze this distillation column given that the equilibrium between vapor and the liquid is described by this equation that equation is given to you that's what you derive in the thermodynamics course so this what we do is look at thermodynamics here I am going to look at the two laws and the constitutive relations as far as the two laws of thermodynamics are concerned you must tell you the first law came after the second law first law of course is about constancy of energy in the second law is about ever increasing nature of entropy but basically there are some fundamental concepts that we assume that everybody understands so I will just state them in sort of keep going and occasionally somebody may disturb those foundations first thing is the elementary concepts you know all that elementary but use the word elementary so nobody asks you questions by definition elementary concepts are concepts that you are supposed to understand so there is heat there is degree of hotness this is one this is a second one the third one is work see mechanics came long before this thermodynamics came so they had already assumed that you know what a force is we assume that force times the distance moved by the point of application in the direction of the force gives you work and so on so people knew what mechanical work was people knew what heat was intuitively so these are assumed we concepts and we will add other concepts as we go along this list is not really complete because from time to time you will come up with ideas mostly these but you will come up with small ideas and then if it gets very difficult to explain I will put it under elementary concepts if it is not so difficult to explain in relation to others will come under theory okay as I said basically thermodynamics should be divided into three parts the first part will be thermodynamic theory which is very rigorous which is a nice set of logical arguments deductive arguments the second part constitutes equations of state and other empirical information about this constitutive relations the third part is applications so far whenever the application does not agree with experiment we have always found that if we improved the second part thermodynamic theory does not have to be touched at all you if you improve the second part where you understand properties of matter and its interrelations from experiment if you improve that the application always turns out to be theory turns out to be right it predicts things correctly so far that is the experience but that is not the end of the world because the number of things you have to measure when it comes to properties is enormous so there are at least a thousand labs all over the world measuring properties continuously for new systems because you do not know whether a new system behaves exactly like an old system or it is different you sort of predict on the basis of analogies but you always have to make a measurement so industry sponsors a lot of this work for property measurements in fact I think 75 to 80% of literature will consist of property measurements and the big complaint is that nowadays after the computers have come in the kids do a lot of mathematical modeling and simulation without worrying about measuring properties measuring properties not easy accurately so you take the easier way out of modeling with existing properties with the number of people making such measurements is reducing so rapidly and at some point you are going to have difficulty so let me get back here as far as the first law is concerned I would although the history is different we will deal with the first law first and you should read if you have time I think you have time it is a matter of organizing it you should read Jules experiments and I won't go into detail he simply went into a large number of experiments in which he converted work to heat as I told you Jules is famous for having sent many of the members of the Royal Society scurrying for the backdoor and in the apparently had to close the backdoor quickly otherwise they lose all the members from the Royal Society nobody wanted to listen to Jules but when you are first establishing a principle what Jules said was everybody knows that there is heat and work as exchange mechanisms for exchanging energy with the surroundings but Jules was the first one to simply assert that there are exactly two ways of doing it every energy exchange is either a heat exchange or a work exchange and there are no other ways of doing it so essentially assertion is that there are exactly only two ways two fundamental ways to exchange energy between or I will say for exchange of energy between system and surroundings so I will put under elementary concept system although you can define a system is anything that for which you can define a boundary well defined boundary anything inside it is a system everything outside it is the surroundings in thermodynamics so only two ways and he said essentially and there exists a property of state and put it here but not all of these are indefinable these are essentially concepts that you are supposed to understand these are definable elementary concepts this is property of state I will tell you what property of state is there exists a property of state he called it internal energy such that the change in internal energy was a perfect differential whereas work and heat were functions of path this is of course for this in a particular case of a closed system so let me introduce here under system there are three kinds of system so I will step back a bit system is any region of interest for which there is a well defined boundary a system is isolated when it has no interaction with the surroundings the only truly isolated system is the universe okay there is no other but many systems are effectively isolated in the sense that their interaction with the surroundings is negligible a closed system is one that exchanges energy with the surroundings but not mass so which chemists mostly deal with closed systems chemical engineers mostly deal with open systems because they have flow systems processes have mass coming in mass going out plus energy exchange with the surroundings there is no real conceptual difference the isolated system is very very useful conceptually because you can write you can write laws for isolated systems whatever you say about an isolated system you can maintain is right because nobody can verify it okay but the trick here is to say things that are meaningful from what you say about an isolated system you should derive results for a closed system which can be measured and verified otherwise they what you say are the rankings of a madman or a loner it does not matter you can say what you want you have a constitutional right but nobody will listen to you if you want collective activity you have to say things about an isolated system that lead to results for a closed system that can be verified experimentally for example Gibbs when he did the statistical mechanics of molecular systems of large systems he said a large a macroscopic system can exist in many microscopic states the simplest example would be temperature for example I am jumping the gun a bit temperature is there is a measure of the average kinetic energy of molecules in the system all the so you can have one molecule going a little faster one molecule going a little slower and maintain the same kinetic energy so you can have many possible states that is each molecule can be in different states but the total energy can still be the same so there are many many microscopic states that correspond to a given macroscopic state that is when you make measurements on us beaker of water like this you think the whole thing is quiet if you had the bit to see the molecules should just go mad in the molecules will be running around at 10 to the power 5 centimeters per second on an average so they will be hitting this every 10 to the power only a few centimeters so every 10 to the power minus 5 seconds you have a collision and if you could hear it you would go mad again I mean imagine thumping at the rate of 10 to the power 5 times a second that is the minimum and there are 10 to the power 23 molecules there so you are talking of 10 to the power 28 collisions per second so the whole thing is a madhouse luckily you do not see it because you are seeing averages and the average behavior is constant therefore you claim that it is at equilibrium it is at rest and so on so that is only an illusion the real fact is that there is a tremendous amount of activity and you have so Gibbs said in an isolated system all microscopic states that correspond to the same macroscopic description are equally probable it is pure philosophy because you know nothing about it the only way to do it is to do it equitably now since I know nothing about the states I assume they are all equally probable but that statement would have had no meaning except from that he derived laws that corresponded exactly to the closed system loss for in classical thermodynamics so similarly what you have to do is you have to realize that isolated systems are very useful conceptually but you have to derive results for closed and open systems chemists use closed systems and you can derive all of thermodynamics for chemical engineers from closed systems this book by Denby which is my favorite book is the only book I read cover to cover in thermodynamics Denby's book has practically only closed system tell a little bit of treatment about open systems I think he has added as an apology afterwards his first edition didn't even have it then we wrote this book on principles of chemical equilibrium which I like very much my recommendation is the following the many many books in thermodynamics are very good but if you go to the library what happens is you read one book you know sort of get bored then you read the other next book and you read another book you read 25 books all of them you will read chapter one so you won't get anywhere my recommendation is just pick the first book you got make sure it's a decent author don't pick a lousy book take a decent author's book and read the whole of it and then formulate it in your own mind that's the easiest way to do it ultimately it's nobody's special possession once you understand it it's yours as much as anybody else's if you do that you will be much better off in fact there's an old principle let me take this chance to tell you anyway there's some principles of teaching the first principle is nothing can be taught means this goes my job okay but the fact is a teacher can only facilitate learning and you have to be in phase after all I send out a message if you are in a mood to listen you will receive the message otherwise you won't you will be thinking of something else which is alright because somewhere along the line you hear these words and they'll come back to you later and even if they don't come back it's not a big loss it's only human experience that you are gathering you will have gathered somewhere else so the first principle is this second principle this is a very important principle that are in the enunciate he says suppleness and comprehensiveness of mind is actually developed by multiple approaches to the same problem not by solving many problems equivalent of these words the idea is that many problems you know if you use many approaches to solve a problem you understand the physics of it very well you can apply it any time to any other problem of interest and when problems come in real life that are interesting to you will use these techniques the idea is only take it teach your technique old again saying that the education is not about filling a bucket about teaching a student to open the tap in Madras sometimes it's a problem tap doesn't give you any water but you can never the less the idea is simply to teach you techniques the methods of science are always much more important than science than the results because results can change think it is also another quotation in very good one I forgot them there's an overlaught in chemistry who said he was appalled at the number of things he had insisted that students learn that turned out to be wrong afterwards this is part of teaching in any case but coming back I would say suggest that you try and do one problem in many ways and never everybody recommends that you do a large number of problems I myself haven't done a large number of problems but I found it very useful to study a problem and see if it's different from the previous one if it's not don't do it if it is do it is one more last story contrast is some of these stories is told by a mathematician I may have told you this before there are my favorite stories I think both the mathematician a faces were given a glass full of water has to make tea so they made went through the process put leaves and boiled make tea then they were both given an empty glass and has to make tea again so the mathematician filled it with water put it on the table and said QED by previous theorem T is made you don't actually get T with the mathematician but he simply tells you that there is a proof that he can be made my recommendation is use the method of the mathematician as far as possible do not keep doing the problems again and again because conceptually it doesn't give you understanding anyway let me get back here so the idea here what Joule did was to take his classical this thing was a calorie meter had a stirrer it had an attachment by which he measured the input of work he stirred it and found the temperature went up yet of course the thermometer which again brings you back to what a thermometer is again it's an empirical device for measuring degree of hotness and the things have been done experimentally then you have the degree Fahrenheit and the degree Celsius these have been introduced all these you know so we stick a thermometer in he measured the temperature rise by putting in a certain amount of work what he did was he had a system of pulleys and so on so that he defined work as simply the moving up and down of a weight so you could calculate the exact work done and by moving this up and down he had a series of pulleys which cost this stirrer to rotate and the temperature went up all this has to be done very accurately he insulated the calorie meter measured the temperature is then he cooled it back and the same temperature is he cost by a certain addition of heat then he did this in a thousand different ways every time he found that when he brought the integral over a cycle of ? Q – ? W was equal to 0 over a path whereas the actual work done could vary with the path so the work will be very different but in mechanical system thermo mechanical system mechanical systems he showed that the cyclic integral of ? Q – ? W was equal to 0 although the cyclic integral over ? Q itself or ? W itself was never 0 so Q and W are functions of path but the difference is independent of path therefore he said this quantity can be called the perfect differential and he wrote this is the you this is a summary of 200 years of work you might say and I write DU is equal to ? Q – ? W it is like the old saying that science is very accurate Newton says just F is equal to ? and the whole thing is very clear to everybody it is got all the elements in it whereas look at Shakespeare in order to communicate human confusion he writes a whole play called King Lear and you cannot summarize the whole thing in one sentence and communicate any idea you need a lot of redundancy so that you get some idea of the conflicts in life and what comes through and so on so that is what they said but actually this is false because when you write F you assume what a forces then you have to ask what is a force so it simply science is a language that we all accept and therefore we communicate with one other we are able to communicate but there is a lot of history behind writing F is equal to M whereas in language you still need this redundancy you do not have simple ways of expressing the whole thing because there are many subtle ways of doing so anyway so this what this does is then empowers you to use you in calculus this brings you to first I must have told you what a state is I am sort of putting the card before the horse the state of a system is simply the number of variables required to be specified before you can reproduce the system in another place okay the number of variables you suppose I have a beaker of water I have to tell you what the pressure is what the temperature is and say it is water so three statements tell you the constitution it is pure water I said set room 25 degrees C and one atmosphere pressure then I have completely specified the state of water how do I know I have completely specified it only by experiment I know the number of variables required finally Gibbs derived a phase rule but in the phase rule you know its number of components minus number of phases plus 2 that is the famous Gibbs phase rule but the number of components is suspect if the number comes out to be wrong and the state changes that means you did not measure all the components they may have been one component that you did not measure or there may have been a phase that you have missed if it is a solid state it can come in several phases without you are knowing it unless you examine it very carefully so in a sense while that rule is correct it assumes that you know the number of phase in the number of components so the number of variables required to specify the state of a system is a completely empirical thing so state of a system simply means specification state is defined by the assignment of values to a minimum number of parameters such that can be reproduced exactly in thermodynamics we do not worry about the container shape you are only interested in this system say water if I was interested in the system shape then I have to specify the container and all its properties as well so if your system is simply water then you have to give me only two variables for example if it is pure water so this is an empirical quantity in state variables are simply these variables that you have to specify so what this does is to say that you is a function of state if I know the state I know the internal energy exactly because if I go over a cyclic path and come back to the state you returns to its original value and only a function of state can return to its original value because a function of state implies that it is not dependent on the history of how it got there I could have got this water from kohm I could have collected it from rain water but if it is finally pure water at 25 degrees one atmosphere it makes no difference may make an emotional difference to you if I ask you to drink it if I say from kohm and I say from rain you will drink one very happily in the other you want although all of us will be forced to drink very soon recycled water there is no choice but any case the that is a different issue that is why human beings cannot be modeled in thermodynamics because they have a memory if I describe a person then I can say what is state is I can say he is so tall he is so fat he is so heavy and so on all this I can specify but his emotional state cannot be specified in terms of just current variables and to say how he was treated when he was one when he was two you know all that comes into play the history of the system so when you say state variables and thermodynamics is confined to description of systems that can be described in terms of state variables that means I only talk about systems without a memory okay if they have very short memory it is okay you can sort of gloss over it and say I will integrate everything and talk of properties over a 5 minute interval by which time he will forget if there are many organisms that forget many biological systems are like that they have such short memory that you do not have to worry about the memory but with human beings with anything that has a long memory you have to worry you cannot do thermodynamics of systems with memory so we have these state variables I have this discovery of June and therefore he said you is a function of state if you tell me the state there is a variable you which is uniquely fixed.