 Now let us begin our session formally, now you can, we will now follow more or less quickly in the scheme of things that we have. What I will do is I will quickly go through this and since I need some soothing time for my throat, maybe every 15-20 minutes I will have a discussion session as required. First thing is, this is for us and also for our students, go through our exercises sheet and at the back of the title page you will find a list of text books and references. So these are the five books which give a general broad perspective. Each one is unique and has its own style of presentation. For example, the third one Sears and Salinger which is even currently available and Zimanski 4th edition of 1957, there are later on, later editions but in particular I would recommend this edition. These are the two books which are written by professors of physics, however their treatment of thermodynamics, basic thermodynamics is really good and that is why we always ask our students to refer to these books as background material. The book by Sears and Salinger is the standard textbook for maybe our own physics students here and it is commonly available in India whereas Zimanski 4th edition would essentially be available in the library, may not be available now. Later on there are newer editions of Zimanski, now there is a co-author, I do not think professor Zimanski is there in now, Zimanski and Dickman but they have become so physics oriented that they cannot be really appreciated by non-physics engineers whereas the other three books one three and four, one two and four by Chutan, Moran and Shapiro and Sontag, Bortnak and Vayan. The Sontag and the book that authors and their list order keeps on changing, so may be there is a newer edition with a different, these are engineering thermodynamics books essentially written with mechanical engineers as the target group and in particular I would recommend Moran and Shapiro and Chutan are the books which would be more or less exposing the reader to thermodynamics in our scheme of things and at some places in the exercises you will notice that I have recommended as part of the exercises, some exercises from Moran and Shapiro, Chutan, even Sears and Salinger and Sontag at least in the early part where it is essentially basic physics of thermodynamics rather than applications. Now the evaluation scheme is not something for us to really worry about because many of you do not have any control over it but I will just say that because thermodynamics is a subject which starts from basic physics and goes into application, if possible the best evaluation scheme for thermodynamics would be more or less a continuous evaluation scheme. Now continuous evaluation scheme cannot be parallel evaluation scheme with teaching, so I personally like the scheme which of course in a fully autonomous place like IIT, Bombay I can implement it is every second week you will have a quiz, so in a 12 to 14 week semester you end up having 6 or 7 quizzes and the quiz will be just my quiz as my students know here it is just one sheet of paper A4 size with the question written here and student has space to write his name and roll number at the top and the answer has to be written in this space as well as in this space and it is a small quiz may be at short as 15 minutes sometimes as long as 25 minutes, I do not think I have ever conducted a quiz more than 10 to 15, 15 to 20 minutes is the normal thing, the advantage of such an evaluation scheme is not only the student learns what he has learnt or not learnt and also the teacher understand what are the difficult part for a student and this has to be no great thing a simple small question which relates to what has been taught in the last two weeks and just to find out whether the student has understood it no great acrobatics is required in these quizzes. Now when we start teaching thermodynamics typically in the second year first semester I think that is the place thermodynamics finds itself sometimes in the first year second semester but that is very rarely but sometimes in the second year second semester. So the question arises and the students are not yet clear or not completely clear about what is engineering, what is mechanical engineering and what is the place of thermodynamics and so quickly what I explained to the students since you are teacher I will not spend much time I explained to the students that look we are human beings we want a comfortable life good quality of life. So whatever we do should be to sustain that good quality of life and the job of any engineer is to provide that quality of life and for that the resources are only natural resources nature at one end humans at the other end the engineer sits in between making use of the resources provided by nature to provide us a good quality of life. Now where does mechanical engineering come into play so if we say nature at one end and humans at the other end and provide good life is the job of an engineer if so I propose that the where does mechanical engineering come now all of us are told that mechanical engineering is about machines but again the scheme remains the same we have nature at one end and we have humans at the other end and mechanical engineers are also engineers so they should do the job of providing good life to humans but for us the main scheme is machines. What type of machines first or one of the main theme is use natural resources materials stores of energy to provide power useful energy this power sometimes can be directly used for good of humans of course this power can often be used and is used for drive machines and of course not all machines provide power there are machines which provide power specifically to drive machines there are machines which produce machines machines with produce many other goods which are in turn made use of for the welfare of humans so although machines are at the heart of these things remember that machines which are looked at by mechanical engineers are of the type where natural resources are used to convert it into power power can be used for human consumption as well as to drive machines machines can also be used to produce machines and many other things which are used for the good of humans I think once you give the students this idea of what mechanical engineering is typically about in fact if you look at the history of engineering a mechanical engineering was the early branching of engineering you go back some 500 600 years or go to a linguist and he will tell you when was the first word when was the word engineering used for the first time at that time there was no classification but one characteristic of humans is that humans feel well when they are secure they are always interested in our security security of us as persons security of our family security of our group our tribe our nation and all that so anything which we do we first look at the security aspect subconsciously at least so any effort any new scheme the first implementation would be that of security so when engineering was first developed catapults were developed to throw cannonballs at the enemy so was bows and arrows so were sharp instruments like spears then later on people realized when many of the security concerns were apparently taken care of that engineering has other non-security applications also so the security applications were known as military applications and in military you have military officers and civil engineers so civil people civilians so engineering got classified into the military engineering and civil engineering if you look at the civil was from the non-military point of view so the civil engineers that civility comes from the word civilians in the military scheme of rankings if you look at the history of engineering in India one of the oldest colleges which is now the IIT Roorkee was earlier University of Roorkee and if you go still back before it was formalized as University of Roorkee it was some I think Thompson College of Military Engineering so old Roorkee alumna I call themselves Thompsonian I do not think anyone of them is around but if you go through the history you will find so the first branching of engineering was military and civil so all non-military applications were supposed to be taken care of by civil engineering then what happens as the applications grew civil engineers found that they had to handle power equipment they had to produce machines they have to also establish roads bridges and houses so the structural part was kept by civil engineers and mechanical engineers specialized into the machinery part but of course there were common things for example hydraulics flow of water it is something on which mechanical engineers and civil engineers still have a common thing and if I am not mistaken there are a few institutes in India which have both engineering departments of mechanical and civil but they have a huge big excellent hydraulics lab which is chaired by both the departments AICT may not like it but that is the ground reality you know flow through channels whether closed or open interest both to mechanical engineers and civil engineer similarly even on structures when it comes to steel structures whether you are a mechanical engineer or civil engineer it does not really matter but when it comes to concrete earth work and etc. Well mechanical engineer perhaps do not want to dirty their hand with earth work they want to dirty their hand with oils whereas civil engineers do not want oil they do not mind dabbling in earth and cement and concrete just to show that even after separation branches of engineering contain a lot of overlap between them because these branches are to some extent arbitrary if you look at it the branching of science into physics chemistry even mathematics for now even chemistry and biology is to a large extent arbitrary if you take physical chemistry a chemist will call it physical chemistry a physicist will call it chemical physics and if you go to the library you will find a very reputed journal called journal of physical chemistry and another journal by the American Institute of Physics called journal of chemical physics JCP so JPC exists JCP also exists of course they might have separated into series A series B now. Now after this you know mechanical engineers found that well they are into too many things so from mechanical engineering electrical engineering separated and of course electrical engineering later separated into electrical and electronics and all that. Then chemical engineering separated then metallurgical and materials separated then aerospace separated of course each one of them then separated for example chemical and metallurgical initially had a lot of overlap aerospace has a lot of overlap today with basic mechanical electronics CS and all that. What has happened is in spite of hiving out many of these disciplines mechanical engineering never really switched itself off from many of these so that is why you will find in traditional mechanical engineering curriculum there are many subjects and topics which sort of overlap with. Of course this has been a digression let us come back to over scheme of things in mechanical engineering since we have machines which either produce power from natural resources or consume power or doing producing machines or doing something nice handling of power or energy is one of the major scheme in mechanical engineering. And if you look at the natural resources the only long term natural resource which we have with us is the sun you go back in history I think all our energy seems to have come directly or indirectly because of the existence of the sun creation of the planetary system and all that. So you can say solar energy is the primary energy but because of the history of earth we have sort of stored storages of solar energy over very long term and these are known as fuels mainly the so called fossil fuels coal oil gas and their variations are very long term concentrated storages of energy essentially from the sun and the sun earth system. And these fuels release their energy by default by a process of combustion and this combustion is a process which takes place at a reasonably high temperature and what they provide is what we call thermal energy, energy available at a reasonably high temperature and the branch of engineering mechanical engineering which handles thermal energy is by default known as thermal engineering. So thermal engineering is that part of mechanical engineering which handles fuels thermal energy for any purpose may be direct use or conversion into power now it turns out that the basic thermal energy tends to be localized you cannot distribute it haul it over long distances you can haul fuels but once you convert them into energy it is difficult to haul that energy in the thermal form and when it comes to utilization we want energy in different forms we want mechanical energy to run over pumps, cars, trains etc. We want electrical energy for lighting and running other electrical devices so it is necessary for us to convert this into mechanical power or mechanical energy and this conversion is at the heart of thermal engineering and the first thing we realize is that thermodynamics is that part of thermal engineering which traditionally links such things as heat, work and temperature to be formally defined yet but if you look up history these three words are something for which even a you know early teenager for a late single digit age or we do not have a name for it preteen has a feel people tend to work out so some effort is to be overcome for working out so the idea of work is there the idea of heat sun provides heat fire provides heat gas stove provides heat electrical geyser provides heat that idea of heat is also there and because of fever and all that and running temperature the idea of temperature is also there so these are only idea you ask them for definitions they will tie themselves up in knots but they will oh this is hot high temperature this provides some heat and you have to really work out to open a jammed door or lift a heavy package so those application fields are there but there are no formal definitions which are appreciated or understood in day to day life there is no need for us to really appreciate the difference between heat, work and temperature or even what is energy many of us go through excellent contributions in life without ever worrying about this but as mechanical engineers and particularly as teachers in mechanical engineering we must understand very formally and unabiguously what these mean and the study of thermodynamics essentially means understanding these and related concern if you look at a basic definition of thermodynamics again you cannot define thermodynamics unless you use some terms which are within the scope of thermodynamics itself for example a very common definition is thermodynamics is a study of interaction of energy between systems I think you will agree that such a definition or very similar definition will be found in any textbook and you might have used this definition but remember that we are not developing something strictly mathematically or logically so when you provide this definition words like an interaction energy system are yet to be defined so to that extent we define thermodynamics without really telling them what exactly those details mean if somebody asks you sir what is a system you say a system is a thermodynamic system wait a lecture or two and we will define it what is an interaction wait a few more lectures and we will define an interaction for certain what is the proper definition of energy that waits still few more lectures and we come to first law we will define it. So if you look at it this is some sort of a circular definition which we are using now at this stage there is nothing wrong in defining something as a circular definition because we want to compress a lot of ideas in one word and without reference to any one of those ideas one or more of those ideas it will be impossible to give that compact definition. So we will accept this circular definition but later on our effort throughout would be to define terms like heat, work, temperature, energy in many other terms without falling into the trap of providing a circular definition. If you go to your library or talk to your colleague in computer science and engineering there is a very famous person his name is Professor Donald Knuth, Knuth KNUTH I think he is East European Polish or something but he has settled maybe he is born and settled in America, readily person known for the tech and latech document preparation schemes and also a very eminent person in basic computer science. His series of books called the heart of computer programming are famous you go to the first volume I do not know I think searching and sorting or something title but I would like you to go to the library find out that book and go to the index and look for circular definition and it will say C definition, circular. So you go to D from C and well there is an entry for definition and under that there are number of types of definitions direct, indirect, illustrative and circular in alphabetical order and you say definition, circular it says C circular definition. So is this a definition? It is not a definition but is it useful? Yes it is very useful because it really makes you understand what a circular definition is. In fact if you look at a circular definition it means A implies B and B implies A. Finally which one is two you do not know. So this is a type of definition which makes you understand things without really defining what is circular definition. With this thing you know what is circular definition but you cannot define it unless you give this story. So in thermodynamics I will ask yourself the question go to your traditional thermodynamics books. See how heat is defined and see how temperature is defined. Fortunately or unfortunately both my daughter and son are mechanical engineers and when they were studying one of my very entertaining past time was to go through their standard prescribed books. Of course being a professor of mechanical engineering myself I had my favorite books also sort of imposed on them which they did not really resist but for me it was very entertaining to go through their books particularly those of thermodynamics. And what I find is in many many of those books written specifically for their college, their university, their syllabus. If you look at the definition of heat and you look at the definition of temperature you will find very innovative uses of circular definition. Heat was defined as a form of energy which can flow from a body at a higher temperature to a body at a lower temperature. So heat is defined in terms of temperature and temperature is also defined as there is something called a higher temperature and something called a lower temperature. I think many of you would be familiar with this technique. Then somewhere either before or after that you come to the idea of temperature. Temperature is defined as a degree of hotness. I think this world you all of you are familiar with right. Without defining what is hotness, without defining what is degree of hotness okay. And the degree of hotness is defined in such a way that heat energy can flow only from a higher temperature to a lower temperature. So when you put these two together I think what are you doing if this is not a circular definition in a very convoluted way what it is. It where mathematicians and physicists who sort of straightened this out but we will come to that slightly later. So once having defined thermodynamics the next thing to do is to put it in the scheme of things. For example, since mechanical engineering is about machines, we worry about handling of energy, we worry about the design of machines, we worry about manufacture of machines and we worry about the operation of machines. When it comes to handling of thermal engineering the subjects which we will look at and this is what you should interest on students is thermodynamics which is our absolute basic subject. And you tell them that in thermodynamics we will be using typical working fluids like air and water which we use not only for our day to day purposes but also for significant engineering applications. And since these are the things which flow the next thing we learn sometimes parallely with this is fluid dynamics. Now you tell them that although we define heat temperature and energy and we talk of heat flow from one system to another, thermodynamics never tells us how to make that heat flow or at what rate that heat will flow if certain facilities are provided. Thermodynamics never talks about rate of heat transfer. As a derivative it may but it is not the job of thermodynamics to say that the rate of heat transfer from the water here to the surrounding air if the water is warm is so many watts. For that we study a science and engineering which looks at the rate of heat transfer and it is known as science of heat transfer. And then you say that these are the three subjects which form the basis for thermal engineering. And after that what comes are only applications, applications to phenomena like combustion, applications to equipment like power plants or engine, applications to refrigerators, related stuff like in air conditioners, cryogenic equipment and all that. And many other applications sometimes just for fluid handling or sometimes just for transferring heat in large scale from one place to another and so on. So this is the scheme of thermal engineering and you should impress on the students that thermodynamics is at the base at the top of here but you can always start from the bottom and show that like a tree all the things go. The main basis thermodynamics immediately followed by fluid mechanics heat transfer and then applications will be all branches of that. And of course impress on them that the other branch of mechanical engineering where you worry about the design, detailed design of these machines and the other branch where you worry about what materials to use and how to produce those machines also have a similar things. For example if you go to the machine design branch design engineering you start with equivalent of thermodynamics may be engineering mechanics there. Equivalent of fluid mechanics and heat transfer would be subject like solid mechanics, then kinetics and dynamics, strength of materials then followed by applied courses like design of various elements and various type of assemblies, subassemblies and bigger machines. The next thing you should talk about is the precursors and followers. By that we mean that I do not know here before a student learns a course it is supposed to have cleared what are known as prerequisite courses. That means subjects which provide the required background for learning this given problem. So what are the precursors of thermodynamics? Of course it is something which we have seen thermodynamics heat transfer but which are the subjects or which are the topics one should learn so that the learning of thermodynamics would be smooth. What is the background material? For example we consider that arithmetic into some extent geometry, basic geometry, elementary geometry is required for us to study and appreciate algebra. Algebra is required for us to study and appreciate calculus. Calculus is required to study and appreciate say differential equation, then partial differential equation and so on. So there is a reasonably neat order in which you should study the subject matter and even within a subject we have this a reasonably neat order for studying the topic. So similarly if you say precursors thermodynamics requires some tools and some background. For example high school level physics and chemistry where you know something about gases, liquids, some vague may be incorrect idea of what heat is, what energy, what temperature is, at least these terminologies you should be comfortable with. So one is high school physics and chemistry then mathematics. Well everything of high school level is okay plus the way we are going to learn thermodynamics is some calculus, differential calculus mainly also integral calculus. Particularly the calculus leading to what is known as exact differential. This will be very useful in thermodynamics. And of course since thermodynamics works with energy, any other branch of physics which handles energy in some form or the other, for example we have electrical energy, we have mechanical energy in springs. Some exposure to those will also be useful in thermodynamics. One should remember that thermodynamics if you look at the physics point of view is a proper branch of physics and has the same status as mechanics, fluid mechanics, electricity, magnetism and what have you, gravitation. So thermodynamics does not partition itself off from other branches of physics. It lives with it in a proper happy fashion like a happy family. So a study of thermodynamics can really never be complete if you switch yourself off from other branches of physics. That is something you should impress on students. Now what is thermodynamics about is we have already said that thermodynamics will generally have our main scheme of thermodynamics will be something like this. We will not, we will need to define this. We will have something called system A which could be anybody like me or this bottle of water or this pen or this lamp whatever and a system B. In thermodynamics we will study interactions which will be energy interaction. Tell them that many of these terms are to be defined. So tell them that this is only a trailer. All these terms will be defined in due course as we proceed. Then let us complete the first topic or first set of introductory topics by looking at contributors. Actually thermal engineering if you go back in history really started when human beings or our predecessors realized that the theory phenomena, natural phenomena called fire was very dangerous but also very useful. There must have been lots of accidents maybe tribes must have been simply burned to ash by accidents. But then of course there were always you know brave people, curious people who tried playing with fire as we say and slowly they realized that with proper care it is possible to control fire, to create fire when we need it and douse it when we do not need it anymore. So perhaps the first contributors to thermodynamics where those who discovered the control of fire and you look at the earlier philosophy earth, air, fire, water were supposed to be the four elements in the European scheme of things. Then we have those Panchamahabhutas Prithvi, Aap, Teja, Vayu, Akash that Teja is essentially which is energy fire radiation which is at the central scheme of our scientific philosophy. So although this started and we started understanding that something is hot, something is cold, something is thermal energy, there is something non-thermal energy in a falling rock and some energy in the form of fluids flowing and wind blowing. Perhaps the first person who formalized something about thermodynamics was Karno, an engineer, the mechanical engineer to Bhut. What we today say is the second law of thermodynamics was first proposed as a statement by Karno who looked at mining equipment, essentially pumps and engines which pumped water out of mines and hauled material out of mines. And he started thinking of course being an engineer you have to be good at economics also. He said look this much work I have to do, this much water I have to pump out, this much material I have to pull out and I have to burn wood, coal to run my engine. And of course if I can remove the same material from the same amount of water by burning less coal it is good for me, less cash has to be spent. So the idea of an efficiency of an engine was first put up in his head by Karno and he, what a flight of fancy but he came up with the idea of reversibility and the idea of the maximum possible efficiency of an engine. He had no idea of what heat meant, he had no idea of what temperature meant, he decided that look if I can make my engine reversible then I will be consuming the least amount of my fuel for producing the same amount of work. That means hauling the same amount of material or pumping out the same amount of water. After Karno there were many engineers for example what recently Keenan who contributed to it. But of course when some phenomena comes physicist, chemist and mathematicians start looking at it. So if you can look at physicist then we have the count room 4, Benjamin room 4, then we had Joule, chemist also you can put Gibbs, Lausius, Kelvin, physicist and physical chemist. All these people have contributed to thermodynamics and of course no great physicist you know ends his life without saying something or writing something about thermodynamics. There were mathematicians who started looking at the proper structure of thermodynamics because engineers said look we have something to do with engines so long as we make our engines efficient we do not care about the laws of thermodynamics. Physicists want to understand but physicists never were happy with the structure of thermodynamics which they created because they knew that there were internal circular definitions, internal inconsistencies in that. It took mathematicians to straighten this out and the first person to straighten this out was a French mathematician physicist called Carre Theodore. In fact his structure of thermodynamics is considered from the differential mathematics point of view, from the continuous behavior point of view, the most consistent structure of thermodynamics. Of course it is mathematically very involved so although we will be following his treatment when it comes to first law of thermodynamics, we will not be following his treatment when it comes to second law of thermodynamics because we just do not have the appropriate mathematics background. The second law of thermodynamics we will follow the Kinan and others formulation, Kinan-Kelvin's formulation. After Carre Theodore a few other mathematicians tried their hand but there was another mathematicians absolutely pure mathematicians by the name Giles or Giles I think I do not know Richard or Rudolf or something like that whose mathematical foundations of thermodynamics his work has been published in that form is perhaps one of the excellent ways of looking at thermodynamics where you do not consider anything to be continuous. I mean Carre Theodore assumes that energy is not quantized everything is continuous. You can work in terms of D E, D W, D Q, D T and all that everything is in terms of differentials. We brought in the idea of exact differentials and when it comes to Giles, Giles only talks about states and changes of state from state 1 to state 2. He never brings in the idea that properties and interactions could be continuous. If they are continuous so be it. So his work is on differential concepts geometric concept. Giles work is essentially based on topology and since for some reason engineers are not exposed to topology and we do not really need topology we will just not look at Giles formulation at all. There are other people for example one name which I will write between engineers and physicists is Bridgeman P W Bridgeman engineer physicist. In fact it was his work which led to a proper understanding of thermodynamics and we will be referring to his work as we proceed here and these names we should know because these are the historically significant contributors to thermodynamics. Now any questions on this before we come to basic ideas and definitions. The question from Professor Kulkarni is what is topology. Now topology is a branch of mathematics considered pure mathematics but has enough applications. That is a branch of mathematics where properties of only links and arrangement is considered. For example if you take our normal geometry if I take a straight line and bend it it is a different line but topologically a straight line and a curved line are equivalent because you have a set of points arranged in a particular order the direction does not matter. For example if I take a sheet if I bend it it is geometrically different now instead of a flat one it is curved or it is even closed. Topologically so long as I do not close it it is equivalent because the arrangement is the same but if I close it it is different because you are making a connection which did not exist earlier. So topology considers situations where any sort of change of shape or size does not change the properties. Only a rearrangement changes the property. For example whatever I do with this so long as I do not reconnect it or tear it apart or punch a hole through it topologically they are all equivalent. Applications of these are in thermodynamics in cosmology and many other branches of things. And topologically for example a ring of any kind is equivalent to any other ring. And topologically if I take this out this bottle is equivalent to a flat sheet because what is a flat sheet something which has one single edge. This is also something which has one single edge. There is no hole here, there is no hole here. And in principle I can melt this and make it into a flat sheet without tearing at top or punching a hole. So this is equivalent to this. So our ring or a you know a typical South Indian medu vada provided it has a clear hole through it, they are equivalent. Or you take a solid piece and just drill a through hole through it that is equivalent. So what are the common properties of these is something which is looked at by topology. Seems very clear but there are good books which will make you understand topologically to the extent it is possible with us now. Any other questions? I have one. Galileo is considered as basic contributor for the thermodynamics in the perspective of temperature. Temperature issue that has been raised by Galileo and later on has been confined to one particular definition. I think we can consider him as a contributor for the thermodynamics. See my list of contributors is not exhaustive. Actually the greatest contributors have been lost in history. Those who really develop the basic idea. See because that is what I said we sort of we seem to have genetically inherited from our predecessors the idea of what is energy, what is hot, what is cold and what is something temperature. Without really understanding it but those who brought up those ideas in however way they have been lost to history. And of course if you really start studying thermodynamics I will have to give you may be 100 names of there is a curve code then there is a Glaston and there are number of people who have contributed to thermodynamics. One question is what was the objective condition where such a hypothetical assumption Karnat has made. See the greatness of people like Karno or Joule lies in the fact that they did some experiment however crude. But they could see through all those you know crudeness and approximations and come up with some basic idea. For example you look at Galileo Newton's first law that in the absence of a force acting on it body will keep on moving in a straight line or in a state of rest for an indefinite time so long as a force does not come and left to itself that will what will happen. Galileo worked with falling object Galileo worked with you know balls and sliders moving on a surface. He tried to reduce the friction by using oil and smoother and smoother surface but he never could and we know a zero friction surface is almost impossible to create. But he could see through all that and imagine and propose it as a first basic principle that if I have a frictionless surface which today in his honor we call a frictionless surface a Galilean surface and we say if I push something it will just keep on moving indefinitely till somebody else comes and does something with it. The greatness of those people lies in there being able to see through all those you know realities on earth and go to the heart of physics saying if I idealize this is what it will be. For example Carnot's engine the efficiency was nowhere near that of a reversible engine. None of his processes was anywhere near reversible even today's processes are not reversible. But his greatness lies in the fact that he could come up with the idea of a reversible process by which an engine could work either as an engine or as a refrigerator. He never had an idea of what a refrigerator was but the idea of reversibility came up and then the idea that if I make everything reversible I will spend the least amount of fuel for a given task. It's a great leap of imagination but that's where the greatness of Carnot lies, Carnot and others like him lies. It's not a derivation like 1 plus 2 is 3 so 2 plus 1 must also be 3. It's not a logical derivation. It's inductive logic of the extreme kind. There is no proof. They said so we found that in reality it is so, so that's where it lies. Sir, as we have considered the combustors as the control of fire. We compare it with the control of energy and interaction with the system and surrounding. It is. We will finally put everything on one single setup where energies of all kind will be combined into one term and we will say that look there is nothing special about the way energy is defined in thermodynamics. There are other branches of physics which define that energy and will make use of those characteristics.