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.


For decades, sometimes furious battle has raged among scientists over the extent to which elevated salt consumption contributes to death, with one camp calling it a public health hazard that requires vigorous attack, and another claiming the risk of dietary salt excess are exaggerated, even to the point of calling salt reduction probably the largest delusion in the history of preventive medicine. The other side calls this denialism ethically irresponsible, especially when millions of lives are at stake every year. Describe two sides of the debate may be falling to the trap of false equivalency, though. As the superhero sounding world hypertension league points out, there's strong scientific consensus that reducing salt saves lives, and like the climate change debate, most authorities are on one side, with only the industry affected and their paid consultants and a few dissenting scientists on the other. Nearly all government-appointed bodies and nutrition experts who have considered the evidence have recommended we collectively cut our salt intake about in half, described as extreme, though, by those defending the industry. After all, just a small fraction of Americans actually get their sodium intake that low, therefore the scults, the salt skeptics say the human experience for very low levels of sodium consumption is extremely sparse. Extremely sparse the reality is the exact opposite. The human experience is living for millions upon millions of years without Cheetos or a salt shaker in sight. We evolved to be salt-conserving machines, and when we're plunked down into snack food and KFC country, we develop high blood pressure. But in the few populations left that don't eat salt, that continue to eat as much as we have for millions of years, our leading killer risk factor, hypertension, is practically non-existent. And when you take people out of control hypertension and bring them back down to the sodium levels we were designed to eat, the ravages of the disease can even be reversed. So why is there still a debate? If salt hidden in foods kills millions of people around the world, why are efforts to cut dietary salt being met with fierce resistance? Well, salt is big business for the processed food and meat industry. And so, according to the head of the World Health Organization's Collaborating Center on Nutrition, we get the familiar story. Just like the tobacco industry spent decades trying to manufacture doubt and confuse the public, the salt industry does the same. But the controversy is fake. The evidence for salt reduction is clear and consistent. Most of the quote-unquote contradictory research comes from scientists linked to the salt industry. However, it takes skill to spot the subterfuge, because the industry is smart enough to stay behind the scenes, covertly paying for studies designed to downplay the risks. All they have to do is manufacture just enough doubt to keep the controversy alive. The likes of the World Hypertension League have been described as a mere pop-gun against the weapons-grade firepower of salt encrusted industries who looked disdainfully at the do-gooder health associations who erect roadblocks on the path to profits. Lest we forget, notes this editorial in the Journal of the Canadian Medical Association, high blood pressure is big business for the drug industry, too, whose blood pressure billions might be threatened should we cut back on salt. If we went sodium-free and eliminated the scourge of hypertension, not only would big pharma suffer, what about doctors? The number one diagnosis adults see doctors with is high blood pressure. Nearly 40 million doctor visits a year. And so maybe even the BMW industry might be benefiting from keeping the salt debate alive.


New plans announced for second season of Crossroads on the National Television Network, NTN. The prime time show of the Ministry of Youth Development and Sports highlights young persons making a difference within the communities. We'll feature new segments and target youth in a variety of sectors. The aim of the program is to really dive into communities and find young people who are making a difference. We started last year. This year we're hoping to have a wider cross-section of young people from the arts, culture, sports, youth development, etc. And we're hoping to add some new segments in fact. We're hoping to reach out to the schools and we're hoping to make some young producers out of the students across the island and secondary schools to be specific. And these are some of the things that we can definitely look forward to. The Director of Youth Development welcomes season two of the television program expected in March and encourages the general public to nominate young persons to be guests on crossroads. We are now preparing for season two of Crossroads and I would like to encourage persons out there to nominate young individuals to be a part of this program so that they could highlight some of the achievements and you could have a discourse on youth development in this nation. I must say that season one was a success and the intention is for season two to be even bigger and better. Interested individuals can be nominated by filling out an online form available on the Facebook page of the Ministry of Youth Development and Sports or calling the youth division at 468-5404. Marvin St. Louis reporting from the Ministry of Youth Development and Sports.


Good morning and welcome to today's products and focus so looking at the US 30 right there You can see we have multiple bounces trying to get through 18,000 and 112 And a failure to do so yesterday and actually a bearish engulfing pattern there being posted now We're getting quite close to that 18,000 potential support level Moving averages are flattening out as we've been unable in US 30 to break up that much higher I think the SPX 500 actually managed to reach an entity high before biotech earnings dragged the whole thing down and As you can see there, we've actually just recently had a negative cross on the slow stochastic there above the back to the 8% level there So certainly in the short term, there'll be a little bit of pressure there But as it is earning season anything can happen But and certainly 18,000 could be the next pivot point for the US 30 going forward So looking at the UK 100 we almost briefly touched The second highest level that this market has in its history only then to jump right back down again strong doji formation Right there and we flat lined again a little bit there today all the technicals looking relatively flat Mac D Not really showing anything RSI is neutral and almost slow stochastic there a few days ago posting a negative cell signal But we're a little bit away from both moving averages So we might get drift just as the the Fed actually is about to begin its two-day meeting To think about interest rates, so I think that concludes on Wednesday I'll come back to that in just a second, but the FTSE trading at 70 75 right now So moving on to Japan 225 and you do have bank Japan's session Geo on Thursday for there as a very small possibility that might be more Stimulus involved right there, but Japan 25 doing quite well. I presume a dollar yen is probably ticking above 120 right now So above 20,000 which is looking quite quite tasty there But the longer-term potential resistance is 20,868 uptrend channel still firmly in play First I'm a pattern to the other end and this is Matt these neutral as is RSI with almost slow stochastic Showing a little bit of negative divergence. They're actually something to be careful off, but we're in about 20,095 Was an old resistance level which now might be expected to act as What was a new potential support might act as potential resistance again? So let's try to drop that on there a little bit more actually there we go Okay, so moving on to dollar yen just slightly below 120 in fact Drough actually a bit of negative divergence between dollar yen and Japan 225. It's a little bit unusual actually But nevertheless looks to be run about 119 and this has been in play for quite some time as it seems to be kind of Oscillating around this level Most other technicals looking pretty neutral matter of fact everything's looking quite neutral As we begin just to get a narrow a narrow consolidation rate here run about 119 And it's a breakthrough that either bounce higher or break down below that that's gonna be the next phase for dollar yen Obviously if there's a rise in interest rates in the US anytime soon that could be the breakout catalyst So moving on to West Texas Crude at 2015 highs at the moment the conflict in Yemen the other unrest in the Middle East helping to push this back up higher But we do appear to be entering another period of consolidation a very tight narrow range between 57 and 54 spot 85 Technicals, you've almost got a crossover in the MACD You've got a cell signal in the RSI and very close to having cell signals for the stochastic So not that surprising after this little uptrend right here unable to break up that little bit higher But it's still something to bear mine. I think the most recent reg data that came out the US show There's a big decrease in the number of regs for exploration That's a positive for Crude all West Texas and you've had the US dollar wobble a little bit as well Which helped me push this up a little bit higher. So moving on to gold Gold had a great day yesterday bearish engulfing pattern after almost an entire month of slow declines Trading above the moving averages all the other technicals are flat lining all depends on the US dollar now 1218 potential resistance 1186 potential support now finishing up now with your dollar And GBP USD so your dollar touching this potential downward sloping resistance line One spot 07 86 is still the potential support level that also coincides with the 21 pure SMA Other type of technicals are relatively neutral if we do break above here This would be the first time it's actually made some higher highs of significance for the whole month So be interesting to see if we can actually just get above here So anything above one or 940 could be seen to be bullish in the short term as Greek try as Greece tries to Furiously tries to come to some sort of deal with his creditors That's adding short term potential support to the euro just as the dollar begins to continues to wobble on mixed data So looking at cable cables been absolutely smashing it as we're getting quite close to the general election on May 7th One spot 51 85 was a potential resistance from the broken one spot 54 24 the next potential Resistance technicals are moving into overbought territory not that surprising after this this decent rally is basically gone from 145 all the way up to 152 and a very short period of time so that's not that much surprising but one spot 51 85 could be the potential support level to be aware of if we do get a drift down there That could be an interesting springboard action So Mark a calendar wise today. We've got UK GDP. You've got US retail sales And you've got some CCI over in the US there make sure you got your recurring alerts set for that anything That's set here red. It's gonna be worth being aware of in fact. I have my alert set for there So let me just quickly add that on their recurring alert and if you fast forward on the Wednesday You got German retail sales UK house prices from nationwide and German CPI US GDP Actually got loads housing index from the US Weekly petroleum sales for those of you looking at Cuddle West, Texas, and you've got the FOMC Fed decision rate plus statement Due tomorrow at 7 p.m. UK time so that two-day meeting starts today Finishes tomorrow and that's gonna be a could be a little bit of an interesting announcement when details emerge Later on tomorrow. Well, anyway, join me again tomorrow to find out what happened next


Namaste. In the previous session we studied convolution operations. In convolution operation we define a bunch of filter and we use each filter to calculate activation at a particular point in the image. In this session we will study how to slide each filter across image by setting strides. The output of convolution operation is usually smaller than the size of the input image. In order to keep the output of the same shape as the input we use padding. We will study padding in this session. Apart from convolution there is second important operation in CNN which is called pulling. Pulling aggressively down samples the output of the convolution. After understanding pulling and convolution operation we will use them in a practical setting to classify handwritten digits from MNIST dataset. Let us begin. We set strides while sliding across the image. It provides a way to calculate the next position along each axis to position the filter starting from the current position. By default we take stride of 1 which is the most common choice. We can specify different strides across different axis but we use that particular thing quite rarely. Such a strided convolution tends to down sample the input by the factor proportional to the stride. So, let us try to understand how the stride works. So, this is our 28 cross 28 handwritten digit image and we have a filter positioned at the initial position of the image. So, we use a stride of 1 and the stride of 1 helps us to calculate the next position of the filter. So, the current position is 1 1. So, we will essentially take a stride of 1 in this particular direction. So, the next position of the filter will be. So, the filter got shifted by one column to the right. Once it exhaust all the columns we start shifting it downwards by rows. This is how we slide the filter across the image and try to match the pattern in the image. So, let us say we have 28 cross 28 cross 1 image and we have filter of size 3 cross 3 with depth of 1. So, you can see that we will be able to position the filter at 26 possible positions along the width as well as on the height. So, the final position of the filter will be at position 26. So, we get in all 26 possible positions of the filter along the width 26 along the height and we have depth of 1. So, this is how we get 26 cross 26 cross 1 output of the convolution. So far, we looked at how to perform a convolution with a single filter. In a convolution layer, we typically used k different filters. We define all these filters with con 2D layer. In a Keras command in a tf.keras API, we use con 2D. We specify the number of filters. We specify the size of the patch. We also specify the activation, the input shape. So, in this case, you can see that we have 32 filters. Each filter is of size 3 cross 3, the size of the filter. Then we specify the activation that we want to use after linear combination of weights of the filter with the values of the pixel in the image. And finally, we specify the shape of the input. The size of the filter and the stride which is 1 by default is applicable across all the K filters. After applying convolution of K filters, we get 3D tensor with the same number of rows and columns for each filter. So, let us say this is our handwritten digit image which is 28 cross 28 cross 1 depth of 1. And let us say we apply 32 filters. So, we will have each filter of the same size. So, we have this is 3 cross 3 filter. This is filter number 1, another 3 cross 3 filter, filter number 2 and so on. And this is let us say 32nd filter. When we apply each of this filter to the images, we essentially get 26 cross 26 cross 1 as an output. Since the filter has the same depth as the input. So, here the depth is 1. The depth is normally not specified in the filter size. We get another output from the second filter and so on. This we get from the 32nd filter. Let us say this is the output of the first filter, second filter and 32nd filter. What we do is all these outputs are combined. This is the output of the first filter, second filter and 32 filter, 32nd filter. So, we get number of channels to be 32 each having 26 cross 26 output. So, concretely for our MNIST example, we get 3D tensor as an output with 26 rows, 26 columns and 32 channels, 1 for each filter. The total number of parameters for this filter will be 320 because we have 10 parameters per filter. So, we have 32 cross 10 parameters which is 320 parameters for all the filters. If you want convolution output to have the same shape as the input, we use padding. So, after applying the convolution, what happens is the input gets shrunk by some amount. If we do not want our input to get shrunk, we use padding where we add some dummy columns and rows to the input and then apply convolution on it. So, for a convolution of size, for a convolution with filter of size 3 cross 3, we add 1 dummy row and 1 dummy column to the left and right and top and bottom. We add a dummy column to the left and to the right and a dummy row at the bottom and at the top of the image. This ensures that we have the shape of the output same as the shape of the input. Convolution have a couple of key characteristics. The patterns that they learn are translation invariant. After learning a certain pattern, convolutional neural network can recognize it anywhere. They can learn spatial hierarchies of the pattern. A first convolution layer will learn small local patterns such as edges. A second convolution layer will learn larger patterns made from features from the first layer and so on. This allows us to efficiently learn increasingly complex and abstract visual concepts. So, let us say we have a convolution neural network that is trying to recognize a human from the image. So, the first convolution might capture some local patterns like some simple patterns like edges. This happens in the first convolution layer. In the second convolution layer what happens is we combine the output of the first layer and we learn even more complex patterns. As we progress, we learn increasingly complex patterns based on the output of the previous layers. Finally, this pattern will help us to detect a person in the image. The second important concept in convolutional the second important concept in convolutional neural network is pulling. Pulling tends to down sample the output of the convolution aggressively. It is conceptually similar to the strided convolution. It consists of extracting a specific window from the input feature and compute the output based on the pulling policy. Pulling is usually done with a window of size 2 cross 2 with stride of 2. Let us look at pulling with a concrete example. So, pulling defines a window of size 2 cross 2. So, this is the positioning of the pulling window on the convolution output and we apply the pulling policy on these 4 numbers and select a number based on that policy. We use either max pulling or average pulling as the pulling policies. Second important point is we apply pulling operation on each channel separately. For example, if we have the output of convolution. So, let us say the output of convolution is in multiple channels. While pulling what we do is we apply pulling on each channel separately. So, here what we will do is we will separate the channels on each channel separately. So, we select one of we select one number from this particular patch based on the pulling policy. We use one of the following two pulling policies. The first policy is called max pulling and the second is called average pulling. So, let us say these are 4 numbers in the max pulling window. The max pulling will return 6 which is maximum of these 4 numbers. Whereas, average pulling will return the average of these 4 numbers which is 4. So, let us try to see the max pulling in action on the output of the convolution layer. So, there are so, this is the first instance of a pulling, then we tried by 2 and positioned it on this particular patch. So, this is the second patch where the max pulling window will be positioned and this is the third patch where the max pulling window will be positioned and this is the final patch where the max window where the max pulling window will be positioned and each of these windows will return one number based on the pulling policy. So, we get 2 cross 2 output on the 4 cross 4 input using 2 cross 2 window of max pulling. So, we get the value of 6 which is the largest number in this particular window 2 over here, 8 over here and 9 over here. Similarly, if you are using average pulling as a policy, we will compute average of the numbers in the patch. So, if you apply max pulling on the output of a convolution say let us say output is 26 cross 26 cross 1 and if you apply a max pulling of 2 cross 2, we get the output of 13 cross 13 cross 1. So, you can see that there is a down sampling happening from the output of the convolution when we apply max pulling on it. Note that max pulling does not have any parameters. In practice we set up a series of convolution and pulling layers in CNNs. The number of convolution and pulling layers is a configurable parameter and is set by the designer of the network. In current example, we use 2 convolution and 1 more convolution layer. In the current example, we use 2 convolution pulling layers and 1 additional convolution layer at the end. We use 32 filters in the first convolution layer and 64 filters each in the second and the third layer. Each filter is 3 by 3 in size and we use a stride of 1. We have not used any padding in any of the convolution layers. We used max pulling for down sampling with a window of 2 cross 2 with a stride of 2. It is not necessary that every convolution layer should be followed by a pulling layer. Sometimes we can have pulling after a few convolution layers as well. Now that the model is built, let us look at the model summary. Let us work out the number of parameters for each convolution layer. We will write the shape of input and output tensors for each layer and then work out the number of parameters from that. The input to CNN is a 4D tensor and the 4D tensor the first axis corresponds to samples. The second is number of rows or the height then width and the number of channels. In the case of MNIST, we have a single channel because we have a grayscale image. So, this is the 4D tensor corresponding to the input image. So, we apply convolution operation on this where we use 32 filters. Each filter is of size 3 cross 3 with stride of 1. So, this gets us because you are applying 3 cross 3 filter this input gets transformed into another 4D tensor having height and width of 26 and having 32 channels. Each channel corresponds to a filter that we used during the convolution operation. We apply max pulling on this output with max pulling window of 2 by 2 and stride of 2. So, this gives us another 4D tensor with height of 13 width of 13 and having 32 channels. We can see that there is a down sampling that happened from the output of the convolution as we applied the max pulling on it. Then we apply another convolution with 64 filters. Each filter is 3 cross 3 filter with stride of 1. So, we get 11. So, we get a 4D tensor with shape none with height and width of 11 and number of channels equal to the number of filters that we use in the convolution which is 64. Then we apply max pulling on this 2 cross 2 window size and stride of 2. So, we get a 4D tensor with height and width of 5 and number of channels as 64. We apply another convolution with 64 filters each width size 3 cross 3 and stride of 1. We get a 4D tensor with height and width of 3 and number of channels equal to 64. So, this is the output that we get after applying convolution pulling 2 times followed by a convolution operation. Let us work out the parameters for each of the layer. So, we can see that in the first convolution we use 32 filters each width size 3 cross 3. So, because we use 3 by 3 filters we have 9 parameters corresponding to the positions of the filter and one bias. So, there are 10 parameters per filter and there are 32 filters. So, there are in all 320 parameters. We learn weights of each of these parameters during training of the network. The max pulling layer does not have any parameters. Let us come to the second convolution layer. The size of the filter here is 3 comma 3 comma 32. So, we have 3 by 3 filters with depth of 32 which is equal to the number of channels in the input that generates about 288 parameters plus 1 bias. So, there are 289 parameters per filter. So, for 64 filters we get 18496 parameters. The max pulling layer again does not have any parameters. So, for the final convolution layer here we have the size of the filter is 3 comma 3. The shape of the filter is 3 comma 3 comma 64. We have we have 3 cross 3 filter with 64 channels. So, the number of parameters here will be 3 into 3 into 64 plus 1 bias which makes it to 577 per filter and we have 64 such filter. So, we have in all 577 into 64 which comes down to 36928 parameters. The number of parameters in the convolution layer depends only on the filter size. It does not depend on the height and width of the input. It can be observed that the width and height dimension tend to shrink as we go deeper in the network. We started with height and width of 28 each and after couple of convolution pulling followed by a single convolution operation we got height and width of 3. The number of output channel for each convolution 2D layer is controlled by the first argument. The number of filters used in convolution are normally 32 or 64. Typically as the width and height shrink we can afford to add more output channels in each convolution 2D layer. Now, end of this particular operation we got an output of 4D tensor which has height and width of 3 and number of channels 64. What we do is we feed this output into a dense layer to perform the classification. So, what is really happening here is we take an image we take an image we apply bunch of convolution pulling operations that gave us a representation that will feed into feed forward neural network which will give us the label corresponding to the digit written in the image. Let us compare this with traditional machine learning flow. In traditional machine learning flow given an image we used to first perform feature engineering using computer vision libraries and the features used to get fed into any machine learning classifier which after training will give us output. Now, you can see that the feature engineering part in the traditional machine learning is getting replaced by CNNs. So, we can think of CNNs as a way of generating features automatically for a given image. The beauty of this approach is that the right representation is learned during the model training freeing us from expensive and tedious feature engineering task. We will use feed forward neural network for classification task. Let us see how to set this up. So, we will add a flatten layer that will take the output of the convolution layer and flatten it into a 1D tensor. We feed in the output of the flatten into a dense layer containing 64 units. We will use ReLU as an activation. MNIST has 10 output classes. So, we use a final dense layer with 10 outputs and a softmax activation. Let us understand it with an illustration and work out the parameters and work out the parameter calculations ourselves and we will compare that with the parameters shown in the model dot summary. So, here the input is comma 3 comma 64. We pass it through the flatten layer which gives us 576 numbers which are fed into a dense layer which is the output of which is fed into another dense layer. Flatten has no parameters. It outputs 576 numbers which are input to each of the 64 units in the dense layer over here. So, each of the unit in the dense layer has 576 parameters plus 1 bias which makes it to 577 parameters per unit and we have 64 such units making it 36,928 pattern 36,928 parameters. So, this produces 64. This produces 64 values one corresponding to each unit. So, the final dense layer has 10 units. Each unit receives 64 values from each unit receives 64 values from the previous layer. Adding one bias parameter to it makes it 65 values. Adding one bias parameter makes it 65 parameters per unit. So, total so, in total we have 650 parameters for the final layer. So, if we sum across the CNNs and fully connected top layer we have total of 93,322 parameters. So, let us compare our calculation with model dot summary. So, you can see that we arrived at 93,322 model parameters which is matching with the output of model dot summary. Let us set up the training of the model. We use sparse categorical cross entropy loss with Adam optimizer. Let us train the model for phi epochs with training images and training labels. After phi epochs, the model has achieved more than 99 percent accuracy in recognizing handwritten digits on the training data. Let us check the performance of the model on the test data. We used evaluate method of model class for calculating accuracy of the model on the test data. We passed test images and their labels as input so, that the statistics can be calculated. We observe that we achieve here we observe more than 99 percent accuracy on the test set. It is interesting to compare this architecture with fully connected feed forward neural network that we used in earlier exercise. Let us set up the feed forward neural network and compare it against the CNNs. So, we input the MNIS data set and we set up a feed forward neural network with a hidden layer with 128 units. You can see that this feed forward neural network has more than 100 k parameters as compared against 93 k parameters that our CNN has. So, we can see that in case of CNN, we are defining patches and we are taking a patch performing a convolution operation with the filter. This is the image patch and this is a filter. And what we do is we perform a linear combination of each position in the image with each parameter in the filter. So, you perform linear combination followed by non-linear activation. While in case of feed forward neural network, you take the entire image, you flatten it so that we get a single array of in this case since you have 28 cross 28 image, we get an array of 576 numbers which you are passing to a hidden layer with 128 units followed by a dense layer of 10 units to get the output. If we come up with a equivalent flattened representation, what really happens is we have these 9 values and we have a node. These 9 values are connected to this particular node which is a neuron or a unit in neural network which performs linear combination followed by activation. So, you can see that we are doing, you can see that we are capturing local patterns in case of CNN. So, this is CNN and this is feed forward neural network. So, CNN proceeds by capturing local patterns whereas in fully forward neural network, we learn global pattern involving all the pixels. Today, we learn about CNNs which are extensively used in computer vision applications. We discussed key operations in CNNs and demonstrated their usage in recognizing hand written digit task. We compared CNNs with feed forward neural network. We learn about CNNs ability to automatically generate features from the given image. In the next few sessions, we will learn about using pre trend CNN models for image classification task and visualizing what CNN layers are learning. See you in the next session. Thank you.