 So we now come to the next topic in the scheme, basic ideas and definitions. As we said thermodynamics is a proper branch of physics and has to live in harmony with other branches of physics. This means that we have to accept principles, ideas, definitions which are defined in other branches of physics as well they have defined it we will use it. These ideas or entities which are defined in other branches of physics are known as primitives. Primitives are things defined elsewhere and used here and each branch of physics has its own primitives from mathematics and other branches of physics and so has thermodynamics. For example if you take the geometry part of mathematics from geometry the idea of a distance or displacement, the idea of area, the idea of volume, volume is very important for us we will just be accepted as what they are in thermodynamics, we will not redefine them. They are defined elsewhere, we will use those definitions and whatever interactions between them we will accept to be true. From mechanics we will accept things as four, kinetic energy, potential energy or say gravitational potential energy, we will accept things like velocity, acceleration as need be anything which is defined there. In pressure mechanics or fluid mechanics, from electricity, magnetism, voltage or electric potential, current, charge what have you, if we have a more complicated phenomena which is in which some other branch of physics is involved we will say whatever that branch says about non thermodynamics principles we will accept, yes sir, each branch of physics will define its own state in thermodynamics we will define our own state okay and whenever agree since there are issues in thermodynamics which are common to various branches for example energy, energy is defined in thermodynamics in a way but we will define it in such a way that it is consistent with other ideas of energy from other branches of physics. We will not do anything, no branch of physics will do anything which will lead to an inconsistency when combined with other branches of physics because then the whole structure of physics will become weak. Since we are only a branch of physics we will not do anything which disturb the whole overall structure of physics, they are interrelated and we will accept that many things are interrelated. But whatever is for example we will consider many of these including the idea of work which comes in mechanics which comes in electricity this idea will also be a primitive, we will redefine it, we will appreciate it properly, we may if we have defined it in a different way we will call it thermodynamic work not the mechanical work or gravitational work. And the idea of work in mechanics is different from the idea of work in thermodynamics, we will differentiate that but we will not overrule their idea of it, let them do whatever they want in their branch. When it comes to thermodynamics our definition of thermodynamics work will be this. That is the basic idea and so on. So these are primitives, the second things are premises, a premise is essentially an assumption, things which are assumed to be true. So these are premises in thermodynamics, sometimes these are known as assumptions, sometimes these are known as principles, sometimes these are even known as postulates. For example you take Euclidean geometry, classical Euclidean geometry, the idea of a point, idea of a straight line, idea of a circle, these are all primitives, the 5 postulates of Euclidean, the 5th one being that of parallel lines, so called the famous 5th postulate, if you delete that you get into lots of non-Euclidean geometry. These are primitives, similarly what is a mass, mass is a primitive in mechanics, suppose we have some characteristics but we do not define mass, we assume that mass is a characteristic with any mechanical system we will have and its further properties are derived but basically the idea of mass is a primitive. Similarly in thermodynamics there are a number of premises or assumptions, only 3 of them for some reason are given the status of laws, the first law, second law, 0th law in some order but there are a number of premises for which for some reason have not, I should say not yet been given the status of a law, perhaps for some reason because compared to 0th law, first law and second law they are considered secondary and weak enough so that you can still continue with thermodynamics by deleting a few of them, in that case you end up with things like kinetic theory, statistical mechanics and such stuff. For example one of the premises which we will need is that all our systems are part of a continuum, we will remain in the continuum domain, we will not consider a system to be made up of a large number of particles and things like that is a premise which we make, this automatically means that we are in the macroscopic domain, not the microscopic domain which is used in kinetic theory and statistical mechanics. Then there are other premises which we will make en route, for example there is a premise regarding equilibrium, I have not defined what is meant by equilibrium, then there is a premise regarding state of a system. So this is something which we will make now, but these other two premises as we proceed I will emphasize equilibrium premise the state of a system and then the fourth premise is scale independence, continuous means all interactions are non quantized and related to that is the scale independence which means that we are not looking at systems at a given scale. We are saying that our thermodynamics should be applicable whether we are considering a system the size of a millimeter cube, so consider a system the size of say a liter or a few tens of meter cube or thousands of meter cube, we are going to be scale independent. So we will never challenge an idea where somebody says I will provide an interaction of 3.56 kilo joules, we will never challenge that by saying no 3.56 is not possible, you must give either 3.5 or 3.6, you will say there is no scale involved. So you can say 3 kilo joules it is acceptable, you say 3.14159 mega joules that also is acceptable, you say 300 peta joules that also is acceptable and power consumption of say 2 milliwatt that also is acceptable. So this is a scale independence and of course there are 3 laws and if there are other premises we will discuss those and mark those out as premises, saying that look for any premise there is no proof. We work with the assumption that they are true and we continue to work with that assumption because all our applications and all our observations we find that those turn out to be true. So that way they have the same form or the same status of the 3 laws of thermodynamics. There is no proof for any one of these 3 laws, they are only generalizations of nature but in my opinion the 3 laws of thermodynamics have been given the status of those 3 laws because they seem to be more deeper generalizations of nature and the other things for example scale independence, the continuum premises, these are sort of weaker premises we can develop thermodynamics in a different way by deleting one or more of those premises. The same way that for example our high school geometry is all Euclidean geometry based on the 5 postulates or 5 basic premises of Euclidean but out of those the so called 5th postulate parallelism of lines can be deleted and if you delete it then depending on whether you replace it with something else or replace it with some other premise you get a set of non Euclidean geometry, for example spherical geometry is one in which 5th postulate is deleted. Similarly there are n types of geometries which are non Euclidean geometry so non Euclidean geometry is not one geometry depending on what you do with the 5th postulate what you replace it with you can have n sets of geometry. Basically thermodynamics understanding of thermodynamics so basic understanding depends only on primitives and primises after that are derivations these are simply logically true mathematical treatments of whatever we have defined. Now the second thing we look at are definitions why are we spending some time on definitions we are spending some time of definitions for the simple reasons that definitions help us a lot. If you see my name is UN Gaeton Day it is a definition if I were not to use that describing who is sitting here will be a very elaborate procedure the person who is sitting here at this time of the day or you ask somebody to go and meet a person you say you go to that hall and find out who Professor Gaeton Day is all that person will do is just the way I did come here and say who is Professor Gaeton Day somebody will raise his hand otherwise if that definition were not given to him that the name is Gaeton Day he will say person with white shirt with brown checks of this spacing vertical and horizontal half sleeves and all that all that this type of spectacles this difference in the shape and size of eyes and ears color of gray color of hair all that it will be a very complicated. If we do not have definitions our life will be complicated so definitions are of two or three types first definitions are short forms second definitions are names or labels the third definition is and these are the important definition operational definition a short form definition is something which we have for example we will define enthalpy as the combination of properties u plus pv. So this is a short form another definition we will use this process is a short form for a change of state. Now a short form definition means when I say h equals u plus pv absolutely nothing goes wrong in a text on thermodynamics wherever I see u plus pv replace it by h or wherever I see h replace it by u plus pv. When I say process is a change of state in a thermodynamic textbook I say I do not want the word process so wherever there is a process use a word processor replace it by a change of state or appropriate changes of state okay make it grammatically okay and you can have a whole book of thermodynamics without the word process only what will happen is the book will now be 10 pages thicker and so much costlier okay. So these are useful short forms so long as we everybody understand what that acronym is now I may be Uday Nara and Gaitonday that is one big thing but many students and people here call me by the name know me by the name UNG there was a time when my son and daughter introduced themselves and I am professor Gaitonday's son they will say who? Which department does he work in? Mechanical engineering oh you are UNG's son so that was how the definition was clear okay so these are short forms they save time they save space and they save ink and paper and make our life easier that is the job of an engineer okay. Now operational definition it is something which is more involved and operational definitions were first proposed by Bridgeman in his book a very small book you will find it in your library the nature of physical theory although he was a physicist his main interest was in thermal physics and his main forte was doing experiments with materials at particularly at very high pressures in fact his contribution to engineering is what is known as the Bridgeman seal which becomes better and better and higher and higher pressures he has measured various physical properties of fluids at pressures as high as 40,000 atmospheres 50,000 atmospheres and so on. His physics of high pressure textbook or it is considered a classic so where is two small books the nature of physical theory and the nature of thermodynamics and the significant thought of his went to definitions which are operational definitions the word operational is important because his idea is when you define something except when the definition is a label or a short form you must specify a procedure for implementing that definition. For example when you want to define the mass of a system so you should define it by specifying an experiment by which you will be able to measure or quantify that mass. So you define either a spring balance or a you know tan balance and naturally then you will realize that if you use a spring balance you depend on the gravitational force so you will define what is known as the gravitational mass whereas if you use a spring and acceleration then you will define what is known as the inertial mass of the system. So you have to specify an experiment by which that entity is defined for example the volume of something how do you define the volume of a something you must define it by prescribing an experiment by which that volume is measured or quantified that would be the operational definition. And following Bridgeman most of the things which we will define in thermodynamics will follow one of these definitions either it will be a label or it will be a short form or it will be an operational definition. Right from our first definition that of a thermodynamic system we will see to it that we follow an operational definition. Sometimes an operational definition it is always a procedure but instead of quantifying we will have to specify a procedure by which that label is true or not. For example we say the cap of this pen has a color yellow. So how do you define a color yellow? Maybe we will the operational definition would be something like this. Go to your spectroscopy lab in the physics department. Have a lamp whose spectrum is equivalent to that of the visible light spectrum or solar spectrum. Expose this to that spectrum. Find out the reflected radiation, put it through a spectrometer, find out the spectrum and take the intensity average of all the wavelengths and if that average lies between say 3000 angstrom units and 3030 angstrom units I think roughly that is the range of the so called yellow. If it lies then we will say that the cap is yellow otherwise we will say the cap is not yellow. Now all of us understand what a yellow is but you ask us to define what is meant by yellow we will say is a jodhikta that is yellow but that is not a good definition and that is not at all an operational definition. Maybe we laugh at it and I also laugh whenever I provide many operational definitions but that is the proper way of defining things because I can define whether a thing is yellow or not yellow. There are in many colors here but that way we can also define a red thing or a violet thing appropriately. Sometimes these experiments will be very convoluted, very complicated but those experiments are possible. Similarly for the volume of this liquid we may define a standard measuring cylinder. We will say to determine the volume of this liquid all that you do is open this, do not drink anything out of it pour everything into that measuring cylinder and see to it that the last drop is transferred. Then put that measuring cylinder on a horizontal surface and read out the graduation at which the level exists and that graduation mark is the volume in so many cc or meter cube or meter whatever it is that would be the operational definition. The advantage of an operational definition is we are absolutely clear about what we are talking about. There is no confusion at all. Operational definitions are not specific to thermodynamics. Operational definitions after Bridgeman's work have been used in all basic thermodynamics ideas. Bridgeman is a Nobel laureate. He got his Nobel prize I think in 1945 or 46. I think soon after the second world war. He is one of the most influential physicists of the 20th century. We remember only Einstein and Penman but there are other half a dozen physicists. One of them is Bridgeman. There is still some time. So we will look at our first definition is that of a thermodynamic system. Now since we are doing a study of thermodynamics, the adjective thermodynamic will be used so often that by default we will soon drop it. Whenever we say system we will say we are talking of a thermodynamic system. Whenever we say process we will be talking of a thermodynamic system. Otherwise I cannot finish this in a 3 day workshop and I will use 20 pages instead of 15 pages. This is number one region of space of current interest. That means of interest to us at this moment. Second thing all boundaries must be defined. Don't know will not be accepted as an answer. Don't know, don't care. These are just not accepted. What does it contain? It may contain anything. So long as we define the region of space and define all boundaries, however complex they are it is okay by us. For example my system could be the water inside this bottle. That is what I am interested in. I am looking at it. Can I define its boundaries? Yes. The boundary is the top surface of the water. The boundary is the inner surface of the bottle with which the water is in contact. The upper boundaries etc. they don't come into picture because my system contains only the water. Now some boundaries are flexible. It keeps on changing its time. So what? But at any instant of time I can define where the boundary is. Sometimes it is possible that the boundaries may be complicated. You know, multiply connected because of bubbles. Doesn't matter. But I can take a high speed camera, take a photograph and define at any instant of time what the boundary is. Boundaries may be flexible. They may extend. Of course water is not compressible but suppose it is compressible I can even change the volume. Doesn't matter. The definition is very flexible. The requirement is that should be our region of space of current interest and I must be able to define the boundaries at any time. The boundaries may shift. The boundaries may change shape, change size. There may be multiply connection. A set of drops, if I throw it around you will have a set of drops. There will be multiple zones of my system. Doesn't matter. If I define it, so long as I know the boundaries, those are defined. Boundaries may be flexible. They may be extensible. They may be multiply connected. They could even be disjoint. They could be physical or they could be even defined. For example I can say consider a volume which is a rectangular parallelo pipette. The base of that parallelo pipette is this A4 side sheet, the top of this. And the height of that parallelo pipette is 20 centimeters from here. So you are all engineers. We have all gone through courses in engineering drawing. So I can imagine a volume here, this 210mm by 297mm by 200mm. All of you can imagine. You can even sketch it with dotted lines. So that is my system. What does it contain? It contains air, some dust particles, something, maybe water vapor thrown as a lecture here. Doesn't matter. It may even contain part of this bottle. But I know what the boundaries are. One boundary is physical, the other boundaries are defined. And then I say as time progresses the top boundary goes on rising by say 1 centimeter every minute. I have defined it properly. At any instant of time I know where the boundary is. The top boundary will be a moving boundary. The side boundaries would now be extensible boundaries, extending boundaries. Doesn't matter. But at any instant of time the boundaries are defined. So my system is defined. So remember that a region of space of current interest with fully defined boundaries is the operationary definition of a system. So whether some given something is a thermodynamic system or not, find out whether it is a proper region of space as defined by properly defined boundaries. And a boundary means there is something which is on one side of the boundary, something which is on the other side of the boundary. Only then we call it a boundary. In thermodynamics we use sometimes a world which is common with other branches of physics and that is universe. You know in many papers we will find entropy, determine the entropy change of the universe. That universe is thermodynamic universe. The astronomers universe, the cosmological universe with which Einstein worked and Eieriker works and many other people work. Is that a thermodynamic system? That is a typical question. According to our definition it is not a thermodynamic system because astronomers and cosmologists have not yet been able to tell us whether the universe is bounded or not. If it is bounded what are its boundaries? Because the moment they say universe is bounded, you will say show us where the boundaries are, define where the boundaries are. The moment they define the boundaries they have to say something about what is there on the other side of the boundary. Since the boundaries are not defined, the physical universe or the astronomical universe is not a thermodynamic system. Many good students will ask you these questions. I am sure many of you would have faced this question from the students. The answer should be this, that anything which you can show confined within defined boundaries can be a thermodynamic system. Since the natural universe or the physicist universe cannot be shown to be defined, shown to be confined with the physical boundaries at least as yet. So we say it is beyond the state. Because we cannot define, we do not say that thermodynamics is not applicable. We say thermodynamics may be applicable. But so long as you take a part of that universe with defined boundaries, we will apply thermodynamics. So thermodynamics can be applied to the earth, earth and its atmosphere, it can be applied to the sun, it can be applied to the solar system, it can be applied to the Milky Way galaxy or may be the supercluster of galaxies in which Milky Way and Andromeda exist. But when you consider the whole universe, we cannot define it, define its boundaries. So we say that look, we are unable to define a proper thermodynamic system which defines the universe and hence we are unable to apply our laws of thermodynamics to it. Now traditionally textbooks define what is known as a surroundings and quite often the definition is anything outside the system is a surrounding. We will not do that because that means giving a separate status for something called a surrounding. In thermodynamics, we will always consider rarely just a single system situation. Usually we have a situation where we have two systems, system A and system B and then there is an interaction. The whole of thermodynamics can be developed considering system A, system B, sometimes only system A for more complicated situation may be system A, system B, system C and so on. Any number of systems interacting with each other. Quite often it turns out that there is a primary system, for example if I this water is too cold for me to drink. So what I will do, I will wait or I will try to heat it up and during that process the water happens to be my system. But I am heating it up by holding it in my warm hands or I am keeping it near a source of heat. So there are other systems with which it is interacting. If I consider the effect of air to be negligible, I hold it in my hands then my hands or my whole body is immediately in contact with it or interacting with it in some way. So that is my secondary system. Both primary and secondary systems are properly defined thermodynamic systems. So it is proper for us to shorten this by saying instead of primary system and secondary system, we call this as the system and we call this as the surroundings. Notice that by this definition the surroundings has to be a thermodynamic system in its own right. We just cannot leave it as if this water is my system, everything surrounding it other than outside the system boundary is my surrounding. That is not true because that way we are not defining the boundaries of it. Suppose I am interested in knowing what is the interaction between this and the bottle. I will say okay, water is my system, maybe the air above it inside the bottle is my system B and the bottle itself including the cap is my system C. So if I say neglect whatever I am doing to the bottle, we will say that look of interest to us are system A, water, system B, the air part, system C, the bottle itself. And then we can say rather than ABC, water is my system and air and bottle is my surrounding. But remember air and bottle if I combine the two systems are by themselves properly defined thermodynamic systems. Do not just leave it saying that surrounding is something outside the system boundary, everything outside the system boundary that is not true. In the surroundings of this water, President Obama is not included okay. Make it very clear, not everything, such loose things as everything, all that is outside the boundaries these are things not to be used. And we may use the word surroundings because that is of secondary importance. But remember that surrounding has to be defined as a proper thermodynamic system in its own way. Unless you define it as a proper thermodynamic system, you cannot call it surroundings or I cannot call it any other. But remember that the best way to do it system A, system B for primary system or secondary system or just to be traditional, the system and the surrounding. So we have seen the importance of boundaries, the question of disjoint boundaries we will soon come. Now we come to classification of systems, the words you all know closed, open, isolated. Now although traditionally these are classifications of systems, actually these are actually should be taken later because a system by itself is not closed or open. Only when it executes a process, a term which we have yet to formally define, during a process the system may remain closed or system may remain open or system may become isolated. If I say this water in this, is it a closed system or an open system, then somebody will say when it is a closed system nothing is changing, no water is getting added, nothing is added to it. But somebody can say that look now I open this cap, is it a closed system or open system. Mr. A will say it is a closed system, no mass is changing. Somebody else will say look there is a possibility that I can pour more water in it or there is a possibility that I can drink some water out of it, then it becomes an open system. But when you do that you are always imagining a process. So the idea of a closed, open or isolated system is always related to a system undergoing a process. A system by itself need not be or perhaps in a stronger way cannot be defined as open or closed. A system is a system. Only when it undertakes a process it is likely to be closed, open or isolated. Otherwise the traditional of closed, open isolated is very simple. Cloth system means mass can not flow out of the system. Once you define a system, whatever is the mass inside the system remains inside, no exchange of mass is permitted. Exchange of energy by any means is permitted. If you allow mass flow inside or outside that is an open system, standard definition. But one trap here is for example I have a tank with a inflow line and an outflow line and suppose I have my outflow line flow, outflow exactly balancing the inflow in which case the amount of mass in the system is not changing with time. But the identity of the mass in changing with time, some packets of mass which were in the system now might have moved out, some new packets have come in. So mass remaining steady is not a definition of a closed system. It is a consequence of a closed system. The definition of a closed system is put any sentry anywhere on the boundary during the process that sentry will find that no mass has crossed either out of the system or into the system. So if an item of mass was inside the system it continues to remain inside the system. That is the definition of a closed system. Isolated system means neither mass exchange nor energy exchange of any kind that is isolated. So these are our standard definitions, we need not worry anything about. So we have seen that closed, open, isolated. These are the boundaries pertain to a system during a process. Process is yet to be defined. So I will put a question mark there from our earlier studies. Close system, no mass should cross boundary. But when we have flexible boundaries or when the boundary changes, boundary can relocate. For example, I take a say a bladder containing water. Inside surface of the bladder is my boundary. You take a balloon, you take a car tire, you take a, no, no, no. Let me take an illustration. You take a car tire, the tube in a car tire. See, no leak, no nothing. The air inside the tube is my system, the air. So the air to inner boundary interface, inner side of that tube, inner surface of the tube is my boundary. It is a closed system. It does not matter. But now I press the tube here, it gets balloon somewhere else. I change the boundary of the system. But whatever is the air inside remains inside. So long as my air is the system, it is a closed system. The boundary changing shape, the boundary may even be changing size. I may be expanding it compressing it. What will? Right now the position of surface, I call it say a boundary. Now I tilt it. So it has crossed my physical boundary. Some boundary has changed its shape. Some boundaries have got extended, some part has got contracted. Boundary has totally changed the shape. Why? I can even compress it like this. The boundary has changed the shape. But the system is a closed one. The mass in the system remains mass in the system. So we are saying that we will change our boundaries so that whatever goes out will remain within the boundary. So we have defined water as our system. Yes. But at every instant boundary has to be defined. The water or whatever is inside must remain within that boundary. Nothing else should come in. Nothing inside should go outside. So system, its definition itself contains the boundary, contains and boundary. That is why I said 1 and 2. See that way you can even ask does a closed system exist because it all depends on our observation. If I really look at it, some water molecules are going into air, some vapour molecules are condensing. So that way it is not really a closed system. Finally our attempt is to understand things by doing certain simplifying assumptions. To what level you are going to do that assumption, it depends on that. So you know an adiabatic system, an isolated system and to some extent even a closed system are idealization of real life. We approach them, some of them for example something which is really sealed, you know so called hermetically sealed is really a sealed closed system. But an isolated system we will later on look at the two types of interactions, the work interaction and heat interaction. We will see to it, we will observe that the work interaction because of the nature of the interaction can always be suppressed if we need to. But the heat interaction is difficult to suppress. So that way creating an adiabatic system, creating a zero work system is easier but creating a zero heat transfer system that is an adiabatic system is very very difficult because we do not have so called a perfect insulator. And hence creating an isolated system is difficult. So actually for heat transfer temperature difference is the driving force. And if a system is said to be in the dead state and there is a state to be in a dead state. What is a dead state? Means as per ambient conditions, what ambient conditions? If the system is at ambient pressure and temperature conditions then definitely there would not be any heat transfer taking place. And if there is no work transfer taking place then can we call that system to be isolated? No look at it, if that there is no temperature difference between the system and the ambient that is its immediate surrounding. There will be no heat transfer. But if you say that the system pressure is the same thing as the ambient pressure. And then you say there will be no work transfer that is not right because pressure difference means no expansion or contraction, no zero, no pressure difference. But you can have electrical work, you can have stirrer work, you can have magnetic work, there are so many different types of work. So that work interaction may take place. So we cannot call it as an isolate. No, the system which is for example neglecting some heat transfer because of my hand touching it. This is if I loosen the cap, this is at ambient temperature and ambient pressure. But that is no way it is an isolated system. So what? I can always heat it up with my hand, I can always play with it. But when I define it to be as a dead state then the meaning is that nothing is extractable. You are confusing what we are going to do in combined first and second. Nothing is extractable does not mean no work interactions cannot take place. Yes, for each system involved you have to actually you cannot say something is an involved system unless its boundaries are defined. See if we are just interested in what goes there, what comes from there without worrying about what happens to it then we can leave it at that. But suppose you are asked to say that so much heat is being lost from the system to the surrounding. What is the temperature rise of the surrounding? Then you will have to define the boundaries of the surrounding. So let us not leave surroundings as something loose. If that system the other boundaries of no consequence you can say okay put the boundaries at a distance of 1 kilometer but you have to define the boundary. Otherwise you will have to say immediate surroundings not so immediate surroundings further surrounding why complicate matters. Best thing is in my opinion you should say system A and system B or primary system secondary system. But I still like system A system B because you can then have system C system D any number depending on the complexity of the process. And we say that boundary acts as a continuum breaker. No continuum is a very general word. Since all our systems are part of a continuum we cannot say that the boundary is a continuum breaker. That means on one side of the boundary we have continuum on the other side of the boundary we have non continuum that is not true. That is not true. But the mass of this fluid that we have considered is it separated? Yes so there is a difference in identity. For example I can have air here as one system water here is another system. So the two systems have different identities. One contains air another contains water and maybe a third contains the plastic of the bottom. But everything is a continuum whole thing is a continuum. Some properties like densities may be varying in a discrete way non-continuous way. But the idea of a continuum exists throughout. That is the main canvas. So these are marked boundaries for our convenience. And remember that a system boundary and hence a system is to be defined by us. Nature will never dictate that this is our system. For example this brings us to why do I consider the whole of this water as one system? Maybe I can consider the top half as one system, bottom half as one system with an imaginary boundary in between. Suppose I am heating it very slowly from the bottom. Then it is possible that the bottom half will get heated up first. The top half will get heated up slowly. If I want to study the difference in temperature of the two using some model maybe some principle of heat transfer I will have to have boundaries in between. And in heat transfer and fluid mechanics we have derived equations by considering various slices each slice at distance x of height dx. Those are systems we have created those small control volumes. For deriving your Navier-Stokes equations you take small control volume of dx, dy, dz. Those are systems defined by us. Remember it is for us to define a system. Nature will not, nature will provide some physical boundaries. It is for us to decide whether those are appropriate boundaries for us or we need something else. Boundaries are defined by us and hence the extent of a system is also defined by us. And we should be able to handle the situation properly. In fact the answer to Professor Sudarshan, BMS College Bangalore, we are almost coming to his answer. For example his thing is if a system is made up of disjoint you know number of say droplets of water as in a spray or in a rain. Question is can we consider all this one boundary, two boundary totally as one system. If we can solve our problem by considering the whole thing as one system it is okay. But suppose I want to know what is the difference in temperature between one set of droplets and another set of droplets then no. If I want a detailed temperature distribution then maybe each droplet should be considered as a system. But if I just want to know that something is being sprayed before spraying the pressure was this, after the spray the pressure is this. What will be the rise of the temperature on an average? Then you can have one whole system. But if you want to know that the center of the spray has one temperature, edge of the spray has another temperature then you have to define system definition depends on us. Remember that nobody can take that freedom of example. Now the next thing is state of a system and properties of a system. Now the state of a system is something which is in fact some workers for example Giles. Giles does not define system and state separately. He includes the definition of system in the definition of a state. He has his reason. But let us be traditional and since we have defined system as an entity with proper boundaries completely enclosed in defined boundaries. Now let us define the state of a system. See in thermodynamics we have said that we have a system A system B. They will interact with each other. I have some transaction and because of that there will be some change in system A. There is likely to be some change in system B. We want to quantify this change. So we will say that look I am observing the system. If something changes I will be able to observe that change. Now the question is what are we observing? We are observing the situation that the system is in. For example when I observe this system by default of my illustrator system it is water. I am looking at its volume. Maybe I can put a small pressure gauge here and measure its pressure. You can put in a thermometer or a thermocouple and measure its temperature. And of course I can drink some water and then I can also measure the change in its volume. So I have decided that volume, mass, pressure, temperature are the so called properties of the system. And combination of these will give me the state of a system. So the state of a system is we say is defined as a set of relevant characteristics each one properly quantified. This is a verbose definition and let me explain. First thing is mark the word characteristic and relevant. Characteristic is things like what we are going to do. So volume, area, mass, pressure, temperature, color, what have you, smell. More complicated the system, more is the number of characteristics. Now the word relevant is important because if you ask 10 different people what are the characteristics of this system which is that water in this bottle. Those 10 different people will come with 100 different characteristics. Some will say oh the total area of the water, top surface, side surface, the total area of the boundaries is a characteristic. Somebody will say no even the shape of that boundary is a characteristic. So the question is we are going to study the heating of this water when I say put it up on a warm plate. Question is is the shape of that boundary going to matter? Whether is it here or like this is it going to matter? Maybe sometimes it does. If I am going to consider a spray the area of each droplet, the total area is going to be a characteristic. But for such a simple problem the area may not be a characteristic. Maybe the shape of the surface, inner surface of the bottle is not relevant in many of the conditions that we consider. So the question of whether a characteristic is relevant or not is left to us, our understanding of the situation. Thermodynamics will not tell us which are the characteristics which should consider and which of them are relevant characteristics, okay. And so characteristic is what we can observe, measure. Relevant I have already explained and remember properly quantified. So that means an example, let me take an example, the state of a system. Let us say one of my favorite system is you take a cylinder and there is some gas. Let us say it is closed, there is a valve and it is closed. And the inner surface of this gas, inner surface of the cylinder is my boundary, usually shown by dotted lines and the gas inside this cylinder is my system. So this is my and then I decide that to study the behavior of this system, its pressure, its temperature and its mass are the relevant characteristics. Then somebody will say what about volume, then you can say that look it is such a solid robust cylinder that in the behavior from one room to another, from kitchen to the veranda, it is unlikely to change, let us not complicate matter. So we have decided that volume is an irrelevant characteristic. Then we say that look some cylinders are thin and tall, some cylinder flat and narrow, that also is not going to matter. Shape of the cylinder is also important. We will say let us work with these three characteristics, pressure, temperature and mass. So the first part we have taken care of, we have listed out characteristics and decided that these three are relevant. Then we do some experiment, how to do that let us not worry about and we say pressure is 16 bar, temperature is say 34 degree C and mass is say 18 kg. When I do this, I have defined the state of my system and this is my system. So remember the state is defined by one, a list of relevant characteristics and two, value or quantification of these. Sometimes it will be a number, sometimes it will be an adjective like red, yellow and all that. For example in some radiation problem the so called color may be of important. A black surface, a white surface, a shiny surface may have different characteristics. So these adjectives which may be further quantified if necessary but do not be under the impression that this will always be continuous number. These relevant characteristics are known as properties. So a property is nothing but a short form for relevant characteristics. A definition which is a short form and how useful this short form is, you can see that in your book on thermodynamics what would happen if you were to replace every word which says property by relevant characteristics, properties by relevant characteristics. It will still be a good book on thermodynamics or a proper book on thermodynamics but page length will increase, the book length will increase. So this is simply a short form. And what is the state? The state of a system is defined if we have created one, a list of 11 properties or 11 characteristics and two, provided appropriate quantification for each. Now here we have looked at a system from a macroscopic point of view and hence we have selected properties like pressure, temperature, mass. This we did because we have decided to remain in the continuum domain. If we do not make the assumption of being a continuum domain, if we consider particulate domains, then instead of a macroscopic view point we can go to a microscopic view point. But then we will end up with kinetic theory, statistical thermodynamics. So let us not discuss that, let us remain in the continuum domain and let us go to the next point that is properties. So now we are going to look at characteristics of properties or properties of property or let us say classification of property. Now the idea of a state and idea of a system and idea of a property is not unique to thermodynamics. Even a mechanical system has a system definition, a state definition, a property definition, everything. The particle is moving in this direction at this velocity, this acceleration. Particle is the system, the velocity acceleration, position, all these are its property, mass properties. So just the way we have ideas which are primitives, then properties can be primitive. So primitive properties are those which are defined by other branches of physics. For example, mass, volume, pressure, velocity, area, whatever these are defined by other branches of physics. Temperature is for us to define. Temperature is not a primitive property. Electrical field, charge, current, voltage, potential, gravitational potential energy, kinetic energy, all those things are primitive. But things which we will define energy, thermal energy, temperature, entropy, enthalpy, those are our property. So those are known as basic thermodynamic properties. These are defined laws of thermodynamics. Maybe of the premises which we talked about, the three premises are given the status of a law. There is no society or something which says that this is a law and this is not a law. But sometimes I feel that because these three laws or these three premises define each one very relevant property of thermodynamics, they have been given the status of a law. Other premises like the continuum premise or the non quantizing premise, scale independence premise does not tell us anything about a property. So they remain premises. There are three laws we are going to look at, 0th, 1st and the 2nd. Each one of these will define a property. For example, 0th law will define a property called temperature. 1st law will define a property called energy. The 2nd law will define a property called entropy. So these three and only these three are the basic thermodynamic properties. Of these three, the energy is common. Since energy overlaps, there are various components of energy and we will soon identify one component of energy which we will call the thermal energy, U. Instead of E, you can consider U to be a basic thermodynamic property. It is a small variation. Now if we want, we could have developed the whole of thermodynamics in terms of primitive properties and these three basic thermodynamic properties. However, we will find that quite often we come across combination of properties. So these are known as derived property. For example, the combination of thermal energy U plus the pressure volume product. This turns up so often, particularly when we are looking at open thermodynamic systems that we define this, a short form for this is the enthalpy H. Another property is the compressibility. This is isothermal compressibility. If instead of temperature, we use entropy, entropy constant that will be isentropic compressibility. This is isothermal. Similarly, we have the isobaric expansion coefficient. What will that be? Change in volume with temperature and constant pressure. This is expansion coefficient and there are several others. There is no limit to the end of derived property. We have the enthalpy, then we will have the Gibbs function, we have the Helmholtz function, many other combinations. If you feel like you can define another derived properties for your own use.