 There is another important way of classifying property and that is extensive or intensive. They are not exclusive in the sense that a property need not be either extensive or intensive, there can be properties which are neither extensive nor intensive. Look for example this situation, consider a system and let phi be one property, some property. Now just partition the system into two by putting a maybe imaginary surface through the system. Separate it into one part A, another part B. So the system now consists of two you can say subsystem A and B. If my system is whatever are the internals of this bottle system A could be the water, system B could be air. Then if, now measure the same property phi for A and B. If phi turns out to be phi A plus phi B then we say that it is extensive. Whereas if it turns out that phi is equal to phi A is equal to phi B then it turns out to be it is called intensive. We will revisit this because we are jumping an idea here. We will come to that in a few points. Take for example the volume. Now remember that every system must have a boundary whose extents and locations are defined. So every thermodynamic system at any instant of time must have a defined volume. Remember that the moment you define a system one property always exists and that is its volume. That is something you cannot escape. In a particular case it may be irrelevant but that property exists. There is no thermodynamic system for which you say volume. There will be a volume for every system. Maybe of relevance may not be of relevance but every system will have a volume. Now look at this. Is volume an extensive property or an intensive property? Extensive property. By basic geometric definition volume is an extensive property. Mass, extensive property. For such a liquid which is not getting heated or cooled what about its temperature? Intensive property. If I neglect the gravitational gradient pressure will be an intensive property. We are all familiar with that. Can you give me an illustration of a property? Can you derive a property which is neither intensive nor extensive? The total surface area of the boundary of a system. Is it intensive or extensive? Or neither? Consider this water. You know the total surface area. Now chop it into two. When I chop it into two I am creating additional area for each boundary. That boundary will be counted twice on the right hand side. If you take the surface area of a system when I redefine a system A and B together has the total surface but the A part has that part of the original surface plus that additional surface which I have opened up. Similarly B will have the original part of the surface plus the additional surface we have opened up. The surface area of a system, the total surface area of a system is a property which is neither extensive nor intensive. You can very easily derive this. For example, mass of a system is a property, extensive property, square of a mass of a system, m square. It is a property. It is derived property, mass into mass. What is wrong with it? Is it extensive? No. Is it intensive? No. So there is nothing special about extensive and intensive. We should not have a mental set that a property is either extensive or intensive. We can create enough illustrations of properties which are neither. There could be an entity which is neither scalar nor vector. Actually in thermodynamics there is nothing vector because there is no direction involved except direction of time which is before and after. So if you include vectors in thermodynamics that would be a very convoluted way of including that. That has been done. For example, when it comes to radiation equilibrium we have what is known as a pointing vector but that is a, there is a field involved, physical field involved so there is a sense of direction there. Yes but there is no space involved. It is only before and after. So there is only an arrow of time. There is no arrow in a space direction in thermodynamics. So there is the idea of a specific property. It turns out that many extensive properties are useful and since mass is also an extensive property, it turns out that an extensive property divided by mass, this turns out to be an equivalent intensive property and this is known as a specific property. So we have volume as an extensive property, small v, volume per unit mass is an extensive property. We have thermal energy as an extensive property, specific thermal energy is an intensive property. So you can define H and then there is only one exception to this. The reciprocal of specific volume mass per unit volume which is also quite often considered a specific property. Although it is not per unit mass, it is per unit volume. This is an exception. Otherwise specific enthalpy means enthalpy of the system divided by mass of the system. Useful for, it is not really required to derive the properties or characteristics in thermodynamics, it is useful for tabulating properties. That is about all. Why we are using equivalent symbol instead of an equal to symbol? I was about to explain that. Equal to is a mathematical equality. When I use equivalent that means the left-hand side is defined as the right-hand side. It is congruence but for my symbolism and our symbolism here we have been using since my student days in thermodynamics. Three horizontal lines means left-hand side has its definition on the right-hand side. So that is why I think earlier I do not remember H was defined as u plus p. Did I write it like that or no? I do not know but that is the way it should be written. This means H is defined as. So this is for us in this course is defined as. So if you see anything else H related to something else that cannot be the definition. It can only be a derivation out of this. For example under certain class of processes, certain type of process H delta H equals m Cp delta t. That has to be a derivation. It cannot be a definition of delta H. Now remember that the state of a system was something like one property, another property, some property, some third property, how much was it. Now this reminds us of remember a point in three dimensional space x equals 2.5, y equals 1.0, z equals 3.9. This says that this is a, when you say x is 2.5, you can imagine a point in the three dimensional space. So that way this is 3D geometric space. This we call thermodynamic state space and now you realize that each property is similar to a geometric coordinate and hence a thermodynamic property can be considered as a thermodynamic coordinate. So in this model I can say that state of a system can be represented in a thermodynamic state space and can be, each one of the coordinates can be a thermodynamic property. For example I can consider for our earlier system one coordinate to be pressure, second coordinate to be temperature, third coordinate to be, and we have said pressure of 14 bar, how much was the mass, 18 kg temperature 34 degree C, mass 18 kg 34 degree C. So this projection from here to here will be 34 degree C and then this will be the state as defined. This is a physical depiction of the current thermodynamic state space of our system and in which one point defines our state of the system as it exists now. The system cannot be shown but the state of a system can be shown as a point in thermodynamic state. Now here you see the equivalence of the properties with the coordinates, hence properties are considered coordinates, thermodynamic coordinates of the thermodynamic state space and every point represents a state of a system. Now the question always possible represent a state of a system, I am not writing because whenever I say state it must belong to a system by a point or more state space, answer could be yes, answer could be no. For example if I neglect gravitational pressure gradient at this instance if I look at my favorite system, you can say yes, pressure is uniquely defined, temperature is also uniquely defined, mass is definitely uniquely defined. So yes I can represent it but then suppose I keep it out in the sun or near a hot thing, after some time I will find that the temperature is not uniform. If I am putting it in the centrifuge there will be a significant pressure gradient, the pressure will not be uniform or even if I stir it, pressure will definitely be not uniform at some instant of time. So it is possible that when we observe a system we may find out that the state is such that you cannot represent it by a point in state space. Now a very important definition, if the answer is yes then we say that the state is a state of equilibrium, the system is in a state of equilibrium. No we will say not get this idea clear because the word equilibrium is used in many branches of science. We have even economic equilibrium, so even non-science or social equilibrium, social science is used. For us equilibrium pertains to the state of a system and if a system is in state of equilibrium it is equivalent of saying that that state can be represented by a point in an appropriate thermodynamic state space and that means each and every relevant characteristic, each and every property has a unique value associated with it. This has nothing to do with balance of forces absolutely nothing. Thermodynamic equilibrium means this and we will come across this very often. There are many terms which we use in ordinary life in many branches of physics which has a different meaning, which have different meanings there. They may be very properly defined there, we will not bother about it. For some historical reasons we continue to use the same word in thermodynamics but in thermodynamics we cannot just say as defined there we cannot leave it as a primitive. We will define it for our purpose in this way and we will not confuse it with other equilibria defined somewhere else because you know we have social equilibrium, we have political equilibrium, we have economic equilibrium, you also have mechanical equilibrium and chemical equilibrium. In general in a crude way thermodynamic equilibrium, now this is just a divergent not definition. Usually, I will write here that, usually means that a system is in mechanical equilibrium, chemical equilibrium and in thermal equilibrium. Combination of this is not perfectly equivalent as we will soon see. A mechanical equilibrium means sum of forces on a particle is 0. It is a body sum of torques also is 0. Which one? Both. That is why you know idea of equilibrium there is different. But how dare remember, if you take a particle, sum of forces is 0 but a force may be acting. But there are other forces acting which make the sum of forces to be 0. Here we do not talk of any forces. We do not talk of force means system A acting on system B in some way. Those are involved. In thermodynamics it is not so. Thermodynamic means I do not care what happens. Are the properties uniquely defined? That is all that it means. Yes, chemical means the chemical potential is uniform. There is no possibility of a chemical reaction and thermal means the temperature is uniform. But we have yet to define that because I am showing you this because thermodynamic equilibrium is distinct from thermal equilibrium, chemical equilibrium and mechanical equilibrium. But a system which is in thermodynamic equilibrium will definitely have thermal equilibrium but may have chemical equilibrium and may have mechanical equilibrium. I am putting this slide just to show that there are different equilibria in different branches, physical chemistry, physics. This is our own home ground which we will come to later when we come. Now before we go away from here let us say that this is our thermodynamic state space and let us say that our three properties are simply x1, x2, x3. If I say there is a point then I know this is an illustration of a system in equilibrium. There is a point you take projections and you know what the properties are. Suppose I say that I have a system and I know it is not in equilibrium. I cannot measure at least one property uniquely. How will I represent it on the thermodynamic? Actually there is no way you can represent it on a thermodynamic state space because it will be some nebulosity, some cloudy thing. The system is somewhere there. The property set is somewhere there. I cannot do anything better than that. So remember that a non-equilibrium state or state not in equilibrium is very vague. We cannot represent it on thermodynamic state. If we were to represent it by point it must be a state of equilibrium. Now just as an illustration I took a simple system in which just we had three relevant characteristics. So question that arises is how many properties, how many properties are needed to define the state of a system property. When we come to zeroth law we will show that minimum one. In fact thermodynamics does not tell us how many. But there is a that brings me to the state postulate. In fact I have gone up and down a bit here, does not matter. Let me come to what is known as the state postulate or state principle. One because there is 2, 3 and all that. There are number of them. This is a primitive, sorry, primise. No proof but seems to be true because this way this is the reason why thermodynamics is a separate branch of physics. It can stand on its own way. This says that the state of a thermodynamic system can always be defined in terms that means it is not necessary for us to use thermodynamic properties to define the complete state of a system. For example the state of this, the volume of water this system can be defined in terms of primitive properties like volume, mass and pressure. It is only for convenience that you may use temperature otherwise it is not necessary to define temperature. And that means each and every thermodynamic property which we are going to define can be expressed for any system in terms of its primitive properties or primitive variables. This is a undefined thing and that is why it is a primise. And this is necessary because unless we have this, we cannot define our energy, we cannot define our temperature because for defining those we will have to use operational definitions and operational definitions will not allow us to use something which has not been defined. And since all thermodynamic properties have not yet been defined, the moment we try to define the first thermodynamic properties, the only tools available to us are the primitives. So unless the state of a system is derivable or expressible in terms of purely primitive properties, we cannot proceed. This gives the uniqueness of thermodynamics. It can be partitioned off from other branches of physics and that is why in our textbook of physics thermodynamics is a separate chapter. And this is true of other branches of physics also. Similar postulates must be existing in other branches of physics but we look at it from a thermodynamic point of view. So although we know that the state of a system is very comfortably expressible in terms of its mass, pressure and temperature typically a fluid system. Mass and pressure are primitive properties but we use temperature only as a matter of convenience not because it is necessary to use temperature. We can always define the state of a system in terms of mass, pressure and some other primitive properties. For example, specific volume or density that is always possible but do not go into molecules because we are at the continuum level. We are not talking of collections of molecules. So unless absolutely necessary, we will not talk of molecules. When it comes to kinetic theory, we will talk. That is where because we have decided. The next topic for us is processes. Again we will have a very simple definition, short form. For us a process is nothing but a change of state. And since we are talking of a state, there must be a system involved and if it state changes, we say that the system has undergone a process. So a system executes a process or system undergoes a process is perfectly equivalent of saying the system has undergone a change of state. The system initially was in state one. After some time when I observed it was in state two. That means at least one property was different. Point shifted from one position to another in the thermodynamic state space. We say that it has executed a process. So the minimal requirement is an initial state and a final state. Let us say, let us call the initial state one, let us call the final state two. And then all we will be saying is in this we had an initial state one, the final state. This is the minimal depiction of a process. The question is what happens in between? Let me just consider a situation where I show it in two dimensions so that we do not get confused by the three dimensions. Three dimensions are not confusing. We are very comfortable with three dimensions but this surface and the projection is two dimensional. So why confuse with projection of a three dimensional space in two dimensions? Let us say initially these are, if you want you can write pressure, volume or temperature whatever or x1, x2 if you are comfortable. Let us say we have an initial state one and a final state two. If we define one as initial and two as final this is all that is needed. Now what happens in between? If during the process we keep on observing the system at a very fine intervals of time, very keen accurate observation then there are two possibilities. One is the system does not tell us what it is doing. We cannot even measure some properties and we can say look initially it was definitely at one. Finally it is definitely at two but I do not know what happened in between. That is one possibility, a very general possibility. The other possibility is every time you observe the system behaves in such a way that you can define its state properly. So at some time you will find the system is here, at some time you will find the system is here. In fact you can even perhaps have a proper locus. Let me draw this correctly. That means at every stage the system was in a state of equilibrium. The state went from one point to its immediately neighboring point with very small differences in properties as I kept on observing and hence there were intermediate states which we could define very properly creating a locus or a path which may exist. If so we call the process a quasi-static process. A quasi-static process means a process such that at any time during the process, any instance during the process you will find the state, the system to be in a state of equilibrium somewhere in the state space. Need not be on a straight line joining one to it. Can go all over the state space and come back. But well every time you know where the system is. State can be uniquely defined. That means all properties can be uniquely defined. If you are mathematically savvy you can even fit an equation to this curve. May be very complicated but you can do that. Parametric, non-parametric using all the functions which exist in the modern calculator. If not otherwise a non-quasi-static process will be depicted like this. Need not be because time and actually scale of time it is something which does not enter into thermodynamics. In thermodynamics? No, no, no. So with respect to what? That is the question. The definition is anytime you observe it has to be in a state of equilibrium. Your question is how do I execute a process as a quasi-static process? Then the question that arises is see in principle a process cannot be executed as a quasi-static process because if I want to change the state I must change at least one property and when I change a property I am not sure that the property will change uniformly across the system. That is too much to ask for. So what I will do is I will change a property very slightly and expect it to be soon occur uniformly all over. Now this means that I have to execute it as a reasonably slow process. But let us leave it at that. You can consider that a very close process is a quasi-static process. In fact there could be very fast processes which are also quasi-static. There are very slow processes which will be perhaps non-quasi-static. So a non-quasi-static process we know only the initial state and we know the final state. So let us give an example of a non-equilibrium process. A volume which is separated by a membrane with one phase having some gas and the other phase vacuum. The membrane disappears and when the gas expands the property is not uniform throughout the volume available. Yes, that I agree. We are not able to define a state. That is a perfect example of a non-equilibrium. It has nothing to do with slowness or fastness. Obviously but we get an idea of what a non-quasi-static process is. So here what we do is actually except for the initial and final state we have nothing else to show. But as a question of tradition what we do is we join the initial state and the final state by means of a dotted line and show an arrow. Arrow is just the direction from initial to final. The location of the line has nothing to do with intermediate state. Just a link from one to two. Yes, the location of a dotted line is of no consequence. You can show it straight, you can show it up. But in this case if I have a path I can have tomorrow execute another process like this. This is a distinctly different quasi-static process because I know that although the initial and final states are the same the intermediate states are all different. Whereas in this case this is an extreme case of a non-quasi-static process you can have intermediate things. I can go half way in a proper quasi-static fashion and then suddenly decide to be non-quasi-static. In which case I will have a situation where I will start off like this and then we will say non-quasi-static. So this is partly quasi-static partly non-quasi-static but overall it is a non-quasi-static process because requirement is throughout the process it is in equilibrium. Throughout the process this is not in equilibrium. That can be integrated but beyond that you cannot go. Then if you want you can define a system a state here say 3 and 1 to 3 you can do all sorts of things mathematically but beyond 3 you cannot go. Some books they have given the quasi-static process is a reversible process that is why we can show it in a continuous line. No, being able to show in a continuous line has nothing to do with reversible. A quasi-static reversible process is something which we will define in the second law of thermodynamic that is a much stricter requirement on a reversible process. We will show that for a process to be declared reversible it is necessary that it be quasi-static. Not a stronger version. It is not a version. Being quasi-static is a necessary condition for being reversible but being reversible is not a necessary condition for being quasi-static. The two are different. In fact a reversible process is more linked to an adiabatic process as an isentropic process than to a quasi-static process. When we come to the second law we will. Yes one generation to the next generation of students, teachers. Worse thing it passes from one generation of authors of thermodynamics books to another generation of authors of thermodynamics. Sir can it be clarified by means of a practical example quasi-static and non-quasi-static process? See a process being quasi-static or non-quasi-static is an idealization. Just the way even a state of equilibrium is an idealization because if I keep it like this the pressure is not really uniform because of gravitation. Even the temperature is not uniform because although I am not heating it but there is radiation from that lamp, radiation from this lamp I am touching it once in a while. So even temperature is not uniform but what we have said is just the way we said that some properties are relevant, some properties are irrelevant. Here also we have said that small pressure variation is irrelevant. So I will say I am measuring the pressure at the bottom and for me that is accurate enough for all my purpose. And I will put a thermometer somewhere roughly in the middle and I will say that temperature is the system temperature for my practical purpose. So this is something such approximations we will always have to do because if you want to be mathematically exact we will never be able to determine the state of a system and declare it to be of equilibrium. In similar way when whether the process is quasi-static or not is for us to define. We observe it every time if our observations are detailed we will find that no process is quasi-static. But then we will not be able to analyze as much except the initial state and final state and some links between them. If we want to mathematically integrate we need to have a function. Now the question is whether that function is exactly defined or defined by us according to our convenience. If we define according to our convenience then that means we have forced the definition of quasi-static on that thing. These are all approximations. Now we have classified the classified systems, properties, now processes. So process we have seen just a change of state for a given system and we have classified it as quasi-static or non quasi-static. The last thing which we have to do with cycles. Again a cycle is defined as a process such that final state is same thing as initial state. So on our state space whatever you can write x1, x2 if you feel like 1 and 2 must be the same state. This is the minimal depiction of a cycle. Initial state is final state. What happens in between? Why should I care? My system underwent a process. It was here now. I went somewhere and came back. It had come back there. So it must have executed a cycle. Somebody will say but it never moved from that place. I do not care whether it moved from that place or not. Initial state here, final state the same. So that is a cycle. Yes definitely. I cannot say that 2 minutes, 2 hours, 30 minutes, 32 seconds it was here, 2 minutes, 20 minutes, 32 seconds it was here. There is no change in time. So there is a change in time. There has to be a before and after. So this is the minimal realization. For example if I do something like this, this is a fully quasi-static cycle. I put another loop that is a different quasi-static cycle. And if I draw something like this, this is a non-quasi-static cycle. Simple enough. The basic ideas and definitions in the last thing we will let me say some mathematics or calculus of properties. Remember that if let us say P does not mean pressure. If P is a property, then it depends only on the state because it is a property of state, the location of a point. And consequently over a process say 1 to 2 change in property delta P12 which is defined as P2 minus P1 that will be our definition. It will depend only on states 1 and 2 because it depends only on state 1 and 2. You write any two properties here, your favourites. So I can even write here. This means that this will equal integral 1 to 2 dp along any path joining 1 to 2. Now this when I say any path here, this is a mathematical path. It need not be the actual path executed by the system which executes a process from 1 to 2. So consequently let us say this is the initial state and this is the final state. I may have one path, I may have another path, but integral dp will be independent of the path. This also means the following. Mathematically this means that dp is an exact differential and it also means that which is nothing but delta P for a cycle will be 0 because state 2 using differential calculus it can also be shown that if you have a function P such that integral dp is an exact differential it is equivalent. It is not this implies that it is equivalent to that. And in thermodynamics we will use this characteristic if we find that some function of interactions is independent of the path. We will say we have discovered a change in some property and that is the way we will create a definition for energy using the first law and entropy using the second law. The basic idea is this that a property is a function of the state of a system. Change in property is independent of the path taken between the two states. So any entity which is independent of a path we will say represent a change in some property. We will use that as a basis for a mathematical basis or a mathematical trick if you also feel like for deriving some useful properties particularly the energy in first law and entropy in the second law. Now before we complete the basic ideas and definitions we will just provide an idea of what is interactions. Interaction is a formal word used for transfer or exchange and in thermodynamics these interactions are transfer or exchange of energy which formally is yet to be defined. But then we say that our scheme of thermodynamics let me come back again to our two bubble thing system A and system B. Now when we allow them to transact some interchange between them what will happen is system A will go from state A1 to say state A2. System B will go for state B1 to state B2 but why because something has happened between them and this interaction in energy transfer we call I. Interaction not a definition but we understand an interaction as a transfer or transport or exchange of energy in some form between two systems which quite often but need not always lead to change in the state of the two systems. And the general characteristic or general purpose of thermodynamics is to classify these interactions as of the work kind, work type or heat type. The symbol for this will be W, the symbol for this will be Q. In fact W is a primitive we know gravitational work, we know electric work, we know magnetic work, we know expansion work, confluent mechanics, mechanics, electricity and magnetism. We need not worry about how to define work but however since work is defined in several different ways by several different branches of physics it is necessary for us to put all those work definitions on a proper thermodynamic basis. And that is where we now lead to, that is our next topic, the work interaction.