 second item basic ideas and definitions. As teachers we should spend a reasonable amount of time on basic ideas and definitions for the simple reason that in thermodynamics as in many other sciences or many other subjects, we use terms which are commonly used for many other purposes. We use a term called system. Now a system is used in mathematics, we have a system of simultaneous linear equations, we may even have a system of differential equations or partial differential equations. You go away, we have economic systems and we have social systems. So system is a word which is used not only in thermodynamics but in many other fields scientific or even social scientific or general. And even terms like work, energy, heat, cold, hot these are the things which have been used in various other branches of science and even we use it in our day to day life. Today it is hot, tomorrow night is likely to be very cold, my sun is running temperature. So we use these terms energy, hot, cold, temperature in a very general way. In our day to day life we understand it but when we want to quantify it in thermodynamics we must be very careful about what we mean and what we do not mean. And hence it is absolutely necessary for us to define terms in a very proper way. Although we do this so that our understanding and study of thermodynamics proceeds without any glitch, it is necessary to simultaneously be careful when we use these terms. Because when we go out and use these terms the person whom you are talking to may not necessarily have studied thermodynamics or the thermodynamics the way we have learnt it. So we may say something and he or she will not appreciate it the way we want it to be appreciated. So one has to be careful. Similarly as I said we will now even define certain type of definitions so that we will not start using a term without really defining it and without really understanding it. We will not do something by which I would soon come to a funny definition called circular definition. Any science thermodynamics is no exception to that. It does not get developed or does not exist in isolation. It always works and has to work with other branches of science. Thermodynamics is no exception. Any science will use ideas, concepts, definitions which are developed by other branches of science. And again thermodynamics is no exception. In thermodynamics we use terms like pressure which is defined in somewhere else, mechanics, fluid mechanics. We use velocity which is defined in mechanics, mass which is defined by other branches of this. We use current, electric potential, voltage, even power defined somewhere else. Volume, surface area defined by geometry. Such ideas which are defined by other branches of science and used in thermodynamics are known as primitives. These are defined elsewhere, used by us. By us means students and teachers of thermodynamics. So these are for example p, pressure, v, velocity or volume, force, electric potential, electric charge, electric current, what have you, distance, area. These are all primitives defined by other branches of physics, chemistry, mathematics like geometry and we know they have defined their characteristics properly. We just assume that they are true and go ahead with it. Then the next thing is what is known as premises. Primises are what we call basic assumptions. There is much more to this than basic assumptions. For premises there is no proof. They are supposed to be our understanding of how nature behaves. Some of these premises we will call laws. For example, the first law of thermodynamics, the second law of thermodynamics, the zeroth law of thermodynamics. In other branches of physics for example, Newton's laws of motion. These are premises. These are basic assumptions. They are not derived from certain other principles in which those in case that it is so the other principles would be premises and what we call laws will be derived entities. But for some reason not all premises are given the status of laws. Some are left with the title postulates or principles. For example, we have the state postulate or the state principle. This is true in other branches of science also. For example, those who are keen on mathematics particularly in geometry would realize that Euclidean geometry is based on five postulates. They are known as the five basic postulates of Euclidean. The characteristic of a point, the characteristic of a straight line, characteristic of a circle, characteristic of parallel lines and so on. You cannot derive them. Point is supposed to be an entity in three dimensional space which has a location, a position but no extent. Why should it have only a location and no extent? We do not know. Such an entity exists and with that characteristic of a point we start deriving other properties of points and lines and geometry. So, these are the so called premises. We will look at a number of these. Three of these will be given the title of laws, 0th law of first law and second law of thermodynamics. But there are other basic assumptions without which we just cannot proceed. But for some reason these are not given the status of laws and we will call them principles or postulates. Particularly we call them state postulates in thermodynamics. After premises we come to definitions and derivations. Definitions are essentially short forms or labels. We will come to definitions again and again as we proceed. And then derivations. Derivations are logical conclusions, primitives for using primitives, premises and definitions. When it comes to definitions, we will have two types of definitions. One type of definition is a short form. For example, sometimes we come across certain terms quite often. In thermodynamics we will come across this combination of properties u plus pv. We will come across this combination of properties so often that we will define it as a short form h. This triple line, triple horizontal line equal to which is in mathematics essentially means equivalence. I use it means is defined as. So we can say h is defined as u plus pv. And that means h is a mathematical short form for u plus pv. And that also means that it is mathematically equivalent and it is perfectly okay for us to replace the term u plus pv wherever we see it by h and vice versa. Nothing goes wrong except that some expressions will become longer, some expressions will become shorter. We want our expressions and our talks and our books to be shorter and not longer and thicker and bulkier. That is why we have such short forms. Another short form in terms of word which we will use later is a short form for process. Process is nothing but a short form for a change of state. So in a book on thermodynamics wherever you see a process if you replace it by the set of words a change of state it is perfectly okay. Only thing is that your sentences will become longer the book will have more number of pages. So this is a very useful short form and we will be using such definitions quite often. Not only in thermodynamics we have been using such definitions all throughout our lives. The second type of definition which is a more complicated one is what is known as operational definition. Now this is a proper definition used in physics by means of which various physical quantities and entities are defined. And the key word here is operational. This idea was developed by the great physicist who has contributed significantly to thermodynamics Bridgeman. PW Bridgeman Nobel Laureate worked in various aspects of physics particularly thermodynamics and his thermodynamics or properties of fluids at high pressures is considered a classic. More of a combination of physicist and engineer than a pure physicist. Here we define anything any entity by providing or specifying a set of operations either word or the applicability of a word or to quantify something. I will give you an illustration there is some water in this water. I want to determine the volume of this water. What is the operational definition of volume of a liquid? The operational definition would be the following. Take a cylinder known as a measuring cylinder which will have a uniform diameter nice graduated height scale. We will put it on a horizontal surface. Horizontal surface as designed by a plumb line or a bubble gauge or something like that. Pour this water completely into that. Measure the level at which the mark at which the level exists. The mark corresponding to the level is the volume of water in this bottle. That would be the operational definition. That is the second type quantify something like volume of this bottle. Now I say the cap of this bottle is blue. Now the cap is blue is a statement which is true or false the first type. I have to check the truth of this word. How do I check it? Maybe the proper operational definition would be take this cap take it to a physics lab. Expose it to standard white light or expose it to sunlight. Capture the reflected light from this surface onto a spectrometer. Determine the spectrum. Find out the weighted average of the intensity and if it lies within a certain narrow wavelength band then we will call it blue. If it lies in some other wavelength band we may call it yellow or red or green. For example I have something yellow here. If it is somewhere near maybe 300 nanometers or so we may call it yellow. If it is somewhere at the other end of the spectrum we may call it blue or if it is still further down we may call it violet. So these are operational definitions. You have to set up or specify a set of operation or a proper procedure to either determine whether an adjective is applicable. For example, blueness of this cap or yellowness of this cap or to quantify something for example the volume of this water or even if I drain this bottle of all water what is the inner volume of this bottle. Then the operation would be a bit more complicated. You will say that look take the bottle drain it of everything which is inside and then pour in it a liquid which does not evaporate so easily like water or oil completely fill it with that liquid then drain that liquid into a measuring cylinder. See to it that each and every drop is drained and then measure the level at which the measuring cylinder is filled. The same thing you can do with mass, velocity everything else and in thermodynamics we would like to use operational definition and remember that while doing this the operations have to be completely specified. You cannot say oh that I will specify later such a thing is just not accepted. Let us start defining things in thermodynamics and since many of these are well conversant with we are well conversant with these I will go reasonably pretty fast. The first definition in thermodynamics as we all know is a system. Actually system is a short form what we are defining is a thermodynamic system. But if I start saying thermodynamic system, thermodynamic process, the thermodynamic boundary of a thermodynamic system I will be using the word thermodynamic or thermodynamical so often that I think half of us will run away from thermodynamics for the rest of our life. Now what is the definition of a system? The definition of system is nothing but a region in space of our interest but with defined boundaries and I should not spend less time in underlining this defined boundaries because the system is defined by its boundaries unless the boundaries are completely defined we will not say that a system is defined because when we completely define a boundary naturally we are enclosing some volume of space and hence every system will have one characteristic and that is its volume. We cannot leave that thing open if some boundary is ill defined or not defined we have not defined our system properly. The importance of boundaries is of utmost importance. However, the boundaries can be very flexible. For example I can define the water in this bottle as my system. What are the boundaries? One boundary is the inner surface of the bottle which is in contact with water reasonably regular but reasonably complicated and of course the top surface of the water. If I hold it very steadily I will be able to properly define that surface but if I am not steady or if I shake it the proper surface becomes flexible moving but if I have a camera at any instant of time I can define its location that we will do. Boundaries need not be fixed they can be moving they can even be flexible I can bend the boundary. Sometimes a boundary may even break into in case of complicated systems. We can have some enclosures, air pockets which are not part of the system. Sometimes boundaries may even be defined boundaries. For example in front of me I can imagine top of this a cylinder of this diameter and may be 50 millimeter in height. I can imagine that particular volume but there are no physical boundaries. If I sketch a drawing I can show this as a surface and the other surfaces are dotted lines but by means of a drawing I can define what those boundaries are. Those are geometric boundaries but those are not physical boundaries. I cannot touch those boundaries. If I try to touch my finger will go through and we create such systems quite often. We have done it in solid mechanics. We have done it in fluid mechanics for deriving our continuity equation. We have said let there be a region in space of size data x by data y of data z. So that also is a proper thermodynamic system which has properly defined boundaries but the boundaries are not physical boundaries. They are mathematically or geometrically defined boundaries. Boundaries can change shape size they may be simply connected, multiply connected under certain restrictions we will come to those later. So importance of boundaries can never be over emphasized and because of the boundaries remember that every system must have one characteristic associated with it and that is volume. You cannot say a system you may not worry about its volume. Volume may not be a significant characteristic but volume has to be a characteristic of the system. Then the other type of classification which we usually find is this a closed system an open system or an isolated system. We know what this means. Cloth system is one which does not allow any mass to flow across its boundaries. Open system is one which allows the mass to be which allows the mass to flow across the boundaries. Isolated is one which allows neither the mass to flow nor any type of energy flow across the system boundaries. You know all this but remember that these are not really the characteristic of a system or classification of a system. This is really is classification of a system during a process a system at any instant of time need not be closed or open. It is what happens to the system that makes it closed or open. For example if I say that my system is the water and the air above the water in this bottle. You will say the cap is closed. So it is a closed system. Well that is okay but now if I open the cap and say there is no draft of air so I can neglect any air movement in and out of the bottle then my system which is air and water in the bottle is still a closed system. But if I start drinking part of the water then during the process of drinking some water has come out of the system and obviously some air has gone into the system. So during that process of taking some sips out of the water during that process it was an open system. Again if I replace the bottle the cap of the bottle it is a closed system. So remember that although we discuss this as classification of systems these are the classifications of system during a process. We have not yet defined the process but we will define it. Now the next thing is the state of a system or in full the thermodynamic state of a thermodynamic system. Why do we have to define the state of a system? We have to define the state of a system for the simple reason that we have to study what happens to the system when there is a transfer of energy in the form of heat or work. That is the subject matter of thermodynamics. So because of some transfer in or out of energy in some form system is going to undergo some change. This water is going to get heated or the water is going to get compressed. Something is going to change with the water or the quantity of water is going to increase, decrease, it is going to get contaminated. So that observation of the situation that the system is in is generally known as the state of a system. But what is the operational definition of the state of a system? The operational definition of a state of a system requires two things. First we need to make a list of relevant characteristics. Remember the word relevant characteristics. Characteristic is something which is related to the system and relevant is something which in our experience is relevant in the sense that useful to study. For example if I am going to study my system which is water in the bottle and I am going to study it as I keep it near a hot lamp or keep it in the sun, then may be the mass of water is of importance. The volume of water may also be of importance. May be the pressure under which it exists is of importance. The surface area occupied by the boundary is of importance. But depending on the way it is getting heated may be at some stage volume is not important or if the mass is remaining fixed being a cold system, mass is also not of that importance. Or the color of the cap of the bottle in which that water is filled may be that is irrelevant. What is relevant and irrelevant is something which thermodynamics will not tell us. Out of our experience we will be able to decide whether a particular characteristic is relevant or not. This relevant characteristic is known as a property. So the state of a system is defined by first list making a list of relevant characteristic that means a list of properties because the property is nothing but a relevant characteristic. Another definition which is a short form and two we must quantify by some means each property. Take for example I have a bottle and I have some water in it and let us say that this water is my system and I will say that look mass, volume, pressure and temperature. We have not defined temperature but let us assume we know something about it. These are going to be my relevant characteristic then half of the definition is implemented and then I take this onto a measuring cylinder and say this is 200 centimeter cube. Then I say it is open to atmosphere and measure using some barometer the atmospheric pressure. Let us say this is 1.0 bar. Use a thermometer to measure the temperature in say 24 degree C and go to the physics lab and use a pan balance to measure first the mass of the bottle with the water then drain out the water somewhere else and measure the mass of the bottle. From difference I can determine the mass of the water may be 200 gram. So all that I have done is I have created a list of properties each one of them relevant characteristic and by means of some experiments direct or indirect. For example I may not have directly measured the pressure but indirectly I have measured the atmospheric pressure and concluded that since it is open to atmosphere the pressure of the water should be the pressure of the atmosphere. So directly or indirectly I have quantified this and this I say is now the state of my system which is shown here and is made up of water. So we have defined the state of a system we have defined a system we have identified its boundaries. Usually boundaries are shown by dotted lines we are all conversant with that and we have quantified the state. Now notice that this quantification which we have done is we have done using what is known as the macroscopic view point. This is the most common view point we have considered that the water is a continuum that means we consider it to be some continuous medium which is flexible compressible and so on. We did not while listing the relevant characteristic take note of the fact that it is made up of so many 10 raise to n molecules of this kind which are randomly moving and interacting with each other and with the surface of the bottle. If we do that that will be the microscopic view point. In microscopic view point we will have to consider each molecule for each atom separately. There is a very large number of them and for each molecule you will have to determine the position, the velocity, the orientation and which keeps on changing every instant of time. So not only will you be talking about these, you will be talking of all of these very large number of variables as a function of time something which we just cannot handle and then you will say okay let me talk about the average velocity, the average momentum, the average location and we will go into fields like kinetic theory, statistical thermodynamics and so on. So the microscopic view point we have a few lectures on kinetic theory later, so we will get exposed to that leads to kinetic theory, kinetic theory, statistical mechanics or statistical thermodynamics. Compared to that our thermodynamics is known as the continuum thermodynamics or phenomenological thermodynamics. We worry about phenomena of a continuous medium rather than that of individual molecules which have to be finally handled in a statistical way. So we will restrict ourselves to the macroscopic view point and we will not look at except next week when we talk about, oh we are not included in kinetic theory, sorry I made a mistake. So nowhere here are we going to talk about the microscopic view point. Now actually before we go ahead we will write down some postulates, the first sorry first assumption for first premise is that any system which we are going to study is a continuum. We do not have to worry about particles, we do not have to worry about atoms, molecules and things like that. We are also going to now say that any quantity that means any property or later on any interaction, so this is one, this is another is also a continuous variable. In particular we are going to say there is no quantization. We will not say that energy can only be 1 kilo joule, 2 kilo joule or 0.1 joule, 0.2 joule. If it wants to be pi kilo joules, let it be pi kilo joules. If it has to be some funny irrational number in joules, so be it, we have no objection to that. The third thing we are going to say is our systems and our properties are going to be scale independent. This also means there are going to be no large scale effects and no small scale effects. We will say that in our domain of things thermodynamic systems can be as small as a few drops of water as large as the atmosphere of the earth provided we have defined our geometry properly. And the phenomena will be the same whether they are applicable to the large scale systems as well as to the small scale systems. Of course you can always say there will be system so small that our assumption of a continuum will break down. We agree in which case the laws of thermodynamics as we study it will not be applicable there. One question comes up of that of the physical universe or astronomers universe, the cosmological universe. Is it a thermodynamic system? This is a question some students will ask you because later on there will be arguments that look the entropy of the universe will always be increasing and all that. The answer to that is we today nobody not even the best astronomer knows what the boundaries of our universe are. So since we cannot define the boundaries of our universe, we cannot lay out a thermodynamic system which encloses the universe and hence we say that today we do not know how to apply our laws of thermodynamics to our physical universe. If we can define the boundary of the so called astronomers universe properly define them then maybe we will be able to apply our laws of thermodynamics to it. So there is going to be a microscopic limit to our thermodynamics and there perhaps is also a macroscopic or upper limit to our laws of thermodynamics, our study of thermodynamics. We will come to more premises as we go. The next thing we should be talking about is classification of properties. The idea of properties is not unique to thermodynamics. We have mechanical properties, we have fluid dynamical properties. Each branch of physics defines its own set of relevant characteristics and properties. So our basic classification would be first primitive. Like a primitive idea that means primitive concept something which is defined in other branch of physics or chemistry and used here. So similarly any property which is defined in other branch of physics chemistry, geometry and is used in thermodynamics. We say that look that other branches define all its behavior all the relations related to it very properly. So we will simply use it. These are primitive properties for example pressure, mass, area, volume, electric potential, charge. All these things are primitive properties. Thermodynamics does not define them. Thermodynamics says mechanics has defined it. We will use that idea as is required by us. We will not do anything more. The second type of property is basic thermodynamics or simply basic in thermodynamics. These are defined using laws of thermodynamics. We are going to basically study three laws. The zeroth law, the first law and second law and in turn these will define properties like temperature, energy and entropy. Three laws, three basic thermodynamic out of these three properties, energy is a property which is partly primitive, partly thermodynamic because energy is such an all pervading idea that there are other branches of physics which have defined energy or components of energy based on their ideas, their premises and hence we have the mechanical kinetic energy, the gravitational potential energy and so on. Consequently, after taking care of all those energies, in thermodynamics we will come across a component of energy which we will call U, the so called thermodynamic energy or the internal energy of the system. So you can say TES or TUS are going to be the three basic thermodynamic properties and the third set is the so called derived properties. These are combinations of properties, either addition, multiplication, derivation, differentiation and so on. For example, as I have already said enthalpy, we will define it, all derived properties are definitions. This will be defined as U plus PV. Similarly, we will have the Gibbs function, the Helmholtz function and so on. We also have for example the, for a fluid system the isothermal or isobaric expansion coefficient. This will be rate of change of volume with respect to temperature at constant pressure per unit volume. Similarly, we have the bulk modulus, let us say bulk modulus, isothermal bulk modulus. This will be defined as the rate of change of pressure with volume, isobaric conditions, but again it is relative volume. So we have a V here and again because almost always as volume increases, pressure decreases. So to get a positive number for kappa T, we put a negative sign. So these are all derived properties, definitions. Wherever you see the left hand side, you can replace it by the right hand side and vice versa. These are short forms and any property which we are going to use is going to be of this kind. There is another type of property and that is another type of classification is intensive and extensive. For that we consider for example a system S. This is our system and let a property be phi, some property be phi and then all that we do is put an arbitrary surface, chop the system into two and let us say we have a part A of the system and a part B of the system. Then let the property, the corresponding property phi of A be phi A and that of the other partition B be phi B. Now we sometimes find that if the property of the total system is the sum of the properties of the two partitions of the system, then we say that phi is an A extensive property, depends on the extent. But if it turns out that phi equals phi A which in turn equals phi B, then we say that phi is an intensive property. It is important to note that there may be some properties and we can create any amount of any number of illustrations of this that it is not necessary that a property must be extensive or a property must be intensive. There are properties which are neither intensive nor extensive and illustration would be the surface area of our system. You know that the surface area of the total system will not be the surface area of A plus surface area of B because of that intervening partitioning surface and hence a surface area of the system will not be a property which is either intensive or extensive. Then the third type of property which is quite often talked about is specific property. Specific property is usually defined as an extensive property per unit mass of system. For example, if entropy is the extensive property, the intensive property usually represented by small s is the entropy of the system divided by the mass of the system and so on. Usually, a specific property or an intensive property will be represented by small letters and extensive property will be represented by a capital letter. There are again some exceptions for example, pressure is an intensive property. By default, we use small p for pressure but temperature is also an intensive property. But for some traditional reason small t is reserved for time and capital T is reserved for temperature generally. Now going back, we would have seen that the state of a system is defined by a list of properties and their quantified values and that brings us to the following idea. Let us look at again the state of a system. Let us again take our system to be some fluid, I will not call it water, some fluid in a bottle and let us say that the bottle is rigid. So, we will say that look, since everything in the bottle is a system and the bottle is rigid, the volume is not going to change. So, volume I may neglect as a relevant characteristic and then maybe I will say mass is 1 kg, temperature is 24 degree C, pressure is maybe if it is a sealed bottle, it could be a gas under pressure, let us say 4 bar. This could be the state of a system. Now look at the analogy, when I say m is 2 kg, t is 24 degree C, p is 4 bar. You know one can think of geometry as this is one coordinate, x equals 1, b, y equals 24, z equals 4. So, I can imagine in this case a three dimensional situation. So, a coordinate axis 3, but instead of x, y, z, I will have m 1 kg, I will have temperature 24 degree C and I will have pressure 4 bar and maybe this would be the point representing my state. So, what we have done? We have created a geometry in the appropriate number of functions. In this case we had three relevant properties, this mass, temperature and pressure. We created three axis and using that three dimensional geometry, we could show that this is the point representing my state. Such a space, geometric space is known as thermodynamic state space. Notice that in this state space, each coordinate represents a property and hence each property is also known as a thermodynamic coordinate in the thermodynamic state space and each point in this thermodynamic state space will represent the state of my system. Now immediately the question arises is actually a few question arises. One, how many properties are required to define the state of a thermodynamic system? That is an open question. Which ones? That is another question. Third one, is it always possible to represent by a point? So, this let us discuss this. Actually, at this stage we do not really have answers to many of these. How many properties? This depends on the type of system. Thermodynamic does not put any restriction on this. Which ones? Actually, thermodynamic says something about this, but it leaves us a choice. It does not dictate that these must be the properties, but it says a premise. This is another important premise, which I call the state postulate one. The state postulate one says that the state of a thermodynamic system can only represent the state of a thermodynamic system. It is always defined in terms of primitive variables or primitive property. We need not do so, but if we want to do it, we can always do it. For example, here we have selected mass, temperature and pressure. We know that mass and pressure are primitive properties, but temperature is not. But we have selected it as a matter of convenience. We will define it formally later, but whatever we know about temperature, we have done it. But if we say that look, I do not want to use a thermodynamic property, then maybe using mass, pressure and volume or some other primitive property, I should always be able to define the state of my system. That is what thermodynamic says. There is no proof to this and that is why this is a premise. It is state postulate one that the state of a thermodynamic system can always be defined in terms of primitive properties. It may not be very convenient to do so, but this is always possible. This separates thermodynamics properly from other branches of physics, because I can study the mechanics of this without looking at its thermodynamic state. If I want to start defining the thermodynamic state, that primitive properties are enough. Now the third question, is it always possible to represent the state of a system in thermodynamic state by a point? The answer is sometimes yes and sometimes no and that brings us to the idea of equilibrium. In fact, the idea of equilibrium is not unique to thermodynamics. We have mechanical equilibrium, we have chemical equilibrium, maybe in electricity, magnetism, there could not be an electronic or electrical or magnetically equilibrium, but mechanical equilibrium is something which all of us know, that a point particle is in equilibrium if the net force acting on it is 0 or the sum of all forces acting on it is 0 or a rigid body is in equilibrium if the sum of forces acting on it in total is 0 net and also the total net couples acting on it, couple acting on it is also 0. So, momenta acting on it is 0, forces acting on it in some are 0. In thermodynamics, the idea of an equilibrium is slightly different. It has nothing to do with momenta and forces. All that we say is a state of equilibrium or state in equilibrium or system which is in a state of equilibrium means it is representable by a point in state space and that means each and every property or all properties uniquely defined. So, if I have a system say mass, temperature, pressure or you write any properties if you feel right and this is a state in equilibrium. This could be some other state in equilibrium this here could be a third state in equilibrium. I am putting those circles just to emphasize the point, but each point and each point in state space means position of a point in geometry that means it has location but it has no extent. So, location means all coordinates are defined we are talking of a thermodynamic state space. So, thermodynamic coordinates are defined and hence each and every property must have unique values associated like P equals 1.2 bar temperature is 26.7 degree C mass is 327 grams to any level of precision that you need at that particular point. Whereas, if at least one property is not uniquely defined we are not certain about it then maybe we will have a state which is not in equilibrium at such a thing is very difficult to put in a state space. For example, it is difficult to change the mass, but suppose I open it and play with it allow it to go on spilling some heat it up and shake it to such an extent that even the pressure is not uniquely defined. Then I will get a system whose state may be will lie somewhere in some zone here I will not be able to say what it is. So, maybe this is a crude representation of a system with state is not in equilibrium it is very difficult to sketch or represent the state of a system which is not in equilibrium like this. So, this is our idea of equilibrium in thermodynamics I leave it to you as an exercise to compare it with the idea of mechanical equilibrium or chemical equilibrium. Thermodynamic equilibrium is something which will come to later, but again we cannot prove it, but one can demonstrate that a state a thermodynamic system which is in a state of equilibrium will always be also in a state of mechanical equilibrium will be in a state of chemical equilibrium and all parts of it will also be in a state of thermodynamic equilibrium. Thermodynamic equilibrium is something which we will come to when we study the zeroth law. Now, the next thing is what is known as a process a thermodynamic process a process is defined as nothing but a change of state short form for a change of state and that means the minimal requirement is because we are talking of a system of a state there must be a system which undergoes the process there must be an initial state and there must be a final state and I forgot to mention unless otherwise stated hence forth we will consider all the states that we are talking about to be states which are states in equilibrium unless for some reason we say that we consider a system in a state of non-equivalent. So instead of a three dimensional one I will sketch my state space in two dimensions that is easier and let these be if you want you can write p v here or if you want you can write p t here or if you want to be more general you can write x 1 y 1 here or x 1 x 2 choice is yours any two properties the initial state will be a state of equilibrium represented by a point the final state would be another state of equilibrium represented perhaps by another point usually we will call the initial state by the later I later one or I final state is usually given the symbol 2 or f now the question is if we are looking at it geometrically this is the minimal realization of a process but then what about a path question then arises is that well again may be and that again gives us this idea that look to determine whether there is a path or not will what will I do we will observe in all detail the system as it goes from this initial state one to the final state two it is possible that my keen observation tells me that I can measure the properties uniquely for almost uniquely during this process as it goes from one to two at any point I will know that look it started from one then it went to somewhere here somewhere here somewhere here somewhere here and then came to two I can sketch a path like this and arrow to just show what is the initial state and what is the final state this means that during this process all intermediate states states of equilibrium then we call such a process quasi static process else we will call it a non quasi static process for example non quasi static process means it went from one to two I know the initial state I know the final state however I do not really know what happened in between I could not measure some properties in a unique fashion in which case we will not be able to represent the process by a continuous locus at shown here but just to show that this was the initial state and this was the final state we will call it by convention by means of a dotted line the position of a dotted line is immaterial if I sketch it like this or if I sketch it like this it does not matter these are just two non quasi static processes they are shown distinct because may be they are distinct so these processes say f and g are non static processes and there could be similarities between them or they could be totally unrelated there is no way to make out whereas this process A is a quasi static process and I am sure that these were the intermediate states as indicated by this locus this would be another quasi static process and it sure is different from the process one to two through A because that was one set of intermediate states and this B has another set of intermediate states as indicated by that more loopy line so this is the representation between a quasi static set of processes and some non quasi static processes now thermodynamics does not say that state one should be distinct from state two a cycle is defined as a process such that initial state is the same thing as final state so the minimal representation of cycle if you do not like x y replace it by p v or whatever you want the minimal representation of cycle will simply be one point one and two in between it might have gone somewhere it might have come back to two must have come back to two then this is the cycle this would be a quasi static cycle you can sketch another cycle this is another quasi static cycle this would be a non quasi static cycle the location of the loop is immaterial just want to indicate that it is a non quasi static cycle it is almost one o clock and may be what I will do is I will just talk about a one point change in properties during a process let phi be any property so delta phi during a process is defined as property of the final state minus property of the initial state since properties depend only of the state and not on the way that state is arrived at this does not end on the path and that means it does not depend on whether the process is quasi static or non quasi static because a property being a property of state we define the change in property as final state my property of the final state minus property of the initial state does not and will not depend on the path if a path exists that is quasi static process then delta phi which is phi 2 minus phi 1 will be remember this will be true any path this means two things first if phi is a property then this implies mathematically that d phi is an exact differential and also derivable from this is integral of d phi which is delta phi for a cycle will be 0 and we will use these conditions sometimes actually twice once during the first law and once during the second law to derive properties particularly the energy and the entropy we will now break for lunch and be back here exactly at 2 o clock thank you very much and see you again.