 Another way of looking at properties is as extensive or intensive property and for this we look at a system like this. Let us take a system, I will just show it like this a big bubble and then I will consider that to be partitioned into two systems. So this is our system and let us say it is partitioned into two parts or two subsystems A and B. So A and B together they form our system. So you can say system is A plus B and let us say we consider some property of the system, let us call it phi. We measure that property and let us say it is phi and for the part A we measure it and say it is phi A and for part B we measure it and let us say phi B. Now if you find that the property of the whole system phi turns out to be phi A plus phi B then we say phi is extensive, phi turns out to be equal to phi A and also equal to phi B then we say that phi is intensive, simple definition and here we should note a property neither intensive nor extensive and your first homework today evening is to think over and find out or set up a property of a thermodynamic system which is neither intensive nor extensive. It is not necessary for a property to be either extensive or intensive, it can be neither you can set up such a property. Now we come to that part of thermodynamics but before that let me complete this part of the property discussion. Sometimes we define what is known as a specific property. A specific property is nothing but extensive property unit usually with one exception which we will soon see. Examples, you take say pressure or temperature, these are intensive properties. You take mass, volume, energy of various kinds, these are all extensive then specific volume and as volume per unit mass, this is a specific property. Similarly, energy per unit mass, this is known as specific volume, this also is a specific property, it will be known as specific energy. Similarly, specific enthalpy will be h by m, specific entropy will be, the only exception which I will not write down is density which is not per unit mass but it is mass per unit volume. It is the reciprocal of specific volume but that is also a specific property in some sense. Now we come to at some stage, we have to come to the discussion of view points. A discussion came up in my interaction earlier. When I said that state of a system is a quantified description, we have listed the relevant characteristic and we have quantified it but the relevant characteristic can be from a macroscopic view point, remember A or it can be from a microscopic view point. So, here the scale is macro, large, micro, small and as somebody said there is a wide gap in between which is mesoscaling. So, you can have a mesoscopic view point but let us not confuse with mesoscopic which is a mixture of macroscopic and microscopic. We look at macroscopic and microscopic. Now when it is macroscopic, we look at our system as a continuum on a large scale, we are not going to look at microscope and electron microscope and see minute details of the system. The microscopic we are going to say that it is made up of a large number of particles. When we have a continuum, the microscopic domain we look at a small number of properties, even for the most complex system the properties will not exceed may be a dozen or so. For simple systems 3, 4, 5 is more than sufficient for microscopic. So, here I will say n is of the order of may be 10 for reasonably complex things. Here n is of the order of 10 raise to Avogadro number 23, 25 whatever a very large number and for every particle you are going to have 3 components of position, 3 components of velocity assuming that those are point particles. If they are extended particles, they have three dimensional particles then you have their attitude locations. So, it is going to be very complicated. So, because there are small number of particles, we have to have a few equations. So, this is ease of handling. Here too many equations. So, what do we do? This just cannot be handled. So, we talk about averages and we end up with statistical thermodynamics. Out here we discuss phenomena, the way nature behaves, the way continuum behave on the large scale. So, we end up with classical or phenomenological thermodynamics. Statistical thermodynamics is useful in its own right, particularly when you go at micro scale you have to look at statistical thermodynamics. But for a large number of mainstream engineering applications particularly in mechanical engineering, the continuum approach is good enough and in this course we will restrict ourselves to the classical view point of thermodynamics. So, whenever we describe a system, we will be describing it using the continuum model and hence we will be firmly remaining in the domain of classical thermodynamics. Now, let us discuss something more on properties and now you look at our system. Let us say system A and let us define the state. Let us say for the time being the state up is made up of mass, pressure and temperature. Let us say that the cylinder of gas is very rigid. So, there is no question of changing the volume. So, volume tends to be a variable to be noted but not of that relevance because it is not going to change. So, let us say mass of 14 kg, temperature of 32 degrees C, pressure of say 22, this is state of system A. I have to write three properties for simplicity. You could add volume, you could have energy, you could have whatever you want. If it is a gas made up of two component gases say P and Q, you could have mass of P to be 14 kg, mass of Q to be 12 kg, number of variables will go up. When you look at this, we are naturally reminded of coordinates. I can say that look in a coordinate system, I can have a point x equal to 14, y equal to 32, P equal to 22 and one might as well sketch this like this. We can have mass axis, we can have a temperature axis and we can have a pressure axis and we can say that 14 kg mass, 22 bar pressure and may be 32 degree C temperature. So, this height is the same thing as the height here. So, this point A, I can say is state of, what I have done is I have sketched a coordinate system, each axis of which represents one thermodynamic property and in that coordinate system, a state can be shown as a point. Such a coordinate system is known as a thermodynamic state space. The thermodynamic state space is the coordinate geometry analog of ordinary space, each axis represents one property. So, a property now becomes a thermodynamic coordinate in the thermodynamic state and each point, each point represent one state of our system. A different point will represent a different state of the system. For example, a slightly higher pressure may be the same mass, the slightly higher pressure of 24 bar and the slightly higher temperature of say 40 degree C will give a state A prime, a different state of the system. Now, remember that the state can be represented as a point in the thermodynamic state space, but the story is not over here. The question is, is it always possible to represent a state on a thermodynamic state space by a point? Now, let me simply say that this is some mass, this is some temperature, this is some pressure, our thermodynamic state space. Is it always possible to represent a state? I will keep on dropping the use thermodynamic, otherwise it becomes long, otherwise here the full sentence should be, is it always possible to represent a thermodynamic state as a point in thermodynamic state space? So, out here and out here, if you are a purist, add the word thermodynamic. The answer is sometimes yes, sometimes no. Take, for example, I have this bottle, the mass of the water contained in the bottle, the pressure of the water contained in the bottle and its temperature. If I do measurement and get unique values for it, I will be able to represent it by a point on our thermodynamic state space, say point X, but suppose I have churned the bottle significantly and I have heated it up by keeping it next to a hot space, then as I do my measurement of temperature, I will find that I will get different readings at different places. I measure, try to measure pressure, I will not get a unique value of pressure, significantly different pressures as I do different measurements, in which case my answer will be no. If at least one property is such that I cannot get a unique value for it, then my answer will be no and in that case, I will not be able to show it by a unique point. Maybe I will be able to show it by something, state it somewhere there, I cannot make out where it is. Such things happen and many of our real life systems will end up with a situation like this. This brings us to the idea of equilibrium. When it is possible for us to represent a state by a single point in thermodynamic state space, we say that the state is in equilibrium and when it is no, we say the state is not or if you want to be more specific in thermodynamic. So, a very important definition is that of thermodynamic equilibrium and the important thing is we say that the state of a thermodynamic system is a state of thermodynamic equilibrium or the state is in thermodynamic equilibrium. Only when it is representable by a point in the thermodynamic state space, that means we are able to assign unique values to each and every property. If we are not able to do that, at least there is a variation or a non unique value for at least one property, then we say that the state is not in thermodynamic equilibrium. This is going to be our definition of thermodynamic equilibrium. Now, what we have looked at so far is idea of a thermodynamic system, importance of boundaries, state of a system, properties of a system, classification of properties and viewpoints, microscopic, macroscopic. Idea of a thermodynamic state space where each coordinate represents the property on some scale and the idea of thermodynamic equilibrium. Our idea of thermodynamic equilibrium, although thermodynamic is a big word, equilibrium is also a big and complicated word but our equilibrium, our thermodynamic equilibrium just means the ability of a state to be represented in thermodynamic state space by a single point and that means each and every property which means each and every relevant characteristic uniquely defined a unique single value. Now, the question how many properties are required define the state of a system? The first thing to note answer in thermodynamics but now we come to our state postulate one. What is this state postulate one? Thermodynamics cannot tell us, we cannot derive using thermodynamics how many properties. We will come to state postulate two after the first law of thermodynamics when we give a number to it but the first state postulate is one the state of a system in full form the thermodynamic state of a thermodynamic system can be defined using only primitive. This is our first state postulate. This means that you need not use properties like temperature, energy, entropy, enthalpy for defining the thermodynamic state of a system using appropriate primitive variables like mass, pressure, velocity, density, volume you should be able to define but this ability does not mean that defining a state only in terms of primitive properties is the most convenient way of doing things. It may not be convenient, we find that it is very convenient to define the state in terms of temperature and that impresses on us the importance of the quantity or characteristic or temperature, property called temperature but thermodynamics says that you can define the state of a system using purely primitive variables. It may be an inconvenient way of doing it but it can be done that is state postulate one and this means that once you define a state using primitive variables as dictated by state postulate one all the thermodynamic variables now become functions and or dependent only on primitive variables. So, this state postulate has in it the basic idea known as the equation of state. I am writing a plural here because once having decided or define the properties using primitive variables then when it comes to thermodynamic properties temperature will be dictated by those primitive variables. So, there is a functional relationship between primitive variables and temperature that is an equation of state. So, our classical ideal gas equation of state we have not discussed it formally yet but all of us know it PV equals MRT or temperature equals PV divided by MR. Temperature is related to purely primitive properties pressure volume mass. Similarly, energy or internal energy will be related only to primitive properties entropy will be related only to primitive properties and these relations we call in thermodynamics equations of state do not take it as a definition just now we will come to this later. This is Gayatonday from Bombay. Do you have any questions over NIT Trichy? Over to you. Can you tell the contributors from mathematician to thermodynamics? Can you name some of the contributors? Mathematicians got into development of thermodynamics rather recently. If you look at the early days you know in the 19th century scientists were good in physics chemistry mathematics altogether. So, when you say people like Kelvin they have contributed to physics, they have contributed to thermodynamics, they have contributed to mathematics also. So, but they were known mainly as physicists. In the 20th century there are two mathematicians who have contributed significantly to thermodynamics. The first one and the more famous one was the French mathematician Konstantin Karatheodori. His so called the differential formulation of thermodynamics is what is considered to be among the mathematically perfect formulations of thermodynamics and later on when we go to the first law of thermodynamics we are going to use the Konstantin Karatheodori's form of the first law of thermodynamics. His form of the second law of thermodynamics is also well in the words of professor Sukhatme if I may paraphrase them it is mathematically very beautiful. However, as engineers particularly as mechanical engineers it is rather difficult for us to appreciate that mathematics and hence we will be remaining in the physics and engineering domain when it comes to second law of thermodynamics but when it comes to first law of thermodynamics we will be using the Karatheodori's formulation. The second mathematician in the 20th century who contributed to thermodynamics but for some reason he is not that famous and we do not even know what happened to him after his early contributions to thermodynamics is Giles. A mathematician whose thesis on the mathematical foundations of thermodynamics has been published in a book form. His formulation is purely topological in the sense there is absolutely no differentials involved in it. It is only transitions between states and his contribution to thermodynamics according to me is that he had shown that there are six and exactly six that is six necessary and sufficient premises for developing the mathematical foundation of thermodynamics. So three of them are equivalent to our 0th law, 1st law and 2nd law and three are equivalent to the different types of state postulates. Over to you. Thank you sir. Hello, this is Anand coordinator N.A.T. Tiritchi. Some of the feedback I received from the party's friends I would like to bring to you. What are the topics you are delivering? If you give the suitable textbooks for the particular those topics it will be really useful for the participants then that material can be taken into the students when they are likely to deliver thermodynamics subjects in their college. Over to you. Thank you. Professor Anand I have listed five textbooks and as I said at the beginning in fact I have the five textbooks here. Unfortunately none of these textbooks have been written from the point of view of a teacher who has to teach a first level thermodynamics class in mechanical engineering. They have been written for engineers in general and many of them say this book is good for a textbook for say the first or third semester mechanical engineering thermodynamics course. It is also useful as a reference book for you know practicing engineers. Now I find it very hard to believe that a 500 page textbook can do justice from a second year mechanical engineering student also to a 40 year old engineer who is designing turbines and worrying about the control of boilers. Because of this these books get into too many applications boilers, turbines, refrigeration, air conditioning systems and to keep the thickness of the book in control they sort of pad up or they make the initial contributions pretty small. Consequently when it comes to development of the basic ideas of thermodynamics may be none of these books are good enough. You will have to use them in combination. So for example whatever these introductory topics which I am talking about they are almost in any one of those five books and they will be particularly well explained in Achyuthan, Sears and Zimansky. Maybe what I will do is today evening I will spend some time and try to say tell for which topics which are the books one may refer to. But if you find that topic 1.1 is in this book, this chapter, topic 1.2 is this book, this chapter, this section, I do not think that will be possible. Over to you. There is no further question. Thank you very much. Over to you. Thank you very much. Any questions from your end? Over to you. The problem seems to be the timing problem, the internet bandwidth problem and some associated, you know network management problem. We are taking a status situation. The status report will be available to me soon after the session is over. So I will inform what is the action to be taken by us or by you tomorrow morning. Those who have received zero mark should not worry about it. Actually the test one was essentially a feedback which we needed for the purposes of our study. The zero marks do not mean anything. That is just a fluke of computer programming. Do not worry about that. Over. V. N. I. T. Nakpur, any questions? Over to you. My question is from mechanical engineering standpoint the default approach is that of classical thermodynamics rather than that of statistical thermodynamics. Is this a correct perception and my humble opinion is that while teaching thermodynamics a balanced exposure would help the understanding of abstract ideas like entropy. Over to you, sir. Nice question. In fact, thermodynamics can be developed from the classical point of view. It can be developed from the statistical point of view. However, whether you study thermodynamics ab initio in physics, chemistry or engineering, the development has always been first classical then into statistical. The transition from classical to statistical can be done at various stages. We being mechanical engineers, we go as much as possible in the classical mode and then if need be go into statistical. For example, at least in IIT Bombay at the undergraduate level, we do not talk of statistical. It is only at the post graduate level course in thermodynamics. For example, the corresponding course at the post graduate level means about a 4 or 5 week review of undergraduate thermodynamics that is the classical one and beyond that it is statistical mechanics, kinetic theory and such stuff. It is wrong to assume that entropy can be appreciated only through the statistical means. In fact, I have been teaching and there are good books and I have also been taught a very proper understanding of entropy without any thought of statistical or randomness or disorder or anything like that. This idea many students come to us saying entropy is the you know a measure of disorder but you never showed it like that. I said I do not have to show it like that. All the characteristics of entropy we have derived. In fact, entropy itself is derived as a useful property in our traditional classical way and that is how it has been used by thermal engineers all these years. So, there is nothing wrong in remaining at least for the first course in thermodynamics for mechanical engineering purely in the classical. Over to you. We appreciate your views. Thank you very much. Over and out. Velour, this is from IIT Bombay. Any questions? Over to you. Thank you. I think I get the question something like this. Your question is something about processes and how do we mathematically model the processes? I will tell you that I have just used the term we have not yet defined the process correctly, not characterized any processes. So, we will continue with that in the basic definitions. The only definitions which I have given you so far is that of a system and may be of thermodynamics. The formal definition is only that of a system. System, its state, all that we will define. Then we will define a process. This sometime till we come to the processes, their characteristics and their modeling. Just wait for an hour or a day. These ideas will automatically be developed in due course. Over. Sir, one more question to you sir. We know about microscopic and macroscopic approaches sir. What is meant by mesoscopic approaches? Can you show some materials or give some definitions? Is there any? We want to know the related topics there. Mesoscopic. Over to you sir. See, I understood your question. It is a question about the scale and the type of modeling. Traditionally, we have been modeling or partitioning thermodynamics as microscopic and macroscopic. We will be remaining more or less firmly in the macroscopic domain. Now, recently because of development at the micro-nano picol levels, thermodynamics at the microscopic or the micro-formulation of thermodynamics is being looked at again. But you know like things in real life everything is not absolutely black and absolutely white. There is a lot of funny in between and the mesoscopic scale is the in between scale of microscopic and macroscopic, where macroscopic effects are also significant, microscopic effects are also significant. So, we will have to take the best of both worlds and being able to model that. In this course, we are remaining firmly in the macroscopic domain because this course is for teachers who are going to teach thermodynamics as the first course in mechanical engineering. So, we are going to remain in absolutely basic traditional thermodynamics which is macroscopic. I hope you understand.