 just now I see only two centers who have raised their hand NIT Trichy and Pillai Panvel. So, let me go there just two questions per center and I will restrict myself to may be three centers these are two here and I will wait for I will take questions from one more. Good morning sir, enthalpy equal to u plus p v sir, everything internal energy pressure volume all our properties why do you require this extra property H and this H is any direct relation with heat transfer that is first question and second question is in free expansion like half of the part of the vessel is filled with vacuum and half of his vacuum and another is some matter is there if you remove that partition inside the inside the total vessel that molecules are moving. So, thereby they are doing some work. So, they are doing some work means some energy is they are giving. So, where that energy is coming from you said that dq is 0 and dw is 0. I think some work is going on there might be some change in enthalpy that is what I want to say over to you sir thank you and one more one doubt is which is a which properties neither extensive nor intensive thank you sir over to you. Since in one short you have asked three questions I will restrict myself to the answering these three questions. The first question was what is H well we said that there are different types of properties we said primitive properties like pressure, volume, velocity then basic thermodynamic properties or inherent thermodynamic properties and there are just three of these one property defined by each law of thermodynamics. First law defines energy 0th law defines temperature and today we will use the second law to define entropy. So, when it comes to property in our set we have primitive properties plus three basic thermodynamic properties and these are simply e or u t and today we will take up s. Apart from this we have what are known as defined or derived properties. These are just short forms and these are forms for convenience one such property is the enthalpy H and this is defined as u plus p v that is it. Do not try to as ascribe any direct meaning to these because we will see when we come to open systems and we have already seen that even for fluid systems when you have a constant pressure process this u plus p v turns up together. So, it is useful to have a short form H for it. Similarly, we have seen yesterday C v and similarly C p these are defined or derived properties these are not basic properties it is convenient for us to work in terms of C p for many fluids over a reasonably useful range of temperature. We find that u and H are almost linear functions of temperature and hence the slope of that if we define we can given the temperature difference we can easily determine the either the enthalpy difference or the internal energy difference. Hence it is good to define these short forms C v and C p. Later on we will come across other short forms on Monday they will be you know Gibbs energy Helmholtz energy and so on. So, there is nothing special these are just short forms for convenience I think that takes care of question one about the free expansion. You talked that free expansion means molecules moving from one side of the system to another side of the system and because they are moving they are doing work I would like to mention here that we do not have to go and talk about molecules. We know from our school physics and chemistry background that all matter including gases liquid solids are made of molecules. But our classical thermodynamics engineering thermodynamics all the basic stuff including second law entropy can be derived without talking about molecules. So, we do not have to think of free expansion in terms of molecules. If you realize that there is something like that it is ok. In fact just as a side tracking or a diversion we will talk about how free expansion in principle can be reversed and we will talk of a funny creature called the Maxwell's daemon. But that is not really our main stream thermodynamics that is on the border line of classical and molecular thermodynamics. Then you made a statement that just because a molecule is moving it is doing work that is not true remember even if you consider that single molecule as a system with a boundary surrounding it well it is a thermodynamic system at the microscopic level. But when it does work it has to interact with some other system just because it is moving it is not doing any work. Yesterday we took an illustration that in vacuum a free falling body say a ball neglect air resistance a ball going up and down as a projectile it is not doing any work all that is happening is its energy is being maintained constant because there is no heat transfer there is no work transfer. But it is the total energy which is remaining constant it is the as it goes up kinetic energy reduces potential energy increases when then as it comes down potential energy decreases kinetic energy increases. There is only a redistribution of energy there is no work done because remember for work to be done there must be two systems and there should be an interaction between the two systems that means work should be done by system A on system B and system B should say yes I am being worked upon by system A. Then the third thing about extensive and intensive properties these this is simply a classification and I have already given you the definition I think all you wanted was an illustration of a property which is neither intensive nor extensive. And this can be created but one property which is obviously neither extensive nor intensive is area if you take a volume as our system and lets its area be A naught. And consider a partition which splits it into say a part A I will use small letters here so as not to confuse with the capital A for and then you will notice that the area of A and area of B do not sum up to the total area A naught because the area of A will be the area on the outer surface which contributes to A naught plus the area on the partition which does not contribute to A naught. So, when you sum up this area you will not have it equal to A naught and you agree that in the general case A naught is not equal to area of B nor equal to area of B. So, the area of a system surface area of a system is a property which is neither extensive nor intensive. We do not have to really worry about this because area by itself at least in our illustrations on thermodynamics does not play a very major role. Now, that was enough from Trichy. Let me go to Panvel. Over to you Panvel. Can you elaborate the degrees of freedom for a vapor phase? The question was the degrees of freedom in the vapor phase. Let me say that when we have the phase diagram, let me draw the reasonably complete phase diagram. This is the triple point, this is the critical point, this is solid, liquid and vapor phases. Degree of freedom means that let us take a simpler version because we are not going to look at mighty component mixtures in this course. For us degree of freedom means how many of these intensive properties P and T, we can vary slightly and still remain in the same type or same phase of system. For example, if you are here what we call superheated vapor then I have some pressure some temperature. I can vary the pressure slightly without changing the temperature and I will still be in the vapor phase. Similarly, I can change the temperature without varying the pressure and I will still be in the vapor phase. That means I have the ability to slightly vary pressure and temperature independent of each other and still remain in the vapor phase where I was earlier. Same thing will be true if I am within the liquid phase or I am within the solid phase. So, when you have only solid or only liquid or only vapor, we say we are in a single phase domain and we have two degrees of freedom. That means P and T can be independently varied and that also means that to locate a point on this, I have to specify both pressure as well as temperature as in case of superheated steam. Superheated steam at 10 bar does not mean anything. You have to say superheated steam at 10 bar and may be 250 degree Celsius or 300 Celsius something like that. Now take a point which is on this line and I am considering a location x and at x I have liquid and vapor together. So, the characteristic of the system is liquid and vapor in equilibrium. Out here it was vapor only, no trace of liquid, no trace of solid. Now this is a two phase situation. Why two phase? Because you have a fixed pressure, you have a fixed temperature, but if you take various parts of the system, the specific volume or density is not uniform. If you take a small part of the system which is in the liquid, suppose there are droplets of liquids and bubbles of vapor, consider a small subsystem in that which contains only the liquid. It has a density, a slightly higher density. Take another subsystem which is in the vapor part say in a bubble, then it has a lower density. So, at the same pressure and temperature you have parts of the system which have distinct density. These parts are known as phases, that is a basic definition of a phase and because you have two distinct phases here, one liquid and one vapor with two distinct specific volumes or two distinct densities. We have a two phase situation and the phase rule you have the formula and if you substitute number of phases two, you will find that there is only one degree of freedom and it is consistent because I want to remain in the two phase situation and if I want to remain in the two phase situation, I cannot change the pressure while keeping the temperature constant because if I keep the temperature constant and increase the pressure, sorry if I keep the pressure constant and increase the temperature, I will go into the superheated phase, single superheated zone with a single phase. I will get away from my two phase situation. Similarly, if I reduce the temperature, I will go into the liquid phase. Again, I go away from the two phase situation and the same thing if I maintain the temperature constant and only increase or decrease the pressure, I will end up with the single phase liquid or a single phase vapor. So, if I want to remain in the two phase situation, then if I change pressure, I have to change my temperature correspondingly. If I increase my pressure, say from here to here, I must increase my temperature from here to here, I have to go along the curve and that means, if I select to change P, I have to change T. If I still want to remain in the two phase situation and that means, I cannot select P and T independently. If I change P, there should be a corresponding change in T and if I change T, there should be a corresponding change in P and that means, out of P and T, I can select only one and that means, I have a one degree of freedom. I think that explains that. Now, let me take one more center M K S S S Pune. Come in Pune, over to you. Good morning sir. I have a question regarding the zeroth law. In the discussion of the zeroth law, two systems were considered by separated by a diathermic wall and it was asked to pick the state of system A and try out various states of system B and check whether there occurs any heat interaction. My question is, without defining the temperature, yet how we can check whether there occurs any heat transfer. This is my first question and second question by the state postulate first, first state postulate. The state of the system can be defined only by primitive properties and in Mollier chart, we still can define the state of the system. Then, can we call H and S as primitive properties, over to you sir. The first question was about zeroth law and I think by saying talking about that state postulate that the state can always be defined in terms of primitive properties. You have answered it more or less yourself, but you have not been able to appreciate the link. You said that like yes, we take a diathermic partition and we have two systems A and B, fix one system in a state say A 1 and try out various states of system B. Then, you asked we have not defined temperature. So, how do you define the state of system B, different states of system B and the answer is in that state postulate. The very first state postulate that we talked about that the state of any system can be defined only in terms of primitive variables. That means, if it is a fluid system I can take mass pressure volume as the variables and if I change of course, it will be a closed system simplicity. So, you can change volume and pressure and you can have different states of the system B. So, that is the first part. The second question you asked related to Mollier diagram, see the state postulate says that it is possible, it is always possible to define a state only using primitive variables or primitive properties. But, since other properties now get related to this primitive properties, remember the next state postulate that there is only a restricted number of properties which are needed to define the state of a system. If you take a simple fluid system number of two way work modes is one. So, for a system of fixed mass you need only two properties and for a fluid system the two properties would be two primitive properties for a fixed mass system would be say pressure and volume. So, all other properties can be defined in terms of pressure and volume, but you do not always have to define the state in terms of primitive properties. You can define the system the state of the system in terms of any two convenient properties. Now, it turns out that of the two primitive properties which easily come to our mind that is pressure and volume. Pressure is very easily measurable, but volume is something which is not so easily measurable except when your system has a very regular geometric shape like a sphere or a rectangular parallelepiped real life systems will have very complex shapes. So, measuring volume and keeping track of changing volume is not that easy whereas, pressure measurement is easy keeping track of changes is also easy. So, instead of pressure and volume we take pressure and some other variable typically from the ease of measurement and appreciation and feel temperature happens to be the other variable. So, that is why whenever we talk of a state of a system by default we talk of pressure and temperature, but pressure and temperature are not the only useful properties you have energy you have specific volume or density we have enthalpy so, in Mollier diagram we use enthalpy and entropy because later on when we consider open systems and second law we will find that entropy and enthalpy and entropy are significant variables and because they are significant variables we plot H s diagram, but H s diagram is not the only diagram which we should look at depending on what we are going to study what we are going to appreciate and what we are going to analyze. We will be looking at projections of state space on the p v plane, the p v diagram, the temperature entropy diagram, sometimes the temperature volume diagram and for some traditional reasons the refrigeration people plot their cycles on the pressure enthalpy diagram. So, there is the common thing is two properties because we are using fluid systems which are simple compressible systems which two properties that is left to the person who is handling that system who is analyzing that system. I think that should satisfy you I think it is coming to 9.30 and today I want to spend enough time on the second law of thermodynamics so, I am stopping the interaction at this point just now.