 We are starting the session. As is our normal format, we will visit a few centres which have already raised their hands. I see two here already. And after that our normal session today will begin. First I am going over to YC College, Nagpur. Good morning. YCC Nagpur. Over to you. Good morning, Professor Gayathunde. This is Mukta here. Over to you. So, I think the flight was uneventful. You seem to have landed in time. And how are the things there? At least from here the impression is reasonably good. Over. Yes, sir. I have just had a chance to interact with the participants. It seems they all seem very interested. And I have had the chance to talk to just one person so far. But he is very happy. Apparently he was a student of yours way back in the 90s. And he is very happy to have got the chance to learn from you all over again. Over to you. Thank him very much. And I see a reasonable amount of crowd. I think you have a full house today morning. And now before I say over to you, since I am already in touch with them, let me ask them, do they have any technical questions which I take every day morning? If so, you can hand over the mic to the one who wants to ask the question. Over. No technical questions today, Professor Gayathunde. And I would like to tell the AVU team that the audio and the video is excellent. Absolutely no problem about that. Over to you. And I will over and out. Thank you very much. Good morning, Panvel. Any questions from you? Over to you. Good morning to you, sir. Sir, it is regarding PER-11. Experiment that will use this relation to determine the CP without any energy measurements. Over to you, sir. Okay. I will have to look it up. But this is something which is left to your imagination. Because if all that it says is you have to CP will be TV beta and DP by DT at constant S. Now the question is how do you determine DP by DT at constant S? Because remember temperature is directly measurable, V is directly measurable and beta is 1 over V, partial of V with respect to T at constant P. So, that is also PVT measurement. The only thing we have to do is DP by DT at constant S. That is the variation of pressure with temperature at constant entropy. And if you can set up a simple experiment in which you can measure this. I am thinking of a acoustic measurement in which you remember that the nearest to any isentropic process that we have in real life is sound transmission. Because if you go back to the history of the velocity of sound, Newton was not very comfortable with thermodynamics. Derived an expression for the velocity of sound in air. But he got an expression assuming air to be an ideal gas to be square root of pressure and specific volume. That is square root of R T. Because there was an unknown assumption in his derivation that it is an isothermal process. Later on, it was realized that the pressure variations and the corresponding density variation that the process as my sound gets transmitted from my vocal cords to the ears nearby here is essentially an isentropic process. It is a quick small compression and it is an expansion. And when that is considered, the velocity of sound measured and the velocity of sound predicted in gases matched excellently. Now, I should not even say reasonably well there were excellent matches. So, you can have such cavities, resonating cavities in which there is a neat periodic variation of pressure and a neat periodic variation of temperature under isentropic conditions. So, if you measure those variations of pressure and temperature, you will be able to get d p by d t at constant s. Once you do that, you will be able to measure your c p. Over. I had another question. It is a general question. We had studied 0th law, 1st law and 2nd law also. So, which is the common terms among these three laws? Question is, we have studied the three laws and which is the common theme or common terms between those three laws, except that they are laws of thermodynamics and the way we use them or the way we propose them has been developed over the years. That is perhaps the only thing common. And I think as I said sometime earlier, it is generally accepted that these three laws form the basis of thermodynamics. The statements of each of these laws may slightly differ. For example, we have considered the Kelvin plan statement as the basic statement of the 2nd law. There are alternative statements. The most common alternative statement of great interest to mathematicians and physicists is the Karate-Hodori form of the 2nd law or Karate-Hodori statement of the 2nd law. So, there are variations. But then, there are proposals by which the whole set of laws are replaced by either another set or a single all-encompassing law. For example, Hexopolis and Kinan in the 50s and 60s developed what they called the general thermodynamics in which they proposed one all-encompassing law, something called the law of stable equilibrium. And from that, they argued out that the laws of the, argued out the 1st law, the 2nd law. And they claim that 0th law automatically follows. You do not have to extract it out of that law. They have a big book. If you go to the library and look up under Hexopolis and Kinan, you will find that I think it is known as principles of general thermodynamics. It is a big fact book almost as thick as a dictionary. But it is not easy to read and the arguments are not easy to follow. Unfortunately, they have provided a large number of verbose arguments rather than symbolic quantitative arguments that is mathematically robust argument. That is why it has not become popular at all. Of course, it is agreed that the Karate-Hodori's form is very robust. But for those who are not conversant with details of differential geometry and think projective geometry and such topics, it is not very easy to follow. That is why at least for engineers, I feel that Karate-Hodori's formulation is ok for the 1st law. But for the 2nd law, I would be more comfortable with Kelvin-Planck formulation. There is another formulation that by Giles. But that has 6 premises. But to appreciate that, you really require facility in topology. That branch of pure mathematics which we hardly ever studied. So, that is where it stands. For us, I think we should consider three laws 0th, 1st and 2nd as three basic aspects of thermodynamics. Three laws defining three basic thermodynamic properties, temperature, energy and entropy. I think we should leave it at that. Over to you. Thank you very much, sir. Another question is, what is the difference between polytropic process and adiabatic process? You will notice that we have not used the word polytropic process ever. But I will tell you the history of that. Notice, we have already shown that if you have an adiabatic quasi-static process of an ideal gas, only PDV work or ideal gas, I see that there is a difference between isentropic process. Then, either under these conditions, either one of them, the process equation turns out to be PV raise to gamma its constant. Now, real life processes are not first not of ideal gas and not isentropic or if they are ideal gas, they do not satisfy all these requirements. So, a real life process is a model quite often just for the sake of being able to manage and integrate and things like that as PV raise to n is constant. This is just a convenient model for us to be able to analyze processes typically in an IC engine or earlier in the steam engine. Steam engine is nowhere near an ideal gas, but an expansion process is quite often modeled as PV raise to n is constant, where n depends on the type of process. For steam, they have found that n between 1 and 1.3 is a common range and if you have a near adiabatic and good quasi-static process, superheated steam will have n of around 1.3 saturated steam or wet steam will have n around 1. So, that gave the idea of this convenient model called a polytropic process. So, this where n is not necessarily equal to gamma is known as polytropic process. In fact, you will find that in the old textbooks, the process in which PV equals gamma, PV equals constant is executed. Now, we know that this represents an isothermal process for an ideal gas, but it could represent an expansion process for any fluid and such processes did happen in some type of steam engines under certain conditions. That was known as a hyperbolic expansion process. Hyperbolic simply because x, y equals constant represents a rectangular hyperbola on the Cartesian coordinate. So, PV equals constant is on the PV coordinate which is the expansion compression plane. This is called it hyperbolic expansion. That is it nothing more than that, over to you. Let me go to NIT 3G. Good morning NIT 3G over to you for questions. Good morning sir. This is Sudhakar here. I have got a very basic question. Sorry to ask this question again and again. Sir does human being and living organisms obey law of thermodynamics? If so, what kind of work interaction and heat interaction is taking place between them? Over to you sir. This question does come up again and again. Is a human being us? For that any living matter? First thing is yes, we know what is inside us, what is outside us. So, for any human being, the boundary of a human being can be very properly defined. So, yes, human being can be considered to be a thermodynamic system. In fact, nature has given us the outer cover, generally known as skin, very well defined which sort of properly separates us from the rest of the world. So, it is a very well defined boundary. The shape may be very crooked, very odd, but we are all familiar with that shape. We can define it very properly. So, it is a thermodynamic system. It obeys the laws of thermodynamics. However, we have our work interactions, heat interactions across our boundaries, but the problem with the human being is that it is a very complex system or very complicated system. For example, the e part of the human being, delta e part of the human being because of the complex composition will have various components. Delta u, our normal thermal which may be depends only on temperature. Our pressure does not change much. Delta u plus, we will have some delta e chemical of various kind plus all sorts of electrolytic processes are going on. So, there is a delta e electrical. Our nerve impulses are microelectronic impulses. So, there is a change in energy associated with them. Another thing which is the weakness of our model of thermodynamics is that remember that we lay great emphasis on the so called equilibrium. We have, we work with very simple systems like a gas or a mixture of gases or a simple mixture of a few chemical compounds where the internal energy is made up of may be a few components not many and we can always consider the system to be in equilibrium. Whereas, a human being the system is never in equilibrium. Hence, the state is always in a flux and hence although the laws of thermodynamics are applicable, we do not have detailed facility of properly applying those laws to human beings or any living beings. But, there is a branch which looks at this thermodynamics applied to biology and there are people right from Schrodinger to who was Prigogin, the great physical chemist and thermodynamicist and a few others have written papers and published some books on this. You can refer to them in any good library. Over to you. Good morning, sir. One more question, sir. You derived the Maxwell relation that in NLGHs it is a function of volume and pressure specific volume and pressure. On the right hand side it is a function of entropy and temperature. I want to know why the Maxwell relation is a function of volume, specific volume, pressure, entropy and temperature. Also, particularly in the inside temperature with volume, temperature with pressure and also another relation entropy with volume and entropy with pressure and also here also they are giving entropy and temperature also. What about the other properties which are not considered in this final Maxwell relation? Over to you, sir. The question is about Maxwell's relations and the question is why is it that only PVTS in some order are related to each other and not other properties like for example enthalpy or Gibbs function and all that. There are two reasons for it. The absolute basic reason is we are considering these are Maxwell's relations for a fluid system and for a fluid system apart from the basic thermodynamic properties velocity, temperature and entropy. The other property which comes into operation is P that is one thing. The second thing is notice that Maxwell's relation is nothing but the mathematical expression of the fact that if you take a reversible cyclic process represented on a PV diagram and the TS diagram we know that the area is the same on both of these and because of this naturally the four variables PV represents area under this curve represents the work done TS area under the curve under certain conditions represents the heat transfer and that is the reason why Maxwell's relations for a fluid link only PVTS nothing more. Maxwell's relations are not the compact form of all relations in thermodynamics. This is one important subset of relations. Other relations will have to be derived using Maxwell's relations and of course the other basic laws of thermodynamics. For example, the basic property relation which will always be there but of course you can say basic property relations at the top of everything every all other relations including Maxwell's relations follow from the basic property relation and all derivations and definitions of other properties like enthalpy Gibbs function and Helmholtz function over to you. Thank you very much sir over and out. Good morning Jabalpur over to you. Out the assignment announcement which you want to make in yesterday's lecture I think you have made that regarding assignment of participant to be submitted after the course. Thank you over to you sir. Okay nice for reminding me I have already been thinking about that either on the last day or soon after that on the moodle side I will set up the assignment. I am trying to set up an assignment which can be individually done. However if I find that something is really heavy I will provide the facility or part of the assignment may be done by a group of people. I am sure none of you is working alone and if not in your own college in nearby college and definitely by email contact you will be able to work in small groups of maybe at most three or four people. I do not know how many of you have a facility like a plotter or a plotting software like GNU plot or graph or graphic plotter on windows available to you. But I think one college every college will have at least one machine on which some screen plotting facility will be available. So there will be some plotting assignments also in that. And the deadline for this will be something like 15th July so about 20 days after 20 or 22 days after the end of the session you will have 2 or 3 weeks. I am told and I thought this is good because many of you may still have some exam duties and other preparation to do. So I am not pressing you for time. The deadline for me for setting up the assignment is 26th June. I wanted it to be 25th June but there is a full day assignment for me out of Mumbai on 25th June. So 26th June evening time you will by that time you will definitely get the assignment on Moodle. Anybody should be able to look at it and 15th July will be the deadline over to you. Thank you very much sir over and out. Good morning over to you Sivakasi. Adiabatic process we have reversible adiabatic and irreversible adiabatic. Similarly for other process if it is constant pressure or volume or isothermal we have reversible isothermal and irreversible isothermal process. What you sir? The question is that when it comes to an adiabatic process we have a reversible adiabatic and irreversible adiabatic. We consciously make a distinction whereas for constant pressure or isothermal process whether such a distinction exists or not. The answer to that is first thing is remember that in thermodynamics right from first law through second law and of course in a negative form for the zeroth law the adiabatic process is a very important process because the basic theme of thermodynamics is that there are energy interactions of the non-work kind and they lead to the science of thermodynamics. So long as thermodynamics was not developed all interactions were considered to be of the work kind and that is the domain of mechanics fluid mechanics etcetera fluid mechanics encroaches on thermodynamics because fluids expand and contract and very easily get heated up and cool. But in the classical mechanical domain everything is work interaction. They take care of non-work interaction by saying you know conservative forces and non-conservative forces. But they never explore that in any detail that is left for thermodynamics to do. The basic premise of thermodynamics that there are interactions of energy which cannot be defined as work we call that interaction heat and all the characteristics of heat and related to that like temperature temperature differences later on entropy etcetera derived. And because of that adiabatic process is very important hence reversible adiabatic and irreversible adiabatic has a distinction which we make in the second law of thermodynamics. Similarly, when you have a constant pressure process there is a reversible constant pressure process there is an irreversible constant pressure process. Similarly, in isothermal processes you have a reversible isothermal and irreversible isothermal and there will be some distinction and you can derive those distinctions. For example, if you take a vapor system or a gaseous system a fluid system then a reversible isobaric process would be a process in which only p d v work will be done and it will be an isobaric process. In fact, for a fluid a reversible process is one in which only p d v work will be done heat may or may not be transferred but the work if at all it is done it will be the expansion kind of work. But if you say an irreversible isobaric process then of course p d v work will be done and there may be some other kind of work also and similar distinctions you can derive for an isothermal process but those will be derived distinctions. The defined distinction between a reversible iso adiabatic and irreversible adiabatic is that for a reversible adiabatic process the change in entropy will be 0 because we have seen that a adiabatic reversible process has to be an isentropic process whereas for an irreversible adiabatic process the entropy change through the process will be greater than 0 over to you. Another question, the reversible and irreversible adiabatic process follow the different path whether the other process non-adiabatic that is constant pressure volume the reversible and irreversible follow the different path or the same path. Notice that again I think earlier I have made this distinction adiabatic refers to the interaction across the boundary it does not refer to any path when it is adiabatic reversible then we have a path defined because that is a unique process the isentropic process whereas when you say a constant pressure process or a constant temperature process these are specification in terms of certain properties say pressure is constant or temperature is constant and whereas being adiabatic you do not dictate any property and when you dictate a property for a constant pressure or constant temperature process you have already dictated the path. A constant pressure path is a horizontal line on the standard TV diagram a constant temperature path is a vertical line on say T P, T V or T S any diagram in which T is on the x axis over to you. Thank you sir over and out. There are two centers and let me just take only two centers Amrita and J N T U other centers if they have any questions I will take them later because by 10 o'clock I want to start our main theme today first to Amrita Coimtor over to you Amrita at Coimtor. Sir this is Amrita the question is there was a question in the second test regarding the form of water in atmosphere and the right answer was given as a super heated steam so will you please explain this over to you. I think I will not explain it now because this has been explained earlier perhaps twice during such interactions and the explanation of this is already on the Moodle participants forum so will you please look at it over to you. Okay sir thank you over to you. Okay I am before going to J N T U Hyderabad I am taking up a question which has been asked to me in the text mode from Indore may be there audio or video link is down. What is the practical application of property relation and Maxwell's relation? The practical application of this is the basic idea we are able to get relations between properties which help us understand the thermodynamic state space better for example take the perhaps one of the most important things is the Clausius-Clapeyron relationship but before I come to that and discuss that in detail let me go back and say what I have already said and that is that these property relations put a relation or a restriction on the way properties behave they will never dictate the absolute values of property using this property relations you cannot tell what will be the density of air at 3 bar and say 75 degree Celsius. You will not be able to tell us what is the temperature of saturation for water vapor at one atmospheric pressure we know it 100 degree C as a matter of measurement we have measured it to be 100 degree C. However you look at the Clausius-Clapeyron relation you take the Clausius-Clapeyron relation we have D P by D T on the saturation line is S F G by V F G can also be written down as H F G by T V F G. Now look at this here we have temperature difference in specific volume between liquid and vapor and the latent heat on the right hand side and the way pressure changes with temperature on the left hand side. It tells us for example that given T and V F G not changing if I have a fluid with larger latent heat for a small temperature rise I will have to increase the pressure by a very significant amount whereas if I have a smaller latent heat for a given temperature rise the rate of change will be the required change in pressure would be small. You also look at it the other aspect of this write this as S F G and denominator you write as V G minus V F and notice that this is reciprocal of density of the gaseous phase this is reciprocal of the density of the liquid phase. We also know that the density of the gaseous phase will always be lower than the density of the liquid phase. We do not have a fluid or generally at least I do not know of any fluid where the vapor is less dense is more dense than the liquid. So, in a liquid vapor situation in a gravitational field it is the liquid which always settles. But now here we are looking at the liquid vapor equilibrium it is also applicable as much to the solid vapor equilibrium or say the solid liquid equilibrium d P by d T sat but say for solid liquid this will be S liquid minus S solid part divided by specific volume of the liquid minus specific volume of the solid and this is reciprocal of 1 over density of liquid and this is 1 over density of solid. The density of liquid is lower than the density of solid, solids sink in their liquid but there are exceptions and one exception is water a very common exception is water for water density of the solid is lower than density of the liquid at least around ambient pressure but over a very wide range and because of this ice floats on water. Now what does it have to do with our understanding? Now notice that if density of the solid is less than density of the liquid that means specific volume of the liquid is less than specific volume of the solid and that means this denominator is negative we know the latent heat of ice as it makes positive. So here we have a denominator which is negative we have a numerator which is positive and that means our d P by d T on the saturation line for solid liquid is a negative number and what does that mean? That means as if you want a temperature rise you must reduce the pressure or if you increase the pressure you are decreasing the temperature and that is why on the P T diagram from the triple point the ice water equilibrium line is towards the left because as you increase the pressure the temperature decreases. So we know that if you put ice under pressure it makes faster there are experiments in the school books to explain that and now you will notice that the liquid vapor line has a shallow slope the solid vapor line has a sharp slope. The variation of pressure with temperature with pressure is not very significant and that is because of the relative magnitudes of delta s and delta v across the solid liquid phase. So this is the application the first direct application the understanding and appreciation of the fact that mating point of ice reduces as you increase the pressure whereas boiling point of steam increases as you increase the pressure that is perhaps is the even junior student can understand now the important of property relations. I think that is the answer I wanted to give to indoor and I think others have also appreciated it and that brings us to the end of the question answer session.