 Good morning, we are beginning the third day and as we did yesterday, I will take up a few questions in the first may be 20, 30 minutes and then we begin our formal sessions. I am first trying out Jabalpur. Good morning sir, is there any difference between no heat interaction and only work transfer over to you. Good morning madam, that is our definition. In fact, one of the things which I said near the end is that we define work interaction, then we define energy through first law and then we define heat interaction as a non-work interaction. So, our definition of heat interaction is the relation Q equals delta E plus W. So, heat is really an interaction of the energy kind, which is not of the work type. So, what you said is right, heat interaction is everything other than the work interaction. Naitith Ritchie, good morning any questions from you over to you. Good morning sir, this is Sudhakar from Naitith Ritchie. I have got two questions sir. The first question is regarding the thermodynamic process like adiabatic and polytropic process. What is the real application of this process in the engineering point of view? And second question is what are all the research topics possible out of work interaction and first law of thermodynamics? Over to you sir. Our idea for adiabatic etcetera are the ideas and definitions used to develop the laws and develop the derivations of thermodynamics. If you look up the English dictionary, I think historically adiabatic may be a Greek or Latin derived word meaning no heat transfer or heat transfer prevented, but those were the days when you know heat was not properly understood, work was not properly understood, the links were not properly understood. But the word adiabatic was already used. So, we recreate the definition of adiabatic to put thermodynamics on a proper footing and define it as work transfer only. After developing first law of thermodynamics, then just now as I discussed earlier adiabatic then means that no heat transfer will take place. That is the answer to your first question I suppose. The second question is what are the basic research topics regarding fundamental thermodynamics? I think the research topics pertaining to fundamental thermodynamics have been more or less exhausted. At least for us engineers there is hardly anything to do in thermodynamics. A reasonable amount of effort is still needed just the way we are doing it in making thermodynamics easily understandable to students. My exposure to teaching and learning of thermodynamics in many colleges engineering colleges in particular is that thermodynamics for some reason is considered a scary subject. If not a terror subject, I will use the mild word scary subject. And now you have computer graphics and animations and such stuff available. And maybe what the effort should be for at least engineer teachers like us and serious students in engineering who want to take up teaching is to create ways of explaining thermodynamics through what we call electronic technology, communication technology, educational technology. So, that learning thermodynamics becomes a pleasant experience rather than something to be afraid of. Over. Sir, another question is this thermodynamic subject is being offered for other branches like electrical engineering, marine engineering. So, how to approach the subject for other branches of engineering other than mechanical? All to users. See the basic ideas will remain the same. You will have to take applications from those appropriate branches. For example, if you teach thermodynamics to electrical engineering, you will have to discuss energy dissipation in electronic components, the cooling and thermal management of electric motors, electric machines and all sorts of. You will notice that today all electrical and electronic components tend to be compact. That is smaller is better or small is beautiful as they say. But then you will notice that the more compact you make the heat transfer and thermal problems arise. And today if you see the limit on the compactness of mobile phone, the limit on the compactness of a car engine, the limit on the compactness of the projector which we are using for projecting this. And the electronic equipment which we are using that those limits are essentially thermal. So, we will have to take illustrations from those fields for electrical engineers. For marine engineers, I do not think marine engineers would essentially be looking at thermodynamics as the marine power plant engineering. So, if you take care of their any special requirements in the marine environment, otherwise it is essentially mechanical engineering thermodynamics. But when you go to non-mechanical engineering, remember that the fundamentals that we are discussing here will have to be subdued a bit and the more emphasis should be on their applications. Because they are going to simply apply thermodynamics. They are not going to develop thermodynamics nor are they nor will they generally be expected to teach thermodynamics at the basic level. Over to you. I will try Amrita. Good morning sir. This is Uday from Amrita Koyamutur. I have a question in work interaction question number 5. It is given that mass and density are constant in work interaction 5, problem number 5. Whereas volume is defined as mass over density and if both are constant, there is no appreciable change in volume and integral p dv will become 0. So, how can we calculate work done in that problem? I think I discussed this late evening yesterday, work interaction 5. I brought your attention to the third line where when you read it, you have missed the word in the brackets almost constant. And that is the most important word although it is in parenthesis. Now, almost constant means do not insist that it is mathematically constant. As you seem to assume that if it is strictly constant, I agree. If the density does not change since mass is fixed, density also is fixed then volume is fixed. Then if volume is fixed in any process dv will be 0 and there will be no expansion compression type of work done. But along with that, notice that you have the bulk modulus which has a large value 2 into 10 raise to 12 dine per centimeter square. And the definition of the bulk modulus is change in pressure per unit fractional change in volume that is minus v partial of p with respect to v at constant t. So, it is isothermal bulk modulus. The value is large that means you need a large variation in pressure to produce a small change in volume. So, there will be a small change in volume and hence there will be a small amount of work done and that is what we are expected to compute out in this. I am just looking at pressure and volume. If you have a gaseous fluid then we know that if let me say that this is some volume v naught and this is some volume say v naught by 2. And let us say this is some pressure p or p naught and this is higher pressure. Now, suppose we have something like a gas and if we start compressing it isothermally, we know that if you compress it typically to half its volume the pressure will more or less double. So, for a gas the compression process will be something like this. At this approximately this will be 2 p naught this will be approximately v naught by 2. Whereas, if you take a liquid or a solid which are essentially incompressible a doubling of pressure will not reduce your volume it will reduce your volume, but it will reduce your volume very little like this. And you will end up with a new volume which is only slightly lower than v naught. So, if this happens to be the change in pressure delta p this happens to be a small change in volume delta v. And notice that if delta p is positive delta v is negative. And then the ratio of this and because notice that p is an intensive variable whereas, volume is an extensive variable. So, we do not want an extensive thing here we want it to be an intensive property relation. So, we multiply this by v or make it delta v by v and we add a negative sign to make this number positive. So, that we can tabulate just positive numbers it is just like using minus k instead of k in Fourier's law of heat conduction. So, this is the basic idea of the bulk modulus the proper definition instead of large difference of delta p delta p the proper definition is as given in the partial of p with respect to v. And since this compression can be done under isothermal conditions it can be done under isentropic conditions. So, we have to specify the condition under which it is executed and that is partial of p with respect to v at constant t over to you I think that has explained it. Yes sir, if there is a steror work alone takes place in the system is it a rudimentary system or not over to you. See the definition of a rudimentary system is that it can do no two way mode of work. So, for a rudimentary system a steror work is it is a one way mode of work and mind you a steror work when you say very specifically steror work it is assumed that you are stirring a fluid in which case it is a one way mode of work. And it is admissible for a rudimentary system to have that mode of work. However, many students and many teachers also are under the impression that the tau d theta type of work is a one way mode of work. Whereas, a p d v type of work is a two way mode of work that should not be right because a tau d theta type of work can be steror work in which case stirring a fluid is a one way mode of work. But remember that springs particularly helical springs used in clock work and many toys they also have the mode of work which is tau d theta you crank them up and they get uncranked as the toy works as the clock proceeds. There the tau d theta although it is very similar to the steror type of work it is a two way mode of work that spring can be you know energized or you can do work on the spring by putting a tau d theta and the spring can do work on its surroundings or whatever mechanism it is driving by unwinding itself. So, that is a for a spring tau d theta type of work is a two way mode of work only when it is stirring tau d theta type of work is a one way mode of work over. Sir, actually adiabatic work is path independent mean why over and out while executing such a I mean while having such a work in a system go ahead Amrita the process can be isobaric isothermal when the processes are different the path will be different does not it sir can you explain that. The question is an adiabatic process does not necessarily mean a unique path an adiabatic process only means work transfer only and that means no heat transfer and an adiabatic we will come to this when we come to some exercises in the first law of thermodynamics may be later in the second half today. An adiabatic process can have different paths, but if you manage to link two states for a given system state one and two by two different adiabatic processes the first law insist that the work done in the two processes is the same and we can have enough illustrations of that even numerical ones we will have those illustrations with us later today. What is the difference between control volume and system? Oh what is the difference between control volume and a system control volume is a so called open system during a process mass is allowed to flow or does flow across its boundaries currently all our formulations are based on closed systems that is the basic idea of development of thermodynamic laws. So, a fixed mass is in the system across the boundaries the interactions are only of the work kind and heat kind most engineering systems are of the open kind and may be sometime next week we have the session in which we will convert our closed system thermodynamics laws to appropriate forms for open systems and then sports we will be very comfortable in managing all open systems open systems are also known as control volumes open system and control volumes are very very common names both are used equally frequently for a closed system the equivalent name called control mass is rarely used you may find it some oldish textbooks, but a closed system it simply a system or a closed system the world control mass is only rarely used over. Good morning sir we have two co-sensor one is regarding the first law definition the first law is basically the statement of the first law is basically defined for the adiabatic system which says that during an adiabatic for an adiabatic system during the process the work is basically path independent when the same first law when it is applied for a closed system it becomes path dependent the work becomes path dependent can you please explain sir. I suppose there is some basic confusion here see first law and everything so far we have restricted ourselves to the first law anyway our first law and all development so far is for closed systems. So, what we have said is the first law is our understanding of how adiabatic processes behave and our statement of the first law is if you have a system and say this is the simple state space of the system initial state one final state two and you take any adiabatic path quasi-static or otherwise the work done is the same it is not only independent of path but independent of any other detail for example if a non quasi-static process is executed of the adiabatic kind there is no path as such. So, but the requirement is that the initial state be fixed the final state be fixed and all the processes that we consider between them must be adiabatic then the work done should be independent of the path. Now, we use this characteristic to define the energy in terms of energy difference we defined it as minus w adiabatic the minus sign is only matter of convention and then we said that if we have a non adiabatic process and during that let the work done be w then we define our heat transfer as the work done during a non adiabatic process between 1 and 2 and minus work done during an adiabatic process between 1 and 2. If you ask me a question which adiabatic process I will say it does not matter because first law says that if you take any adiabatic process the work done would be the same. So, I do not have to specify which adiabatic process here and then we said that this now becomes equal to because of our definition of delta E w plus delta E. I think I will explain this a bit further this should have come later in the lecture consequences of the first law but I will do it here because I think it is appropriate to do it here. Remember that our final form of the first law is q equals sorry you can translate it as like this out of this this depends only on change of state why does it depend on the change of state because it is equal to w adiabatic with a negative sign and first law says that this is independent of the path. So, it depends only on the change of state the initial state and the final state whereas each of these are interactions. So, they depend on initial state they depend on the final state and they depend on the process whereas this side depends only on the initial state and the final state. So, a question can be asked saying you have 1 kilogram of some system say 1 kilogram of water in a closed volume closed system and it changes its changes its state from an initial state of say 1 bar 30 degree Celsius to a final state of 5 bar 80 degree Celsius what is the change in energy well we can calculate that all we need is the initial state and the final state. But if you ask during this process what is the work done or what is the heat transfer then we will have to ask the detail of the process how did it go from 1 bar 30 degree Celsius to 5 bar 80 degree Celsius. We will do these problems today afternoon after we study zeroth law and something about basic idea some basic ideas about equations of state over. We have another question sir this is regarding the classification of the property sir the classification one way of classification of the property is in terms of extensive and intensive the definition of these are the understanding of these classification is ok with in terms of the operational definition. But can you explain it without going with the operational definition. I would not like to go away from the operational definition because operational definitions are the neatest of definitions ok. You know what the operational definition is but if you just take the words and extensive property by its dictionary meaning not by its thermodynamic meaning means that it depends on the extent of the system. If you make the system larger say if you make it double in size double in mass everything else remaining the same well the an extensive property is likely to double whereas an intensive property well it depends on only what the system is that is the intent of the system not its extent. So, an intensive property does not depend on the extent whether the system is smaller or larger it does not matter. For example if you take water at just now I said 1 bar and 30 degrees C what is its density you can say what is density is without knowing what its mass is. If I say it is 1 kg of water at 1 bar 30 degrees C or 5 kg of water at 1 bar 30 degrees C its density will remain the same because density is an intensive property. Whereas if I say what is its mass then the mass will definitely be different because in one case it is 1 kg in one case it is 5 kg if you ask its volume you will say in the first case it is approximately 1 liter in the second case it is approximately 5 liter. So, volume and mass depend on how much of the system we have the extent of the system. So, these are extensive properties whereas properties like density specific volume specific heat specific entropy specific enthalpy these are intensive properties. So, they do not depend on how much of that system we have over. Sir, myself Vikram Rathod from SVNIT Surat. First of all I would like to ask about the over and out let me go somewhere else. Pump having water having pumping application how work is calculated. You are asking a question on open systems you are asking a question of open systems just wait for a few days and we will have precisely an exercise on pumping of water over. One more question sir that is for the imaginary boundaries can you focus some on imaginary boundaries over to you sir. I think imaginary boundaries are a bug beer, but imaginary boundaries are boundaries defined by us. So, they need not be physical boundaries for example, I can say that in front of me assume a volume in space this much width say 20 centimeter width 20 centimeter height and 20 centimeter depth with an x y z coordinate starting from here x like this y like this and z like this. Not a single boundary is existing, but I can imagine that much as my system. It will be an open system, but well I have defined my boundaries in my space. We use such boundaries for deriving differential equations of say heat conduction differential equations of fluid mechanics. The continuity equation is defined in this way by taking a small control volume of size delta x delta y and delta z. You sketch the control volume, but you ask the teacher where is this surface you say it is a surface you can put it wherever you feel like it need not be aligned with a wall or it need not be aligned with a physical surface. I hope that explains it anyway I think now I have spent about 45 minutes it is time for us to come to our mainstream topics today. After completing the study of the first law of thermodynamics we have reached a stage where we know something about the energy of the system let us look at the. So, just now I said earlier few minutes ago while talking to someone that we have here a change in state as represented by delta e related to interactions. The first thing we know is w we know is made up of components we have the expansion work we have the stirrer work depending on the type of system we will have electrical work and so on. When scientist and engineers started exploring delta e we delta e turned out to be made up of a number of known components delta e kinetic when the system is in motion delta e say let me say potential or gravitational potential when it is in a gravitational field plus change in electric energy when you charge a battery its electric energy increases when it discharged it gets decreases. But then apart from this it turned out that there is a component which was earlier confused with the heat interaction and that we call delta u this was known earlier as and even now it is known as thermal energy internal energy. The word internal is funny because there was a time when some of these components were split into internal energy components and external energy components we do not have to worry about it. So, we will neglect the word internal and we may simply call it thermal energy, but there are text books and even many of us continue calling it thermal internal energy or simply internal energy. The correct word today would simply be thermal energy of the system. So, the thermal energy of the system is that energy component which remains when you take care of all the other energy components from the delta e which is defined by the first law of thermodynamics. Now, some questions arise if delta u is going to be a reasonably important component on what does it and related to this, but more or less general is how many properties are needed to generate thermal energy. Uniquely define the state of a system two related questions because the moment you define the state of a system its thermal energy would be defined. So, the question which still remains is how many properties are needed to define and how does the thermal energy depend on those properties and that brings us to the second state postulate. The first states postulate we looked at when we looked at I think day before yesterday afternoon thermodynamic state space. The first states postulate was that the state of a thermodynamic system can always be defined using primitive variables and out there is the essence of the so called equations of state that means non-primitive variables or thermodynamic variables should always be able to be related to primitive variables and those relations are our equations of state. We will come to equations of state again soon formally. The state postulate two unlike the state postulate one, state postulate one says state is defined or definable only by primitive properties. It does not say how many properties are needed. State postulate two provides you a number and say these many properties are needed to define uniquely the state of a system. Now, let us look at state postulate two. Remember yesterday we defined the complexity of a system. We said that the number of two way work modes defines the complexity of a system. If it is 0 then we say it is a rudimentary system. If it is 1 we say it is a simple system and if it is greater than or equal to 2 we say it is a complex system. State postulate two says that the number of independent intensive properties required to define the state of a system equals very simple formula the number of two way work modes plus one. This is our state postulate two. Again it is a postulate it is a premise. So, so far we can say we have looked at formally three premises in thermodynamics. State postulate one the first law of thermodynamics and state postulate two. The hidden postulate or hidden premise which I may call state postulate zero is the assumption throughout that when a system is left to itself it will come to a stage of equilibrium or a state of equilibrium. That is a hidden assumption and a hidden premise in all that we do in thermodynamics. That means you will generally find a system left to itself in a state of equilibrium and hence we can work with it that is one of the basic premises. So, we can say we have looked at state postulate zero state postulate one state postulate two and the first law of thermodynamics. So, four premises so far we are going to come to two more those will be zeroth law and the second law. Now, what is the consequence of this? First let us look at it. We are talking here about the definition of the state of a closed system. Closed system means the mass of that system is fixed and is identified it does not change and we are talking of independent properties and independent intensive properties. We are not talking of extensive properties here and we need not because we have a fixed mass. Now, why is the word independent used here? Just now we need not bother about it, but later on we will notice that in some part of the state space for fluids like water. We have the liquid phase of water and the vapor phase of water in equilibrium together and when that happens we have the phase rule which is applicable and which says that when you have a liquid and a vapor in equilibrium pressure and temperature are not independent variables. If you fix pressure the temperature gets fixed, if you fix temperature the pressure gets fixed. When we study properties of water we will come to this situation and that means in that case pressure and temperature are not independent. So, you cannot select them as the pair of properties if you need to select them. Now, let us see where this leads us. The consequence of this is if you take a simple system number of two way work modes is one and two properties define the state of a closed system and that is why for many simple systems like systems containing air system containing a gas system containing water. These are all simple systems number of two way work mode is one and we are always happy with two properties. We say steam at 10 bar 300 degrees C we know all the properties are determined. Generally we have not asked ourselves a question why is it that only two properties pressure and temperature say for example are sufficient and any good mechanical engineer who has studied mechanical engineer and is using it. We will say that look you give me pressure temperature I can determine steam properties. You give me pressure and enthalpy I can determine the state of the steam. So, this two properties requirement comes out of the state postulate two. We have water in a closed system that is a simple system. So, two properties define the state you take a complex system say an electrolyte which can also expand can also be charged and discharged then three or more properties are needed to define its state. But now look at a rudimentary system the number of two way work mode is zero and what does this mean? This means that only one property defines its state. This does not mean that a simple system will have only two properties of significance. It does not mean that a rudimentary system will have only one property of significance. For example, you take a system containing air the properties are pressure temperature density or specific volume you have thermal energy you have entropy you have enthalpy we can define many properties many more than two. However, the state postulate says that any two so long as they are independent can be used to define the state. For example, if you define take select the pair as pressure and temperature then everything else specific volume density entropy enthalpy energy thermal energy all these things will depend on the two properties. And the relation between any third or fourth or fifth property to the two properties which we have already decided as the independent property that relation we call the equation of state. Similarly, for a rudimentary system you may define more than one property, but one is sufficient. And the second third fourth properties which you have defined will be functions of the one property which you have taken as independent. Thermodynamics dictates the number not the properties. For example, for water thermodynamics does not say that use pressure and temperature. Pressure and temperature may be convenient may be ok if they are independent thermodynamics says select two you can even select enthalpy and entropy. And we know that from our Mollier chart given enthalpy and entropy we can read out and determine other properties. Thermodynamics says two properties because the closed system containing water will be a simple system. So, two properties define the system.