 So, welcome to the second day of our workshop. Today's program is as scheduled. In yesterday we could complete exactly as planned. Today the four sessions will be devoted to first law, zeroth law and thermometer and part of the properties of fluids. So, you will notice that properties of fluids extends till tomorrow morning and that is the plan. Let us see how it goes. Before I begin the first law, some comments based on what happened yesterday. There seemed to be two points of confusion. The first confusion is about the idea of universe. Now if we say the astronomical universe or the physical universe, question is whether is it a properly defined thermodynamic system or not. Well it is a system, but we cannot define it properly because we do not know where the boundaries are and we cannot set up a boundary. The astronomers are still arguing whether the universe is a finite one or an infinite one whether it is a pulsating one, steady state one or all sorts of things. So, we cannot say that laws of thermodynamics cannot be applied to the universe. To any part of the universe which we can delineate by defining the boundaries, yes we can apply the laws of thermodynamics provided we can measure or guess what the interactions are. But if you take the complete universe, we do not know what the boundaries are and hence we cannot define the boundaries and hence we are unable to define it as a proper thermodynamic system. So that we can apply our laws of thermodynamics. The second confusion seems to be on the word quasi-static. Now the word static here comes from it links with mechanics. Something which is not moving, something which is at one place, it is static. Something which is moving, something which is changing is dynamic. So the static here means something equivalent to our state of equilibrium. A point in thermodynamic state space representing a state of equilibrium. Now quasi-static means quasi usually means almost quasi-steady means almost steady but not exactly steady. Similarly quasi-static means almost static or almost in equilibrium but may not exactly be in equilibrium. So quasi-static which is related to a process would mean that during the process, if you want PV or anything else, there is nothing special about this. Suppose this is your initial state, this is your final state. The process will take you from state 1 to state 2 but if during the process we are able to define all intermediate states properly and maybe we get a path like this, then we will call that a quasi-static process. A quasi-static process has nothing to do with a process being reversible. We have not yet defined what a reversible process is. We will define it when we come to the second law of thermodynamics. Till then we do not have to worry about the adjective reversible. Again when it comes to second law of thermodynamics, we will define a so called thermodynamic universe as distinct from our physical universe. Thermodynamic universe is a very restricted concept and for some reason it is called thermodynamic universe because some textbook started using it entropy rise of the universe, entropy change of the universe but what they mean out there is a thermodynamic universe properly defined in the local context and not the physical universe. Again when it comes to quasi-static, get rid of the idea that it has to be a slow process or it has to be a reversible process is nothing. Our definition of quasi-static process is a process such that any time we look at the system while it is executing the process, you will find that the state is in equilibrium or the state is almost in equilibrium. So, you can represent it by a point and since all intermediate states are in equilibrium, all these points will link up with each other following the locus as shown here. Now it is possible that the system may go from state 1 to state 2 following some path in such a way that at least during part of the process we will not be able to assert that the intermediate states are states of equilibrium in which case at least part of the process cannot be shown by a continuous line. I have shown here a dotted line just indicating that I have a process in which all I know is I start with the initial state 1 at the final state 2, but I just do not know what has happened in between. Now I think with this explanation let us go to the next topic and that is topic 5, the first law of course of thermal dynamics, something about the history of the laws of thermal dynamics. Again the way sign convention is arbitrary, the nomenclature of these laws is also to some extent arbitrary. People started physicists and engineers started developing the ideas in thermodynamics and we ended up with a so called law and since it was the first one to be proposed it was called the first law. Before this we had Newton's law and we had Newton's first law, second law, third law and we had Kepler's laws of planetary motion and so on. Newton's law of gravitation was only one so it is just called Newton's law of gravitation. So we had first law then we had second law and then it was decided that temperature requires its own law and it was assumed that or it was perceived at that time that the temperature has to be defined before energy is defined or before entropy is defined. So instead of calling it the third law they called it the zeroth law. Making thermodynamics one of those rare parts of physics where a zeroth law is defined. In fact if you say first law or second law some generalist may ask you which first law are you talking about, whether it is first law of Newton or first law of thermodynamics. Similarly second law is it the second law of Newtonian mechanics or is it the second law of thermodynamics. Same thing is true for third law but zeroth law I think has a special status it exists perhaps only in the science of thermodynamics. But if you really go back in history the science of thermodynamics really began with Carnot and his ideas today are formalized as the second law of thermodynamics. In the work of Ruhm-Ford and Joule led to what is known as the first law. But the nomenclature is second and first because the first law was formally developed first and then the second law came into being. And finally in the early part of the 20th century we had the zeroth law. Number of people Fahrenheit, Caratheodory, Lansberg many people contributed to the so called zeroth law. Because it was at that time that the science of thermometry reached not perfection became very mature. And hence the zeroth law had to be proposed because the idea of temperature was properly absorbed leading finally to what is known as the international practical temperature scale. It is redefined every year because developments in measurements and electronics and sensors and post processing help us being more and more precise in the measurement of temperature. Now what is the current status of these laws? In fact I was surprised when I really started studying it that if you look at the set of laws pertaining to thermodynamics as a structure of laws it is not unique. If we go back yesterday we have defined work properly that as a primitive. But we have to define properly the following quantities in thermodynamics in some order. And these quantities are temperature, the heat interaction, the energy E and the entropy S. Everything else follows from some interrelation of these properties. There are many structures of these laws which develop these ideas in different ways. And even zeroth first second the triplet of laws that also is not unique. Hexopolis and Kinon have proposed a single law so called law of stable equilibrium from which they tend to derive what we call the zeroth law the first law and the second law. However the arguments are so complex and very difficult to understand that it just has not become popular. And hence the traditional treatment of thermodynamics with three distinct laws continues. Again in that there are the various formulations. By formulations we mean how do we propose these laws and how do we state these laws after looking at some general behavior of nature. The general behavior of nature seems to be that look there is something called thermal equilibrium leading to temperature, idea of temperature. There is an interaction other than the work interaction giving us the idea of the heat interaction. In fact this led to the earlier caloric theory of heat because we say heat flows and they said if heat flows it has to be something like a fluid flowing. So the idea of a thermal fluid or the caloric came into being. Then the idea of conservation of energy and the idea that processes take place only in one direction. These lead to the various laws of thermodynamics. But we have to formalize these laws put them on proper mathematical structure. And there are earlier formulations where we define heat in some way. Then we come to the first law and define energy. And then we have the second law and define entropy. And of course zeroth law is independently used to define temperature. This is what is known as the classical Gibbsian formulation. But then there are other formulations which start with from work. They go to first law and define energy. Then define heat. Then go to zeroth law and define temperature. Then go to second law and define entropy. And there are various other formulations. There are some formulations which put heat in the beginning and work afterwards. This is just to impress on you that what we are going to study is just one way of studying and proposing the laws of thermodynamics. And there is nothing unique about it. Tomorrow you can come up with another consistent and neat structure of thermodynamics and then there is nothing wrong in it. Now remember nature behaves in its own ways. But there is a method in its madness. It is always consistent. We know if nature behaves like this, today it will behave like that tomorrow. It will not behave in any different way. Our understanding of this behavior lead to laws of physics. And laws of thermodynamics are also laws of physics. And this our understanding depends on who we are and the way we look at the behavior of nature. For these laws of physics there is no proof. So a question like state and prove the nth law of thermodynamics is meaningless. Because this is just our understanding of how nature behaves. Now if there is no proof, why do we believe in those laws? Why do we say that if something violates the first law of thermodynamics or something violates the second law of thermodynamics then there is something wrong in the way things are proposed or things are designed or things are expected to happen. Why do we have such great faith in these laws? We have such great faith in these laws simply because we have seen over years, decades and in some cases over centuries that well we have we seem to have properly assimilated the behavior of nature in these laws. And our faith in these laws today has grown to such an extent that if we come across a situation where a particular laws seems to be violated. We do not jump to a conclusion that law is wrong, that law has been disproved or anything like that. We say that look there must be something wrong in the way we have observed that occurrence. We made an error or we did not observe it completely or we missed out noting down some facts. And always when we relook at it and we analyze it in detail we will always find or we have always found that there is nothing wrong with the laws the way we have looked at the things is incomplete or incorrect. That does not mean that the laws are eternal. We have cases in physics for example we know the Newton's laws of motion are not perfect in all aspects of physics. When you come to very small interactions this quantum mechanics they fail although when you come to very large distances, very large gravitation effects and very large relative velocity that is the realm of special and general relativity there also they fail. So maybe the same thing is true of the laws of thermodynamics. We have made an assumption that there is no quantizing effect and everything is continuum. Tomorrow we go to a situation where things are quantized the laws as we know them today will not be applicable. They will get modified. After having said so let us come to the first law. For the first law we are going to follow the formulation of the friend scientist Karatheodor. So this is Karatheodor's formulation or Karatheodorian formulation. He used the concepts of geometry and exact differential equations and integrating factors to bring out in a very solid mathematical way. Mathematics, calculus, differential geometry, the laws of thermodynamics. Derived the idea of energy, derived the idea of entropy, derived the idea of temperature. Temperature has an integrating factor. We will use this formulation for the first law of thermodynamics because it is straightforward and is understandable to us. Although his second law of formulation is also mathematically very robust, we do not have our comfort label with that type of mathematics is not very high. So when it comes to second law of thermodynamics, we will follow a different route. We will follow essentially the Kelvin, Planck, Kien and formulation. To begin with now we have to define a new word which is adiabatic. We have not yet defined the word adiabatic and the traditional meaning of the word adiabatic means something which prevents it transfer. An adiabatic boundary is something which prevents it transfer. But we would not define it that way. Karatheodor did not define it that way because the heat interaction is not yet defined. We have defined only the work interaction and hence we cannot and we should not define adiabatic using something which is not yet defined. So we will now define adiabatic meaning work transfer only. Now remember that once work transfer takes place across a boundary. So the adjective adiabatic can be applied to a boundary. An adiabatic boundary is the boundary across which only work transfer takes place. Any interaction across it, we check it out using our operational definition discussed yesterday. That turns out to be an adiabatic boundary. If we find that all interactions are purely and fully work interaction. It can be of course boundary, surface, wall, partition, interface. All these things can have the adjective adiabatic associated with it. Meaning only work transfer is allowed. Only work interactions are allowed across it. Now is work is done always by a system or on a system. So this adjective can always be applied can also be applied to a system. An adiabatic system means a system which is constrained in such a way that it can do only work type of interaction. So naturally that means such a system will be fully bounded by adiabatic walls or adiabatic partitions. Now an interaction almost invariably leads to a process. So the word adiabatic can also be applied to a process. An adiabatic process is a process in which the only interaction which takes place will be the work interaction, some type of work interaction. So an adiabatic process will be executed by an adiabatic system and this system or such a system will be bounded by adiabatic walls. So adiabatic finally means work transfer only. It is a short form for this set of words work transfer only definition. And then our first law of thermodynamics is our understanding or the statement of the behavior of adiabatic systems. Now we come to the statement of the first law of thermodynamics. This is after Karatheodori. Karatheodori said that he got the inspiration from Jules experiment. If you look up the history, Jules did an experiment to determine how much energy is needed to raise the temperature of a given mass of water from a specified initial state to a specified final state. He did various combination but our school textbooks say that he tried to measure the energy, determine the value of a calorie by taking 1 gram of water and raise its temperature from 14.5 degree C to 15.5 degree C. That is a story but he did different experiments essentially to determine the energy required to transfer a system from a given initial state to a final state. And one thing which we generally do not notice is that he did all his experiments in an adiabatic fashion. And Karatheodori generalized it as the first law of thermodynamics. And the statement of Karatheodori is like this. You write whatever you want here. I am writing simply x and y. If you want you write p, v, any properties known to you. Let us have a system and let us take it from an initial state 1 to a final state 2. You take a closed system, process is 1 to 2 both fixed and then you say that consider a number of adiabatic paths, adiabatic processes between 1 and 2. Some quasi-static, some non-quasi-static. But all are adiabatic. The statement of the first law is work done during any adiabatic process between states 1 and 2 of a system is independent any detail of the process. By any detail we mean the way it was done, what were the work modes, whether it was quasi-static or not. All that is required is fixed initial state, fixed final state and that the process considered must be an adiabatic process. So, although I have written it in short, if you want to write it in big statement, you will say the first statement of the first law of thermodynamics is work done by an adiabatic system while executing a process from a fixed initial state 1 to a fixed final state 2 is independent of the path and any detail of the process, any other detail of the process because some details of the process like initial state, final state and the fact that it is adiabatic is fixed. So, you could say any other detail if you feel like other than these 3. This is the statement of the first law of thermodynamics. Now everything else including our some other definitions will follow from this. For example, a consequence of this is since w adiabatic 1, 2 is independent of path, following consequences follow. Integral d w adiabatic 1 to 2 is again independent of path. That means depends only on states 1 and 2. And hence it should represent a change in some property of the system. Other way you can look at it that this also means d w adiabatic would be because the integral is independent of the path and depends only on end states. d w adiabatic must be an exact differential and hence d w adiabatic would represent the differential of some property. This is the first conclusion. The next thing is what is this some property? It turns out that to be consistent this property has already been explored by other branches of physics. And hence to be consistent with other branches of physics, Karathiodori called this property energy. He did not define it to be energy. He said that this should be defined as energy because that way we will be consistent with other branches of physics. Remember thermodynamics is a part of physics. So thermodynamics cannot do something which will disturb the well established structures of other branches of physics. And hence to be consistent with mechanics electricity and all other branches of physics, he defined this property to be the energy E. And he called it energy not to redefine energy but to be consistent with other branches of physics. And also to be consistent with the nomenclature used in other branches of physics, remember this d w adiabatic integral sorry w adiabatic between 1 and 2 represents the change in some property or d w adiabatic represents the differential of some property. That property he called energy and linked the two by the following relations definitions delta E 1 2. This is E 2 minus E 1 which is delta E. This is defined as minus integral 1 to 2 d w adiabatic. This is the defining relation for energy. In differential form we can write d E is defined as minus d w adiabatic. This is definition of now question is why this negative sign. Let me use some other color. We have a negative sign here. We have a negative sign here. This negative sign let me again say is a matter of convention. So, this is the second sign convention that we have come across. The first sign convention was when we came to the work interaction. We said raise in weight means work done by the system is positive and work done on the system is negative. Of course, chemists etc. They tend to use the other way that work done on the system is positive, work done by the system is negative. If that were the case maybe we could have used a positive sign here. But remember that our first sign convention for work was work done by a system is positive. The second sign convention we have used here is if an adiabatic system does positive amount of work the change in energy is negative. If an adiabatic system has a positive amount of work done on it or if the system does a negative amount of work then the change in the system is positive. So, if you do work you get exhausted your energy reduces. You can remember it that way. But again remember that this negative sign is just a matter of convention. There is nothing thermodynamic about it. Now before we go about the details of energy let me complete the basic formulation and then we will come back to it. What about non adiabatic processes? Again let us consider a system. Again I am writing x, y and let us consider two states of a system 1 and 2. And let us say that we have joined 1 and 2 by means of some adiabatic process. So, let us say 1, 2, adiabatic is any adiabatic between fixed states 1 and 2 of a system. And now let us consider this process any general process need not be adiabatic and I am not talking about quasi-static or anything. Only thing I am saying is this process is adiabatic do not ask me whether it is quasi-static or not. If you do not want it to be quasi-static show it by means of a dotted line. Similarly, the second process which I have shown without any I will just call it process 1, 2 no special marking on it. It is any general process by general means you be at general as you feel like. If you want to make it adiabatic make it adiabatic. If you want to make it non adiabatic make it non adiabatic you want to make it quasi-static make it quasi-static. If you want to make it non quasi-static just show it by dotted line and say it is non quasi-static you make it as complex as you feel like. Now, since this is not necessarily given to be adiabatic all that we know is w W12 need not be equal to W12 adiabatic. This means need not be equal to. I am writing this because mathematically W12 not equal to W12 adiabatic means that they are distinct but here we do not want to use it in that perfect mathematical sense. We want to say that not equal to means well it is generally not equal to but it could even be equal to because it is a general process it could be adiabatic. If it is adiabatic then naturally equal to applies but even otherwise once in a while perhaps it could be equal to that equal to is not excluded from here. Now we come to a definition of what? We will now look at this difference W12 minus W12 adiabatic. We will define it as Q12 and we will call it the heat transfer or heat interaction during the process 1, 2. The non adiabatic or not necessarily adiabatic process joining state 1 and state 2. Again let me say that this is the definition of the so called heat interaction and I have it is not very clear but again there is a sign convention here. We have defined it as W12 minus W12 adiabatic. We might as well have defined it as W12 adiabatic minus W12 nothing wrong in it that again a matter of sign convention. So, remember that hidden in this is a sign convention 3. First sign convention for the work interaction, second sign convention for the definition of energy here. So, this is sign convention 2 and this is sign convention 3 and absolutely nothing wrong if you use the other sign convention. Some signs in some follow up equations will change accordingly. Now remember that in this equation again I will write Q12 is W12 minus W12 adiabatic. This part is independent of path that is first law. This part could be path dependent because we do not claim W12 to be process 1, 2 to be adiabatic and hence a combination of something which is path dependent with path independent would also mean that this is path dependent. Now before we go further one minor consequence of this sign convention is that in our traditional terminology Q12 is positive when we say heat is absorbed by the system and Q12 is negative when heat is rejected by the system. These now become the definition of heat absorption and heat rejection. Heat absorption is when Q12 as defined by this relation is a positive number. Heat is rejected by the system when Q12 as defined by this relation turns out to be a negative number. Now let us look at what we have said is the following. W12 adiabatic is independent of path. Hence delta E12 is defined as minus dw adiabatic. The third thing we defined is for a non adiabatic process Q12 is defined as W12 minus W12 adiabatic and if you combine these two you will get Q12 is W12 plus delta E1. I made a small mistake here let me correct it this is not. On the other hand we can say that dw adiabatic is an exact differential. Hence we can define a property such that dE is minus dw adiabatic. The differential form of this would be dQ will be defined as this will be definition dw minus dw adiabatic for the same small process element and combining this and this you will end up with dQ equals dw plus dE. Writing or removing this 12 which is now the common subscript we will end up with Q equals W plus delta E for the full process or in its differential form dQ equals dw plus dE in its differential form. These two are now known as the final form or final forms of the first law of. I will now make a statement which many of you may find it difficult to absorb but that is a correct statement and if you follow this you will not get into a large amount of trouble later in problem solving and discussing thermodynamics. What I will say is this statement and of course its precursor this is a final statement is the only statement linking the heat interaction Q with the rest of the word through W and delta E. Any other relation which we see between Q and any other relation which you have set like Q equals m Cp delta T Q equals m into h fg or for a constant volume process Q is m Cv delta T for some sort of process Q equals delta h capital H. All these things are relations which are a consequence of this relation and they are not independent relations by themselves. The only basic relation between Q and the rest of the word is Q equals W plus delta E or dQ equals dE plus delta P the two boxed relations or framed relations on this page. Now with this we complete the definition. Now I will say this is the definition of heat interaction and now let us move further. We have said that look Q equals delta E plus W although this is the final form of first law. We know that from a study of the other branches of physics we know number one that W can be a combination different modes of work and similarly delta E can be made up of some of different components. Just the way we know that W can be made up of depending on the details of the system made up of expansion work, stirrer work, electrical work, may be surface tension work what you have. Similarly energy is something which is common between thermodynamics and other branches of physics. In fact energy is something which pervades almost all of physics and chemistry. We know that delta E is made up of various components. For example, delta E kinetic because of velocity, delta E gravitational potential plus delta E electrical plus delta E magnetic plus there will be many other components. Now it turns out in observation that other branches of physics tell us how to prevent a change in delta E kinetic, prevent a change in velocity that can be done by preventing any force acting on it. Delta E gravitational can be made to be 0 by seeing to it that the level of our system in a gravitational field does not change nothing goes up nothing goes down. Similarly, delta E electrical, delta E magnetic can be made 0, but even then it turns out that you can have some work interaction and hence you can have some Q interaction and hence what remains finally when all other components are taken care of is a component delta U which is known as the full name is the thermodynamic internal energy or thermal internal energy, but commonly known only as internal energy. So notice that delta U is only a component of delta E and delta E is not by default equal to delta U. Although quite often we write Q equal delta U plus W straight away that is not a safe way to do because one can always come across situation or create exercises and problems in which delta E is delta U plus some other components. Hence always start with Q equals delta E plus W and then write may be using an assumption that delta E equals delta U. You will find that in some cases that assumption is not valid in which case you will have to take care of the other components. Before we complete the discussion of the first law what we have done so far is we have looked at the Karatheodori's formulation, defined the word adiabatic, defined the first law or stated the first law as work done by an adiabatic system between two fixed states is independent of the path. So differential of adiabatic work must be an exact differential that gave us the definition of change in energy that gave us letter for non adiabatic processes the definition of heat transfer and then we came to the final form of first law of thermodynamics. We looked at various components of work, various components of delta E and by writing these components in expanded form we can have an expanded form of the first law of thermodynamics. We will now do a final discussion, we can write first law in a slightly different form just by transposing term or in differential form on the left hand side both Q and W are interaction and hence they are path dependent here these are in exact differential. So if you want you can write them as d dash Q d dash W this is an exact differential. So delta E depends only on end states these being interactions depend on end states and also on path. Again you should know that Q and W being interactions are forms of energy in transit you cannot have just one system and talk of interactions for Q and W because they are interactions at least two systems must be involved a donor system and a recipient system. Whereas when you talk of delta E only one system is involved we are talking of delta E of a system that is one. Second one our definition of delta E is the definition of delta E or d E and this implies that absolute values of E significant because we will always be working with delta E or d E a change or a small differential. Let me complete this by giving you an analogy since W and Q are energies in transit these are two systems which are involved in an analogy given is that of I found it in a text book. So it is not original I think the author of the text book is Boxer it is a small thermodynamics text book barely found somewhere. We talked about rain as what is rain? Rain is water in transit from clouds to the surface of earth the rain falling on a lake. So rain is the interaction between one system the cloud the other system the lake formed by the collection of rain water. You do not say the cloud has so much rain in it we do not say that the lake has so much rain collected in it what is collected is water. So water is like energy it could be in one form in the cloud it could be in another form in the lake. Rain is simply a water in transit like traffic between two cities. Bombay may have lots of vehicles in it Pune may have lots of vehicles in it. When vehicles in Mumbai go to Pune we say there is a lot of traffic from Mumbai to Pune interactions are something like that. Two systems must be involved in the energy must be in transit that means must flow from one system to another system and there is another minor issue here that because two systems are involved the interactions whether Q or W those interactions must be between the two systems and interaction cannot vanish halfway in between. It is like what they say double entry bookkeeping the moment something comes out of one account it must be entered as an entry input in another account. So if you have two systems interacting it is always heat transfer from system one to system two. Get rid of the old ideas that heat absorbed by system A and heat rejected by system B it is always proper way to say heat transfer from A to B and work done by A on B or by B on A whatever. Heat transfer from A to B cannot vanish in between work transfer between A and B cannot also vanish in between because Q and W are interactions they depend on the process and they depend on the way the system is defined. I will give you one example this is a rather you can make it a rather complex example but I will just ask you one thing we have you know in our hydraulic slab or engine slab we have dynamometer they help us absorb the energy produced by the engine and measure the amount of power developed one of them is the brake dynamometer is the rope dynamometer. So all that you have is a drum and if you take a break you have let me show a break only on one side. So you have a break and you have and you measure the force on the brake the friction on the brake and all that may be you have a fulcrum and then you have a force F. Now we know that the energy is transferred from the drum to the brake. Now what is this interaction is it a work type of interaction or is it a heat type of interaction. Before you do that be careful where you are sketching the system boundary your system boundary is within the wheel itself if this is the separating boundary within the rim of the wheel whatever is outside its system B system A is whatever is within this red dotted surface then you will find that it is one type of interaction which one I will leave it to you to analyze. Whereas on the other hand if you decide that your boundary it just outside the wheel part of the brake is also included in the boundary then you will find that the same interaction turns out to be the other kind of interaction. In one case it will be work in the other case it will be the heat type of interaction. And now that this here where we have the difficult part what happens if we have the boundary exactly at the interface of the drum and brake then it may turn out that we are in a situation where we are unable to quantify without looking at much more detail or without moving the boundary according to our convenience either inside the drum or inside the brake to determine what exact type of interaction it has. Finally the interaction is a combination of Q and W but we may not be able to separate the two interactions properly. But remember that is not an issue a system is defined by us the boundaries of the system are laid out by us they need not be matching exactly with physical boundaries and physical surfaces we can define a boundary of our system anywhere we feel like. So that freedom remains with us we use that freedom and simplify the solution of problem.