 I find that you should in the very first set of exercises which quite often will be the exercises on the work interaction. You should spend may be double or triple time because not only the work interaction part is to be emphasized, but emphasize sketching of system diagrams, assessing of process diagram, then step by step solution methodology, taking care of units dimensions and significant figures. This is also important. I wish there will be some subject in which this would have already been emphasized, but by default for some reason it ends up in the domain of the thermodynamics feature. It has been so 30, 40 years ago and I think it is so today that perhaps because thermodynamics is one of the early courses starting mechanical engineering, but it seems good. We have enough illustrations of doing that in our course. Now coming to the first law of thermodynamics. Before we really getting to the first law something about the history of the laws of thermodynamics. In your quiz yesterday one question was of the 3 laws of thermodynamics 0th, 1st and 2nd which is the earliest historically and which is the latest. And I think not even one of you has given the correct answer. I may be wrong, but my browsing through indicated that some combination has been given, but the fact remains that if you go back in history the idea of the laws of thermodynamics first came with Carnot. His idea that one can have a best engine, the most efficient engine. If everything out there he did not use the word reversible, but we can today translate his idea that he had the idea of what he meant by reversible. If you idealize all sub processes, all transfer processes, remove friction, remove leakages then you will get the most efficient engine. And he may be had a vague idea that that efficiency will not be 100% because he said most efficient engine, but he never said 100% efficient engine. That was before any other idea of thermometry, conservation of energy nothing was formalized. So historically based on Carnot 2nd law is the earliest although it was formulated much later put down on paper and pencil as the 2nd law. At that time nobody thought of even thermodynamics as a science. If you go back in history the work of Carnot is the first formal work in thermodynamics and his work is today formalized as Carnot theorem a significant part of the development of the 2nd law of thermodynamics. So historically speaking I did not ask I said of the 3 laws of thermodynamics which is the earliest historically I did not ask formulated historically. Earlier thoughts were of the 2nd law of thermodynamics by Carnot, thoughts of the 1st law formulated by Jules experiments and all that came later. 0th law came only in the early part of the 20th century. But the formulation of 1st law came first, formulation of 2nd law came later. So that is why they were called 1st law of thermodynamics and 2nd law of thermodynamics. Then in the early part of the 2nd 20th century it was realized that to put temperature on a formal footing you need a law of thermodynamics and at that time it was thought that that law of thermodynamics should precede because temperature being considered the most important thermodynamic quantity at that time. It should precede the 1st and 2nd law they did not want to change the names of 1st and 2nd law so they called it 0th law. As a consequence thermodynamics is perhaps the only branch of science which has a 0th law. There are other law there are Newton's laws of motion but they are 1st, 2nd and 3rd. Thermodynamic laws they could have been 1st, 2nd and 3rd but because 1st and 2nd law were already formulated they did not want to renumber them and they did not want to renumber them for a very special reason. The 2nd law of thermodynamics is one of those very very special laws in physics. It is one of those rare laws which end up with an inequality. All other laws of physics as far as we know are laws of equality or laws of definition. The 2nd law is an inequality and because of this unique nature even some great physicists are uncomfortable with the way we formulate the classical 2nd law of physics. And because of this when somebody says let us discuss 2nd law without saying whether it is 2nd law of mechanics, 2nd law of Kepler or 2nd law of thermodynamics. It is assumed that if you say simply the 2nd law you must be talking about the 2nd law of thermodynamics. So there are even books in the library the 2nd law no thermodynamics but everybody who sees that knows that it must be the 2nd law of thermodynamics. So the 2nd law of thermodynamics has the unique status of being the 2nd law of the world. And because of that they did not want to renumber it as 3rd law and then they said we will renumber we will number the law regarding thermometry as the 0th law. So till around 1930s the way was 0th law for temperature, 1st law for energy, 2nd law for entropy. But then people were not really happy the way 0th law was formulated and the way the laws were explained. So people mathematicians physicists started looking at the way the laws were formulated. Some people thought that why should there be 3 laws perhaps we could do only with 2 laws. There were attempts to merge the 0th law with the 2nd law. There were also attempts and some success in formulating the whole thing in terms of one law the so called law of stable equilibrium. But the formulation is so complicated and so ununderstandable to even teachers of thermodynamics that I dare not consider it as good for explaining to even college teachers like you forget students. So we will remain with our 0th, 1st and 2nd laws of thermodynamics. However we will by the way before we come to this the law of stable equilibrium we still use as a premise and although we have not written it down it is there at the back of all our thinking is that you know yesterday we defined equilibrium and we continue with a state in equilibrium. The question is asked that look why do you say that a state is equilibrium. What guarantees that this water here is a thermodynamic state in equilibrium the air in this room there is some movement some temperature variation but it is a good approximation for a state in equilibrium. The reason for that is a premise is that any thermodynamic system which is isolated tends to a state of equilibrium. So you create a thermodynamic system totally nowhere near any point in state space isolate it and just leave it to itself it slowly tends to some state of equilibrium. This is a premise in thermodynamics and some people like Keenan and Exopolos have tried to put it formulate it formalize it as a law of stable equilibrium from which they tend to derive 1st law, derive 2nd law and derive 0th law but we will not do that but we will take a different route. We will follow the route of Karatheodori for the work of 1st law because his formulation is considered the most proper neat in classical thermodynamics. Then we will go to 0th law. So our order will be 1st law, 0th law, 2nd law. This way we do not fall into the trap of defining heat in terms of temperature and temperature in terms of heat but many people and many of you will be uncomfortable with this initially because we tend to define or we will define the heat interaction without any reference to temperature. And then we will go to 0th law where we will define temperatures but we will appreciate that 0th law does not define temperature as a level of hotness. It defines it as something labels on isotherms and till we come to the 2nd law we will keep on at the back of our mind that only the 2nd law tells us what is a higher temperature and a lower temperature. 0th law does not tell us, 0th law only tells us temperature A is different from temperature B that is it. 0th law does not tell us which is higher and which is lower. We use thermometers to arbitrarily number them as higher and lower but a thermodynamically proper definition of higher and lower temperature comes up only after the 2nd law is studied. And we will follow that formulation because in my opinion that formulation is the most consistent one and not just my opinion I have implemented that thing in teaching to our undergraduate students and there is absolutely no difficulty in their absorption of this formulation. So, although historical is 2nd, 1st and 0th formulation is 1st, 2nd, 0th. First in the time of Joule and Gibbs, 2nd by Kelvin Planck and others, 0th mainly by Landsberg and Carrethiordori. Our study will be in the order 1st, 0th. Now it is necessary at this stage to again emphasize on students that the laws of thermodynamics like other fundamental laws of physics, the other fundamental laws which they know by this time is Newton's laws of motion in classical mechanics. These laws have no proof, you cannot prove or you cannot derive Newton's 1st law and 2nd law and 3rd law of motion. On the other hand Kepler's laws of planetary motion are not fundamental laws of nature. Then Kepler developed them, they were assumed to be fundamental laws of astronomy. But when Newton developed his laws and Newton developed his ideas of calculus using the laws of Newton and mathematics of Newton, one can derive using the universal law of gravitation and Newton's laws of mechanics, all the 3 laws of Kepler. So, Kepler's laws are actually now derivations or theorems based on Newton's law of motion and law of universal gravitation. But the basic Newton's law and the basic laws of thermodynamics are laws, fundamental laws of nature, no proof. Then why do we believe in it? Our belief is very strong because over decades and over centuries, we have not found any contradictory evidence of these laws and our faith in them has grown to such an extent that if we come across a situation where we have a conclusion which apparently violates that law. In fact, I will say apparently violates that law. We do not come to a conclusion that that law will be misconstrued or is not proper. But we immediately try to analyze the situation and measure the situation in proper detail because our immediate conclusion is look, although there is an apparent violation, we are almost sure there is no violation when we look at it in proper in all its detail. That is the level of faith that we have in these laws. Having said that one should appreciate that these laws are restricted to thermodynamic systems and when we are looking at them from a macroscopic point of view. So, our premise is that our systems are continuous and there is no quantization of interactions, energies and states in the thermodynamic state space and that they are scale independent, small or big does not matter. Only when these premises are true, the laws are true. When you go to scales which are cosmological scales which are molecular level, these laws are not on their proper ground, remember that. But for a vast majority, very, very vast majority of engineering applications, particularly mechanical engineering applications, these laws are perfectly in order. Now, after this we come to the basis of the first law. The three laws of thermodynamics, if we look at, are our understanding of the behavior of nature, but some aspect of nature. For example, I can say that the first law is our understanding of the behavior of adiabatic systems. What is adiabatic? We have not defined, but it is a short form which will make it very clear what adiabatic means. Zero law is a behavior of systems which are non-adiabatic. We will have another short form for the word non-adiabatic and we will define what is adiabatic. We will define what is that non-adiabatic is and then the second law is our understanding of the behavior of what we call as engines. Second law can be derived looking at many different things, but we being engineers, particularly mechanical engineers, engines is something at our heart interest. So, second law will be based on engines. So, for that we will deviate from the Karatheador's formulation and we will go through the Kelvin Planck formulation. In the first law the key word is adiabatic. In your quiz there was a question, what is an adiabatic process? So, naturally that means adiabatic is an adjective. Our definition of adiabatic is this. Adiabatic is a short form. First thing adiabatic is an adjective. Adiabatic by itself means nothing. Adiabatic is an adjective which modifies something like a process, system, boundary, so on. It means work, transfer only. That is what it means. Adiabatic means work, transfer only. So, an adiabatic it can be applied to, for example, an adiabatic boundary. A boundary across which only work transfer can take place. It can be applied to an adiabatic system, a system which is constrained in such a way that it can do only work transfer, no other mode of energy transfer. It can be applied to a process, a process in which the only interaction is work transfer, no other interaction is permitted. And why do we define this? We go back to yesterday's definition of work interaction, the operational definition of work interaction. That definition always accepts the possibility that some interaction will not be a work interaction or will be a fully work interaction. And that itself is at the heart of thermodynamics. Thermodynamic science came up because there are interactions other than work interactions. If there were no other interactions other than work interactions, thermodynamics would not have existed as a science. Of course, the world as we know would not have existed if there were not non-work interaction. That restrictive part of science in which only work interaction takes place is adiabatic. So, if you have a boundary across which only work interaction takes place, we call it an adiabatic boundary or an adiabatic partition or an adiabatic wall. A system is adiabatic if it is restricted only to work type of interactions. So, such a system will be covered totally in adiabatic boundaries because any way energy transfer can take place across any boundaries by work. So, all such boundaries of an adiabatic, all boundaries of an adiabatic system would be adiabatic boundary. And such a system when it executes a process, it will execute an adiabatic process because only work interaction can take place. So, this is what is meant by the word adiabatic. The adiabatic, remember adiabatic is an adjective and it means one that permits work interactions only. And typically, this adjective is applied to a boundary, a system and a process. So, we should now be very clear what is meant by an adiabatic boundary or adiabatic wall or adiabatic partition or an adiabatic interface, different names for a boundary, an adiabatic system and then adiabatic process. Work transfer only. Moment you say adiabatic, that means you are restricted in it to work transfer, whatever is involved with that adiabatic thing. So, now the next thing, the first law tells us something about the behavior of adiabatic systems. Now rather than give you a very verbose solution, verbose statement, let me say, I will sketch, let us say this is our system and let us say that it is adiabatic. It may do any type of work with its surroundings but only work, no other interaction is permitted. And let us say that an appropriate state space, consider any two processes, any two states of the system, 1 to 2. And this is exactly what Joule did and experimented with. It is generalization of the so called Joule's experiment, where he restricted himself with water going from 14.5 to 15.5 Celsius and all that. But our generalization is this. We have an adiabatic system which we take from some initial state 1 to a final state 2 by some adiabatic process. Select this be one adiabatic process, quasi-static. Let this be some other adiabatic process, also quasi-static. Same initial state, same final state. We could even take it from 1 to 2 by some non quasi-static adiabatic process. We could take it by some other non quasi-static but adiabatic process. And then we measure or compute, let us say this is process A, this is process B, this is process C, this is process D. Then we evaluate or compute the adiabatic work done during the process A, that done during the process B, that done during the process C. I am emphasizing AD because all are adiabatic processes. And same initial final states 1 to 2, 1 to 2, 1 to 2. Joule discovered and stated that all these work interactions are the same. So work done by an adiabatic system during a process from a fixed initial state 1 to another or some fixed, may not be another, some other fixed state 2 is independent of the path and any other detail of the process. The requirement is fixed states 1, 2 and adiabatic processes. The work is independent of the path. So our basic statement of the first law is work done during an adiabatic process from 1 to 2 is independent of path and other details. That means whether it is quasi-static non quasi-static. I use the word other because one detail which is common is adiabatic. All other details do not matter. This is going to be our first law. Now this as a statement is rather useless because what do we gain out of it? Remember of the 3 laws of thermodynamics. Each of the law of thermodynamics, whatever we do, whatever we say the statement, finally we come up with a useful property out of those 3 laws. The first law will help us extract a useful property called energy. Second law will allow us to extract a useful property called entropy. And 0th law will allow us to extract a useful property called temperature. So that is the final point. The beginning point of first law is w adiabatic 1 to 2 is independent of the path. That means it is not a path function. That is something great. So if it is not a path function then how do we use it? This implies that w adiabatic is not a path function. This implies many things. Mathematically it means that the differential of w adiabatic must be an exact differential. Physically it means that for a fixed state each state can be labored with a unique value which will be w adiabatic 1 to that state. Each state i because I execute a adiabatic process from the reference state to that state and a unique number can be assigned to it because the detail of the process do not matter so long as it is adiabatic. And now what is that which we label of piece of piece? So these labels or we should say this label can be considered to be a property of the system. Because it does not depend on the path with reference to our reference state it can be considered a property of the system. Or mathematically since it is an exact differential we can consider w adiabatic itself as a change in some property. I will show this on a state space. Let us consider just some state space x1 x2 of our system. I take this as my reference state say 1. I consider this state say 2 and I will say I label this with phi 2 is w adiabatic 1 to 2. Then I take a state 3 and I label this with phi 3 is w adiabatic 1 to 3. Similarly I can do with state 4, state 5 whatever. Then I claim that these phi 2, phi 3 etc are a property. Is my claim true? My claim will be true if the variation of this remember the variation of a property from state 1 to state 2 is independent of the path. Now let me see what about phi 3? What about phi 3 minus phi 2? Will it be independent of the path? Because of w adiabatic. So, phi 3 minus phi 2 which will be w adiabatic 1 to 3 minus w adiabatic 1 to 2 will have to be w adiabatic 2 to 3. So, because of this the discovery is phi represents some property. And mind you everything is with reference to some state. So, phi does not seem to have an absolute value. We need a reference state because we are always talking of a process. So, if we want a unique value it should be with respect to some reference state. But when it comes to differences between properties that is a unique value. Now this is the main thing to be consistent with other branches of physics. We realize that phi represents energy of the system. Why do we call it energy of the system? Simply because this is consistent other branches of physics. Other branches of physics have already developed ideas of what is energy? What are their components like potential energy, kinetic energy, magnetic energy, electrical energy, chemical energy. And there also the idea is that energy is not absolute. It is the only the change in energy which is of importance. When it comes to kinetic energy it is with respect to a reference frame in which the velocity is 0. That is the reference state. When it comes to gravitational potential energy it is with respect to some datum level. So, what we define is this. We define the thermodynamic energy as is common we will drop the word thermodynamic. We will define energy E with this relation data E12 is W adiabatic 1 to 2. And what is data E? Data is nothing but E2 minus E1. This is the definition of energy. So, we have taken two steps so far with first law. We have said first law represents characteristic of adiabatic system. The statement of first law is that the work done by an adiabatic system while going from fixed state 1 to a fixed state 2 is independent of the path and other details about the process. Other because adiabatic is one restriction. And that is the only restriction about the process. The process could be quasi-static. The process could be non quasi-static. It may have one work mode. It may have thousands of work modes. But only work modes are allowed. Any non work interaction is prohibited because it is a adiabatic process. It is a restrictive process but it is a special process because the work done between two states is independent of the path. Because it is independent of the path, we can consider it to be representing the change in some property. Because change in some property between two states is independent of the path. And each state has a unique value of the property associated with it. So, each state has a unique value of the adiabatic work associated with it provided if the adiabatic work is from some reference state. And that property or the change in that property represented by adiabatic work we define in thermodynamics as the thermodynamic energy. And the immediate question arises if sir energy has already been defined in other branches of physics. Why do we redefine it here? We say that look we call it energy because calling it energy here is consistent with other branches of physics. So, we are not really defining energy ab initio. We are just perhaps extending the definition of energy as used in other branches of physics into thermodynamics. And that also is proper because we know that first law finally represents the principle of conservation of energy. And conservation of energy is not the unique domain of thermodynamics. Conservation of energy exists even in mechanics. But there there is a restriction. For example, in mechanics or physics you would have come across the term a conservative force field and a non-conservative force field. You say that when a set of particles moves their sum of their potential energies plus sum of their kinetic energies is invariant provided the force field in which they are working is a conservative force field. That conservative force field immediately sort of restrict itself to adiabatic processes that means no heat transfer is taking place or no dissipative processes in which heat transfer is not taking place. So, that restriction to conservative force field it immediately indicates that they are not encroaching on the domain of thermodynamics. In thermodynamics we accept that there are interactions other than work interactions and hence the if we do not talk of force fields here but if there were force fields we could have non-conservative force field. But we are extending the definition of energy to take care of those by restricting to begin with to adiabatic processes. That is one question. So, we are not encroaching we are consistent with other branches of physics. The second question is why this negative sign? Remember yesterday when we defined that work is plus M1 G1 H or M2 G2 H. We had a sign convention we said work done by a system is to be considered positive work done on a system to be negative. And we say it is a matter of convention and there are people who can work the other convention. Here also it is a matter of convention and being consistent with the idea of energy used in other branches of physics. We can live with this negative sign but then many of our equations will have a negative sign there. And this is if physicists use this because this is consistent with our idea that when we do work by say kneading dough or working on a trade mill we are doing work we feel exhausted. Why do we feel exhausted? Our energy level goes down. So, that is why energy going up when work is done on the system energy level going down when work is being done by the system that also makes it psychologically convenient. But remember this is a matter of convention. There will be 4 sign conventions that we will come across. This is the second one. The third one will soon follow and the fourth one will come to when we define entropy. The first one was the sign convention for work. The second one is the sign convention for energy. The third one will be the sign convention for heat transfer. Fourth one will be the sign convention for change of energy. Now the next thing. So, the steps in first law we will again come to this because using one statement first we define what is made by adiabatic. What is meant by adiabatic? Second thing we said the behavior of adiabatic systems. Then the third one was W adiabatic was like change in some property and the fourth one was delta E is minus W adiabatic. This is definition of delta E. That means we have systematized first law without talking about heat transfer. But we know that finally we have to come to delta E is Q minus W. That is the final form of first law student knows from his Einstein standard. Now we have to define the next step is definition. We consider the following. Let us say that we have a system goes from an initial pro state one to a final state. Let us say that we have a choice of two processes. I am not emphasizing that they are quasi-static. Let us say there is a process I will call it adiabatic AD. One AD2 is an adiabatic process. And let us say that I have another process quasi-static or otherwise which I will simply call 1 2. So, the process 1 2 is this one. Process 1 2 AD is this one. This is adiabatic. This is may not be. It is a general process. And I am not claiming they are quasi-static or anything. I am only claiming that one AD2 is an adiabatic process. And one and two are defined states in the state space of a system. Because this may not be adiabatic we can say W12 where the not equal to, remember the not equal to in thermodynamics is not the same thing as not equal to in mathematics. In mathematics A not equal to B means A-B is not 0. They are distinct. In thermodynamics almost always when we say W12 is not equal to W12 adiabatic something like this. It means need not B. In mathematics when we say A is not equal to B, it is perfectly safe to divide by A-B. In mathematics when A is not equal to B, 1 divided by A-B is a very proper finite number. We can work with it. But in thermodynamics when I say W12 is not equal to W adiabatic 12, it means it may not be equal to. I still accept the possibility that it may be equal to. Then we agree to this that it may not be equal to we define Q. The heat interaction is during this process, non adiabatic may not be adiabatic process as W12 minus W adiabatic 12. This is our definition of the Q interaction. But we have already defined W adiabatic 12 as minus delta E or delta E minus W adiabatic 12. So use that and you will get Q equals Q12 is W12 plus delta E1. This we consider as the final form. Is T ready? We stop here. I know you have lots of questions which we will take up after the teacher.