 We will first look at the histories of the laws of thermodynamics and the current status and then we will formally begin the study of the first law. If you look at the history, thermodynamics was not developed in one shot. We learnt many things, we observed various aspects of nature and slowly the ideas of thermodynamics emerged. Mechanics development is not unique to thermodynamics, even mechanics developed like that, astronomy developed like that, then there is a haiku about Galileo, it says that very pithy one, it says that Galileo saw that the earth moved around the sun while the church stood still. So here it was the church which stood still but there were many scientists who initially did not believe the developments taking place, later on they were also converted and finally everybody came together and the laws of thermodynamics were formalized. If you look up the history, you will find that the efforts of Carnot began the formal study of thermodynamics, then came Joule and he extended the law of conservation of mass, conservation of energy to the first law of thermodynamics. Meanwhile the so called cannon boring experiments led to some sort of equivalence of work and heat. I put equivalence in code because thermodynamically we know that they are not perfect equivalent of each other. Meanwhile there were developments in thermometry, many people contributed, Fahrenheit in some way is considered the father of thermometry, but there were many others who did that and based on this we had something known as the formulation of thermodynamics. By formulation we mean a neat consistent method of presenting the laws of thermodynamics. And we have a number of formulations for example, there is a gibbian formulation, then there is a Joule-Kelvin formulation, there is a Karatheodori formulation, modification of that is the not Kelvin, Keenan's formulations, Keenan's has more than one formulation. Some of these for example, the gibbian formulation is favorite of chemists and chemical engineers. These formulations are of useful to engineering people, Karatheodori's formulation is although very rigorous is essentially appreciated by physicists. We are going to follow a route which will go like this. If you look up the historical development and there was a question in the test on that, first came Karno, so the historically the oldest is the second law in some way, although it was formalized much later. Then came first law and the zeroth law is the latest one, belongs to the early 20th century. Traditionally many books teach them in this order, zeroth law, first law, second law. If you look up a book by Zimanski, you will find the first chapter itself is zeroth law and temperature. However, a good way of development of this and a consistent way of development of this is the our way, we will start with first law, then we will go to zeroth law and then we will go to second law. For the first law, we will be using the formulation of Karatheodori. Although it is a mathematical formulation, it is not totally out of our abilities to look at it. zeroth law essentially is from a physicist's name as Landberg, but although it is not really credited to him, I find that he is one of the major contributors to the way, we will appreciate zeroth law. The second law, we will be using the Kelvin, the Keenan that type of formulation. This is a mathematical and physical formulation. This will be an engineering formulation and our progress will this way be smooth without any backtracking or without any forward links involved and mainly without any circular definitions involved. Well, this is not the only way a consistent formulation can be presented. There are alternative formulations and I am presenting this formulation because I find after my efforts at studying and making other study thermodynamics that this is at least for mechanical engineers, this is a very neat and not very difficult way of presenting the laws of thermodynamics. Now, what are the laws of thermodynamics, where do they come from? The laws of thermodynamics are basic laws of physics, they have the same status as the Newton's law of mechanics or the Newton's law of gravitation. In Newtonian mechanics and in Newtonian gravitation, the Newton's laws are not derived from anything, they are premises. The statement of every law is our understanding of how nature behaves. It is based on observations and assimilation, generalization. These are not derived, they cannot be derived. If at all a logic is used, the logic is inductive logic, not deductive logic and that means we find essentially the logic goes like this. We find something in true in case one, case two, case three, case four in a large number of cases and then we say that if it is true in such a large number of cases, it should be true in another situation where the basic circumstances are very similar. That is the idea of inductive logic. Although these are our understanding of the law of nature, it is possible that we have not been able to generalize these perfectly or very properly and that is why many of these laws have essentially been formulated in a crude form and then have better and better and more rigorous formulations based on them. Today, our faith in these laws is of such a high level that if we come across a situation where say the first law or the second law of thermodynamics seems to be violated, we do not immediately rush to the conclusion that our formulation of the laws of thermodynamics is wrong. We say that our observation of that situation may not be perfect or we may not have applied our laws to that situation properly and in all cases so far or let me qualify that in almost all cases so far we have been right proper observation and proper understanding tells us that our laws are good enough, but that means only if we remain in the domain of classical thermodynamics, if you go into a situation where microscopic or mesoscale effects are significant then naturally our formulations will be weak and we will have to take recourse to alternative formulations like statistical mechanics, kinetic theory and statistical thermodynamics. Once you remember that kinetic theory and stat thermo are not alternative formulations to classical thermodynamics, they are formulations good in another domain of physics, the classical thermodynamics is good in our domain of physics. Now let us come to the first of the three laws also for some reason known as the first law of thermodynamics and I will use a word without defining it, we will say first law of thermodynamics is a generalization behavior of adiabatic system, the word adiabatic is not defined as yet and let us now define this. So, what is adiabatic? Adiabatic is a short form for us and adiabatic means work transfer only, it is an adjective and it can be applied to boundaries systems processes. For example, if we take a system A and say we have a system B separated by a boundary and let us say the interaction is I and then we say that if this is the boundary let me say is only work interaction and that can be decided by using our operational definition which we studied today earlier. Then the boundary between A and B is an adiabatic boundary because it has allowed only work interaction across it. So, and suppose A does not have any other interaction then system A executed a process in which only work interaction took place. Then we say that A executed an adiabatic process and we can then say that during this process A was or is an adiabatic. So, we have an adiabatic boundary which means it allows only work transfer across it and that can be checked using our operational definition. An adiabatic process is one in which only work transfer is involved no other mode of energy transfer or interaction is involved and adiabatic system would be a system which can execute only adiabatic processes that means it would be bounded only by adiabatic boundaries. This importance this clarity of definition of adiabatic systems is necessary for us to be able to formulate the first law of thermodynamics properly. Now adiabatic systems were studied and the historical thing always mentioned is Joules experiments. Say Joules experiments for some people say they were measurements of the mechanical equivalent of heat. They were measurements of the energy required to heat water. They were measurements to determine the specific heat of water whatever but we look at Joules experiments in the following way. We generalize Joules experiment and we notice the following. Joules did experiments with an adiabatic system. He took a fixed system and adiabatic one from a fixed initial state one to another fixed final state two and he took it from one to two by different methods some quasi-static may be some non quasi-static. But all the processes had two things in common system the initial and final states were fixed and the process any process one to two where all adiabatic and what did he notice adiabatic means only work transfer and the conclusion was if you have fixed initial and final states of a system and the process is adiabatic for each process w was the same. Actually if you really look at the historical detail of Joules experiment heat systems were not really adiabatic. He tried to make them as adiabatic as possible to the extent possible. He tried to keep one and two the two states fixed to the extent possible at that time we did not have fine thermometers. So, when he said that I am trying to increase the temperature of water by 1 degree C from say 14.5 degree C to 15.5 degree C. How good was 14.5 maybe to 0.1.05 degree C was not exactly 14.5 where they perfectly adiabatic where they were almost adiabatic they were not perfectly adiabatic. So, his measurements of w although crude were such that he never got the same w, but his feel for the experiment and his understanding of the process was such that he realized that if we were to do a perfect experiment he would come with a result that work will be independent of the process provided it is adiabatic and the initial and final states are the same. And that generalization of Joule we formalize today as the first law of thermodynamics. So, the statement of the first law is work done by adiabatic system during a process from a fixed initial state say 1 to a fixed final state say 2 is independent of path any other detail. By other we mean the requirement is that it should be an adiabatic system that means it should be an adiabatic process otherwise no detail of the process matters. And in mathematics or in a sketch we can say that fixed initial state fixed final state one adiabatic process say a another adiabatic process say b another adiabatic process say c also adiabatic say work done from 1 to 2 by an adiabatic process is the same for all processes and is independent of the detail of the process including the path if it can be defined important thing is that it must be adiabatic. Now, what does this mean mathematically it means two things which are essentially the same one way of looking at it is like this. Let us say that we keep a state of our system one fixed and we take various different states say 2 3 4 I can go from 1 to 2 by an adiabatic process quasi static or otherwise I can go from 1 to 3 by an adiabatic process. Since the adiabatic work only depends on the initial and final states for each one of these states we can provide a label which is W adiabatic for a process from state 1. And this can be a simple label because so long as the process is adiabatic if you want you can say for an adiabatic process let us be very clear that can be given as a label. For example, I can give this here label as say 100 units meaning as long as I go by an adiabatic process from state 1 to state 1 100 units of work are needed. This may be 150 units meaning whichever adiabatic process I take from 1 to 2 150 units of work is involved and so on that is an integral or a labeling way of looking at things. Another way is a differential way of looking at we say that if W adiabatic from 1 to 2 is going to be independent of the path then mathematically integral 1 to 2 d W adiabatic is going to be path independent if such an integral exists. And that means d W adiabatic in the definition of calculus is an exact differential. If you go into calculus you will notice that an exact differential is one which when integrated the integral between two points turns out to be independent of the path you take for the integral. Now we realize following consider any property pressure, volume whatever property let us take two states 1 to 2 the property here will be 5 1 the property here will be 5 2 of a system. So, consider a system and some property 5 now 5 2 minus 5 1 is a unique number depends only on the state 2 and 1 that means depends 5 2 on 5 1. If it is written down as an integral d 5 from 1 to 2 will this value depend on the path it will not depend on the path because it has to be equal to 5 2 by 5 1. So, the integral is independent of path this also means which is equivalent in mathematics is d 5 is an exact differential. And if we take 1 to be equal to 2 this is for a process, but for a cycle what will happen cyclic integral say from 1 to 1 of d 5 will be 0. If we look at our adiabatic work by first law integral d w adiabatic 1 to 2 which can be written down as w adiabatic 1 to 2 is independent of path. That means d w adiabatic is exact differential what if I execute an adiabatic cycle what would be w for an adiabatic cycle will it be 0 yes because I start with 1 and come back to 1 I might have executed the cycle without changing the state that means without doing any work. That means if I do an adiabatic work execute a cycle and come back to state 1 the work done in an adiabatic cycle should be 0. And from this we come to the conclusion that w adiabatic 1 2 must be the representation of the change in some property. Or we say that d w adiabatic must represent differential of some property. Now the question is which property this is where we come to a situation where thermodynamics has to work with other branches of physics, other domains of physics. And we realize that the property is energy. So, the realization here is w adiabatic 1 2 represents change in energy. And then we come to this brings us to thermodynamic definition of energy our symbol will be E. We define energy actually we define the change in energy or the difference in energy between states 1 and 2. Define as E 2 minus E 1 we define it as minus w adiabatic 1 to 2. In a differential form we write d E is minus d w adiabatic. Now the 2 questions question 1 why E and why call it energy and question 2 why minus why the negative sign. The answers to these questions are the follows 1 E energy because this is consistent with other branches of physics and 2 negative sign is a matter of convention. And our convention is work done by a system which raises a weight is positive that is our convention. And again if you look at the situation it looks somewhat consistent with our feeling. Now when we do work a human being does work say by running up stairs or walking a mine feels exhausted that means the energy levels go down. We feel hungry we want to have food replenishing our energy level. So, the idea here is if you do work a human being does work say by running up stairs or walking a mine feels exhausted that means the energy levels go down we feel hungry we want to have food replenishing our energy level. So, the idea here is if you do work exert yourself then your energy level should go down. So, a positive w should lead to a negative delta E and a negative w should lead to a positive delta E. In that way also this sign convention is otherwise conventionally better. Consequences of this are units of energy are the same thing are units of work. The dimension of energy is also dimension of work to delta E can be determined by measurement of work by definition adiabatic. We have not yet completed our formulation of the first law. See now we have what have we concluded so far. We have said that w adiabatic is independent of path that is the basic statement of first law. First conclusion w adiabatic represents change in a property of our system. Third step identifying that property as energy this is definition of delta E. Now we come to the following realization we have to come to the definition of the non-work interaction. But before that let me again confirm the following 1 to 2 w adiabatic 1 to 2 is fixed the moment 1 and 2 are fixed and delta E is minus w adiabatic 1 and hence w adiabatic 1 to same thing in another word same for all processes so long as they are adiabatic and so long as they are from 1 to 2. Now let us consider a non-adiabatic process by non-adiabatic processes because it is non-adiabatic means interactions other than work are possible. Non-adiabatic means we are restricted to only work interactions non-adiabatic means we are not restricted to work interactions other type of energy interactions are possible. Let us again consider a system so this is our state space of some system just for simplicity I am showing it in two dimensions you can use any number of dimensions that you feel like. Let us say that we have two states 1 and 2 and let us say we have two processes 1 quasi-static or otherwise an adiabatic process I will just leave it with a adjective adiabatic and another process quasi-static or otherwise which is a general process need not be adiabatic this is definitely adiabatic. Let the work done during the adiabatic process be w adiabatic 1 to 2 let the work done during this process a general process which need not be adiabatic be simply w 1 to 2 I am not using the subscript adiabatic what does the first law says if the two processes were adiabatic both the processes were adiabatic this work interaction and this work interaction would be the same but this process is not guaranteed to be adiabatic consequently we can say w 1 2 need not be equal to w adiabatic 1 2 this is not actually the strict not equal to sign of mathematics this means need not be it could be if it is equal to there is no harm thermodynamics does not say that it must be unequal thermodynamics is it may be equal it need not be equal. So, that way this is either equal to or non equal now if we realize this then we are ready for the next step and the next step is we say w 1 2 minus w adiabatic 1 2 we define this as the q and we call this heat interaction again since we are talking for process 1 2 I should write the subscript 1 to 2 remember this is any process and this is q 1 2 for the same process and this is w adi 1 2 is for an adiabatic. So, this is our thermodynamic definition heat interaction and for a given process again rephrasing this the heat interaction is defined as the work interaction during that process minus the work interaction during an adiabatic process all this from the same initial to the same final state this is the definition. Now, we have defined the heat interaction now the next step is combine definition of the of delta e and q we already know that minus w adiabatic 1 2 is delta e this is definition of delta e we have definition of q which is w minus q 1 2 w 1 2 minus w this is delta e adiabatic 1 2 combine these 2 and you get q 1 2 is w 1 2 plus delta e 1 2 and since now everything is for the same process we can write in short q equals w plus delta e this we say is the final form of first law of and of course, we are always working with closed systems we are not looking at any mass interchange. So, this is for closed systems notice this has come out of many steps first the operational definition of work definition of the adiabatic then the first law of thermodynamics which said adiabatic work is independent of path differential is exact differential which made us realize that it is a change in some property we aligned our self with other branches of physics by defining that change in property as change in energy that gave us delta e is w adiab minus w adiabatic then we define heat interaction for non adiabatic processes as w minus w adiabatic finally, we combine these two to give us the final form of the first law of thermodynamics well the I can rephrase this as notice that the left hand side represents change in state that is represented by change in property and because it is a change in property this is something which depends only on end states path independent on the right side r q and w which are interactions depend on end states as well as the process that means they are path dependent we can write the differential form of first law we can write d q is d w is d w is d w is d w is d w is d w is d w is plus d e again transposing d e is d q minus d w this is differential of a property mathematically it is an exact differential these are differential interactions differentials or small interactions these are non exact or inexact differentials if you integrate d e that will be an integral independent of the path if you integrate either d w or d q that integrate integration will depend on the path if you are able to integrate and because these are exact differentials quite often these are represented either as d q d w or d prime q d prime w you will find some text books doing it it is not always necessary to do that but what is important for us to notice is that these are inexact differentials and hence when you integrate d q you will get q and not delta q delta q is incorrect similarly when you integrate w d w you will get w and not delta w using such nomenclature as delta q and delta w in thermodynamics is wrong now so let us write for a process of a closed system we have q equals w plus delta e for a process element q equals d w plus d e if you feel like cross this to indicate and be conscious that they are inexact differentials now let us integrate this and you will get integral of d q is integral of d w plus integral of d for the process again you should notice that this will be path independent whereas both this will be path dependent now what happens for a cycle for a cycle initial state and final state is the same so integral of d e or delta e for a cycle will be 0 for a cycle integral of d q over a cycle will be integral of d w over a cycle plus so you end up with the cyclic form of the first law which all of us know that the heat absorbed by a system executing a cycle would be equal to the work done by the same system during that cycle this is the first law for now just two things remain one is when we write q equals w plus delta e. We already know that work is made up of different modes it may be a combination of expansions terror electric so work is some of or some over similarly the change in energy is made up of change in energy say potential by that I mean gravitational potential plus kinetic plus electric plus what happened. This is some over different components of energy you should also notice that first law defines only change in energy and that means absolute values of e are of no use they are of no actually meaningless so whenever we talk of energy we will always talk of change in energy but we may have a reference state and with respect to that we can have just the way we have a datum for gravitational potential energy we will have a reference state or a datum. And now the last thing to realize in this is again let me draw let me sketch this q equals w plus delta e remember that using our definition of delta e this becomes the defining relation for q and this is the only link between q other interactions defined by thermodynamics any other relation that we have and when we start solving problems on first law tomorrow these things will be clear any other relation that you know between q and anything else must be derivable from this as a proper logical derivation that brings us to the end point of Jaipur any questions from you over? As the adiabatic work is adiabatic interaction is only the work but in adiabatic is the other interaction apart of the work also. So this other interaction will always be larger by quantum than the adiabatic one or as it can be some time less also over to you San. As I understand your question is when you execute an adiabatic process the adiabatic means you are restricting to restricting the system to do only work interactions whatever be the magnitude whatever be the composition of that for example an adiabatic system can simultaneously do expansion or compression work there could be some stirrer interaction there could be electrical interaction there could be any number of interactions provided each and every one of them can be demonstrated using our operational definition of work to be a work interaction. If an interaction during a process turns out to be a non-work interaction or not fully a work interaction then that process is not an adiabatic process over. Thank you over and out. Jane to you Hyderabad over to you for questions. I will do this thing first thing in the afternoon when we do problem solving and work interaction I will give you practical examples of how either C1 or C2 is set up I think that is necessary I read it a bit in the morning because before lunch I wanted to complete the basic formulation of the first law of thermodynamics. So wait till soon after lunch and I will take this as an illustration over. Thank you over and out NIT Trichy any question from you over to you. Yes sir we have different types of equation of states so how to choose appropriate equation of state for a particular working substance over to you. You are it is nice that you are jumping the gun we will come to equations of state when we complete our study of the first law of thermodynamics and the 0th law of thermodynamics then the ideas of the equations of state will become very clear thank you over. One more question do you mean to say the rudimentary system is a bounded one over to you. By bounded one if you mean with properly defined boundaries then yes any system has to have properly defined boundaries so even a rudimentary system has to have properly defined boundaries over. The difference is that a rudimentary system is such or is constrained in such a way that it cannot do any two way mode of work. I gave two illustrations in the morning one illustration was our simple say clinical or ordinary thermometer it is a mercury in glass thermometer it is a solid piece of glass something is inside but we cannot do anything to that I cannot expand it completely press it like a spring or a gas I cannot twist or untwist it I cannot charge and uncharge it I cannot in fact do any type of maybe I can do some friction provided energy by doing work of friction over it but that is only one way I can rub the thermometer but the thermometer cannot rub me back that is not a two way interaction. So a thermometer is a rudimentary system it has zero modes of two way interaction I gave another illustration if I have a simple non-electrolyte non-magnetic gas in a cylinder piston arrangement then it has one two way mode of work and that is the mode of compression and expansion. However I can freeze the piston by saying lock it at one place or I can freeze the gas in a solid cylinder with no movable wall no piston at all sealed cylinder in which case even that possibility of expansion compression does not exist because we have restricted it to zero. So we have made a simple compressible system into a restricted rudimentary system we have made it a rudimentary system so that was the second illustration over to you. Adiabatic process have been shown in so many so many different parts is it possible. Yes over to you yes it is possible adiabatic process if you have more than one modes of work can take different paths the question arises it is a common question so I will do an explanation if we have a simple system and if we restrict it only to that single two way mode of work and if we say that it is quasi static then an adiabatic process tends to be a unique process otherwise there is nothing special about adiabatic processes again in our first law illustrations I have enough illustrations where you will find from an initial state you can have an adiabatic process which is which goes one way which can go also as an isobaric adiabatic process we can also have an isothermal adiabatic process you can even have a constant volume adiabatic process so there is nothing really special about an adiabatic process. Adiabatic process means only work interactions no heat interactions of course we can say no heat interactions only as a derivation based on the first law of thermodynamics that is not the definition the definition of an adiabatic process is only work interactions over. Sir this is a Harnan coordinator N. A. D. Tiritchi on behalf of the participants I want to ask one question how you relate Delhi with a minus work adiabatic this is a basic doubt is arise from most of the participants if you expand briefly then it will be helpful for the participants over to you. See both work and energy are in a way primitive to thermodynamics because they are defined in other branches of thermodynamics we have defined adiabatic we have defined adiabatic work we generalize behavior of adiabatic systems as the first law of thermodynamics. So when using that we have to define energy we have to be consistent with other branches of physics because before the first law of thermodynamics came up mechanics and electricity and magnetism other branches of physics had a law called the conservation of energy and that was not a perfect law of conservation of energy. Because if you talk to your physics friends they said that conservation of energy was work only in force fields which were conservative and there was a circular definition there was that conservative force field is one in which the first law of sorry the law of conservation of energy is valid. Energy from a thermodynamic point of view that is an incomplete conservation of energy first law completes it by introducing the heat interaction and to be consistent with the conservation of energy principles in other branches of physics we define our change in energy as delta E and put it as equal to minus w adiabatic that way we remain consistent and true to other branches of physics. That way our first law which we claim to be generalization of the principle of conservation of energy remains consistent with the conservation of energy in mechanics for example over. Thank you sir over and out. Over to you Nirma quick with your question. I want to know that whether is it practical to use microscopic point of view analysis to solve a thermal problem and if we solve by both the analysis what difference exist is there any case study for solving a thermal problem over to you sir. Please mute your mic so that the audio is better when I talk. Your question is can I get the same answer or can I solve the same problem using both microscopic and macroscopic approaches well the microscopic approach is aligned by appropriate definitions of temperature pressure etcetera with the macroscopic approach. So wherever in a continuum domain that is macroscopic domain you apply our standard macroscopic thermodynamics or you apply microscopic statistical thermodynamics you will come to the same equations and end up with the same solution only in the microscopic domain where we cannot apply statistical classical thermodynamics will you get a different answer by using statistical thermodynamics as you go to micro and micro levels your ideas or the results of classical thermodynamics and the results of statistical thermodynamics will start differing. In fact you will go away from the classical thermo domain and your results will not be good you better take recourse to statistical thermodynamics. Thank you.