 So, I think before that you probably have figured out that this is going very methodically so that there is absolutely no ambiguity that we are facing. So, though there was a vague idea of what work is and you had heard what heat was, we started by first defining what work was and we did not define heat at all. So, we actually gave a formal definition of what work was, we tried to evaluate work and then we went to the first law where we again redefined energy, then we defined heat. So, it went in a very particular sequence and we never used temperature even at that point and then we went to the 0th law and we decided that there is something called a temperature, but we do not know except that we could label that we did not decide you know how to say whether something is higher or lower. Then there is a science called thermometry where you know you can just put some arbitrary labels based on properties of some substance that you had. For example, you could have had the length of mercury thermometer or the volume in a constant pressure ideal gas thermometer or something like this and you could fix some labels and you come up with some idea of what you know you basically have some basis for putting the labels. The second law in a way is again of course you know based on observations. So, and maybe you know one of the observations people decided was on this framework where you had arbitrarily decided that something is higher low. They thought they saw that oh heat or this so called heat is flowing from high temperature to low temperature and you cannot do it the other way. But this used a definition of high and low which was based on thermometry and we did not really come up with a solid way to put what is high and low. So, again you will realize that this whole effort is to formalize what is high and low by basing it on a log. So, that is what the effort of trying to go in this method is that you are trying to come up with a method to formalize what is high and low and in return we will also come with a property called entropy and we will find out why it is useful especially for engineers it is extremely useful. It decides the limits on processes. So, just as a background you can I will just write down we first did the first law. It had something to do with what we called as adiabatic work. We found out that you could go that between any two points you could do adiabatic work and the path would not matter at all. But the one thing that we never said was is it possible to go from every point A to every point B using adiabatic work. So, for example, if I drawn an arbitrary coordinates some x1, some x2 and let us say I am here A. So, first law just tells me yes you know between A and B I can do adiabatic work using any path maybe it is further static maybe it is non further static I know that WAD does not vary. But can I really go from A to B using only adiabatic work that question was never answered. So, you realize that there is an answered question. Similarly, you can say that people have observed that you have some so for example, let us go to the 0th law. I fixed some labels that is some temperature level which I call A, some temperature level which I call B. I figured out I could differentiate between A and B. But you realize that maybe it is possible that heat gets transferred from A to B, but not the other way round. So, this is an observation you see, but it is not explained by the 0th law. So, it just stops at labeling some of the certain things. Similarly, first law stops at you know telling what adiabatic work is we use it to define heat we use it to you know come up with a more proper definition of energy. But we never set the limits yes is this possible is this not possible. If something is possible till what extent is this possible. So, those things are not set up. So, that is why we need the second law which is of course, again based on experience, observations and you know it is true as long as you cannot find anything which contradicts and that is the situation right now. So, I would say over the years there have been various forms in which the second law has been put forth and you probably I am not sure you know many of you are explaining the second law in what form you explain it. I mean can I have a listing because mostly in mechanical engineering people I have seen they tend to follow one certain manner. Can I have some examples what would you normally say is the statement for the second law Kelvin Planck. So, I have noticed that yes more or less anyone who comes in mechanical engineering they always seem to know that the second law statement they always have been told is the Kelvin Planck statement. So, that is the one statement we will also go by though of course, you know that there is a statement called the Clausius statement there is statement by Carnot. There is also a statement by Carre Theodori in fact that was his statement for the first law was what we followed, but for our proper formulation we will stick with the Kelvin Planck because that is in our logical scheme of things to see to it that we are going from one argument to the next in a particular order. So, we will realize that just by using the Kelvin Planck statement we can arrive logically at many, many other conclusions without you know really deviating much from you know some more or less you can say simple logic. That is why we use the Kelvin Planck statement and while writing down the Kelvin Planck statement we will also notice why we would rather prefer not to use the Clausius statement because you know it uses the idea of temperature which we do not want to use as to what is higher and what is low. It uses the idea that there is some something called a high temperature and something called a low temperature we do not want to use that idea because we still do not know. So, we would rather stick with something where we do not know what is high and low, but we know what that there is something called a temperature. So, that is all that we really need to use to go ahead. So, that is why we will stick to the Kelvin Planck statement. When we come to the Clausius statement we can show that this means the other and we will again reiterate that the Clausius statement is slightly weaker. So, the Kelvin Planck statement I think most of you know is it says that in some vague way it says that there is no possible process which can just take q from a particular heat reservoir and you know convert it entirely into heat. So, for example, so basically this all deals with let us say some cyclic device which executes a cycle. So, by itself it is not really changing its energy. So, it takes q from some heat reservoir which let us say some temperature T1. So, this is the label we are giving we do not know what that label is, but we know that you know yes it has a particular temperature and that is good enough for us. Since this cyclic device you know it is undergoing a cycle it is not changing its state. So, for it this delta E is 0. So, this q is equal to W. So, this we know or this what the Kelvin Planck statement says that this is not possible. I think this is the accepted statement. So, of course, there are 2, 3 small new concept there is something called a temperature reservoir. What is the temperature reservoir? I mean it is correct. So, it is again one of those idealized concepts that no matter how much energy you take out of it the temperature of it does not change. I mean you can say it is some kind of even temperature reservoir is a relative concept you can say. You know for example, if you are a mosquito and you fall in a swimming pool the swimming pool is a temperature reservoir for you because the mosquitoes energy does not affect the swimming pool energy. But if 2, 3 of you fall maybe it affects your temperature and that temperature may change. So, in a way it is a relative concept, but for we can say it is the temperature reservoir for our engine is what we are looking for. So, the T you know does not change then we come to something which is called a heat engine because we were talking of a device which converts Q to W. So, there is a device called as a heat engine. So, the engine is a device which you know probably interacts with a few temperature reservoirs. There is a Q transfer and it itself is a cyclic device. So, it is just taking Q and all it does is you know converting into W. Nowhere are we saying that it is only taking Q. It is interacting with some few reservoirs. There is a Q interaction between this engine and those reservoirs and Q comes out. So, the heat engine is something which you can say interacts temperature reservoirs and outputs work. It is a cyclic device which one here. So, because it is a reservoir whose temperature does not change that is what we are looking for. So, all our argument for second law is based on temperature reservoirs where we say that something is interacting with a temperature reservoir something whose temperature does not change which one? Yes. No, no, no the temperature reservoir is correct because that is the quantity which we are assuming is not changing. See you are removing energy there is no doubt that if you remove energy you expect the T also to change. But that is why I said it is a relative concept. It is so huge compared to your engine that however much energy you remove we assume the temperature does not change too much or it more or less remains constant. And that is the argument we need here because we will talk about interactions with temperature reservoirs as far as our second law goes. Actually we are taking only energy not a temperature. Correct. You are taking only energy you are not taking temperature. So, it continuously supply energy that is why it must be called a energy reservoir. No, no, no. But see we are saying it has a continuous or it has the same temperature irrespective of you know how much energy you remove. So, because we want because we will talk of more than one energy reservoirs if you want to say that I want to put two different labels to it. One has a particular temperature the other has a particular temperature. Now if I start calling them energy reservoirs I mean that is okay but you know I really want to put a label to them. So, I will say this reservoir has a temperature T1 and this reservoir has a temperature T2. So, I would prefer to call it a temperature reservoir. But you are right I mean if you want you can call it energy reservoir but the label is the T1 or T2 or whatever else that I have put on it that is all that we are trying to distinguish. No, I mean I would not say that why are you trying to say that yes. I think we should not get carried away by the nomenclature. The nomenclatures used are temperature reservoir, energy reservoir, constant temperature, energy reservoir, thermal reservoirs and anything. The idea is it is a system whose large enough compared to what we are doing. So that in a few cycles which we will be using for analysis, temperature does not change and this is a realizable approximation either we have what we call later you know large thermal inertia okay so that with a finite amount of energy extraction the temperature changes little if at all or we can have what we saw yesterday that is a or based on steam tables a constant pressure thing with wet steam in it. So long as you maintain the pressure constant the temperature will remain constant and so long as you do not extract such a large amount of heat that everything condenses or supply such a large amount of heat that everything evaporates it will maintain its temperature. So it is easily realized okay let us not get carried away by the nomenclature if you are comfortable with some other nomenclature use it. Later on by Friday we will decide what the nomenclature to use in the final course so I think that should satisfy all. Okay so since I will continue to call it temperature reservoir so what we are saying or we would rather have the Kelvin Planck statement as such. So this cyclic device is the heat engine okay so I can revert the Kelvin Planck statement and say that a 1T heat engine does not exist okay so which means some heat engine which is interacting with only one temperature reservoir okay taking having a Q interaction and outputting W such a heat engine cannot exist so that is that is how we are you know shortening the entire Kelvin Planck statement and you know making use of the word heat engine which you know as mechanical engineers would like to use it that is so this is our preferred way of putting the Kelvin Planck statement that a 1T heat engine does not exist okay so that means you need more than 1 temperature reservoir with which the heat engine will interact okay so 2T heat engine 3T heat engine these are all fine okay so that is what we would want to go ahead. So how would a 2T heat engine look like so I have just drawn a 2T heat engine so there are 2 temperature reservoirs one is at T1 one is at T2 okay and this heat engine this is the heat engine this is the cyclic device in middle that I am drawing this heat engine is interacting with one temperature reservoir you know there is a Q interaction which I am calling Q1 and it is interacting with you know the other temperature reservoir which I have labeled as T2 okay there is a Q interaction and I am calling it Q2 right now I have assumed that you know Q1 is being absorbed and Q2 is being rejected and that is why I have put a minus sign and W in naturally the first law come out to be Q1 minus Q2 okay so this we are saying is possible okay is possible I mean it is possible that this such an engine can exist okay but now we want to argue out our next argument that if this is possible we never said anything about where it should absorb heat from and where it should reject heat from so is it possible for it to do this I should put some Q1 dash some Q2 dash some W dash is it possible for the same engine to run between the same two temperature reservoirs but now absorb heat from the one label T2 and give it to the one label T1 given that the first one was possible or if this is possible is it possible to the other way around correct so the so you will the argument we will put forth okay is that whatever we do okay we will first see whether it will violate the Kelvin Planck statement or not if it does then we say this is possible or not possible okay so you will realize that for us for every argument to be true we will test it with the Kelvin Planck statement okay if it satisfies the Kelvin Planck statement we will say okay this is probably possible if it does not satisfy the Kelvin Planck statement we hold the Kelvin Planck statement to be supreme and we say you know if it violates such a thing is not possible so for example if I have such a process let us say this is possible okay this Q1 values Q2 values are different okay but you know I can since this is a cyclic device let us say you know I run it some n times okay and I run this m times I will run it in such a way that you know m times Q1 dash is n times Q2 and I will put this together this is like a black box for me so when I have done this you realize that I have removed from T2 as much energy that I had put in it using this device I have removed from it okay you will realize that these things you will have an interaction only here this combined device has an interaction only with T1 and it is outputting net energy out so what we realize is that if one of these is possible the other is not possible so if the right side was possible then the left side is not possible or if you find out that the left side was possible then you realize that the right side was not possible so it is only one of the two situations which can be possible both cannot be possible okay because if both are possible you can create a one T heating that is going to be the argument the same thing can be said you know I will not state the plogious statement but I will just say the same thing let us say that there was a heat engine where this was possible between some temperature reservoirs with labels T1 and T2 I could have done this heat interaction okay then I consider two situations now I have the two temperature reservoirs okay I mean I have just drawn this line q either you know you can say directly they are in contact or maybe there is a cyclic device in between whose only duty is to take q from T1 and put it in T2 or it is a device which just takes q from T2 and put it so by itself it is not changing its state in one cycle it just picks up some q from one reservoir and puts it in the other reservoir both the reservoirs have different temperatures okay they are not the same temperature so now you will realize that if this was possible you will realize that you would not mind this happening if I combine this and this okay from T2 in one case you are putting q here you are taking out q okay and you know I can always this is a cyclic device I can always run the number of cycles in such a way that the q's match and you will realize that I can have a net effect where I am not at all the q here I will just balance it out and there is no net q interaction with T2 and the combination will just ensure that there is an interaction with T1 and some net output of work done so that means I realize that if this is possible I have no problems with this but I have problems with this this I will say is not possible okay I have not used the closure statement of high and low I have just used the Kelvin plan to say if something was possible between two temperature reservoirs there is a q transfer possible without anything else without any external work without anything else between T1 and T2 but not the other way round okay why the argument is the same if I combine can I will I violate the Kelvin Planck statement or not Kelvin Planck statement said nothing about you know what is high and what is low it just talked about 1 T heat engines it says a 1 T heat engine cannot exist so I am just showing whether it can exist or not so that is a logical argument is that is that okay so we started with with just one statement saying that you know this is not possible okay so we are just trying to see if you know that statement is getting violated and every time we think it is violated we say yes okay whatever we had assumed then that is not possible because we believe that the Kelvin Planck statement is completely true okay that is true then something which violates it that is not possible so that is how our argument will go on now so I have I have still not I mean you you realize that this is some form of the closure statement that I have put here but I have not used high and low because the closure statement explicitly uses high and low so I am not going to use that right now so I can think of now let us say you know some heat engine which is working between T1 and T2 okay I can think of another engine which I realize I can set it between let me call this q1 q2 q2 dash q3 dash W2 dash W2 dash so though between T2 and T1 I cannot have a process where I remove some q from T2 extract work and you know put the remaining in T1 I can probably find a reservoir where I can remove q from T2 extract work and dump some amount of q in T3 it is always possible of course you will realize that I can have an argument if that this if this independently exists this one then you know I cannot have something reverse you know going that you can take it is the same argument I have used that argument earlier that if one direction is possible the other direction is not possible just because I violate the Kelvin Planck statement okay so right now I will leave you with this statement because I need to go let me save this so we had you know just decided that if you can run an engine between T1 and T2 in this fashion okay you cannot run it the reverse way because every time our only logic was are we violating Kelvin Planck statement or not if yes then we say okay our assumption is wrong so if this is possible the reverse was not possible so then we said is it possible now to probably run an engine between T2 and some other T3 so it is possible probably I mean we will have to test it out probably it is possible now if it is possible to run the engine between T2 and T3 such that you absorb Q2 from T2 reject to QT3 and have some work output W2 dash okay then we know for sure that we cannot do the reverse that is we cannot go from T3 to T2 because we will use the same argument if we do it we will violate Kelvin Planck then we can ask the question is it possible to run an engine between T1 and T3 in this way some Q1 double dash Q3 double dash W3 I will put double dash is it possible to do this your argument will be yes because always this is some cyclic device this is some cyclic device I can always run the this cyclic device and this cyclic device such that these two are equal that is I put in so much Q2 as much as is removed here okay so that means the net interaction with T2 is 0 and this total this total combination is only absorbing from T1 only rejecting to T3 and there is a net work output which is coming from here and here okay so what I have done is a combination and try to give you an engine which I mean the net device is just running between T1 and T3 as far as you know the external world is concerned okay so that means if it was possible to run an engine between T2 and T3 in this fashion definitely it was possible to run an engine between T1 and T3 you can now make an argument can I run the engine between T3 and T1 in the opposite way you will say again no because I have already used that argument for T1 and T2 once you can run an engine between one temperature label and another temperature label I cannot run it in the reverse fashion because I will violate the calculation next. So that means I have come to a conclusion that I can now draw another T4 here and maybe I can run another engine between T0 and T1 and I can keep this going on so I will have a set of levels I can use the same argument with let us say purely the heat transfer that is there is a level here there is a level here T1 and T2 it is possible to go directly like this it is possible to go directly like this it is then definitely it is possible to go directly like this same argument if it is possible to go directly like this I know that if this was possible I know that if this was possible T1 and T2 this is possible I know between T2 and T3 if it was possible to run an engine T2 and T3, then between T2 and T3 a direct heat transfer is possible, I do not violate anything. Then I know that T3 to T2 directly heat transfer is not possible because I already used that argument earlier that if I run an engine between T1 and T2 then this is possible, but this is not possible, this is not possible, this is possible. So I can use the same argument between T2 and T3 for an engine, if the engine works in this way then this is possible. If the engine works between T1 and T3 here then definitely this is also possible because I will use the same argument again and I will know that the reverse is not possible. So we see that definitely yes we are creating a hierarchy now that is from one temperature to another temperature, if an engine is you know you can run the engine such that there is a work output, the reverse is not possible. From the so called you know the temperature from where you cannot run the engine you can always find another temperature between which you can again run the engine. And if you can run let us say between T2 and T3 we have already shown that you can definitely run it between T1 and T3. So we are creating a hierarchy T1, T2, T3, T4, etc. So now you see where this is leading to. So it is as if saying that you know this guy is the bigger guy or bigger person, this is the next person in the hierarchy, this is the next person in the hierarchy and so on because it is as if you know he says this person says I can run an engine by rejecting heat to you, this person says I can run an engine by rejecting heat to you. Definitely the upper person can definitely run an engine by rejecting heat to the next lower guy. So it is you know whoever T2 can run an engine with T1 can definitely run it. So T1 is higher than anyone T2 is higher than. So then we say we are already using this logic that you know there is some kind of a hierarchy. So this is where we now decide to say this is high and this is low. So this brings us to our next step that we say that if I can run an engine between T1 and T2 such that I can absorb heat from T1, produce work and reject heat to T2 I will define this as being T1 higher than T2. So this is my logic for saying what is high and what is low. So I am not going to use thermometry, I am going to use the Kelvin Planck statement to decide what is high and what is low. I know for sure now that I cannot run the engine the opposite way, I can run it in only one direction and this is what I call high and low and now you will realize that this definitely corresponds with the Clausius statement because in the Clausius statement you can have a device which does nothing else but transfer a quantity of heat Q from so called higher temperature to so called lower temperature correct and we are saying yes this is possible and the Clausius statement says you cannot do it from so called lower temperature to a higher temperature and we are saying yes you cannot just take heat from lower temperature using a cyclic device and the net result is just dumping the entire heat into a higher temperature. The Clausius statement used high and low we never use it till now we only first said that we use the Kelvin Planck decided what is high and low based on the Kelvin Planck and we said yes this exactly corresponds to our logic for the Clausius statement that is once we have decided what is high and low we say yes the Clausius statement applies because if this is the direction in which I take Q get W and reject Q2 out then this way is not possible and this is nothing but the Clausius statement is this this is okay. So we have deliberately tried not to use the Clausius statement because it assumes something was high and low okay we did not want to get into that argument because we just went by the law we said the 0th law only you know decided stop that labeling things we did not decide what is high and low so we use the Kelvin Planck to decide what is high and low okay and then we said yes now the Clausius statement sounds reasonable okay but that is why we never went and tried to use the Clausius statement if you already knew what was Clausius statement and if you said yes this is how the law should be you can always try to derive with the other way around okay but we felt that the Kelvin Planck in the strongest statement okay and we can base our entire logic only on this so I think if you go by this logic people will hopefully you know understand yes you know you have not used any other argument except saying that we believe in the truth of the Kelvin Planck is this okay trying to build up the hierarchy of temperature deciding what is high and low so we have again you know we have only decided what is high and low we have not numbered anything we have not said that I know that this temperature is something and this temperature is something we have only decided this is high and this is low okay is this if this is fine then you know let me come to some definitions okay if there is an engine then the efficiency of the heat engine I can always say is the network output upon how much heat it absorbs this is the traditional definition that people have used for an engine because the ultimate aim of the engine is to extract work okay what we provide is the input so you know it is one of the normal ways to define an efficiency what you get out upon what you put in in some sort of way so this is if we stick with this definition this is of course W can be written as Q1-Q2 because that is arising from the first law you know we are not using any other magic there and this can be written finally as 1-Q2 by Q1 so this will be true for any heat engine 1-Q2 by Q1 that is the going to be the efficiency of a heat engine there is also something called a refrigerator you know which is just something which is the other way around you take some Q2 from a T2 you put in some work W and you dump Q1 in T1 okay so this is perfectly possible by the Clausius statement that you can take heat from so called lower temperature and dump it into a higher temperature reservoir if you are actually inputting work okay so there is something external that is happening okay so it is the only the sole thing is not just taking Q2 and dumping Q2 higher reservoir but there is also a W2 this is allowed so this thing is what is called as a refrigerator okay so I mean you know it but I guess this is the time when you are going to introduce it to the students okay what is the concept of a refrigerator that you are trying to keep low temperature region cool okay and that is the objective of running a refrigerator and in refrigerator we do not define an efficiency I guess the only logic here is because you know the numbers will turn out to be more than one what we get is actually we want what we want really is to remove Q2 so we would want to put that on the top in any definition of some measure of performance and what we put in is the work okay so you know you can have it greater than one so you are not really going to call it an efficiency typically you say we call it as a coefficient of performance okay I mean it is just it is just something that we are okay with you know by calling it a coefficient of performance so once you come to this definition okay we will now come to what is called as the Carnot theorem for the second law we will figure out so this is another statement for the second law so you have to just show how each statement is true and for every statement you have to again go back to the Kelvin plane that will be always your logic