 Let us straight come to topic 5 the first law. Now traditionally if you look there are many books which teach the zeroth law first. The order goes as zeroth law first law second law in teaching. It is not necessary to follow that. What we will follow is a more logical way of presenting things because you must have noticed yesterday that I have cut many of you short by saying we have not yet defined it. We will look at it later. Let us not talk about it. Our aim is to always go from something which is defined, something which is understood to something which is to be defined, something which is being explored, something which is being developed. And since I have already spent some time on circular definition we would like to see to it that we do not want any circular definition. We may have forward links. For example we have already started talking about energy without really defining it. Yesterday we talked about heat, sometimes temperature without really defining it. But we have not used those concepts in defining anything so far. So talking about something which is going to come later is one thing but using that idea as if it has already been defined we will likely end up in our creating a circular definition. So look at the history of the laws. Yesterday we said the history of the laws is such that if you go back the idea of the second law was existed in the Carnot's work way back some 300 years ago. And this at that time nobody talked about the laws of thermodynamics. In fact it turns out that Carnot worked using the caloric theory of heat rather than the thermal theory of heat which we have now, the energetic theory of heat. But anyway there was no other theory of heat. The caloric theory of heat was buried only after the cannon boring experiment of Count Room Fort. And it was the new theory was quantified by June. But till then the caloric theory worked and in those days perhaps it worked well because hardly any conversion of heat into mechanical energy took place. Then comes Jules experiment and before that Count Benjamin Room Fort's experiment indicated that heat is nothing but some kind of motion that means some kind of work. So it was the two ideas of work transfer and heat transfer being two modes of energy transfer came up from his work. But it was Jules experiment which finally led to what we call today the first law of thermodynamics. It is possible to develop the whole of the science of thermodynamics based on just these two laws. However that development is not very easy to understand although there are books and there are treatments which work only with these two laws. So slightly more than a hundred years ago when thermometer properly developed we had the third law, third in the order we had the zeroth law. At that time it was understood that maybe zeroth law should be understood first because temperature was considered the absolute basic idea in thermodynamics. So many textbook even today follow the exposition in the form of zeroth law, first law and second law. And even good physics books like Zimansky and Sears they do follow this particular methodology. However when mathematicians got into the act they realized that the structure is very intermingt and it is not a good idea to have zeroth law, first law, second law taught in that order or learnt in that order and the treatment which we are going to follow is we are going to study the first law then we will go to zeroth law and then we will go to second law. So that is the type of order we are going to follow and as we follow it will be clear to us why it is going to be so. When it comes to first law we are going to follow what is known as the Karatheodoris formulation, French mathematician who put thermodynamics in a proper mathematical chamber. When it comes to zeroth law we will follow a formulation provided by Landsberg and others and when it comes to the second law we will follow the Planck-Tienen-Bridgeman exposition. Now question arises with students what are these laws? See laws of thermodynamics are basic laws of physics. They are our understanding of the way nature works and since the nature surrounding us is something which we have not created we cannot say that the nature should work in this particular way. Observations observed and generalized. Here the idea used is inductive logic. I saw something happening today morning at 7 o'clock. I have seen it happening yesterday at 7 o'clock and day before yesterday. So it is very likely that it will again occur at 7 o'clock tomorrow morning. That is inductive logic. There is no deduction here. It is not like 1 plus 2 is 3 and 2 plus 1 is also 3. Absolutely nothing of that sort. And these generalized statements are now given the status of a law. Is there a proof? No, there is no proof. Then why do we believe in those laws? We believe in those laws for the simple reason that all proper observations now seem to be in accordance with those laws. And our belief in those laws not only those of thermodynamics but other laws in physics like Newton's law of mechanics and so on are the belief is so strong that if we come across a situation where a law is apparently violated we hardly ever actually I should say we never jump to a conclusion that there is something wrong with the law. We say that look there must have been some error in our observation or our error in understanding what we are observing. So we make that experiment again in detail with proper measurements. We observe all the aspects of that and invariably we have come to the conclusion that look there has nothing wrong with the law. There was something improper in the way we observed or we conducted the experiment. So newer and newer observations have only allowed us to increase our faith in the law but in the early part those things allowed us to you know fine tune the law properly. This happens sometimes slowly, sometimes after a few decades or after a few centuries. For example you look up Newton's laws of motion. They were considered absolute till Einstein came on the scene. The Michelson-Morley experiment started creating some question marks. Then Einstein came and proposed his special theory of relativity and general theory of relativity to show us that well Newton's laws were good so long as the relative speed between bodies was much lower, much smaller than the speed of light. When the speeds approach the speed of light then a slightly different or more detailed type of physics gets involved and we have the Einstein theory of mechanics and Einsteinian theory of gravitation. But when there are small masses, small gravitational effects and lower speeds that theory automatically reduces itself to the Newtonian theory. So Newtonian theory was not proved wrong but what was proved that Newtonian theory is true in a certain zone of physics. Moment you cross that you are naturally going away from the tenets of Newtonian theory. The same thing is true here. Our thermodynamics because we are assuming that it is a continuum thermodynamics based only on phenomenon not on microscopic particulate observation. So long as we are in this classical domain our laws will work but if you go to the microscopic domain these laws as they stand may not work. These laws may not be proved wrong but these laws will need to be modified. Similarly, today our understanding of physics restricts ourselves to within our observable universe. Now our observable universe is perhaps too small a part of the overall universe may be the unobserved or unobservable part is much much larger than what we have observed. So maybe our laws of thermodynamics will need to be modified when we go to observations much beyond what we are capable to. So these laws are salt of inviolate so long as we restrict ourselves into the domain which we have charted out. Beyond that what happens at today we do not know but we are open that it is possible that these laws will have to be modified. Now we come to the first law. Notice that what we have done so far is we have understood what is meant by a thermodynamic system its state interactions and particularly we are now comfortable with the work interaction. We have created a thermodynamic definition of work and we know how to determine or evaluate the work interaction in certain class of processes. We have appreciated that it has various modes and all that. To follow the Caratheodoris formulation we now define the adjective adiabatic. Adiabatic is defined to mean a short form for work transfer only. So this can be applied to any entity any process anything with which work transfer is involved. Now we know work is a transfer of energy in some form between two systems across a boundary. So the adiabatic adjective can be applied to a boundary or a wall or a partition or an interface different names for boundary. So an adiabatic boundary or wall or partition is a wall which allows only work transfer across it and hence since we have a method by which we can determine whether an interaction is work transfer or not we can determine whether a boundary is adiabatic or not. See what is the interaction across it? If we find that only work interaction is taking place well we do not have to worry about the quantity it is adiabatic. If we find that something other than work interaction is taking place it is non adiabatic. Since boundaries belong to a system this can also be applied to a system. An adiabatic system is one which will be completely enclosed in adiabatic boundary. So only interaction it can have is a work type of interaction. It can also be applied to a process. A process is an adiabatic process if the interaction during that process will be executed by a system. So that during that interaction in during that process only work is done. If you find that some non work interaction is taking place then well it is not an adiabatic process and the system involved is not an adiabatic system and at least some part of the boundary of that system must be a non adiabatic boundary. So this is the definition of our work, the word adiabatic. It means work transfer only. Why do we define it like this? We define it like this because we have defined only work so far. So when we define something else we are going to use only the concepts which have been defined so far. So in the idea of adiabatic we are not going to use the concepts of temperature, heat etc which we are yet to define. Now after having said so the first law. So the first law is the is based on the behavior of adiabatic system and this is the Karatheodoris form. Karatheodoris form says like this take a system must be an adiabatic system. Let it execute a process from a fixed state. So adiabatic system is the one requirement, one and two are fixed states. This is the second requirement and then what Karatheodoris said is execute any process from one to two with the requirement that this be an adiabatic process. I will use the adjective adiabatic. Process may be quasi static, process may be non quasi static. There is no restriction on the process except that it is an adiabatic process and starts from a given state one to another given state two. And the statement basic statement is the word done by this adiabatic system in going from fixed state one to another fixed state two. Any adiabatic process quasi static otherwise whatever no restriction except that it is an adiabatic is independent of the path and any other detail. By any other detail is it is possible that you use one work mode in one process, maybe you use another work mode in another process, maybe in the third process you have combination of the work mode whatever the requirement is that is the consequence of this. So this is the statement absolute basic statement of the first law in the Karatheodoris form. And we use this because what is required is definition of adiabatic which requires definition of work interaction which is already done, requires definition of two states and a process which has already been done. So we are not using any idea which has not been defined. How do you determine whether a process is adiabatic or not? Determine whether only work transfer takes place. How do you determine that? We have the operational definition of work. How do you define state one and state two? Measure the properties, the unique set of properties, state one unique set of properties may be different at least one property is different could be state two. Now consequences, the immediate consequences is WAD12 because it is path independent DW adiabatic must be an exact differential. Path independent that means this integral 1 to 2 of DW adiabatic must be a point to point integral rather than a path integral whichever path you take it would lead to the same value. And now we use the characteristic of properties which we said yesterday that if for a property its differential is an exact differential. So any thermodynamic entity whose differential is an exact differential must be the differential of a property. And this means that DW adiabatic must be differential of some property, W adiabatic must be the change in the property which property this property which we are talking about between states one and two. Now the next question is which is this property? It turns out that Karathiodori defined this property as E and he called it energy. Why energy that we will soon see? The reason is he proposed it like this and he found that it is consistent with all other observations and the derivations and work so far. And he defined this E because DE has to be DW, he defined DE as minus DW adiabatic and which means in the integral form E2 minus E1 which is delta E12 was defined as integral for minus integral DW adiabatic E12 any path. Here it is seen that there is something other than work transfer also. No only the work transfer difference in an adiabatic process is defined as energy transfer. The work has given the name in it. Yes, the work transfer in an adiabatic process is given the name energy difference between those two states that is the definition. Remember everything is adiabatic we have not gone away from non adiabatic to non adiabatic that we will do soon. Now the question is why energy? The reason is after we complete the formulation we find that the final form is absolutely consistent with all our observations. That is the only reason why laws are accepted. Second thing is why this negative sign? Well it is a matter of convention. We are mechanical engineers and mechanical engineers and physicists tend to use this negative sign as a matter of convention but our chemist cousins or chemical engineer cousins they tend to keep a positive sign there. It is a matter of convention. So let me use a different color here. This and consequently this. So negative sign is a matter of convention. No nothing even in work interaction remember that we said raise of a mate means positive work. Raise of a mate we said yesterday was positive why positive we could have made it negative there that was also a matter of convention. So there was one sign convention. I want to give an explanation in the development of thermodynamics PDV was defined. For DV to be positive what to be positive? But even then that is what we feel but chemist feel no it should be minus PDV. Can you take DV as positive? The integral gives us positive work and so that is the condition which you got followed. DV is positive gives you PDV as a positive value. Yes. But it need not be defined as positive work. I can define DW expansion as minus PDV. True but what we accepted is this itself. DV being positive we take DW as positive. Yes but we have accepted it as our convention. Yes exactly but I am saying that may be the reason. So there is convention involved. There is no requirement. What I am saying that is the reason why we could have accepted our area. Agree. Agree. We could have accepted that we could have accepted other. But remember that was a convention which we use. Here also we have used a convention and I am sure there are textbooks which assume the other type of convention. Yes. Now another reason which sometimes I get. Sir this is okay because you know if we say this is energy then you know when I work out I am exhausted. So when I do work my energy reduces so there should be a negative sign. But again that is our feeling. Chemists say that look housewife says that when she needs dough the energy of the dough increases because she is doing work on it. Okay. She says that is the way a housewife looks at it. But that is the chemist or a chemical engineers way of looking at it. Now notice that so far we have come to delta E between two states is minus W adiabatic. If I remove that 1 2 1 2 which is common. This is the first quantitative statement of the first law. You can say that this is the definition of delta E. Of course between two states actually you should have the hidden thing here is this is delta E 1 2. This is W adiabatic 1 2. That is hidden here. Anything which is common. Now the next thing is and mind you again let me make a strong statement. This is the only statement which links change in energy to anything else in thermodynamics. Because this is definition of data. If after sometime we find out find a relation which is delta E is something else which is not obviously or not directly seen as minus W adiabatic. That must be a derivation from this. Now we come to the further development. What about a non adiabatic process. So now let us consider a situation. I am writing x 1 x 2 you can write p v whatever anything which we have defined so far. Let us say we have a system which executes a process from 1 to 2. Let us say because first law as depicted so far does not depend on whether the process is quasi-static or not. Let us say let there be an adiabatic process joining states 1 and 2. Let us call it W 1 2 adiabatic. Let the work done during this process be W adiabatic 1 2. Let there be another process quasi-static or otherwise which I will call without any subscript. So the work done in this adiabatic process is W adiabatic 1 2. Now the blue process let us say that the work done during this process same end states let it be W adiabatic. Simply W 1 2 not necessarily adiabatic. This is adiabatic. This is general. I am not saying asserting it is adiabatic. Now since this is not adiabatic if it were adiabatic we would write W 1 2 is W adiabatic 1 2 that is our basic statement of first law. Since this is adiabatic and this is not necessarily adiabatic we now write that W 1 2 where now here the symbolism is slightly different and we will come across this again and again. In mathematics when I write A is not equal to B. It means A is strictly unequal to B. A is not equal to B it satisfied only when A is say 1 and B is 2. It is not satisfied when A is 2 and B is 2. But here there is a difference. Here not equal to means not necessarily equal to. In fact if you want to be mathematically strict this should be W equal to W adiabatic 1 2 or W not equal to W adiabatic 1 2. Both are acceptable. Whereas mathematically not equal to would mean if you put left side minus right side it has to be 0. Here it may be 0 it may not be 0. So here yes it is conceptual not necessarily equal. Yes if this blue 1 2 the unmarked process if it were adiabatic but followed by the other path instead of that above path if it is in the same path of what. See I am not talking of the path here. Path is immaterial I am only saying let there be one process shown by black here which is necessarily adiabatic and let there be another process shown by blue here which need not be adiabatic need not be. I can assert that it is definitely not adiabatic then I would say this is definitely mathematically unequal because if it is not adiabatic well some other interaction may be taking place and then I am not sure Karatheodori's statement can be applied. Now based on this we come to the next definition. Definition of quantity q let me just call it q. Karatheori defined that q interaction the non-work interaction he defined as w 1 2 minus w adiabatic. So what Karatheodori says is let me go back take a system take two states 1 and 2 and some process at shown by blue here which is not necessarily adiabatic. So if it is not necessarily adiabatic there is likely to be some non-work interaction and he decided to quantify the non-work interaction by means of the symbol q and he defined it as follows that the non-work interaction between the for the process shown in blue between states 1 and 2 of a given system was w 1 2 minus w adiabatic. Connect the two states by an adiabatic process find out this measure this the difference is q 1 2 and he called q 1 2 just for consistency as the heat interaction this is the definition of the heat interaction and of course if I give some numbers to this for example if I call if I call this set of equations as equation 1 and if I say this is equation 2 or relation 2 and then I call this relation 3 equation 1 is the definition of delta E equation 2 is the assertion that process 1 2 is not necessarily adiabatic and equation 3 is the definition of the heat interaction. Excuse me sir yes sir sir is there any specific reason why the definition is defined as w 1 2 minus w ad 1 2 and not w ad 1 2 minus again again a matter of convention ok and finally we will see what would have happened if we were to take a different convention ok. So this is the third convention that q 1 2 is defined as w 1 2 minus w adiabatic 1 2 it might as well have been defined as w adiabatic 1 2 minus w 1 2 if we were to do that we will get a slightly different form but because the sign convention is different when we apply it we will have to plug in numbers with appropriate sign the final result would be the same. Thank you. The quantitative result would be the same now look at equation 3 and look at equation 1 definition of energy or energy chain and definition of the heat interaction. Now combine 1 and 3 because minus w adiabatic is nothing but delta E 1 2 and you get q 1 2 is w 1 2 plus delta E 1 2 and since 1 2 is a common thing we can write in a general way q is w plus delta E or delta E plus w this is I call it. Now I am going to write this equation again on the top of next page because we will spend some time on discussion q equals delta E plus w or w plus delta E does not matter I have a habit of writing delta E first this is equation 4. This we call the final form of first law of thermodynamics but remember that it has in it the following things hidden the basic first law that w adiabatic is independent of the path is hidden there we have made use of that and define delta E. So the link to that hidden first law statement that w adiabatic is independent of the path is the delta E here. Then we have defined q as w minus w adiabatic use the definition of delta E to come to this form which according to us now is the final form of first law. But remember that definition of delta E is equation 1 and definition of q is equation 3 and this is first law plus definition of it. So this although we say is the statement of first law we can say this is the final form of first law and now you see here write down that this includes the first law statement definition of delta E and definition of q. Now I will make a statement which I am sure of you of you will object this statement I have been making in front of my students and initially even my teacher professor at Chuthan objected to it and I had a 1 hour argument with him after which he agreed that my statement was right. Unfortunately I have not come across a simple text book I mean college level text book in which this statement is made. I make a statement that this equation equation 4 here is the equation in this form after including this definition which relates q the heat interaction to anything else involving that system. If you come across any other relation between q and anything else like q equals m Cp delta T or m Cv delta T or m into latent heat that must be a derived form from this equation do you agree? Yes or no? Okay think over if you have a disagreement I am available till tomorrow or even later by email. Now after that let me talk of another thing is there is a plus q here there is a plus delta E here and there is a plus w here. All 3 signs are because of a convention the sign in front of w is plus because we have said that whenever the external effect of the behavior of a system is the raise of a weight it is a work is done by the system. We could have said that work is done on the system give it a negative sign then there would have been a negative sign in this form. Then we said that because of another convention let us define delta E is minus w adiabatic. We have a mental set that if a system does work it gives out something its energy must be reduced. So again a convention because of that negative sign there is a positive sign in front of delta E here. If we were to put a positive sign there this would have become a negative sign. Then we have defined q a positive over equation 3 as w12 minus w adiabatic. We might as well have defined it as w adiabatic 12 minus w12 that would have been another definition of q. Fortunately almost all definitions of q are of that kind I have not seen a group of scientists or engineers using heat rejected by a system to be positive where heat absorbed by a system is positive. So we will link to that because of the calorie matrix. But remember there also is a convention involved. So do not get carried away if you see it slightly different form with a negative sign 1 or 2 negative signs. You must accept it saying that look maybe his convention is slightly different but check that his convention is different. If the convention is the same as ours and if there is a negative sign then there is something wrong. Then now I will rewrite this form in the form delta E is q minus w. Notice that on the left hand side we have something which depends only on the change of state. On the right hand side we have interactions change of state that means delta E depends only on 1 and 2 initial and final state. Because these are interactions each one of them depends on 1 and 2 and process detail. On the left hand side we have change of state of a system involved and hence left hand side talks only about one system change in energy of a system. Right hand sides are interactions so those are energy transfers or energy transports between two systems. So on the left hand side only one system is involved. On the right hand side for q at least two systems will be involved one of them the system which is represented on the left hand side. Again for w two systems must be involved at least one of them a system on the left hand side. If I write this in the differential form for a process element this becomes dq minus dw. De being the differential of a property or differential of a state function point function is an exact differential. The right hand side the dq and dw are not exact differential in exact differential and hence quite often you will find that this d and this d because it is inexact is represented by either a d prime or a d with a cross or sometimes even by a lower case data. Just to indicate that it is an inexact differential you will find many text books strictly following this. I do not insist that we follow it but we must every time remember that dq and dw are inexact differential when you integrate them over a process you will end up with the integrated quantity q or the integrated quantity w. Do not write delta q delta w delta pertains only to a property of a system. So when you integrate d you have delta e but when you integrate dq you have only q. Remember in mechanics the professor spends some time on the difference between distance and displacement between two points in a plane the displacement is the same the vector joining the two but the distance will depend on the path you follow. For example if you take Mumbai and Pune the great circle displacement is you just need to know the latitude longitude of Mumbai latitude longitude of Pune and may be the altitude and you can find it out coordinate geometry that is the displacement. The distance you travel as you go from a given point in Mumbai to a given point in Pune depends on which road you follow or whether you took the train and again whether the train was on the fast track or on the slow track. Which track did it take of the three in the guards or did you follow did you take a flight in which route the aircraft followed. Similarly q and w are like distances depends on all the details whereas delta e is like a displacement. Now you can write this as q equals delta e plus w or w plus delta e or you can write delta e is q minus w these are just transpositions of the whole thing. When you start applying this remember that thermodynamics is consistent with other branches of physics we cannot do anything which puts other branches of physics into trouble. We can augment them we can extend them but we cannot do something which leads to inconsistency. We have already seen that w is made up of number of work modes this would be w expansion plus w stirrer plus w electrical plus depending on the complexity of the system depending on the number of components of work different modes of work. It turns out that something similar is true for delta e other branches of physics have defined other forms of energy. For example in mechanics we have simple minimal thing is the kinetic energy in a given frame of reference. If there is a gravitational field there is a gravitational potential energy complicated mechanical systems like a spring there is a you know elastic energy involved. Then if it is a dielectric then we have the electrical energy involved of charging discharging diamagnetic we will have magnetic energy involved. So we find that delta e is made up of various forms of energy delta e mechanical which could be delta e kinetic plus delta e say elastic plus may be other depends on how complicated the solid is plus we will have delta e gravitational potential plus delta e electrical. Again depending on the type of system and the type of situation the system finds itself in you will have various components of energy. It turns out that even if you suppress a change in all other components of energy there is one component of energy which remains and when you do all that that component we call delta u this is the what we call the thermal energy. So the definition of delta u is subtract from the energy change components of energy changes or energy changes pertaining to any other phenomena like mechanical electrical kinetic potential of all kind and what finally remains is delta u that is because it has nothing to do with any other branch of physics except thermodynamics we may call it thermodynamic energy or simply thermal energy. So this happens to be definition of delta u. Now if we have a situation where our system is at rest so kinetic energy is 0 change in kinetic energy is 0 during a process change in gravitational energy is 0 and no fields affected or if there is a field like gravitational field it does not move in that field in any way move in a general way in which case the changes in energy of other components will be 0 under such conditions if there is an energy change of the system as dictated by first law then that change must be the change in thermal energy of the system and in many of the simple situations we find that for example again heating of water in a bottle or in a vessel all other energy changes will be 0 so the energy change will essentially be energy change due to delta u and hence quite often this thing is written in its reduced form q equals delta u plus w but remember q equals delta u plus w is not a general form it is a form in which we assume that the system is at rest and all other components of energies do not change. So q equals delta u if delta e is delta u assume delta u is delta u as q is delta assumed or demonstrate then we end up with our text bookish form q equals delta u plus delta u but I insist that whenever you derive something from first law or derive or start solving a problem always start so recommendation or maybe I will use the doctor's sign recommend recommendation is always begin with q equals delta e plus w then make appropriate assumption including this assumption if needed and then derive the applicable form see if you look at our equation q equals delta e plus w look at it from mathematical or if you expand this as delta u plus delta e other plus w expansion plus w stirrer plus what you have. Notice that we have just one equation the number of unknowns in that equation will be a reasonably large number even in the most general form there is one equation and three unknowns and as you start putting in the components you will end up with a larger number of unknowns but the equation is still one so there is no fun in this you know large number of unknowns means there are n unknowns n minus 1 will have to be specified and then you extract the value of the remaining n unknowns depending on the process may be we will be able to determine w expansion w stirrer and all that may be depending on the what is happening and our knowledge of other branches of physics we may be able to determine delta e others the question then arises is what does delta e or delta u in this expanded form depend on well it depends on the state of the system no doubt about it but then how many properties do we need to determine uniquely the value of u and what is the relation between those properties and u actually thermodynamics does not really help us u how many properties which once if we come to the conclusion that three property which three property and in what way that means what is the relation if the three properties are say x 1, x 2, x 3 what is the relation between u and x 1, x 2, x 3 or between delta u and delta x 1, delta x 2, delta x 3 because remember that the first law form has only delta e and delta u it only talks of change in energy of some form or the other it does not talk of energy by itself. So continuing these three questions one, two and three it turns out that for one how many properties there is an answer and the answer is known as state postulate or state principle two, second state principle. This says that the number of independent intensive properties independent is more important intensive properties is a minor thing that means you can say number of independent properties for a system of fixed mass the moment you fix a mass even a non intensive property extensive properties can be converted into an intensive property required uniquely define the state of a system equals now remember yesterday I used 2 w, n 2 w number of two way work modes it says number of two way work modes plus one and the moment you uniquely define the state of a system well all its properties including its energies would be defined. So to define the state of a system and define its energy uniquely the number of independent properties needed are the number of two way work modes plus one at this stage we will not prove this take this as a principle or a postulate but after studying the second law and deriving some relations between properties based on that we will come to almost the doorstep of the proof of this the actual proof requires a rigorous differential mathematics we will not do that but we will get a demonstration that how this is consistent with the property relations that we are going to derive. Now as a consequence let us see what happens suppose we have a simple system for simple system how many two way work modes one like a gas simple compressible system one two way work mode. So the number of properties required are two so two properties for example pressure and specific volume pressure and volume we will define the state pressure and volume also happen to be primitive so even the state postulate one is demonstrated by convenience we may use pressure temperature but we have not yet defined what we mean by complex system greater than two rudimentary system note this when it comes to zeroth law now this one means what does this mean this one means that every system will have at least one thermodynamic property associated with it. So that means there is no system in the world which is unaffected by thermodynamics and since there is one property associated with it whatever be the property the energy will be directly related to that property for a rudimentary system every system will have a energy and will have some property at least the energy which is a characteristic and since we have said that any thermodynamic system which should have at least one property and that is volume for a rudimentary property all properties should be perhaps dictated by its volume perhaps okay let us see that was the answer to the first question we have two more questions which ones and what way two and three which properties and in what way thermodynamics does not provide any answers thermodynamics says which properties well choice is yours depending on the type of system if we later on there will be some restriction based on the phase rule if we have a two phase or a three phase system so there will be some restrictions but again thermodynamics does not say you must use this property or you must use that property again which way again thermodynamics does not answer suppose you decide P and V to be the properties which way should you be related to P and V thermodynamics does not put give any answers however after doing second law we will realize that thermodynamics although does not dictate how property should be related to each other it dictates certain restraining condition it says that if pressure varies with volume like this maybe temperature should vary with entropy like this so some linking relations it does like a structure of a Indian musical Raga beyond that you are free to do so long as you follow that structure you are free to do whatever you feel now because of this at this stage we cannot remain with generalities generalities have to be over we have to be more specific so that we can solve some numerical problem because if the relations are not known we cannot do any number and we have also seen that so far apart from basic definitions we have defined the work interaction we have defined the energy as either delta E or delta U and we have defined the heat interaction we have not yet defined what is meant by temperature so we now go to the we say if we remove everything else delta U remains right what remains is delta no but what we remove is also not clear no what we remove is clear because we look at the other branches of physics say for example we say that mechanics defines mechanical kinetic energy so here we are defining complement of delta U without knowing what delta U is no complement of delta U or other branches of energy are already defined in other branches of physics so we take them as primitives so in delta E we write delta E is delta E primitive components as defined by other branches of physics plus if anything remains that is delta U so delta U's definition is delta E as comes out of first law minus delta E all other primitive components so you have a system which has a mass so mechanics comes in oh if it has a mass then if it moves it should have a kinetic energy half mv square so if the initial state as a velocity v1 final state as a velocity v2 mechanics says that the change in kinetic energy is half mv square mv2 square minus half mv square then it says if there is a gravitational field and it goes from a height z1 to z2 the difference in potential energy is mg z1 mg z2 minus mg z1 so that becomes delta E potential gravitational potential then your professor of electricity comes in oh it is electrically charged so in a field if it moves like this the change in energy is this put that on the right hand side. Things that come in thermodynamics that we have not see thermodynamics really ends with delta E is q minus w or q equals delta E plus w these are only the consequences of working with other branches of physics we cannot isolate ourselves with other branches of physics and later on even of chemistry so we have to be consistent and somebody claims that look this much is my money this much is my money so you have to say what remains must be my money that is delta U so definition of delta U is delta E as defined by thermodynamics minus delta E as claimed by any other branch of physics no if somebody else where to claim T, T will not have been a thermodynamic quantity it would have been defined in mechanics it is not defined in any other branch of physics you ask them what is temperature is at what ut is thermodynamics you should tell me what temperature see work is a primitive we have not defined work we have put work on a consistent thermodynamic definition so we have a thermodynamic definition of work because we find that other branches of physics have slightly different definitions of work interaction as we said something just falls down mechanics says that well force of gravitation into the distance is the work done they do not talk of a system A system B in thermodynamics we have to talk about system A system so at this stage we are at the end of section 5