 So, let us continue quick revision, we said first law is the our understanding of the behavior of adiabatic systems, we define what is meant by adiabatic systems, then we generalize the behavior of adiabatic systems understood that W adiabatic is independent of some paths, so should represent change in some property, that property we took as energy to be consistent with other branches of physics giving you definition of delta E that is thermodynamic energy of the system as minus W adiabatic minus is a matter of sign convention, the second sign convention. Then we did the definition of heat interaction that was this, again mind you there is a sign convention involved here, because we could have defined it as W12 minus W12 adiabatic or we could have defined it the other way W adiabatic 12 minus W12, but we define it this way again as a matter of sign convention, because this way we are consistent with the nomenclature or the convention that the heat absorbed by a system is positive, heat rejected by a system is negative, if I were to define it the other way W ad12 minus W12, it would be heat rejected by the system to be positive and heat absorbed by the system to be negative. For some reason historically and traditionally perhaps because of our link with the calorific calorific theory of heat, calorific was a fluid, so when something is gained it is positive, something is lost it is negative, so we have physicists, chemists, engineers all work with the convention, but a convention that heat absorbed by a system is positive, heat rejected by a system is negative and we are consistent with that definition. Now adiabatic work being independent of the path is first law, defining that as an energy change is the definition of energy, for a non adiabatic process agreeing that W12 need not be equal to W adiabatic 12 that is obvious because we have said first law is actually characteristic of adiabatic processes, so the difference if any is defined as the heat transfer 12. And finally the final form can now be written down as I will just drop the surfaces Q equals W plus delta E, this is the final form for any process, the differential form will be DQ equals DW plus DE, at this stage it is necessary for us to emphasize that DE being the differential of a property is an exact differential like DX or DY, whereas DQ and DW are not exact differential and to emphasize that quite often we cross the stem of these or while typing we prime D prime Q or D prime W, it is not necessary to write it, but what is necessary is to understand and be always conscious of the fact that DQ and DW are in exact differential whereas DE is an exact differential and because of that delta E is a property change, it is a point function difference in energy between two points whereas Q and W are path functions, so if you have the same states 1 and 2 delta E for any process between the two states is fixed, it is even minus E2 whereas Q may be different W may be different if the processes are different. Then again to emphasize that the units of E, units of W and units of Q are the same and this is for any process, this is for a differential process, for a process element and mind you for a small change in state this can always be written, but if you go on accumulating that small change unless it is a quasi-static process you cannot integrate this, whenever it is integration of a differential quasi-static process is a necessary that should again be emphasized. Then let us consider a cycle, cycle means one is the same thing as two and hence delta E is 0 and that means Q over a cycle should be W over a cycle something which we know but this is our proper derivation of that. Now before taking questions which I know there will be a number of them, I will make a statement which had sometimes got me into trouble but I have properly come out of it and that statement is that we should now realize that with in our scheme of things, this is not only is the end form of first law and remember the restriction here is we are considering a process and the process is that of a closed system, we are saying fixed mass we have not considered any mass flow here, but what I am going to say is that we should also realize that this is the only equation being the definition of Q which relates Q to the rest of the world. During our study of thermodynamics if we come across any relation which does not obviously look like this relating Q to something else that relation must be a derivation from this relation, there is no other independent relation linking Q with the rest of the world except of course the second law of thermodynamics where it will vaguely get related to delta S but so long as there is no entropy around purely from an energy point of view this is the only relation between Q and the rest of the world and that relation for second law is a relation for delta S, it is not a relation for Q, this is the defining relation for Q and if you have any other relation that must be a derivative of this and derivable from this, questions. Actually now you adiabatic is independent of path, adiabatic is independent of path you are told adiabatic work is independent of path, adiabatic work is independent of path, but actually the work in general is depends on path, yes general work depends on path and that is why we have said that if a process is not adiabatic the work done need not be equal to each other and the work done hence need not be equal to the adiabatic work done. But if you have two states one and two and execute any number of adiabatic processes from one to two the work done in each and everyone should be the same that is the discovery realization which has been used to formulate the first law of thermodynamics. So what I feel now that exactly is the first law, what I have feel now is there must be a only one path between one and two if it is adiabatic it is true or not, no not necessary that will be true if you say that you have only one mode of work the path is quasi static and may be some other restrictions if you put those restrictions then there will be only one path, but adiabatic means only work done if you have more than one mode of work between one and two you can have any number of adiabatic paths. So can you give example? Examples will follow when we do the example, yes madam. We have come across the definition for adiabatic as where there is no heat transfer we call that adiabatic yes, but there are agree that this our definition of adiabatic means work transfer only after defining Q adiabatic is saying equivalent to no heat transfer, but if you try to define adiabatic meaning that there is no heat transfer you have to define what is meant by heat transfer before that. Whether it is between the system and the surroundings. Okay, but how do you define heat transfer between system A and system B, we have not yet defined before defining adiabatic and hence we will not define adiabatic as no heat transfer. It is another way of saying work transfer only okay, but we say work transfer only because still we define heat transfer we do not want to use the word heat okay just the way we have talked about temperature, but we have not defined temperature so we have not related anything to temperature. In fact you will find that unless we define temperature now we cannot proceed significantly beyond this we cannot solve any problems and that is what we will come to now. Professor the W122 minus W adiabatic 122. Yes. Whether the W122 is greater than the W ad12. No, if it is greater than W ad12 then Q12 will be a positive number if it is less than W ad12 Q12 will be a negative number there is no restriction on the sign of Q12 nothing is greater than something else all I said is it need not be equal to and this need not be equal to as I explained beans it can be equal to it can be greater than it can be less than if it happens to be equal to well that net Q12 will be 0 that will be a overall adiabatic process. If W12 is greater than this Q12 will be positive we will say heat is absorbed by the system in our traditional norm of nature if W12 is less than W12 adiabatic then Q12 will be negative and we will say in our traditional terms heat is rejected by the system. Now the next step is the following it was just pointed out that delta E has different components yes W has different components yes so what we will now do is our first law which we said was Q equals delta E plus W we will split delta E into different components and before that we will split W into different components because W came first. So let us say that W is made up of various modes it could be expansion it could be stirrer it could be electrical it could be surface tension plus what have you more complicated the system more these work modes are possible some of them could be two way some of them could be one way and again I emphasize two way one way because we will come back to it when we come to the next version of the state postulate. Now we also know that energy is not unique to thermodynamics the idea of energy it has occurred in mechanics fluid mechanics electricity magnetism gravitation whatever you have. So we know that E is made up of some components for example there will be a delta E kinetic plus delta E potential of various kinds there could be gravitational potential there could be electric potential there could be magnetic potential so you can even sum this up over all such potential energies of other kinds delta E kinetic would be delta of M v square delta E potential gravitational would be delta M g delta H assuming g is uniform or if you have g varying you integrate it out with local g into dh after taking care of all this if you say that you execute a process in which you assure that kinetic energy is not changing potential energy is not changing of any kind but then the question arises that if I execute an adiabatic process in which I see to it that there is no change in the gravitational potential energy it stays where it is there is no change in kinetic energy my system does not accelerate or decelerate there is no change in magnetic field no change in surface area so all other energies are restricted to not change in that case I can still do work on the system that is a discovery and hence we say that there must be an component of internal component of energy which is unrelated to anything else in physics that component that remains we call it as the thermal internal energy the reason why traditionally it has been called internal is that it does not have to do with anything external like position velocity etc so even other components for example kinetic energy it is measurable my means of velocity you have an external frame of gravitational potential you have to measure something with respect to a datum so these are sort of external variables coming into picture whereas electrical energy chemical energy nuclear energy these are all internal there is nothing external to measure we have the potential inside the charge inside and that gives us the electrical energy the magnetic induction in the field inside gives us the magnetic energy chemical energy depending on the concentrations and the components we can these are considered sort of internal energy we do not have to look at external variables so that is why this thermal energy because it does not depend on external variable depends purely on the local state of the system is known as thermal internal energy but a better nomenclature would simply be thermal energy so our nomenclature would be for this thermodynamic energy or the total energy which contains all components and when you remove components pertaining to other branches of physics what remains is the thermal energy and the traditional nomenclature is u and because we are writing in the delta form it is delta u quite often in our simple problems we will not have other components so it is okay to write q equals delta u plus w but make it a habit force the student to write always q equals delta u plus w and make an assumption that delta equals delta u let the student be conscious of this fact because suddenly you have a problem one problem of a sack falling from a height of 30 or 40 meters if you use delta u you will be wrong because there is a change in potential energy which has to be taken care of whenever a student writes q equals delta u plus w and not delta u plus p dv he should be conscious of the fact that delta e could be delta u plus something else so let him make an assumption that delta e equals delta u when you make an assumption you may realize that look apart from delta u there could be something else and similarly let him write it as w and then let him write as w is w expansion only when he stops at w expansion he should quickly think are there other components read the problem does it mention a stirrer does it mention electrical work all these things okay so it is a good idea to solve our first law problems always from this equation and do not replace immediately delta e with delta e let that be the first step as appropriate. Now look at this equation a simple equation three terms so that means given two terms I can find the third nothing special about it but okay I can measure w if q is 0 I can determine delta e or by some reason if I have measured q and w I have determined delta e but see e or delta u the thermal part of it is a property of the system it is not directly measurable I need some property by which I can have a handle over it so now the question that arises is the following and that slowly brings us to the zeroth law delta e is change in some property now the question is on what does e depend and how that is the next question that we have to solve but since we know that e has a number of components let us restrict our self to u because we know how the other components are evaluated if we know the velocity we know the kinetic energy change if we know the change in level we know the gravitational energy change. So let us ask ourselves the more pertinent question that how is delta e to be related to the property other properties of the state and that brings us to the subsequent section how many properties fix the state of a system is it two is it three is it four and which ones that brings us to the state postulate again and that brings us also to the number of two way work modes this which ones are not really dictated by thermodynamics we will take a forward link to one part of thermodynamics which is known as the phase rule we will not derive it but we will use it because we are going to work with water and steam two phases together the phase rule tells us the conditions under which pressure and temperature are independent and the conditions under which pressure and temperature are not independent that is all it does but thermodynamics using the state postulate will tell us how many properties are required to define uniquely the state of a system but thermodynamics will not tell us which properties and that brings us to state postulate which I may call state postulate one but in most books this is mentioned only as a state postulate hardly any book or very few books we talk of state postulate one which we discussed yesterday that the state of a thermodynamic system can always be defined using only primitive variables it does not say how many but it says that only primitive variables are necessary it may not be always the most convenient one but only primitive variables can be used to define the state the state postulate says that if we have a system fixed mass that means a closed system then the number of independent intensive variables intensive actually because of fixed mass intensive now includes intensive as well as specific equals number of two way work modes plus one this is the state postulate the second part of state postulate and because it is a postulate this is a premise we do not have a proof for this now under certain assumptions about type of system and type of work modes using mathematics one can sort of do a differential analysis and show that this is derivable but mathematics using differential geometry so esoteric that we will leave it at a postulate we will not seek a proof of this now what is the consequence of this remember this one is important and that will bring us to our property known as temperature we have seen that suppose you have a fluid like a gas what is the number of two way work modes it has one so how many properties are required to fix the state of a system of containing a gas of fixed mass two that is all it says it does not say which two okay it could be pressure volume it should be pressure temperature mass is already fixed so that is not a variable or anything tomorrow you define entropy maybe entropy temperature would define the state entropy pressure would define the state entropy enthalpy would define the state so long as they are independent shown to be independent by some other thing the number of properties will be two so this means that we have defined simple systems N2W is one so two properties are needed and this is the reason whenever we talk of air water in some such fluid system where the number of two way work mode is one compression and expansion we always say pressure temperature when we say air at 3 bar 300 degrees we are happy we know everything about the reason we are happy is because of state postulate air being a fluid with only single two way work mode two properties are sufficient but the moment you have a complex system say an electrolyte expand contract as well as charge discharge number of two way work modes is two you will need three properties more complex the system higher be the number of properties needed and at this stage many books will have definitions which we should make the students comfortable with a system which has a single work mode is known as a simple system if that single work mode is that of expansion compression we will call it a simple compressible system if that for example the cell in my mobile it is a simple electrical system because the only two way work mode is charging and discharging similarly you take a simple elastic rod extension and compression is the only work mode assume that it is constrained not to get twisted and bent so we will call it a simple elastic system similarly a soft iron piece assuming that you cannot compress it or expand it you can only magnetize it and de magnetize it that will be a simple magnetic system but if that soft iron piece can be extended and compressed then you can magnetize it de magnetize it expand it extend it compress it that will be a complex system two two way work modes so this way because most of the books will be talking of a simple compressible substance simple electrical substance and so on we will not use the word substance everything for us is the system whatever is inside the system with some substance that is okay but we will always define a simple compressible system because unless it is a system thermodynamic system we will not talk about it so the proper thing would be although the books say substance we will say okay the substance which is contained in that system but actually the characteristic of being simple compressible simple electrical is that of the system so we will properly talk about a simple compressible system a simple compressible simple electrical system and so on and now remember that unless we really talk about properties we are not really worried about what is inside a system we have always been talking about the system inside the system is like a black box so long as we know what its state is it can be anything we all need its properties so we do not really have to be talking about a substance we will always be talking about a system now before we go further we have said that there are substances or there are systems which yesterday I called rudimentary systems here number of two way work modes is zero what is the number of properties needed to define the state of such a system one property and that is good because if we were to have a thermodynamic system with zero property we will get into lots of problems what do we do with thermodynamics so this indicates that even if there is no two way work mode there will be one property needed to define the state of a system what is that one property that is what thermodynamics does not say and hence because of that suppose we have a mercury in glass thermometer the only property we know the only thing which can change is the length of the thread of mercury in the capillary we have mapped it to temperature but the basic property is that length of the thread which can be very easily measured that brings us to the idea of a temperature but we must now formalize what we mean by temperature and for that we move to 0th law I do not have to write off thermodynamics although I should really write it I will leave it to write it but 0th law is unique to thermodynamics for the simple reason I do not think there is any other science which has a 0th law associated with it is there one Newton's law is first second in electromagnetism there are some laws which are but there is no 0th law those laws are usually named after people amperes law and somebody else's law maxels laws maxels relations which come out of all those but there is no 0th law now what is 0th law what is your idea of 0th law let us hear because every textbook has usually it does not have a chapter on 0th law but almost all thermodynamics textbooks for some reason talk of 0th law usually in the very first chapter finish it off in about a paragraph talk about something called thermal equilibrium and say something something and say low and behold something called temperature comes out we will not accept that we want the proper formulation of 0th law so what is your idea of 0th law internal the energy transfer from a to b who is talking the energy transfer internal energy we call it as thermodynamics because it is internal energy is property of a system it cannot be transferred anything which is transferred is only energy is transferred energy is transferred in the means energy is transferred okay way by the way something which I forgot a great analogy before going to this again this is something which you have to impress on your student so I will see let me write this as delta E is q minus w this is another way of writing first law okay just transpose terms delta E is change in property of a system okay this q minus w are interactions between so this is not really complete because we are talking of delta E of a system q and w with some other system but we are not yet talked about delta E of that system okay there will be first law applied to them of a system and between system means there must be two systems involved this depends for this state only on the initial state and the final state these depend on initial state final state and the process detail so we must emphasize on students that q and w are interactions two systems are involved and both q and w are energy in transit that means while doing the interaction of either q type or w type there must be a transfer of energy from one system to another two systems are involved a boundary must be involved unless the boundary is defined you cannot talk of a q or a w okay and there are two illustrations one analogy and one illustration one analogy is that of rain which I found in a book by small book by boxer some 40 or 80 page book so he talks of a cloud okay and then he says well I have converted it to we have a lake what do we have in cloud water in vapor form or in droplet form what we have in the lake is water cloud burst and forms a shower of rain what is rain rain is the interaction between cloud and the water in the lake something comes out of the cloud something goes into the lake so rain is water in transit like heat and work we do not say pavay lake now contains so many meter cube of rain it contains so many meter cube of water the cloud contain cloud can't say oh that cloud has 250 millimeters of rain in it no cloud has so many tons or so many meter cube of water vapor in it but when that water gets transferred to the ground the interaction is known as rain if there is no rain the amount of water in the cloud remains what it is if there is no rain the amount of liquid in the lake remains what it is because of the interaction called rain the water in the cloud cloud depletes sometimes to such an extent that the cloud vanishes water in the lake increases sometimes if initial water is zero a lake is formed that is one analogy and the second thing which we should talk about is there is a neat situation where a small movement of the boundary converts a work interaction into a heat interaction and the situation is that of a break consider a simple situation nowadays mobikes particularly front wheels have what is known as a disc break very clearly seen open mechanism so that is an advantage otherwise drum brakes are inside the hub we do not even see what that mechanism is so now consider a situation where I am simplifying it I have this disc which I am considering as a plate and this is the shoe shoes which are holding it together and the plate is being moved I want to know what is the interaction between the plate and the shoe is it a work type of interaction or is it a heat type of interaction and let us assume that the shoes are fixed to somebody the structure of the car or the motorcycle and the plate is moving because it is connected to the wheel ask them to do the problem using two system diagrams in one case say that the system is the plate itself and nothing else and say that the system boundary is just inside the surface of the plate this is one ask them to redo the problem and say that now the system boundary instead of just inside the plate I am extending it slightly into the this is case a this is case b I will leave it to you as an exercise to do this today evening think about it discuss among yourself and do not be surprised if you come to the conclusion the correct one is in case of a the interaction is a work type of interaction in case b the interaction is a heat type of interaction and all that we have done is moved the boundary of our system by maybe just a fraction of a millimeter but this also means that if I make an adamant choice that the boundary of my system is exactly on the interface of the brake and the shoe then I am at a situation where I do not know whether my interaction is purely a work interaction or purely a heat interaction but if I move it slightly into the shoe it is heat if I move slightly into the plate it is work this is an excellent illustration that work is an interaction depends not only on the two systems but on where the boundary is located of course when you move the boundary we are also changing the definition of our system because the system is defined only by its boundary but this emphasizes on the student the importance of laying out the boundaries precisely because if two students assume two different sets of boundaries hence two slightly different systems the answer can be totally different in one case somebody will say oh it is a proper work interaction the other one will say where is the work interaction this is purely a heat interaction.