 Now we should remember that work interaction or work is a primitive. For example in physics we define a small amount of work is done when we have a force F acts on some body and the point of application of the force gets displaced by some amount of distance dx. And this is a dot product so see to it that the force and the displacement are generally in the same direction. If they are not we take either the component of force in the direction of the displacement or component of displacement in the direction of the force. Here we do not talk if you can look at this thing Newtonian basis of mechanics or Newtonian depiction of mechanics. We do not talk of body A doing work on body B. It is only a force point of application and the displacement. Because of that suppose I have something which is in a gravitational field and it is even allowed to fall freely down. We say some work is done. If you do your projectile calculations you will say as the projectile suppose you throw a ball straight up. You know as it goes up and goes down you will say there is a gravitational force initially the displacement is against the force. So initially a negative amount of work is done it decelerates. At the apogee it comes back turns around and the force is in the direction of the displacement now a positive amount of work is done. And then you will say the amount of work which is done increases the kinetic energy but you also say the reduction in potential energy also increases the kinetic energy. We never talk of what is system A what is system B. In thermodynamics such things will not do. So what we do is here we have Fdx there are other situations for example you will have p into dv then this is not pre multiplied by dv then you will have for electrical work you will have p into dq for surface tension acting and extending you will have minus sigma into da. You have a stirrer in a liquid which is being stirred you will have minus tau into d theta. Everything that you will notice is something of the x into dy kind and another thing for us to notice because we have defined properties as extensive and intensive. We should notice that x is a property of some involved system and you will notice that x is generally an extensive variable sorry intensive variable like pressure the charge of sorry the potential of a cell surface tension of a liquid. Well tau is not a property so classification does not come into picture and dy is a small change in some extensive property. So often this is intensive and this is extensive often but not always. But in thermodynamics such ideas will not do. Thermodynamics we have to have some basis by which we have to decide whether when we have a system A and a system B and some interaction takes place and the change of a system A, state of a system A changes from A1 to A2 and state of a system goes from B1 to B2. We have to answer the following questions. Is the interaction I work interaction? If so what is the direction? May be a convention of direction or convention of sign will have to be used and what is the quantity? These are the if we do that we will have a proper definition of work. And now we come based on this to what is known as the thermodynamic definition of work. What is your idea of the thermodynamic definition of work? Which is there in almost all textbooks. Soul effect, he says raising, you say raising or lowering. Do you accept lowering is acceptable? Only raising. What type of conversion mechanisms are allowed? Only pulley block or heisting drum systems. Electrical motor will not be allowed. Can you provide an operational definition which will tell us when an interaction is work or not work? We have not defined the temperature yet so we cannot use that idea. You are taking one particular example of a gath in a cylinder piston area. It could be anything. So what we will do is because this is only a 3-day workshop, let me quickly go through this. We will now consider the operational definition and this operational definition is originally from Bridgeman. Not exactly like this but the credit goes fully to him. And for that again we go back to this. We will consider this to be our requirement. We have a system A and a system B. We know there is some interaction I between them because the state of the system A has changed from A1 to A2 and state of the system B has changed from B1 to B2. So we want an operational definition that means we will now provide a set of procedures, a set of experiments by which you can answer these questions. Is I a work interaction or completely a work interaction? If it is not, it is okay. If it is, then what is the direction and what is the quantity? Then we proceed like this. What we do is the following. It is in two or three steps. We take system A. We let it execute the same interaction I and let it go through the change of state from A1 to A2 but we try to replace B by some contraction C1 which has the same interaction with I with system A but whose output is nothing but rays of a weight. Weight is mass in a gravitational field, mass M1. It is raised not lowered by a height H1. And C1 has to be a primitive device that means you can have pulleys, you can have slides, you can have crank and axles. You can even have electrical motors, 100% efficient because we know that given sufficient effort and money you can have near 100% efficient motors just the way given sufficient efforts you can have frictionless drives, mechanical drives, frictionless rivers and frictionless pulleys and gears, non extensible strings, all these things are possible. And C1 executes only cyclic processes that means when this result takes place the state of C1 does not change. In between it may change but finally it should come back to its original state. That means what we are trying to do is this interaction which is the same because system A does not feel anything different. It says I am doing interaction, shaking hands, interacting I on the other side. It does not notice that on the other side instead of B there is someone else but since whatever is offered is being accepted in exactly the same fashion leading to the same change of state of A, A feels nothing is different. So the interaction C1 does not undergo any change of state but the rest of the world the mass M1 is raised in a gravitational field by a height H1. Notice that C1 executes a cycle means no other external effect other than raising of a weight. Now we try to execute C1 or implement C1 if C1 is possible. It may be possible to do this it may not be possible to do this. Then we say then I is work definition and then this is one I is work then we say that system A does work on system B convention of A system we doing work on system B. And C3 work done by A on B is plus M1 gh1 and work done by B on A is minus M1 g this is the first part of the definition and this is only if C1 is possible. Now if C1 is not possible then go to step 2 let me call this is step 1. Step 2 is very similar to step 1 here in step 1 we replaced the system B by a contraption C1 and tried to see whether we could have the sole external effect of raise of a weight. If successful definition over we do not have to proceed we have identified it is work we have defined the direction we have defined the quantity. Now in step 2 what we do is we remove system A we let system B go from its initial state B1 to B2 by providing it the same earlier interaction I except that instead of A we try to set up a system C2 such that the sole external effect as earlier would be the raise of a weight may be M2 by a height h2 in a gravitational field g and again C2 has to be a primitive system and C2 executes only cyclic processes. Notice the similarity with the previous page C1 was a primitive device C1 was only cyclic processes C2 is a primitive system or primitive device to use the same word cyclic processes only and now we say if C2 is possible C1 is not possible C2 is possible perhaps then we say number 1 I is work 2 we say B does work on A and 3 WAB is minus M2 g h2 WBA work done by B on A is M2 plus M2 g h2 mind you either here as well as on the previous case A does work on B and B does work on A is a matter of convention that is the way we define and again there is a sign convention involved when A does work on B work done by A is positive work done by B is negative and when B does work on A work done by A is negative work done by B is positive if finally if this is step 2 which we will execute only if we are unsuccessful in inventing C1 for step 1 if C2 is not possible go to C2 is also not possible because we come to C2 only when C1 is not possible. So step 3 is now neither C1 nor C2 in spite of our best effort then we say that the interaction I is not fully a work interact it may be totally non-work or it may be partly work partly something else. Now what we do here is there is a sub definition it is may not be possible in case of C1 to reduce it raise completely but the question that comes to your mind it should come to your mind is why am I looking at system A first I might first look at system B first see whether C2 is possible and then come and see whether C1 is possible it can be shown that in either case the final result will be the same it is an involuted proof but proof exists that it does not matter which one you take first. Now based on this as a consequence we find that may be done when two systems are involved there will be a donor system and there must be a receptor system if there is no receptor like free expansion you have a piston but on the other side there is no pressure perfect vacuum there is no system there no material there to receive the work so in that case work will not be done if there is no receptor there is only a donor there is no work interaction if there is no donor only a receptor also there is no working. Now using this definition this is just an illustration of how to perfectly write an operational definition of work otherwise what you have understood from your text that the sole external effect should be nothing but the raise of a weight is the correct definition but all that we have done now is put it on a format of operational definition so there is absolutely no scope for confusion and we have even quantified it in the textbook definition how much is the amount of work is never quantified in this particular case the amount of work is quantified is also emphasized that two systems must be involved A and B we started with that there are no two systems involved there is no question of work because if there is no receptor system there is no question of work being done. So based on this we find that the work interaction in many cases is made up of a number of components of work interactions for example these components could be pdv so called expansion work it could be for a liquid tau d theta sterrer work or could be a spring which is wound and unbound as in case of our old wrist watches it could be electrical work edq it could be surface tension it could be you can think of something for example extended string as in case of the Hooke's experiment minus fdl you will notice that there are some pluses there are some minuses that comes out of our definition of something plus something minus it all depends on the force and relative displacement directions. So things to notice here that one or more of work may be involved in case of a very simple situation it will be a gas expanding it will be only the pdv mode case of your cell phone battery charging or discharging it is only the edq mode stirring a liquid using a spoon or a sterrer it will may only be the tau d theta mode you have a winding clock that is only the tau d theta mode there is no other way you can do work. One thing you should notice is that some modes are two way some modes are one way this is important for example if you take a gas in a cylinder piston arrangement the gas can expand provide work interaction to the surrounding whatever is on the other side of the piston provided it is providing the piston with the requisite balance force so that it can receive the work. The surrounding can also go to a slightly higher pressure and compress the gas so work done by our system could be positive during expansion could be negative during contraption but what about the sterrer? I have a liquid or a fluid in equilibrium I put a sterrer and I stir it I can do work on the system but I take a system in equilibrium quietly put my sterrer in it and then tell the system you do work on the sterrer system is not for the system fluid system it is not possible to do such a thing this is a question this is an illustration of a one way work mode do not be under the impression that only stirring or a friction of something like that is a one way mode work. For example you take your mobile phones the cells are chargeable and dischargeable while charging work is being done on the system while discharging the system our mobile battery does work on whatever is the circuitry surrounding so that is a two way mode of work but you take the typical non-rechargeable batteries which go into our torch lights and things like that they are non-rechargeable so they can do work on the surrounding but there is no way the structure internal structure is set that we cannot charge them so we cannot do work on them so their electrical work mode is a one way mode of work which one but that is a store of energy but I cannot by electrical connection I cannot inject that energy by doing work on it I cannot charge it even if I put a electrical connection on to it there is no way current will go and it will get charged but as per the that we showed it by Tharmada and that we show work this charge can also be used for raising a weight which are the discharging of the battery can be used for raising yes but then the battery is incapable of absorbing it you put a potential no current will flow or if you are if at all it flows it will flow as a resistor so as a system it is incapable of getting charged I am not talking of the mobile battery I am talking of the standard torch batteries so just every day or no we know or whatever so just to illustrate that there are many situations where it is two way and it is one way this is important because soon we will come to a situation where we will find that the two way work modes are important now after this there are some simple things which all of you are familiar and that is evaluation of the evaluation of work involves two steps step one identify modes of work for each mode evaluate or try to evaluate integral x dy with a plus or minus sign as appropriate notice that for two x must be known as a function of y or something similar to some parameter functional relationship should exist and that means the process at least the x y part of the process should be quasi static because only if the process at least on the x y plane is quasi static we will have for every value of y a defined value of x because the function will be completely known the complete path is known and we will be able to evaluate it by integration if it is not quasi static that does not mean that there is no work interaction it only means that we are unable to evaluate the work by the process of integration for a non quasi static process the work evaluation may still be possible but that will be in an indirect way using the first law of thermodynamics now the standard illustrations that work is a path function etc that is common there is nothing special about it I would now come to the item 7 and 8 of this work interaction that is the complexity of systems I have said just now that this some modes are two way is an important things because let us say n to w is the number of two way work modes of a system then we say that if the number of two way work modes is one then we define it as a define the system as a simple system that is our definition of a simple system a simple system is a system which has only one two way mode of work there may be other modes they could be one way for example you take a simple gas we know that the only two way mode of work is expansion compression so the PDV expansion compression mode I can do stirrer work I can do electrical work by having an electrical discharge in it but those are only one way work modes so a gas or a liquid which is not an electrolyte is not magnetic simple gas or liquid fluid is a simple thermodynamic system because it has only one two way mode of work if we have a simple system then it can be further classified that if that one mode of work is expansion compression we call it a simple compressible system if that one mode of work one single two way mode of work is electrical charging discharging like in your mobile batteries you cannot compress or expand them they are solid but you can charge them you can discharge them so electrical charging discharging is the only way the only two way mode of work so this will be a simple electrical system and this way you can have a simple magnetic system and a simple extensible system for example you take a simple spring mechanical spring the only two way mode of work is compress it and allow it to expand or railway buffers they are of that kind to some extent they also have dampers in between but otherwise they are two way modes compress it can expand so those will be simple elastic systems if number of two way work modes is greater than one such systems are known as complex systems for example if you have in a cylinder piston arrangement a fluid which is electrolyte you can expand it compress it that will be one two way mode of work you will be also able to charge it discharge it that will be another two way mode of work so such a system is a complex system so electrically charged gases or dielectric fluids these are complex systems and that is why the science of magneto hydrodynamics where you have electrical mechanisms you have magnetic mechanisms and you have fluid mechanisms all three so magneto gas dynamics is a really complex depending on whether the spring is able to do only compression expansion but if it is also able to twist in the other way it will be a complex but if you have a simple helical spring just two hooks on either side expand compress that will be a simple elastic system which one In a cylinder piston arrangement you can create a complex system yes or you can say my system has a cylinder piston with a fluid in it and it also has attached with it a rechargeable cell the whole two system together with the two parts together yes you can create complex but shock absorber is actually it is a complicated system because not only do you have a spring but you also have a gas volume inside to act as a dampener so but the whole system is such that you cannot if you keep them separate then yes it is complex but because they are internally connected it becomes a simple system because externally you can only do compression expansion you can independently tap the gas separately but together that is like him I have a cylinder piston by the side of it I have a spring I said the total system is this then naturally I have a complex system not necessarily here we are looking at a combination but a electrolyte fluid it is not a combination it is inherently a complex system what is the system there the plasma plasma is it definitely a complex system because there are you can do electrical work on it you can have magnetic field and do magnetic work on it and it is in some sort of a fluid you can confine it and expand and compress it so there are in principle three two way modes of work so it is a complex system that is what I said magneto gas dynamics is a study of really involved complex now the question is are there systems with can you give me an illustration of a system with no two way mode of work non compressible fluid elongation of ductile material elongation of ductile material plastic material ductile my first question is will there be systems in which there is no two way mode of work answer is yes according to him the answer is yes you are giving illustration but the answer is yes and yes there are there are enough systems which can be inherently with zero two way modes of work or I can take a simple system and constrain it in such a way that I cannot do that two way mode of work in which case I will have a zero mode of work for example you take the cylinder piston say I can expand the gas or compress the gas but if I using m seal or nails I fix the piston in one place constraining it to be a constant volume system it becomes a zero two way mode of work system because it is constrained in such a way that although inherently it is possible to have a two way mode of work compression expansion I have prevented that from happen but there are some systems for example you take his illustration of an incompressible liquid it is not constrained but you cannot compress it because it is incompressible it is neither not an electrolyte so you cannot charge or discharge it so there is no two way mode of work even you know something which all of you have our household clinical thermometer is it a system of this type you cannot twist or untwist it you cannot charge or discharge it you cannot compress or expand it it is a solid piece it is like an incompressible liquid which is so that is a system which is a system with zero two way mode of work such systems we will call rudimentary systems the importance of this will be seen although I am defining it just after the work interactions the importance of these will be seen after the first law when we try to answer the question how many properties are really needed to define the state of a system that will be our state principle 2 or state postulate 2 state postulate 1 we have already seen that the state of a thermodynamic system can be defined using only primitive variables but it does not say how many of those variables how many of those will depend on the complexity of our system but we will come to that after the first law of thermodynamics as a consequence of the first law of thermodynamics and we will revisit that at the end of the second law of thermodynamics because they are not a very robust but an illustration of why that number comes up will be made available in fact state postulate 1 is actually a primitive it has no proof but state postulate 2 in a complicated way can be proven so it is not a primitive using first law and second law state postulate 2 can be derived we will look at the way it is derived but we will not go through the complete derivation because it is a very involved derivation.