 that work is also defined in other branches and a general idea is it has something to do with force into displacement. So, if you have a force applied on to a particle on to a body and if the point of application of the force gets displaced or moves and in the direction in which or at least a component of that displacement is in the direction in which force is applied then we say that work is done. And you can do work from the mechanics point of view by lifting a weight in a gravitational field overcome a force of friction moving a charge in an electric field and many other ways. In thermodynamics we do take work as a primitive because it is defined in other branches of physics. However, since thermodynamics does not concern itself only with work it concerns itself also with the non work interaction that is the heat interaction type. We do not want to create any confusion about the idea of work. So, we will soon define or redefine and come up with a thermodynamic definition, but before that let us take some illustration. So, we know what we are confronting with let us take some situation. Let us say that we have a rod of some length L we are holding it and we are pulling it consider the rod as the system it is under a force F. So, the rod itself is whatever it is pulling the rod is pulling back by a force F the force F we will call the tension in the rod you may even let us keep it with F. And let us say that the person who is applying this force applies it in such a way that the rod gets extended by a distance d l then we say that the small amount of work done d w is F into d and we say that look from the rod point of view F is towards negative x d l is towards positive x. So, may be a correct way is to write d w is minus F d l that is one way of representing this small work interaction. Another way is you can consider a system containing a fluid and let us say we have a stirrer we say this is the fluid thick fluid we put a stirrer. And we try to rotate it by applying a torque tau and say under the influence of tau the stirrer moves by a displacement d theta. So, if this is the way suppose I want to move it clockwise then the torque which is imposed on the stirrer will be in the anticlockwise direction the fluid being discussed tries to enforce a torque. So, that the stirrer is restricted. So, again here we will find this is the work done by our system which is the fluid we may call it the stirrer work. We could have say nowadays many of our gadgets mobile phones cameras have an electrolytic cell say a battery a positive terminal a negative terminal with some electrical potential e across them. And let us say that it is connected to whatever is the gadget and a small charge d q passes can write it if you want small current I current I for a small amount of time d t. Then if we take the battery you can say that the work done by the battery is e d q or if you want you can write it as e i d t. And finally, I cannot complete this without our standard illustration suppose I have a suppose I have a fluid gas or vapor enclosed in a cylinder system arrangement. And let us say that the fluid imposes a pressure p on the piston this area is a then naturally the force on the piston is p into a and there will have to be an opposing force f equals p a to keep the piston in place. But suppose I relax the piston slightly. So, that there is a displace when d x of the piston under the influence of this pressure in that case I can write d w is p into a into d x. But since a into d x is the change in volume of the fluid we write this as p into d. So, now I have here 4 illustrations and you will notice that our 4 illustrations end up with the following thing d w turns out to be of the kind x d y with a plus or minus sign here. A few things to note first we note that there is a sign convention involved sometimes we wrote a positive sign sometimes we wrote a negative sign. Then we should also notice that some work interactions are one way some work interactions are two way for example, take this illustration which is on this slide fluid pressurizing a piston. I can relax the piston let it move slightly out may be by slightly reducing the force f. So, that small movement is possible then my d x will be positive d v will be positive and d w will be positive. But I can also slightly increase this to compress it inside in which case my d x will be negative d v will be negative and d w will be negative. It is a two way work mode and now let me go back look at this battery it can be if it is a typically rechargeable battery which we have in our mobile phones it can be discharged making the mobile phone ring and allowing us to communicate. But then we get discharged we connected to a charger and the current is made to flow in the other direction and we charge the battery. In one case the i is in positive direction giving you a positive d w when we use the mobile phone during charging i is in the other direction giving you essentially a negative i giving you a minus sign on the d w it is a negative quantity formula remains the same it is the sign of i or sign of d q which changes. So, this also is a two way mode of work what about this I try to stir the fluid one way the torque is opposing it I try to move the fluid in the other way the torque still opposite. So, if d theta is positive torque is in one direction if d theta is negative torque is in the other direction in any case this work interaction will be negative I cannot put the stirrer in the fluid and say fluid you stir the stirrer that is just not possible this is a one way mode of work whereas, this is a two way mode of work and in a similar fashion this expansion of a fluid is a two way mode of work this is important because later on when it comes to a state principle second law this one way and two way modes of work will help us in understanding the third one which at least a few should have noticed by now is often particularly when we have a two way mode of work x is an intensive property and y is an extensive property take for example, this is a two way mode of work p d v. So, x is p it is an intensive property I consider part of this pressure here pressure here is the same. So, it is an intensive property v on the other hand is an extensive property partition into two volume of one part plus volume of the other part is the volume of the whole system. Similarly, I will leave it to you as an exercise to check that in the previous case that of a battery the potential for the voltage of the cell is an intensive property does it depend on the size I can make a small leclanche cell it will give me 2.2 volts I can make a big leclanche cell it will still give me 2.2, but the charge that it can hold the current it can provide will depend on the size. So, the potential difference across the cell terminals is an intensive variable the charge that it can provide for the current that it can provide is an extensive variable when it comes to this one way mode you will notice that neither tau nor d theta or theta are properties of the fluid properties of the fluid will be pressure volume temperature etcetera. You can go back one more step what about here just confirm to yourself that f is an intensive property and l is an extensive property if you take half of it by equilibrium the force would still be f, but the extension of half the rod will be d l by 2. So, f is intensive l is extensive this is also something to be noted. Now, we have to generalize this and we have to generalize this and formalize it and for that we come to the thermodynamic definition. Most of us know from text books that the thermodynamic definition of work is an interaction which can be completely reduced to the raise of a weight in a gravitational field and nothing else, but that that is the text book definition. Although that definition is we will provide a neat operational definition so that we do not fall into any trap. The basic idea is work interaction is something which can be completely reduced to raise of a weight that means weight is nothing but mass in a gravitational field and it is agreed that if I lift something a mass in a gravitational field I am doing work. So, anything which is completely reducible to that must be a work interaction. Now, by completely what do we mean we can use any fully defined device we can idealize for example, we can use friction less pulleys we can use 100 percent efficient electric motors etcetera. That means we can neglect mechanical friction we can neglect mechanical friction we can neglect electrical friction that is ohmic heating and such stuff but no black box allowed. That means you cannot say that look I have a box here in which you do this and this will come out do not ask me what is inside this that is not allowed. You must define your mechanism fully and you can set up simple mechanisms by which any of the first four interactions which we saw can be shown to be equivalent to raise of a weight. But now we will go to the thermodynamic definition we will set up a procedure we will now set up an operational definition finally, we will become our illustration of thermodynamic definition of we set out to answer this question. We say that let us have two systems system a and system b. Let system a execute a process taking it from state a 1 to state a 2 it may be quasi-static it may be non quasi-static does not matter. While doing this interaction with b let the state of b go from b 1 to b 2 let the interaction be I now our questions would be the operational definition should be able to answer the following questions first question is is I work I is work what is its direction what is its magnitude. These are the questions we seek to answer by setting up the operational definition of work. We proceed as follows we remember that the basic idea of work interaction in thermodynamics is something which can be fully converted by defined mechanisms to nothing but the raise of a weight. So, what we do is we take our system a let it go from a 1 to a 2 but instead of b we try to have the same interaction with some contraption which we want to set up that is c 1 this is fully defined contraption that does not change its state that means it executes cycles if at all and all that it does is raise a weight mass say m 1 in a gravitational field I will just say g and raise it not lower it by some height h 1. We try to set up c 1 which is a fully defined contraption that does not change its state that means if at all it executes a process it executes cycles and which does nothing but raise a mass m 1 by a height h 1 in a gravitational field or against a gravitational field g. Now when we try to set up c 1 it is possible or it may not be possible if c 1 is possible to be set up then we come to one conclusion of this definition we say 1 we conclude that I is work then the second thing we say that a does work on this is our sign convention which we formalize as we say work done by a is plus m 1 g h 1 plus m 1 g h 1 plus m 1 g h 1 plus m 1 and work done by b is minus m 1 g h 1 and this is only if c 1 is possible and if c 1 is not possible we will say go to 2 and after this we say end of definition we do not have to go to step 2 because we have already decided that I is work. Now it is possible that we cannot set up c 1 in which case we will try to set up c 2 in a similar fashion we come to step 2 and here we say that look I have this system b which went from state b 1 to b 2 executing our process by having an interaction I with a but I would like to replace this a by c 2 c 2 again a fully defined contraption as in case of c 1 no change in state I try to set up c 2 whose result should only be raise a mass may be m 2 by a height h 2 against a gravitational field g. So, we try to set up or discover or invent c 2 and then we say if c 2 is possible then we come to the conclusion that again we say I is work then we say in this case b does work on a third quantification work done by b is equal to c 1 by b is equal to m 2 g h 2 and work done by a is minus m 1 sorry m 2 g and that is the end of the definition but the definition is not that way complete if c 2 is also not possible then we will go to step. So, we have made two attempts one to set up c 1 from the point of view of system a a when we try to set up c 1 a still believes that it is interacting with b because it is executing the same process having the same interaction but quietly we have tried to replace b by this contraption c 1 which hopefully can raise a weight if that is not possible then we tried the other way round we said keep a away try to fool b by thinking that it has the same interaction with a executes the same process but a is quietly replaced by c 2 which job is doing nothing but raise a weight in a gravitational field if neither of c 1 or c 2 is possible then we go to step 3 we come to this step is neither c 1 nor c 2 can be set up in that case we say we come to the conclusion the interaction is not possible fully it may be totally a non-work interaction or it may be a combination of some work interaction and some non-work interaction now I will leave it as an exercise to you to show that all four illustrations interactions using our operational definition now we come to a stage where we have defined what is work interaction and now we have to evaluate the work interaction brings us to evaluation of work we note the following there are modes of work interaction they simultaneously so for example the total work may be made up of expansion work plus may be electric work plus may be stirrer work plus depending on the complexity of the system for example you could have a system a fluid electrolytic fluid so it may be doing some e d q type of work simultaneously it could be expanding against a pressure this could be a w electrical there could be a w expansion the p d v type of work there could be a stirrer and the work interaction for the stirrer could be all these things are possible I need paper so we will have to obtain the work interaction by obtaining a sum over various modes or components of work now take a component let us say expansion work we know expansion work is p d v so this is for a process element where a small change in volume takes place but say for a process we will tend to write we can write this but can we evaluate when can we evaluate the answer is if p happens to be a proper function of v throughout the process then we can evaluate it we can evaluate this integral when p is a mathematical function of v that means at least on the p v plane this is a quasi static process if the process is non quasi static we will not be able to evaluate it if for example we take continue we continue with the expansion work suppose I have a say initial pressure is this p 1 initial volume is v 1 let us say final pressure is p 2 final volume is v 2 this is state 1 this is state 2 if the process is quasi static then may be we will have some process like this and then we will be able to evaluate the integral and the integral will be so quasi static process then we have p as a function of v integral p d v is evaluated but if it is a non quasi static process all that I know is I start from here I go to 2 and I do not know what is the path in between non quasi static process w expansion in this particular case is or can be evaluated not be evaluated some of these things will be clear today afternoon when we start solving some exercises on the work interaction so now you notice that at least for the expansion process and instead of p v you could have e q for electrical process and tau theta for the stirring process though for a quasi static process the work done is area under some appropriate curve on an appropriate projection of the state space a different quasi static process would mean a different area so it is very clear that the work depends on the path we do not have to derive anything about it so in thermodynamics we say that work is a path function and now we come to the next thing how did I get rid of that now some definition we define the complexity of a system we have seen that some work modes are one way typical illustration is stirring for a fluid or you take an electrical component which is purely a resistor put a potential across it that is what is known as the ohmic heating heating is unfortunate word there but that is a work interaction which is one way so we consider a system and we say that the number of two way work modes this we count and we say number of two way work modes let me say this is n tu w or n two way now if you take say a simple gas in a cylinder then the only two way work mode it has is expansion and compression and such systems we will call system as a simple for example a gas in a cylinder this is a simple system and the only two way work mode is that of expansion and compression so such a system is sometimes called a simple compressible system you take the rod which we took as an illustration for a simple spring so we say an elastic rod or a spring extension and compression is a the only work mode it has so we can say it is a simple elastic system similarly you have your mobile phones I think all of them are switched off open the back cover take out the battery what type of a system does it have I cannot expand it compress it but I can charge it and discharge it so the only two way work mode that it has is that of electrical charging and electrical discharging so we can say the cell of a mobile phone is a simple electric and in a similar way you can perhaps define a simple magnetic system and many other type of simple systems greater than one we call such systems complex for example an electrolyte which can expand and contract can also be charged and discharge is a complex system there are two numbers of two way work modes charging discharging and compression expansion similarly a spring which is made up of magnetizable and demagnetizable material will be a complex system you can magnetize it and demagnetize it you can compress it and you can expand it so it is a combination of elastic system as well as a magnetic system I inadvertently use the word substance and this is what is quite often used by many textbooks but in thermodynamics we do not really have any special meaning for substance we should always be using the word system because it is always our system you may say a system containing a gas a system containing a fluid a system containing a magnetic material a system containing a dielectric material but it is always the property of a system that we will be talking about we close this discussion by noting that it is possible to have a system such that there is no two way work mode associated with it illustration a system which all of us know the mercury in glass thermometer all of us even kids have seen this we measure temperature typically of us humans how many two way work modes I cannot extend it I cannot compress it I cannot twist it is no two way work mode involved we have used for such systems in thermodynamics let us call such systems as rudimentary systems we can create rudimentary systems for example we take a system containing a gas in a cylinder piston arrangement if we allow the piston free to move then well the expansion work is possible and it will be a simple system but we lock the piston will always be 0 because it is constrained to be 0 we are not allowing the volume to change then this becomes restricted to a rudimentary system and by this method a system can be rudimentary system can be created even from simple systems now that brings us to the end of the basic idea of work interaction defined then we have the operational definition then we looked at various modes of work we looked at the evaluation of work and then finally we looked at complexity of systems depending on the number of two way work modes we will come back to this this is useful at the end of first law and it is particularly useful for when we come to 0 thank you.