 The first job of thermodynamics is to inherit the word work, first thing we know that work interaction is a primitive because students have learned mechanical work, students have learned PDV expansion work, students have learned that work is done when you compress a spring, work is done when you wind up something, work is done when you charge a battery and nowadays earlier battery charging was rare, but nowadays everybody charges the battery of the mobile phone or the camera or whatever you have laptop, so charging, discharging of a battery, pumping water, compressing air, all these things are, they require work that is that vague idea of a work interaction exists, the general work interaction exists. But let us first look at some primitive work interactions and then we will try to combine them into a common thermodynamic mode of work, thermodynamic definition of work. See work interaction to begin with is a primitive, we have come across work interaction in various different ways. For example, take a spring, if I want to keep the spring and if I want to hold it, then I must apply a force F to keep it extended of a length L, let us say this L is greater than its free length L0, just for illustration, in which case I must apply a force F and if I am holding it here, the spring will apply a force F onto me, of course I must also apply a force, but I am showing it from the spring point of it, the spring is pulling whatever is holding it in and then if I am strong enough, I will move it by a distance dL, what is the work done by the spring? F into dL, in which direction? Is it minus F dL or is it plus F dL? Minus F dL, so we say here dW of the spring is minus F dL, another illustration take a cylinder piston arrangement, there is some fluid at a pressure P, if the area of the piston is A, it must be Pascal's law uniform pressure, so a force of T into A will be applied on the piston, so to prevent the piston from flying away, I must have some equivalent force on the other side, let us say that I am holding it with an equivalent force and then I relax a bit and let this change by dx, the piston, let the piston move by dx, what is the dW here? Force is PdA, sorry P into A, moment is dx and A dx is the change in volume, so this we write as PdV, let me take one more illustration, we have a cup, there is some reasonably thick fluid in it and I put a stirrer, I put a stirrer, nothing happens, there is no force on the stirrer and the liquid is in equilibrium, it is not twisted turning everything uniform, as in this, I have put a stirrer, nothing, but I try to rotate the stirrer, as I try to rotate it because of viscosity I find that I have to overcome a torque, so if I try to rotate it by an amount d theta, I have to overcome a torque which is tau, which will try to oppose it, fluid friction and what will be the work done by the fluid on the stirrer, minus tau d theta and my last example, it is say the battery of a rechargeable battery of a mobile or a laptop, let us say this is the positive terminal, this is the negative terminal, I have charged it, it is there in the mobile and my mobile of course it is silent, but it will work, as it works some current I flows for a time dt, if it rings and of course the potential difference here is e from negative to the positive, what is the work done by this system of ours, dw, work done by the battery is e into I dt, which is e into dq, where dq is the amount of charge that it has given up, of course charge is conserved, so a charge at a higher potential is given up, equivalent charge of a lower potential is brought back, because just like mass is conserved, charge is also conserved, so circuit current I has to be completed, if I dt goes like that, same I dt has to come back, so notice these four interactions, there are many such, here there is a minus F dL, here there is a P dV, there is a minus tau d theta, there is an e dq, notice that generally the work interaction is of the type x dy, I will put plus or minus, because sometimes we notice a negative sign, we put a conscious negative sign, you say minus F dL minus tau d theta, we were not keen at all on putting a negative sign when it came to P dV or e dq, so well there was a sign convention involved, we will come to that, but what about x and y, look at the three things, F and L where properties of the spring, yes, state of a spring is determined by what length it is and what force it is applying, similarly volume and pressure are properties of our system, the gas here, P and q are properties of that cell, potential that it provides and the charge that it can hold, what about tau and theta, are they properties of the fluid, if I just put a stirrer there nothing happens to it, I cannot say that this fluid, if I put a stirrer will immediately put a torque of 3 Newton meter, only when I try to stir it, if it is in equilibrium no torque, what torque are you talking about, I cannot provide any torque when I am feeling it, so you will notice that of this x dy, sometimes x and y are properties, sometimes they are not, that is the first thing. Now when they are properties, notice what type of property x is and what type of property y is, look at the intensive-extensive combination, look at the property F, P and on the second page E and look at the property q here and look at the property L and V here, what type of properties are those, F and P, are they extensive properties or intensive properties, if I take half this system, what happens to P, it is not P equals P1 plus P2, it is P equals P1 equals P2, so pressure here is an intensive property, volume extensive property because if I partition it, V1 plus V2 is V, for a spring, if I cut the spring in half, simple mechanical equilibrium tells me that the force must be the same, right, so F is an intensive property, but if I make the spring in half, the length is L1 plus L2 is L or DL1 plus DL2 is DL, so F is intensive, L is extensive, here P is intensive, V is extensive, tau and theta no properties at all, so no question of extensive-intensive, what about E and Q, E is intensive, same type of cell if I make it bigger or smaller, it provides the same potential, your normal dry cell whether it is triple A size or a big D size, it provides 1.5 volts, right, but what about Q? How? Let us finish, you agree E is intensive and you agree that Q is extensive, if you want more charge, you take a bigger cell, you cut the cell into 2 or instead of 2 put 1 cell, you have a smaller amount of charge, how? Now, coming to the stirrer, how do you say tau is a property? No, viscosity is not a thermodynamic property of a system, if a system is in equilibrium, you cannot measure its viscosity, so the characteristics here is X and Y, sometimes properties, sometimes not, properties both, sometimes not both, if you look at all work interactions, you will find this characteristic, why do not ask me, that is a general characteristic of work interaction in all branches of physics, it is of the type X, D, Y, where X and Y are either both properties or both non-properties, this is not emphasized in other branches of physics, but in thermodynamics we take note of this because that is important and where X and Y are properties, X is intensive and Y is extensive, okay, that is one thing you notice, this is one, this is one, another thing you notice is the following, I have this spring which I am holding, if I extend it, my DL is positive, my minus FDL will be a negative number, but I can slowly relax it, in which case my DL will be negative and minus FDL will be a positive number, so this way I can do work on the system, I can do get work done by the system, the work transfer can be from the system to me or from me to the system, similarly I can allow the gas to expand by relaxing myself a bit, extracting work from the gas or I can be more stronger and I can put work into the gas, so these two are properties and I can do work either way, similarly you will notice here charging, discharging of a cell, we know work can be done either way, okay, but what about tau D theta, I can put a stirrer, I can stir the liquid, okay, but as I stir it I am making it non-equilibrium, initially it was in equilibrium, but suppose it is in equilibrium and I put a stirrer and tell the liquid, I stir the stirrer, will it stir it? No, so from its initial state of equilibrium, the process of stirring is not a two way mode of work, I can do work on the system, but I cannot ever expect the system to do work on me, that is another important thing, some modes of work, the sign convention there are different modes of work, four of them we have seen and now let us go back and write the mode of work, this is extension of a spring, this is expansion of a gas, of course by extension I also mean compression where appropriate, expansion also means compression, here it is charging or discharging a cell, this is stirring a fluid, these are the different modes of work and you will notice again something to be noticed about this work interaction which is a primitive for us is that when x and y are both properties and x is intensive and y is extensive, this is a two way mode of work, it is so, it is a one way mode of work, this is important and this is many of these ideas, one way mode, two way mode are at the heart of later developments in thermodynamics and make it a point to emphasize it as two way and one way and see to it that you do not use the word reversible here, sometimes some people feel that a two way mode can be said to be a reversible mode of work, you are welcome to do that but I personally feel that the word reversible and the idea of reversibility is a very special idea in thermodynamics and we should not vitiate that by using it at places where it is not directly applicable, so this is a two way mode of work and that is a one way mode of work, let us leave it like that for the time being, two way means system can do on the surroundings, surroundings can do on the system and because there is a two way mode of work, the sign can change and we have a sign convention depending on the relative directions of x and y, now all these things are accepted by thermodynamics as modes of work but there is a problem, for example, in mechanics work is simply force into displacement, if the point of application, if you see the definition of work, if the point of application of the force executes a displacement then f dot dx is the work done, so the free fall of a projectile, projectile falls down by height h under the influence of gravity force mg, let us say mg h is work done by gravity on that free falling object, mechanics does not ask who is the recipient of the work, mechanics does not ask system A system B, particle it is system A, there is the energy interaction which is the other system which is receiving that work, that mechanics does not ask but in thermodynamics we will ask always for work interaction which is a system A which is a system B in which the work interaction is taking place, because our definition of work interaction is restrictive, it must be an energy transfer between two systems, two systems must be involved, so now that brings us to the thermodynamic definition of work, if you look up any good book and you know all the good books on thermodynamics, you will realize that thermodynamics defines work as something in general can be reduced to the rays of a weight that is the definition agreed to by everyone and they say that it should be completely reducible to the rays of a weight that means mass in a gravitational field and the contraptions which you use to reduce it completely to the rays of a weight should be definable, you should not have any black boxes but you can idealize for example you can consider frictionless pulleys because that is an idealization, if you invest enough you can reduce friction to a large extent, again Galileo thought about a frictionless surface we know no surface is frictionless but this is a definition of what is work, if it is reducible using ideal mechanisms, ideal motors, inextensible strings to rays of a weight then it is work, as a verbal definition it is alright but we need an operational definition and what we will now look at is a good operational definition of work and for that the question first we will formulate the question, let us say that we have a system A and a system B and system A interacts with system B and let me say that the interaction is I just it is an interaction, it is an energy interaction and let us say that the system A goes from state A1 to state A2, let me represent that as the process executed by A, let system B go from state B1 to state B2, let that be the representation of the process executed by system B, now I need an operational definition of work interaction which will answer the following questions, the questions are these, is I, is the interaction I am looking at a work interaction, that is the first question it has to answer or one of the questions it has to answer and second question if I is work then what is its magnitude and what is direction and we want an operational definition that means we must now specify a procedure by executing which we will come to the answers of this question, the operational definition goes in three steps, remember our work interaction says that an interaction is work if it is reducible completely to the rays of a weight, we will essentially use that but formalize it properly, we will say that step one try to set up a system C1 such that I will now show you that such that in, we take system A, we make it execute the same process A1 and A2, so that it behaves it is interacting with a system B and the interaction is I, so system A does not see any difference but we replace B by a system C1, C1 is a system which is completely defined by us, it may contain leak proof, fixed endless pistons, undamped coils, frictionless pulleys, levers, inextensible strings, perfectly chargeable, dischargeable cells, 100% efficient transformers, motors which we know that if we have zero core loss that means superconducting copper and super permeable core, we can think of approaching that limit, C1 is a system which executes only cycles that means including that rudimentary cycle where no change of state takes place and all it does is pull up a mass say M1 by a height h1 in a gravitational field G, it must be up, not down, so this I should show in the end up. Now if we can set up C1, then what does it mean? We have been able to invent or discover a contraption C1 which does not undergo any change, it executes cyclic processes, if at all it executes any process which does nothing but raise a mass M1 in a gravitational field G. So I must be work, then the conclusion is I is work, now we come to the quantification and sign convention, we will use the sign convention say work is done by A on B, this is what we will say and then we will say work done by A on B is plus M1 h1 G and work done by B on A is minus M1 h1 and again let it be clear, for work two systems must be involved, it must be an interaction, the balance of interaction like a two way book keeping, double entry book keeping must be there and interaction cannot just take place with A with a loose end on the other side or imbalance on the other side, if there is an interaction I from A to B, B also should say yes there is an interaction I from A to B, so whatever goes out of A must cross the boundary and go into B and we are trying to define whether that is work or not. Now here there is an if, it is possible that we cannot set up C1, then what? Then the step two, C1 cannot set up, setting up C2, such that, now we turn it around, we say that look, we replaced, for we tried to replace B by C1, we failed, now let us see whether we can try to replace A by C2, so here we keep B in its original position, let it execute the process as earlier B1 to B2, it must be receiving an interaction I, so B does not see any change, but A I am replacing by a contraption C2 which executes only cyclic process or no process at all the last illustration of the cyclic process and all that it tries to do for all that it does is raise a mass M2 by a height H2 in a gravitational region, can we set up C2? Again possibility yes or no, if remember if we have been able to set up C1 it is out, definition is over, we do not come to this step, C2 can set up, then first conclusion I is work, same conclusion as step A, this I should call step two, then we say work is done by B on A, again remember this H2 has to be upward, you cannot say H2 is minus 20 centimeters, no it has to be against the direction of gravity, raise of a weight, do not be under the impression that lowering of a weight is negative work, no it has to be raise of a weight one way or the other, work is done by B on A and WAB is minus M2 H2 G and WBA plus M2 H2, very similar to what we had earlier, here it was positive, here it was negative, here it is negative, here it is positive, because the direction is the other way round and mind you this minus and this plus as well as in the earlier case, this plus and this minus is a matter of convention, here I have assumed a convention which is common in mechanical engineering that work done by a system is considered positive, work done on a system is considered negative, but chemist and chemical engineers use the other way that is work done by a system is negative, work done on a system is positive, but that is a matter of convention all that will happen is instead of delta E is Q minus W, it will become delta E is Q plus W and that plus will become minus in many other derivations in thermodynamics, but finally when you derive in terms of properties for example du equals du minus pdv will remain as minus pdv, because for us dw is plus pdv for them dw is minus pdv when a gas expands, so only when it comes to W there will be a change of positive or negative sign, when W is replaced by something else the equations are identical. Now it is possible that you can set up neither C1 nor C2, then what? Then you go to step 3, neither C1 nor C2 can be set up, what is the conclusion? I is not, I should put completely work, either it is totally non-work or it is a mixture of work and something else, I is not purely a work interaction, it is some other interaction totally non-work or a mixture of work and non-work interaction. Unfortunately this operational definition you will hardly ever find explained in this proper way in a book, have you come across it? I have been hunting because people have hinted at it, people have put it in verbose, they have even said that look you should look at it both ways because the weight must be raised, it should not be lowered, no it is not like charging or discharging, either one way you should raise a weight or the other way you should raise a weight, but you should raise a weight. It would not be work, in fact that is how we will define heat later when we come to first law. If C1 works on cycle it may deliver work, due to this work the weight may be lifted. You are coming to C1 it executes a cycle and all it does is raise this weight by M1, it does not do anything else, it is not allowed to have any other interaction. The only interaction of C is raise of this weight and having this interaction I, it cannot transfer work or transfer heat to any other interaction, no it is only effect of C1 is raise of a weight and of course having that interaction I. Similarly, the only effect of C2 is having that interaction I with B and raise of a weight, it is not allowed to do anything, no bypass, no side effects, no byproducts, only if you can do this it is work and you can show that for the, is it set up, is it possible to set up a cycle only by work interactions without any heat transfer? State is final state, how you go from initial to final that means the same thing as initial is left to you. Cycle does not say that it should only have work interaction, after coming through first law you will come to the conclusion that in a cycle work interaction should equal the heat interaction. So if you do not want a heat interaction that means the net work interaction in a cycle will be 0, that is all the conclusion. So with this we are up to operational illustration of the thermodynamic definition of work. Now after that the next two points evaluation of work and work is a path function that I think we do not have to discuss in any detail except that when it comes to evaluation of work we should remember that there are different modes of work and the system may be doing simultaneously work by different modes and hence the work interaction will have to be summed up. Let me come to evaluation of work a small part and then 7 and 8. Now when we say evaluation of work see a small work interaction the way I have illustrated we considered a gas being expanded or compressed simultaneously we or separately we considered a charging or discharging separately we considered stirring of a fluid. It is possible that I may have an electrolyte the gas above which can be expanded or compressed the electrolyte itself can be stirred or charged or discharged. So it is possible that a system may be doing expansion work simultaneously it must be doing it could be doing electrical work charging discharging plus it could be doing stirrer work. Stirrer work can only be done on the system we have seen it is a one way mode. So a work interaction is summed up over mode that is the first thing to know. Second thing is over a process DW which we can write as let us say pdv plus pdq minus tau d theta should be integrated right from the initial state to a final state 1 to 2, 1 to 2, 1 to 2. Now when is this integration possible? The integration is possible go into the mathematical mode. When is pdv evaluable? When p is an integrable that is in our simple case continuous function of v and that means there is a continuous line from 1 to 2 on the PV plane. That means this evaluation in a thermodynamics sense is integration possible only if the process is quasi-static. If the process is quasi-static you cannot do any of these integrations and you cannot evaluate the work by integration. You can compute it out using some other relations we know work enters the first law indirectly it enters the second law. So you can use that but as a integral over work modes over the process it is possible to evaluate it only for a quasi-static process not for a non quasi-static process that is the part of evaluation of work I wanted to emphasize and then we come to what is known as the complexities. Now a system may have n possible mode of work. Some of these will be two way some of these will be one way. Let me put n 2w as the number of two way of work of a system. If I take a simple gas put it in a cylinder piston arrangement it has only one two way mode of work expansion and compression but if that gas or that fluid is an electrolyte and I have electrodes connected into it I can either expand or compress it or I can charge and discharge it in which case I will have two distinct two way modes of work. I may put a stirrer but that does not change the two way modes of work because stirrer is a one way mode of work. This happens to be an important number in thermodynamics. First we will do some classification based on this and later on again we will come back to this when it comes to the state postulate or the state principle. n 2w is one our illustration is gas in a cylinder piston arrangement or a simple solid non fluid electrolyte as in over mobile battery. Simple one way mode of work you cannot do so simple only single two way mode of work. You can only charge and discharge it. You cannot twist and twist it it is too solid you cannot expand compress it it is again a solid one. We call this system a simple system just a definition. If it is greater than one that is two or more we call such a system a complex system greater than one we are right. For example again coming to an electrolyte which is a fluid system will be a complex system. I can charge discharge it I can expand compress it. You know you take a bubble consider the bubble with a skin as our thermodynamic system. Is it simple or is it complex? A bubble or even a droplet consider surface tension. I can the bubble can expand or compress PDV work either way it can do but a bubble can also stretch its skin sigma da that will be the work done by surface tension. And it can expand giving you positive sigma da it can contract giving you negative sigma da that is also a two way mode of work. In fact the measurement of surface tension is actually by measuring the force required to move a loop for a wire from the surface. So that is a purely fluid system but it is complex two way mode of work two way modes of work. Now let me ask you question can it be zero? Can you think of a system for which there is no two way mode of work? Think of an illustration. But I can always compress and expand it unless it is constrained in a solid box so that you cannot compress and expand it. Then the enclosed container is so rigid that its volume can never change. Because then it cannot you are constraining that system to be a N2W with zero type. But there is another simple system which all of us have used at least once in our life. Very common system. Thermometer, mercury in glass, no expansion, no contraption, no twisting, no charging, no discharging. You can do work on it by friction. And if you want to you know tell somebody or demonstrate to somebody that you are running fever all that you do is hold your hand, hold the thermometer in between and rub it. It will show you 100 degree Fahrenheit without any effort. But that is a one way mode of work. So such systems do exist or a system which is a simple system or a complex system can be constrained to become a N2W equals zero type of a system. Such a system we will call, they are useful for thermometer, we will call a rudimentary system. Now before we close today's discussion something about work interaction. We should remember that work interaction is energy in transit. We should never forget that. And that two systems must be involved. There must be a donor system, there must be a recipient system. And work done by A on B must be negative of the work done by B on A. It just cannot vanish in between. It is like a Rokara transaction. I give you 10 rupees, my balance goes down by 10 rupees, your balance goes up by 10 rupees. There is no middleman in between to take a cut even a small one, no way. It is just across the counter, what goes out from here comes in from there. And second thing is work does not happen on its own. For executing a work interaction, for doing something, there must be a recipient system ready to receive that. For example, you have a cylinder piston arrangement with a fluid in it. On the other side you say is vacuum. You suddenly allow the piston to expand. It may expand till it comes to a halt. On the other side, there is no system to accept that work. So the fluid does not do any work. There must be a recipient system. You must make arrangements for the work to be received. If you freeze the piston, no work can be done. If you allow the piston to simply expand in free space, no work is done. Because there is nothing out there to receive that work. Unless there is a recipient, the system cannot do work on its own. Remember that. That is the basic difference between the work idea as we use in thermodynamics and what we have shown as in terms of that operational definition and the idea of work in many other branches of sciences including mechanics. From a thermodynamic point of view, when a projectile falls over a height h and say velocity goes from 0 to V, mechanics will say the work done by gravity is m g h. The mechanics will say also potential energy reduces by this. Kinetic energy increases by V squared by 2 minus initial 0. In thermodynamics, we will say no work is done. Potential energy reduces agri. Kinetic energy increases agri. But there is no work is done because there is no other system to receive that work. But if I allow the projectile to come down by holding it by a string and as it comes down, raise the weight on the other hand or allow it to extend that string then okay there is some other system to receive that work. Then there is a possibility of a work interact. In fact, I was surprised that in one of the gate examinations, there was a problem on free expansion of exactly what I mentioned that expansion against vacuum. And the question asked was what is the work done? There is no work done but the correct answer was not 0. I had to argue it out. This is some 20 year old story. So, emphasize that work interaction and later on when we talk of heat interaction which will automatically follow from this. Two systems must be involved. A donor and a recipient. If there are no two systems involved, there is no interaction of energy. There is no work done. I think that is enough for today. Thank you.