 Welcome back. While evaluating integral dq by T, we may sometimes actually quite often come across situation where we cannot evaluate the dq part of T or the local temperature. Quite often it is possible that the situation across the boundary separating two systems is such that we are not sure whether the interaction is purely work interaction, purely heat interaction or some combination which we cannot resolve. And one thing we should remember and this is very important is that any interaction work or heat depends on the boundary across which it is taking place. You relocate the boundary, redefine it at a small distance shifted from the original one. Suddenly you will find that what was heat interaction may turn out to be a work interaction or what was a work interaction may turn out to be a heat interaction. A simple everyday situation is what we are seeing now. I rub my hands against each other. Now let me say that my right hand is one system, my left hand is another system and I am rubbing the systems against each other. The boundary is reasonably well defined between the two. It is a bit of a flexible boundary but what is the interaction between the two? Can we classify it purely as work, purely as heat or if it is a combination can we separately quantify the two interactions? It is not so easy to do. Let us make it simple. Let us make one part of that inanimate or maybe even both parts inanimate. Let us make one illustration. This is a solid block. It is a battery and I take my hand and rub against it. Now consider three situations. A situation where the boundary separating my hand and this block is inside this block, may be a fraction of a millimeter inside that block. Case two, the boundary separating my hand in this block has two systems. It is slightly inside my hand and we can define the boundary anywhere we feel like. Let us take the third case where the boundary separating my hand and the block is the actual physical boundary separating the two. And you will find that in one case you may be able to argue that it is purely a heat interaction. In the other case you will be able to argue that it is purely a work interaction. The third case I will not tell you which of the three. In third case you will give up saying it is not possible for me to analyze it in any more detail. Now when such a situation occurs, what do we do? We have to apply the second law. So for that we have found an escape route. Let us sketch a system. Let us say this is our system A and this is a system B with which it is interacting and let us say we have defined the boundary between the two systems to be this. And the interaction across this it is such that we do not know. We are confused or it is not possible to determine or quantify the DQ part of this interaction or it is not possible or easy to determine the temperature at across which this interaction is taking place. The temperature of the boundary at the boundary across which this interaction is taking place. So in this case from the point of view of system A we can evaluate data S for system A. It depends only on the initial and final states of A. We can evaluate data S for system B. Also it depends only on the initial and final states of system B. However we cannot evaluate integral DQ by T for either system A or system B. In which case how do you apply second law to system A or to system B? What we do is we say that look we will not apply second law to system A or to system B separately. We will try to apply the second law to the combined larger system A and B. We note from our studies of the second law that the second law reduces to data S of any adiabatic system must be greater than or equal to 0. And that means if we define an adiabatic system, if we are able to define an adiabatic system, we do not have to evaluate DQ by T because by definition an adiabatic system will not have any DQ interaction involved during its processes. So what we do is we create a combined system, let us say shown like this. And we check whether this combined system, is it adiabatic? If so, then our problem is solved. Now we can apply second law to this combined adiabatic system and check whether it is satisfied or not using this relation. If this combined system is not adiabatic that means there is a third system, let us say this system C with which one of these two systems or perhaps both, let us say system B is interacting with a mode which perhaps includes heat transfer. In which case we extend our combined system to include not only A and B but C, system C. And now ask ourselves this question that this extended combined system is it adiabatic? If the answer is yes, again our problem is solved. Otherwise we go on extending it. So we go on extending our system, combining more and more systems with which the system directly or indirectly interacts using the heat mode of interaction till we come to an extended combined system which is adiabatic. Such an extended combined adiabatic system is known as the thermodynamic universe. And within the course of thermodynamics it may quite often be called the universe. Remember that the thermodynamic universe has to be an adiabatic system and hence the thermodynamic universe has to satisfy the second law in this form. The entropy change of that universe, thermodynamic universe has to be greater than or equal to 0. Now remember that universe is a loaded word, it is a confusing word. There is a physical universe, there is an astronomers universe which is perhaps unique. Of course general relativity theories and cosmologists may say that we are living at just one universe and there are possibly a large number of such universes exist but we are not fighting with cosmologists and astronomers and astronomers. We have nothing to do with astrologists. But we have this idea of a thermodynamic universe because it is a useful idea. Another thing to remember is that the thermodynamic universe is not a unique concept. Given a system and given a process that system is executing, we may be able to define a local thermodynamic universe. Another system, another process a different thermodynamic universe. When it comes to solving exercises, we will see the usefulness of this concept. Thank you.