 The next example, let us say that we have a line, a workshop line in which air is flowing at some pressure and temperature. We have a vessel and we connect the line to the vessel through a valve. We open the valve, fill the vessel with air, a certain amount of air and then we close the valve. So, the only difference between this and the previous example is that in the previous example, we allowed the vessel to be filled from the atmosphere. So, here we are actually filling the vessel from a line. So, it could be a steam line, it could be a high pressure air line and the vessel may be initially evacuated or it may be at a pressure less than the line pressure. We open the valve and allow a certain amount of air or steam to come in and fill the vessel then we close the valve. So, we used to do a thermodynamic analysis of this situation using the system approach. So, we want to define an appropriate system for this case. Since again here also, we have to visualize the process before defining the system. The basis of defining the system is always the same, it should contain the same amount of mass throughout. So, in this case, there could be some mass inside the vessel to begin with, it could be evacuated or it need not be evacuated. So, there is some amount of mass inside the vessel to begin with and there is some amount of mass in the line which actually enters the vessel. So, we define a system which takes into account both these masses which encompasses both these masses then define that as our system and that is what we have done here. This is the mass that is waiting to enter the vessel. This is the mass that may already be in the vessel, the vessel is evacuated this may be 0 otherwise it is non-zero. So, we take these two together and then we define that as our system. Once again the question of what should be the shape or is the shape of this particular system boundary important or not arises, but again we will justify this later I can say for now that the shape of this part of the system boundary is actually immaterial. So, this is what the system looks like at the beginning of the process and then we open the valve a crack providing resistance and making sure that the filling process takes place slowly and as the air or steam from the line enters the vessel the process continues then finally once this has entered this has entered we actually close the valve and this is the final system. So, in this case also notice that the system as defined here contains the same amount of mass from beginning to end and the process takes place slowly thanks to the valve. So, the system boundary which is deforming so this part of the system boundary is actually the one that is undergoing deformation these parts are remain stationary they are undeformed. So, this is the one that is undergoing deformation. So, the part of the system boundary that is undergoing deformation is known at all instance during the process and so the properties of the system and in this part of the system are also known at all instance in time during the process. So, whether it is air or steam is immaterial so the air that is finally in the vessel is identified as a system. So, basically what we are saying here is that there is a certain amount of air or steam in the line and we are filling the vessel with that so the initial mass plus the mass that enters is the mass of the system. So, once we define the system appropriately by using that idea the analysis becomes simple. As we said the part of the system boundary inside the line shrinks during the process as a result of the work done to push it inside. So, notice that here this part of the system boundary you can see that this part of the system boundary shrinks from a certain value initially to 0 at the end of the process which means that the air in the line is actually pushing this air inside the vessel against the resistance provided by the valve. So, this part of the system boundary contracts which from which we can infer that the surroundings are actually doing work on the system. We look at one more example here we have a rigid vessel which contains air and instead of using it to fill a balloon like we did before we simply empty the air from the vessel into the atmosphere but slowly through a valve. So, we wish to do a carry out a thermodynamic analysis of this situation. Let us see how we can define a suitable system. Once again here also we need to think things through before defining the system. The guiding principle always is that the mass that is in the system should be the same throughout and the boundaries must be and the system boundary must be known unambiguously from beginning to end so that the properties are known. So, here we have a vessel and we open the valve and allow a certain amount of air to go out. So, when we close the valve finally a certain amount of air remains in the vessel. So, we use that as the system. So, we define the system based on the final state or the process takes place and then we have some amount of air so we use that as our system. So, this is the amount of air that finally remains in the system. Now, initially when the process begins this would have been the air say for instance like this. So, this amount of air which is shown here this is our system so the amount of air within this boundary is what we are focusing our attention on. So, this air as the process goes on expands and eventually fills the entire vessel. So, the dashed line or the system that we have used here always contains the same amount of mass and this air expands and eventually fills the whole vessel. So, we need to actually think the process through and define the system. The advantage is that when we do this and define an appropriate system the analysis becomes very easy. Once a system a proper system is defined after looking at all the aspects of the problem the physics of the problem then the analysis part becomes very simple as we will see later. Once again the shape of the system that we have initial system that we are the initial shape of the system that we have chosen here is immaterial for the analysis it could have been any amoeba shape. So, we could have chosen something like this as our we could have chosen something like this as our initial system and as it expands it will go and fill the entire vessel at the end of the process that is what is the actual shape is immaterial. What is important is the concept that the final mass that is in the vessel should be taken as a system and we then work backwards and identify the initial shape of the system. So, let us summarize what we have said about this particular example. Once again the air that is finally in the vessel is identified as the thermodynamic system. The initial configuration is shown as a circle for illustrative purposes only as I said the actual shape is immaterial this we will justify in the module on work and heat when we develop expressions for displacement work. The system expands from this initial configuration during the process and eventually fills the entire vessel. So, we can infer then that this system is actually doing work to push the air out of the vessel. So, work is being done by the system in this case and the valve ensures that the process takes place slowly otherwise the air will rush out of the vessel and we will not know the locations of the intermediate boundaries or system boundaries nor will we know the properties of the system at every point in the system it will be non-uniform. So, we will not know the property values unambiguously. The last example that we are going to look at is an air compressor. So, here we have a reciprocating air compressor which sort of resembles piston cylinder mechanism but it has these two valves. So, there is an intake valve here and there is an outlet valve here. So, the way this compressor operates is the intake valve is open and a certain amount of air is drawn in. So, you see the intake valve being open here and a certain amount of air let us say under cc of air is drawn inside the cylinder and then the intake valve is closed then the piston moves like this and compresses the air. So, we want to do or carry out a thermodynamic analysis of the intake stroke alone of this reciprocating compressor which means from the instant the valve opens to the instant when the valve closes. So, system for this based on the examples that we have discussed so far you should be able to define this system for this particular as suitable for this case it encloses the same amount of mass throughout. And the important thing here is that in contrast to the other examples here two parts of the system boundary deformed during the process. This part of the system boundary deforms and shrinks as the process takes place and this part of the system boundary expands as the process takes place as the piston moves to the right. So, the piston moves to the right here. So, this part of the system boundary expands. So, from which we can probably can infer that the work interaction in this part of the system boundary actually such that the surroundings are actually doing work to push this air inside the cylinder against the resistance provided by the valve. And this part of the system boundary is actually expanding. So, it is doing work against the resistance that is provided at the end of this connecting rod. So, it is connected to a motor or it is connected to a crankshaft and so on which will provide a certain resistance. So, this part of the system boundary is doing work against the resistance as it moves to the right. So, the work interaction on this part of the system boundary is the exact opposite of work interaction on this part of the system boundary. So, that is the interesting aspect of this particular example. It also illustrates the fact that the definition of system that we have given and the approach that we have taken in defining it is very general. It is not restricted, we are not restricted to defining systems which can differ only in one part. We can define systems which can deform in multiple parts and the nature of the deformation can also be different. One part it could be contracting, another part it could be expanding, all of which can be accommodated in our definition for the thermodynamic system and we will show that this can all be accommodated in our analysis later on. And when we actually calculate the displacement work for a system like this, it nicely comes out to be the algebraic sum of the all the work interactions. So, basically the work interaction here could be as it the work interaction and it shrinks is of a certain sign surroundings are doing work, here system is doing work on the surroundings. So, when we develop an expression for displacement work, it actually very nicely gives us the algebraic sum of all these work interactions with the appropriate magnitude and sense. So, let us summarize what we have said so far in this particular example. So, the part of the system boundary in the atmosphere shrinks in volume which indicates that work is being done by the atmosphere to push the air inside the cylinder against the resistance provided by the valve. Now, the part of the system boundary adjacent to the piston expands and it does work against the resistance provided by the atmosphere as well as whatever external agent is connected to it which powers the compressor. So, the system deforms while always containing the same mass, it deforms in such a way as to contain the same amount of mass and once again the exact shape of the system boundary in the atmosphere is immaterial and this is something that we will demonstrate later on. It will justify later on. In all the previous examples, the process was guaranteed to take place slowly. In other words, the process was a fully resisted process owing to the resistance provided by in some cases the atmosphere, the mass of the piston, the mass itself, the valve and or an external agent. So, for instance, if you look at this example, the resistance in this case is provided by the external agent on this side and if you look at the previous examples, then in this case the resistance is provided by the valve itself and so on. So, the presence of one of these things ensured that the process actually was a fully resisted process. In contrast, what we are going to look at next is an example which involves a partially resisted or an unrestrained expansion process. This also this kind of process also occurs in real life applications. So, we should see how we can handle, if we can handle a situation like this where the process is partially or fully resisted. Notice that even if the process is partially resisted, the boundaries of the system at intermediate time instance will not be known and the properties of the system at intermediate time instance will also not be known unambiguously. So, whether it is partially resisted or whether it is unresisted is actually material as far as our framework is concerned. Any process that takes place must be a fully resisted process. So, in this example, we have a container, rigid container. On the left half of the container, we have air at let us say some high pressure and the left half is separated from the right half, we remove the partition. Now the right half may be partially or fully evacuated. At time 0, we remove the partition and the air then expands rapidly to fill the entire container and eventually attains an equilibrium state. So, that is the problem description. Now, we wish to find out whether we can analyze this problem using a thermodynamic, using system approach. So, here is the illustration of the problem. So, initially we have air on the left side of this rigid vessel, there is a partition. In the right side is partially or fully evacuated, the partition is removed and the air is allowed to expand fully and occupy the entire container and it comes to equilibrium after some time. Now, it may be tempting to define a system say like this for this particular problem, why not define a system that looks like this. So, this contains the air and we can somehow argue that as the air expands, the system boundary, this boundary will also deform to contain the same amount of air. The difficulty with defining the system in this manner is that the air in this part of the system undergoes a rapid expansion. So, we must have a method by which we can actually keep track of the system boundary and that is almost impossible to do, that is number one. Number two, as the air in this part of the system undergoes a rapid expansion, the pressure and temperature here are likely to be different, if not substantially different from the pressure and temperature of the air at other part, for example, the left part of the system. So, even if we somehow manage to come up with a method by which we can keep track of the system boundary, it is still not a valid system because the property values will not be uniform. So, this sort of a system is actually not helpful for analysis. So, what we need is a system which is like this. So, this system as shown by the dashed line encloses the entire box. So, it could be partially evaluated, fully evaluated, whatever it encloses the entire container. And as the air expands, it undergoes and still occupies the container. So, the system that we have defined here is a valid system and the boundaries of the systems are actually fixed and known at all instances in time, it always contains the same amount of mass. However, we know the properties unambiguously at the beginning of the process and we know the properties unambiguously at the end of the process, but probably not, certainly not during the intermediate stages because it is undergoing a rapid expansion. So, this system is better than what acceptable the compared to what we defined earlier. Although the intermediate properties are still not or properties at intermediate instance are still not known, but that has to do with the nature of the process and nothing can be done about that. But at least this system may actually be used for a thermodynamic analysis. How do we do that? Let us take a look. Oh, I am sorry. We can actually see in this case that because all the system boundaries, so for instance, the boundary here, boundary there, all the boundaries are fixed, we may easily conclude from this that the displacement work for this case is 0 because no part of the system boundary deforms. So, neither the system nor the surroundings are actually exchanging work in this particular case. So, the work interaction irrespective of whether it is fully right side is fully evacuated or partially evacuated is 0. Now, there are actually a lot of misconceptions about this particular problem. The answer of 0 work in the case of fully evacuated can probably be erroneously arrived at by a couple of different methods. So, let us consider the fully evacuated case. The argument in this case goes like this, erroneous argument in this case goes like this. So, we actually define a system like this and this side is fully evacuated. So, this expands. We do not really, the argument goes like this. We do not really need to know the shape of the system boundary at the intermediate instance because anyway the resisting pressure is 0. So, which means work done is 0. That argument is not correct because it assumes that the work interaction depends only on the external pressure or resisting pressure which is we have not really said that to be the case. Now, the other reason why this explanation falls apart may be understood by considering the case when it is partially evacuated. So, it is not fully evacuated, it is partially evacuated. In this case, if you keep the same system boundary which of course we cannot because there will be material here. So, we have to modify this, but what do we do in that case? Do we take the resisting pressure and evaluate the work or do we take this pressure and evaluate the work or do we take the difference and evaluate the work? Turns out that we do not actually have any of these choices. Once we define displacement work and derive an expression for it, turns out that we do not have any such choices. So, in the pathological case when it is fully evacuated, one can actually erroneously arrive at the answer of zero work for this case, but again bear in mind that that is actually not correct. What we have argued here is the correct thing because no part of the system boundary deforms. We may say that the displacement work in this case is zero. That is the correct way to understand this problem and that is the correct way to define a system for this problem. So, this concludes our discussion of thermodynamic system and hopefully by this time you should have understood that what was seemingly a very simple concept system. And now actually is not so simple once you start looking at subtle aspects of what is required to define a system. In fact, you need to sort of go through the physics of the entire problem, understand what is required and then define a system appropriately because as you saw in some of these cases, you need to know the final state before you can define the system. So, the system analysis requires a lot of thought upfront before you actually define a system. But the advantage is that once an appropriate system is defined, the analysis becomes simple because a lot of thought has already gone into defining the system and so the analysis becomes simple.