 We now move on to the second module where as we mentioned earlier in the course outline here we discussed some very important fundamental concepts okay. These concepts are probably already familiar to you, you probably may have encountered them in your high school physics. But what we will try to do now is understand some of the subtleties associated with these concepts. We will refresh the concept and then discuss some of the subtleties associated with these concepts. So we start with the definition of a thermodynamic system. Now defining a system is a crucial first step in any thermodynamic analysis where we are going to adopt the system approach. In case we are going to adopt the control volume approach then we should of course define the control volume before we can proceed with the analysis. So let us assume that we are adopting a system approach. So defining a system is a crucial first step for the analysis okay. Now a thermodynamic system is defined as follows, it is a quantity of matter of fixed mass and identity on which attention is focused for study. Everything external to the system is referred to as the surroundings and the system and the surroundings together constitute the universe. Now heat and work may cross a system boundary but not mass okay. Let us explore this definition further in greater detail, we will dissect the definition and try to understand each and every aspect of this definition. Notice importantly that the last sentence okay, heat and work may cross a system boundary but not mass tells you that in the system approach or indeed in thermodynamics heat and work or interactions that the system has with the surroundings. Which means that whenever a system interacts with the surroundings there can be a transfer of work or there can be a transfer of heat okay. So for heat and work interaction to be present the system must interact with the surroundings that is a very important idea to remember that heat and work are external interactions of the system with the surroundings okay. Certain important points to be noted with this definition, number 1 valid thermodynamic system need not necessarily be useful for analysis. In other words you can define a system which is valid but one which is actually not useful for analysis because it is so difficult to actually carry out analysis with the system. It is valid nonetheless but it is not really suitable for analysis purpose that is quite possible. And the second point is that it is possible to define more than one valid system for a given problem. So the definition of a thermodynamic system for analysis of a particular problem is by no means unique. We can actually define several different systems for the same problem as long as they are valid systems each one of them can be used for the purpose of analysis okay. Normally the choice of which one to use is guided by the information that is given in the problem, the information that is sought and the ease with which we can do the analysis with the particular system. So that is generally what determines which choice we actually use for carrying out the analysis. Let us try to illustrate the idea of a system with several examples okay. The first one simplest possible example. So we have a gas which is contained within a vertical piston cylinder assembly. So we basically have a cylinder which is closed at the top by a piston. So we add heat to the gas until it expands to a certain volume okay. Now we wish to define a thermodynamic system suitable for analysis of this particular problem okay. So here we can see the piston cylinder assembly you can see the piston the gas that is contained inside it can be it need not be a gas it can be any working substance. So this is the cylinder a mass is placed on this to maintain a certain pressure. We add heat to the gas and it expands to a final volume like this and we want to carry out a thermodynamic analysis of this problem. Now definition of a system for this problem is relatively straightforward. In fact it is a no-brainer. The system that is outlined using the dashed line here is the one that immediately springs to mind and that is a valid system. Notice that this system as you can see here initially encloses said amount of gas that was inside the apparatus. And then as the heat is added the system boundary also deforms this boundary keeps moving up along with the along with the gas and so that it always contains the same amount of mass okay. So it is a valid system primarily because it contains the same amount of mass. So the most important part of the definition is that it must contain the same amount of mass throughout not only just the initial and beginning final stages but throughout the process. So the system that is shown in gray so the dashed line is a system boundary and whatever is enclosed within the system boundary is actually the system. So the system shown in gray contains the same amount of matter from the beginning to the end of the process and it does satisfies the definition given above okay. We will discuss the notion of identity little bit later for now we assume that identity remains the same here obviously we can see that the identity remains the same. The mass contained by the system is also the same so it is a valid thermodynamic system that may be used for analysis. Now as I already said some parts of the system boundary remain fixed during the process while other parts actually move or deform during the process. So for instance as you can see here this part of the system boundary so these three parts which are adjacent to the cylinder actually remain stationary during the process but this part of the system boundary which is adjacent to the piston moves along with the piston and undergoes deformation as the process takes place. The shape is retained but the word deformation is used to indicate that it does not remain stationary but it changes during the process. So some parts of the system are fixed some parts of the system deform in such a manner as to always contain the same mass throughout okay which means that we need to know the system boundary not only at the beginning of the process and the end of the process we need to know the system boundary throughout the process okay that is very very important. So we need to know how the system boundary deforms as the process takes place so we need to know the system boundary throughout okay. This is a very very important requirement because if the system boundary is to be known throughout then the process must take place sufficiently slowly that we are able to identify the system boundary at every instant in time okay. In other words let us say that I am adding heat and I add heat in such a way that you know huge amount of heat is added to the gas. Then the gas expands violently and you know the gas begins to move rapidly. So what happens then is that I will not be able to keep track of the system boundary during the intermediate stages because it is moving so fast. We may argue in this case that the system boundary is always at the bottom of the piston but because it is moving so rapidly the pressure, temperature and volume at the intermediate stages will not be known. The reason why we demand that you know the process must take place slowly is to know the system boundary at every instant not only that but also the pressure, temperature and other properties in the system at every instant in time which is why I must add the heat slowly so that the system boundary deforms slowly and at every instant I can get an ambiguous value for all the properties that I am interested in okay. So the requirement that the system boundary should be known throughout implicitly means that the process must take place slowly it also ensures that the pressure, temperature and volume are measurable at every instant and uniform throughout the system. Notice that if I allow a rapid expansion then pressure in say this part of the system boundary during the process may be different from the pressure that I am measuring in this part of the system boundary because the gas there is moving with a considerable velocity. So the temperatures may be different, pressures may be different at different parts which means that I cannot actually come up with an ambiguous value for the properties if the process is very, very rapid so by demanding that the process be slow I am ensuring that the property values are known and measurable at every instant in time and uniform throughout the system. The next point that we would like to observe is the following wherever there is deformation of the system boundary during the process we can easily intuitively understand that there is work interaction between the system and the surroundings okay. For instance this part of the system boundary is the only thing that deforms so you can see that this part of the system boundary is moving up like this which means that we intuitively understand that this part of the system boundary is actually doing work against the surrounding so it is pushing the surroundings away so the deformation is actually creating a work interaction between the system and the surroundings and since the system boundary is expanding we can understand that the system is actually doing work on the surroundings. In contrast if the system boundary were to be contracting then we can easily see that the surroundings are actually doing work on the system. So the important point is any deformation of the system boundary results in a work interaction either the system does work on the surroundings if the system boundary expands or the surroundings do work on the system if the system boundary contracts okay. So that is very important and let us just summarize that here so either the system is doing work as in this example where the piston and the mass are being lifted and the atmosphere is also being pushed upwards or if the piston comes down or if the system boundary contracts then that means the surroundings are doing work on the system we will look at all this with several examples so that these subtle ideas become clearer okay. So as we said the system boundary expands in the case of the former when work is done by the system namely and contracts in the case of the latter this sort of work interaction is called displacement work and we will derive and we will develop an expression later on for calculating displacement work of a system. As I mentioned earlier this system is not unique to this problem we can also define alternative valid systems some of which may be useful for analysis some of which may not be actually be useful for analysis okay. For instance we can define a system which contains the gas and the piston we can also define a system which contains the gas piston and the mass or we can define the atmosphere to be the system everything external to it may be defined as a system. So we can define this the gas alone as a system or the gas and the piston as a system let me just show that so we may define the gas and the piston as the system or we may define the gas the piston and the mass as our system or I may also define the atmosphere as my system for instance like this. So that may also be defined as a system all these are valid systems and depending on what is actually asked for in the particular problem and what is given some of the systems may prove to be easier to work with than others and again so as I said the decision of the choice is made based on the problem statement and what is required in the problem. So in the next example we have an initially empty balloon which is inflated from a rigid vessel so we have a cylinder or a rigid vessel which contains let us say air at a high pressure and and we inflate the balloon using the from the cylinder okay. So we have we have kept a valve on top of the cylinder we open the valve a crack and we fill the balloon with air from the cylinder we wish to carry out a thermodynamic analysis of this particular problem using the system approach. So we would like to define an appropriate system for this problem. So here we can see again the dash line shows the system so you can see that initially the balloon is empty so the dash line contains the vessel plus the empty balloon and as the balloon expands you can see that this part of the system boundary also expands along with the balloon to enclose always the same amount of mass okay. So you can see that the the system outlined by the dashed line always contains the same amount of mass and you can see that all these parts of the system remain stationary while this part of the system boundary deforms from this shape and size to this shape and size finally. So the system shown in gray which is enclosed by the dashed line contains the same amount of matter throughout and hence is a valid thermodynamic system okay. Now how do we ensure that the process takes place slowly you may recall that we we demanded that the process should take place slowly so that the system boundary is known at all instance in time and the properties of the system are also known at all instance during the process. So the process is made slow by virtue of the fact that a valve is present here. So the valve ensures that since you open the valve only a crack the valve ensures that resistance is provided between the high pressure air in the cylinder and the balloon so that the expansion process takes place slowly okay. You can you should also realize that in this particular case the system has two distinct pieces one is this piece inside the vessel the other one is the balloon itself the pressure in the balloon is different from the pressure in the vessel. So can we then argue that macroscopic approach is invalid after all macroscopic approach said that the pressure temperature and all property should be the same everywhere in the system. Notice that here macroscopic assumption is still not violated because of the presence of the valve so there is a mechanical valve which allows pressure difference to exist in different parts of the system so that is allowed had the valve not been there obviously the pressure would have been the same throughout. So the presence of the valve ensures that pressure difference can be maintained without violating the macroscopic assumption. So let us summarize what we have said so far the part of the system boundary which is outside the vessel expands during the process and since it expands we may infer so remember it was it occupied it almost zero volume in the beginning and then it increases in volume which means the atmosphere is being pushed aside so that means the system that we have identified is doing work against the surroundings which in this case or the which in this case is the atmosphere okay. So the air in the vessel is actually doing work to expand the balloon okay. Now there is also an important question namely on the nature of the balloon material okay. So the question is what difference does it make if I draw this system boundary inside the balloon or outside the balloon does it make a difference the it will make a difference depending on whether the balloon material is thin and inextensible or not. If the balloon material is thin and inextensible then like a child's toy balloon then that means that the pressure inside the balloon is the same as atmospheric pressure because the material is thin it cannot really support a pressure difference so which means that whether I draw the system boundary inside the balloon or outside the balloon makes no difference. On the other hand if the balloon were to be made of say rubber or some other material which is elastic in nature let us say it is made of rubber sheet then the pressure inside the balloon can be higher than the pressure outside the balloon which means that if I draw the system boundary inside the balloon then I get a certain work interaction which is the sum of the work done to push the atmosphere aside plus the work done to stretch the balloon okay because I have drawn the system boundary on the inside of the balloon the work interaction that I calculate for the system will be the sum of both these work components. So as the balloon expands as the air inflates the balloon the balloon expands if I draw the system boundary on the inside like this then the work interaction for the system or the work that is done by this system is the sum of the work that it is required to push the atmosphere aside plus stretch the balloon. Now if I draw the boundary on the outside then the work interaction for the system will be the work that is required just to push the atmosphere aside. So the work that is actually the energy that is required to stretch the balloon material will be accounted for in a different way eventually when we write down the first law of thermodynamics but the important point here is that the work interaction depends on where you draw the system boundary and it also depends on the interaction. So if the balloon material is thin and inelastic then it does not matter otherwise if you draw it on the inside we get a certain value for the work interaction you draw it on the outside then you get a certain value for the interaction. So this also shows clearly that work is very much an interaction of the system with the surroundings both the nature of the work as well as the magnitude of the work depend on where you draw the system boundary that is a very very important concept to bear in mind that work is an interaction of the system with the surroundings. So as we said earlier in case the balloon material is elastic the work done by the air is partly utilized to stretch the balloon material and partly used to push the atmosphere aside. So the total work is the sum of both this in case the system boundary is drawn on the inside and as we mentioned in the previous as I mentioned already in both the cases the process is guaranteed to take place slowly by the presence of the valve which provides the resistance so that the process can take place slowly and again unlike in the previous example the piston cylinder example here different parts of the system namely the air inside the cylinder and the air inside the balloon or at different pressures as we already pointed out. So the air inside the cylinder is at a higher pressure the air in the balloon in case it is thin and inelastic is actually at the same pressure as the atmosphere. Now for this case also we may define for instance the atmosphere as an appropriate system so we may actually do something like this and draw so the atmosphere may be taken as a system and we may evaluate the work interaction for that system. Again if additional details are required then it may not be possible to evaluate those with this system but I would just like to point out that this is also a valid system. If you want to calculate only the work interaction this actually probably is a good choice as well okay. Let us try a slightly different variation of this example and then see how things change. So here in this example we are doing the opposite of just what we did just now. So in the balloon example we were inflating a balloon from a vessel filled with high pressure air. In this example we have an initially evacuated vessel and we are trying to fill it with the air from the atmosphere okay so we open the valve slightly as I said before opening the valve slightly ensures that the process takes place slowly with sufficient resistance and the valve is opened slightly and closed after certain amount of air let us say 1 liter of air has flowed inside the cylinder. Notice that if I open the valve all the way and because the vessel is evacuated the atmospheric air will rush inside and it would not be possible for us to define an appropriate system whose boundaries are known at all instance in time or whose property values are known at all instance in time which is why we open the valve just a crack so that the process takes place slowly. So we would like to carry out an analysis of this particular situation using the system approach so let us try to define a system for this case. Now the system for this case valid system for this case looks like this so notice that this actually is that part of the atmosphere which we would say is 1 liter of air okay so we identify arbitrarily 1 liter of air in the atmosphere and we say that that along with this as our initial system. Now notice that as the process takes place the volume of this part of the system keeps reducing once all the 1000 cc has gone inside we close the valve so there is nothing that is outside the vessel okay. Notice that this system shown in dash line always contains the same amount of mass initially is evacuated this has 1000 cc of air finally this has that air which has gone inside so whatever was here has now gone inside here okay. So this is a valid thermodynamic system and notice that this part of the system boundary deforms whereas the other parts of the system boundary remain stationary and they do not deform. Now one thing that we must one question that we must ask is the following how do I define the shape of this part of the boundary I say this is 1000 cc how do I determine the shape of this part of the system boundary. It turns out that the shape of this part of the system boundary is actually immaterial as long as it contains always contains the same amount or the air that is moving in initially it contains 1000 cc and then the this part of the boundary deforms so it should deform in such a way as to contain that initial air that we identified and until the end of the process so as long as it does that it is a valid system the exact shape is immaterial. We will actually justify this later okay. Now in contrast to the previous two examples the previous two examples we actually started with the air that was initially in the vessel and then we allowed it to undergo a process. Here we actually have to visualize the process how the process takes place and then based on the final nature of the system we actually define or the based on the state of the system at the end of the process that is required we define the system. In other words we say that finally the system is going to contain 1000 cc of air and because the system has always contained the same amount of mass we have to use these two facts together and then identify the system. In the earlier two examples it was easier to do here you have to think things through and then define the system appropriately. The actual shape of the part of the system boundary that is in the atmosphere at any instant during the process is actually immaterial we will justify this later. The only requirement as I said is it must initially contain 1000 cc of air and then always contain that air as the boundary deforms okay. Now define in this manner the system that we have shown here gray is a valid thermodynamic system. We can also infer that because this system boundary deforms work is being done by the atmosphere on the system to push the air inside the vessel okay. In contrast to the other two cases where work was done by the system to push the atmosphere aside or stretch the balloon here the system boundary shrinks which means that work is being done by the atmosphere to push the air inside the system. Notice that work is required to be done to push the air because of the resistance provided by the valve. If the valve is fully open then there is no resistance and presumably no work interaction the air will just rush inside. Now we need to do work to push the air inside because we are demanding that it should be a slow process and the partially open valve provides that resistance. So by opening the valve only slightly we provide the required resistance to ensure that the process takes place slowly okay. The vessel may be initially evacuated the vessel may initially be at a lower pressure also it need not be evacuated it may be at a pressure less than the atmospheric pressure also. In all these cases the air will rush in if you open the valve fully so we make sure that the valve is opened only slightly so that sufficient resistance is provided. So this makes sure that this part of the system boundary I am sorry this part of the system boundary is always known. If you open the valve all the way initially it may contain 1000 CC then this 1000 CC this part of the system boundary will disappear in an instant. We do not know the intermediate positions of the system boundary or the pressure inside this part of the system boundary at the intermediate instance because the air is rushing in at high speed. The pressure may not be the same at all points in the system boundary it may even be less than atmospheric pressure because it is rushing at high speed. So the pressure and other properties will not be known at all locations in the system boundary at the intermediate instance in time. So by defining it like this and by saying that the valve is only partly open or partially open we ensure that we know the system boundary at all locations and also the properties inside this part of the system at all instance. So we may also as we just said infer that work is done by the atmosphere to push the air into the vessel against the resistance provided by the valve that is important. So now we have seen both type of interactions one where the system does work on the surroundings by expanding other one where work is being done by the surroundings on the system because the system boundary is contracting. So this is displacement work we will discuss this in more detail later on.