 We now move on to defining property, state and process. Once again, you are probably familiar with these concepts, but again I must emphasize that there are many subtle aspects about these concepts, which you need to understand as you go through the course. A property as you may be aware is simply defined as a particular quantity of quantity whose value depends only on the state of the system and not on the path by which the system attained that state. What do we mean by this? So, here we have a piston cylinder mechanism, which contains air let us say at 2 bar 100 degree Celsius and let us say the air occupies a volume of 0.1 meter cube. Now, you know from your high school physics that these are all properties, the pressure, temperature and volume are all properties of the system, which means that these depend only on this particular state and not on the path by which the system arrived at this state. So, what exactly do we mean by that? So, here I am showing four possible states from which the system could have arrived at this state. For instance, it could have been at a higher pressure and a higher temperature and a higher volume. We remove heat from this, it cools down and then reaches this state, lower pressure, lower temperature and lower volume. Or it could have been at a lower pressure, lower temperature and lower volume. We add heat to this system, it expands and then it attains this state possible. It could also have come from here where it is at a higher pressure, perhaps higher temperature but smaller volume, it then expands and does work as it expands and then arrives at this state. Or it could have been at a state where it is at a lower pressure, lower temperature and higher volume. We transfer work on to the system, meaning we do work on the system, we compress it and then it reaches this state, higher pressure, higher temperature and lower volume. So, this state could have been arrived at from any one of this state or indeed an infinite number of possible states. I am only illustrating four for the sake of brevity. So, now notice that the pressure here will be 2 bar regardless of what the pressure here was or what the pressure here was or what the pressure here was or what the pressure here was. It will always be 2 bar. Temperature here, same thing. It will always be 100 degrees Celsius at this state. Doesn't matter how we arrived at this state from any one of this or from any other state. Same goes for volume. In contrast, let us say that we for the sake of argument we say someone says prove to me that heat is not a property of the system. We can easily do that from this illustration. So, if heat is a property of the system then it must be the same regardless of how we arrived at that state. Notice that in this case, we add heat to the system to arrive at this state which means the sense in which we are the sense of the heat interaction is positive. That means we are providing heat to the system. Here we are removing heat to arrive at this state which means the sense of the heat interaction is negative. We are removing heat. So, the same state could be arrived at either by supplying heat or by removing heat. So, which means that heat cannot be a property of the system and the same argument holds for work also. We could have arrived at this state by supplying work or by extracting work from the system. So, the work is not a property. So, work associated with this is actually not a property. In fact, there is no work that is associated with this because it can be any value and it can be any sense. Work is not a property. So, we cannot associate work with the state of the system. We can associate pressure, temperature, volume and so on. Whichever one is a property, but not quantities which are not properties. And this illustration shows clearly why heat and work are not properties, but why the other thing are properties. Now, the next question that naturally arises here is the following. Let us explore that. Properties may be classified as extensive properties, which means the value of the property depends on the mass of the system. Volume, total energy, total internal energy, total enthalpy or properties that depend on the mass that is contained in the system. Intensive properties are those which do not depend on the mass that is contained in the system. For instance, temperature, pressure, density, specific volume, specific total energy, which is internal energy per unit mass. I am sorry, specific total energies, total energy per unit mass, specific internal energies, internal energy per unit mass and specific enthalpy of course is enthalpy per unit mass. Notice that extensive properties are denoted using capital letters in that is a convention in engineering thermodynamics. Intensive properties are denoted using lower case letters. Now, those that are neither extensive nor intensive. For example, temperature, there is no extensive or intensive version of temperature. Temperature is temperature, we may use upper case for this. Whereas specific total energy is the intensive version of this property, extensive property. Specific internal energy is the intensive version of the total internal energy and so on. So, these are denoted with lower case letters and these are denoted with upper case letters. Pressure and temperature, we may use capital letters. Now, we have defined property of a system. We took a close look at that. Now, let us try to define state of a system. The thermodynamic state of a system is fixed by a certain number of measurable and independent properties such as pressure, volume, temperature and so on. So, what we are saying here is I have actually given in this case three quantities, the pressure, the temperature and the volume. The question that naturally arises after this is how many such properties do I need to specify in order to completely fix the state of the system? So, we know that state of the system is fixed by a certain number of properties. How many do we require? Do I need all three or do I need only two or one sufficient? So, that is the question that we are going to answer here. Notice that there are two things in italics here, a certain number and independent, both are italicized here. So, we will look at both this as we go along. Let us look at independent first. What do we mean by independent? Independent means that the set of properties that we use to fix the state of the system should not contain pairs or properties which are dependent on each other. For example, I cannot say that I will fix the state of a system using density, temperature and specific volume, because density and specific volume are related to each other. One is the reciprocal of the other, I cannot use that sort of a set to define the state of a system. Or I cannot say, for instance, I have water in a piston cylinder mechanism at one bar pressure and 100 degree Celsius. You know that water boils at one bar pressure and 100 degree Celsius. So, the system in this case, if I define it like this system in this case could all be water which is just about to start boiling or it could all be water vapor which is at one bar 100 degree Celsius or it could be some amount of liquid water, some amount of water vapor. So, the exact state cannot be fixed just by saying 100 degree Celsius and one bar pressure, which means that when phase change is taking place, pressure and temperature become dependent properties. They are otherwise independent, but when phase change takes place, they become dependent properties. So, we may normally use pressure and temperature to fix the state of the system, but not when phase change takes place. So, that is what we mean by independent. Whatever set of properties we use must contain only properties which are independent of each other. So, in this case, when phase change takes place, we may use pressure and say specific volume or temperature specific volume and so on. What about the number? How many properties do we require to specify the state of a system? So, the actual number is equal to the number of possible ways why is the energy of the system may be changed. So, if you look at the illustration here, you can see that I can change the energy of the system either by supplying or removing heat or by supplying or removing work, which means that the energy of the system may be changed in two different ways. So, it may be changed through heat and work interactions, which means that the number of properties required to fix the state of the system is 2. This is the simplest possible system and it is called a simple system or simple compressible system, because displacement work is the only mode of work interaction in this case of piston cylinder. So, it is a simple compressible system or simple system, but the number of properties required is 2 because there are two ways in which I can change the energy of the system. Suppose I say that I can, it is possible for me to lift the entire container as a whole. So, if I am able to, if I have the freedom to do that, then the potential energy of the system also changes, which means that I can now change the potential energy of the system also, which means I must have one more independent property, which would be the elevation. So, now I have to start tracking the elevation or specifying the elevation of the system with respect to a datum, so that potential energy changes can be calculated correctly. Now, if I were to set this entire piston cylinder mechanism with a certain velocity, let us say, then the system acquires kinetic energy and so I need to specify one more property, because now I can change the kinetic energy of the system, I need to specify one more property, which would be velocity. This is again an independent property of the system, so that also needs to be specified. Now, what is most important here is to understand that when I say potential energy of the system, I mean I have defined this system, so I lift the entire cylinder bodily, so that there is a change in potential energy of the system. When I say kinetic energy of the system, we do not mean kinetic energy of the molecules inside the system. Remember, we are using a macroscopic approach, so the internal details are neglected, there are no molecules in the macroscopic approach. So, when I say kinetic energy, what I mean by that is, this entire piston cylinder mechanism is translated to the right with a certain velocity. In that case, that velocity also needs to be specified, so that is what we mean when we say kinetic energy of the system. It is not kinetic energy of the molecules, because there are no molecules in macroscopic analysis, kinetic energy of the system as a whole, so the system as a whole starts moving to the right with a certain velocity. So, in each one of these case, as we add more ways by which the energy of the system can be changed, for every additional mode in which energy can be changed, we actually have to specify one independent property. Because once we have done that, any other property has to be expressed as, I mean express in terms of these properties that we have used to fix the state of the system. So, if you use, let us say pressure and temperature to fix the state of the system, any other quantity that we want, for example, internal energy or enthalpy or entropy, specific volume, everything else must be related to pressure and temperature. So, all we have is pressure and temperature that fixes the state of the system, that is all that is required. Any other property of the system should be calculable from these two properties. So, that is what we mean when we say all or any other property must be expressed in terms of these properties through appropriate relations, that is what we mean by this. Here, we again have the ubiquitous piston cylinder mechanism. So, we have a system here, let us say it contains some amount of air. So, there is a piston with a nonzero finite mass and there is also another mass which is placed on top of the piston. So, there is a pressure that is being exerted on the air. So, the system is initially at state 1 as shown here. Now, let us say that I remove the mass. When I remove the mass, the system is no longer in mechanical equilibrium and gas starts expanding rapidly. It goes up to, this may go up to some height and the system pressure will reach a certain value. It may bounce back and forth a couple of times. Eventually, it will reach a mechanical equilibrium and settle down to a final state. Let us say that the final equilibrium state is 2, which is denoted here. Now, I cannot trace the process that the system has taken to go from 1 to 2 because none of the intermediate states are known. Remember, we need two properties to fix the state of the system in this case. And as the system goes through the process at the intermediate instance, I cannot really measure pressure or temperature unambiguously or we may even say pressure and volume. So, I cannot measure pressure and volume without any ambiguity during the intermediate instance. Because it is undergoing a rapid expansion and the pressure at different parts of the system will be different. So, I cannot arrive at a value for pressure or volume may be alright. At every instant, we may be able to measure, but pressure we will not be able to measure without ambiguity. So, none of the intermediate states are known. So, all I can say is that system was initially at state 1, which is an equilibrium state and it is finally at state 2, which is another equilibrium state and the process can be anything. It could have been any process, maybe some process like this or some process like this. It could have been any other process, it bounces back and forth, it could have been some process like this, it could have been any one of these processes, we do not know because we do not have the intermediate states. Now, let us say that to make this situation better, we divide the mass into four pieces. Instead of just having a mass as a single thing, let us say we have four pieces and instead of removing the mass entirely, I remove one piece at a time. So, I remove one piece and then I wait for the system to attain an equilibrium. Now, I can measure my pressure and volume. So, I measure my pressure and volume, I denote that state here, intermediate state. I remove another piece, again I wait until it reaches an equilibrium, I measure the pressure and volume. So, now, I have three intermediate states. I do not know the process in between these states. I do not know what happened in between these states. Again, the process in between these states could be like this, like this, like this, it could be any one of an infinite number of processes, it could have been like this, like this, like this and so on. I do not know the intermediate, I mean I do not know the processes because I do not know the intermediate states. At least I have four, now three intermediate states compared to no intermediate state before, I have three intermediate states. So, perhaps we can sort of eyeball these and say this, the process most likely may be something like this. But still that would only be a guess, we will not know for sure. When will, when can we know for sure? We can know for sure if we divide instead of four pieces, if we divide this mass into an infinite number of pieces and then start removing each one of these infinitesimally small piece one at a time. So, I remove one piece, I wait for the system to reach an equilibrium, I attract the state, I remove one more piece, I get the next state, then I keep doing this. So, now I have an infinite number of states or states which are which are spaced very close together. Now, it is probably alright for me to connect all these states together to get the process. So, the important concepts here are the following. Property, very important, we must be able to measure the property. We use independent properties to fix the state of the system and we need to have intermediate states before we can actually connect them to form a process. So, you can see how all these quantities are related, properties, state and process. We go in this sequence, property, independent properties, measurable, state, measure the properties, equilibrium state only allowed because we can measure the properties only at equilibrium states. So, we measure the properties, then we get the intermediate states and connect them together to form the process. So, let us summarize what we said so far. So, the state of the thermodynamic system is defined by a set of independent measurable properties. For a property to be measurable, the system must be in equilibrium, very important. Process, a path or process is the locals of a set of thermodynamic states that are located only infinitesimally apart. So, what this means is I cannot connect these to form a process, I cannot connect these two to form or to get the process that the system has undergone. I cannot connect these again to get the process that the system has undergone. However, I can connect these to get the process that the system has undergone. So, we need states that are located very, very close to each other or only infinitesimally apart. That is very, very important. Now, let us take a closer look at this, just one more concept here. What is that when I divide this into an infinite number of pieces and I go through this, notice that each one of the state is an equilibrium state. So, the amount of disequilibrium from one state to the next is very small. There has to be a small amount of disequilibrium otherwise no process will ever take place. But that amount of disequilibrium must be very small. So, the mechanical disequilibrium when I remove a small weight is very small. So, the system reaches a new equilibrium state very quickly because it is very small. In the other cases, it will take a while before it can reach the new equilibrium state. But the interesting aspect of this is that I can stop the process at any instant and if I start putting the weights back on, the system will trace this path all the way back to the initial state. In other words, I can stop at any instant and then back up and again attain the same state one by passing through the same path or process. I can retrace this path. So, that is actually the most important aspect of such a process because the weights are infinitesimally small. I can go forward and backward and trace the exact same path going forward and backward. So, from this, it becomes clear that this is what we will call later on as a reversible process. Notice that this is a fully resisted process. This is a fully unrestrained process. This is a partially resisted process and this is a fully resisted process. So, we need a fully resisted process in order to know what the process is. That seems like a tautology, but I think you will gather the meaning. The process should be fully resisted for us to actually even have the process line or process curve. And a fully resisted process is also a reversible process. So, for a process to be fully resisted, notice that it must take place very slowly or in a more formal way, the states must be infinitesimally apart only. So, as we said, the system is out of equilibrium in between two successive states. They may be very close, but still there has to be a small level of disequilibrium for the process to take place. Because if there is no disequilibrium, there will be no process. And the departure, as I said, is quite small when the successive states are infinitesimally apart or it is a fully resisted process. So, in this particular case that we are looking at the origin of the departure from equilibrium is mechanical. Because when we remove a weight, there is a temporary imbalance of forces. So, the pressure exerted is slightly less than the pressure that the gas is at. So, the force balance is slightly out of equilibrium. So, the system very quickly adjusts to this new pressure. So, the origin of this disequilibrium is mechanical. It can also be thermal. For instance, we could supply a small amount of heat. In fact, we can do a thought experiment where you replace this weight with say supply of heat. If you supply a lot of heat in one instant, then the expansion is unrestrained. If I supply finite large but finite amounts of heat, then I have partially resistor process. If I supply infinitesimal amount of heat, then I have a fully resisted or a process which contains only equilibrium states. So, the origin of the departure from equilibrium could be mechanical or thermal. In fact, later on when we look at second law analysis and so on, we will make use of this fact that fully resisted process is reversible. And whether the level of disequilibrium is due to mechanical or is mechanical in origin or thermal in origin, it is immaterial. So, we will take up temperature and the 0th law in the next lecture.