 Today, we are in the second day, but we have a backup backlog from yesterday. Yesterday, I planned to complete the basic ideas and definitions. There are 19 subtopics in it, but we could go only up to topic 13. So, let me complete the remaining before we go to the work interaction and the first law. One of the topics near the end of yesterday's discussion was thermodynamic equilibrium. We said a state is in thermodynamic equilibrium means that it is represented by a single point in thermodynamic state space. That means the system has unique values of… We should note that the idea of thermodynamic equilibrium defined in thermodynamics is somewhat similar, but also different from the idea of equilibrium in other branches of science. For example, in mechanics, there is a mechanical equilibrium. Mechanical equilibrium means that no forces or no net forces acting on a body and if it is a extended body, not a particle, then no net momentum is acting on that, no net moment. So, sigma f should be 0 and sigma, if m represents moments, that should also be 0. Remember that the mechanical equilibrium is not as strict as thermodynamic equilibrium because a particle in mechanical equilibrium with no force acting on it can still be moving at a uniform velocity. If you say that its position is a significant variable, then the position is changing, the state of that system is changing. So, from that point of view, mechanical equilibrium is not as strict as thermodynamic equilibrium. Then, we have chemical equilibrium. When you have a chemical system with different components, chemical equilibrium indicates that there is no net reaction between the two components and this means that the chemical potential is uniform. In our course, we are not going to study chemical equilibrium in any detail from a thermodynamic point of view. So, we will not worry much about it. However, from the science precursor of thermodynamics in school, so called heat, you have some idea of what is meant by thermal equilibrium, not thermodynamic equilibrium, thermal equilibrium. This we will come to when we come to zeroth law and this naturally means that temperature is uniform. In fact, we will use it the other way. We will define what is thermal equilibrium. Then we will look at zeroth law as a thermodynamic premise and then from that we will derive the idea of the temperature as a useful thermodynamic property. This is something we should remember because there are many words. Yesterday, in the discussion which is already on Moodle, the question came up as to whether the universe can be considered as a thermodynamic system and the answer to that was that the universe which universe. We later will define a thermodynamic universe, but if you are looking at the physical universe of the astronomers universe, then I do not think that is a thermodynamic system because we are unable to define its boundaries. Thermodynamics is all about systems. System means we must have boundaries defined. Now, we come to the next important topic and that is thermodynamic processes or simply processes because the adjective thermodynamic we will soon get rid of. It takes too much time and too much space. For defining a process, we will just use this. Process for us is nothing but a short form for change of state of a system. So, when we say that a system undergoes a process or a system executes a process, that means the system has undergone a change of state. So, the minimal description of a process would be the system which undergoes a process and for that system the initial state and the final state. So, if you look at the thermodynamic state space and let me simplify it by saying we just have a two-dimensional thermodynamic state space with some two properties say x 1 and x 2. If you are not comfortable with such abstractism or abstraction, you can write p v or whichever two properties t s, t v, t p, whichever two properties you feel like. Let us say that we have defined a system. So, x 1 and x 2 are properties of that system and let us say this is state 1, this is state 2. So, this is the for a given system, this is the minimal representation of a process. Now, the question that is asked is if this is the minimal representation, the question is what happens to the system during the process? The idea here is any process will require a certain amount of time. So, there is some duration associated with a process, hardly any process is instantaneous. You can always select a scale of time such that it takes some delta t. So, it is possible that the process is such that when it goes from the initial system, goes from initial state 1 to initial state 2 and I keep on observing it. I may say that look, I cannot measure the state, I cannot measure the properties properly as it goes from 1 to 2. In that case, we cannot even, we can only may be link this up by a dotted line saying I only know that 1 is an initial state, 2 is the final state. Do not ask me anything in between and many of our real life processes are of this kind that is no detail available or no detail can possibly be obtained. This is the general situation. However, sometimes the process takes place in such a fashion, slow is not the correct word in it that during the process at any stage system is in equilibrium or system can be observed to be in equilibrium. That means at some stage between 1 and 2, you will find it in a state of equilibrium. At some other stage, you will find it in a state of equilibrium and since it starts with 1 may be soon after the process begins, you will find it in a state of equilibrium very near it and after some time still slightly different state of equilibrium and you will find that if you make enough detailed observations, you will find that you will have an almost continuous locus of states, which you can draw from 1 to 2. From initial state to the final state and here we being engineers and the realistic people, we will say that instead of a system is in equilibrium, we will say perhaps that the system cannot really be in equilibrium because it remains, if it remains strictly in equilibrium, it cannot even move from the initial state because a slight movement from the initial state would mean non-equilibrium, but we will say that the system is in equilibrium with a qualifier almost. How good is this almost is left to us, but if we say that to an excellent approximation at any stage the system during a process remains in equilibrium, then we can draw it by that process by a continuous locus and such a system, such a process we define as a quasi-static. Static is an old name for something like equilibrium. Quasi means half way through or almost there. So, quasi-static process means a process in which the system remains almost in equilibrium throughout. So, if I identify this process as 1A2, A is not a name of a state just a label on that process, then 1A2 is a quasi-static process. Another quasi-static process could be like this, the end states are the same, it is another quasi-static process, but this process is non-quasi-static. I am not sure that the intermediate states are in equilibrium and hence I cannot represent it by a continuous path. I will just show as a convention a dotted line joining 1 and 2 with an arrow from the initial state to the final state and the position of this line does not mean anything. Similarly, I can have another non-quasi-static process, I can show it as D, but I am showing it like this just to distinguish it from C. The position of this line does not mean anything. So, 1D2 is also a non-quasi-static process, whereas for quasi-static processes, this locus 1A2 means something. That means, at some stage during the process, you will find that the system was here, the property was this value of x 1, this value of x 2. At some other time during the process, the property x 1 was this, property x 2 was this. You could have identified the state and marked it on the state space. We say that between the same initial and final state 1 and 2, 1B2 is another quasi-static process because our observations would have shown us this, the system would be here at some time, here at some time, here at some time, here at some time and so on. So, that is the idea between a quasi-static process and a non-quasi-static process. Why do we classify processes like this? The reason is as follows. A quasi-static process, state of system defined because it is in equilibrium throughout the process because the locus is defined. Now, the moment you have a locus, you can operate on it mathematically. You can do operations of integration, differentiation, etcetera. That means a quasi-static process can be analytically handled. A non-quasi-static process cannot be no detail available. So, the characteristic of such a process, say the work done to such a process, heat transfer through such a process cannot be obtained by integration. If at all it is obtained, it has to be obtained by some other means. So, whenever we want to study the detail of a process, it always helps if the process is a quasi-static process or if the process can be modelled as a quasi-static process. That is the advantage here. Most real processes are non-quasi-static and a quasi-static process is only an approximation or a model used by us. Remember this. This is something to be remembered and this is something to be emphasized to our students. The next idea to be defined is a cycle. Our definition of a cycle is nothing but a process such that initial state is the same thing as the final state. So, in a state space, the minimal representation of a cycle is a single state. Initial state is the same thing as final state. In general, the cycle could be or will be non-quasi-static. So, we will only show it like this, just a loop of any kind. This is the general cycle, natural cycle, non-quasi-static. A quasi-static cycle would be, suppose this is whatever is represented by A is a non-quasi-static cycle. A quasi-static cycle could be like this, 1 B back to 1. If this same cycle is executed the other way, through the same set of states, I may call it a different cycle because although the initials and final states are the same, the path traced is in a different order. Of course, I can have another one like this. This could be another quasi-static cycle. Another non-quasi-static cycle can be simply be shown like this. Here, where I show the dotted line and the way I show the arrow is immaterial because all I know is my initial state and final state are the same. In a non-quasi-static cycle, there will be only one state of equilibrium or at least one state of equilibrium. Part of it can be quasi-static but even if a small part is made up of states which are not in equilibrium, it becomes non-quasi-static. So, this is our idea of a cycle. The system comes back to its initial state. So, the final state is the same thing as the initial state. Now, we will get into the heart of thermodynamics. Thermodynamics pertains to situations like this. We have two systems, say system A and system B. System A and B, they interact with each other. That means energy in some form gets transferred from A to B, B to A in some way. There is an energy transaction and because of that system A executes a process and goes from state A 1 to A 2. System B executes a process and goes from B 1 to B 2. For simplicity lesson, let us assume that system A and B during our study interact only with each other and not with any other system. That complication we will do but for our basic study, we will consider such situations. This is the domain of thermodynamics. In fact, if we restrict the transactions of energy only to certain kinds like mechanical energy transfer, then this is the domain even of mechanics. But if physicists studying mechanics soon realize that apart from mechanical energy transaction, which in thermodynamics we will call work transfer, there is an energy transaction of the non-work kind, which we will later formalize as the heat transfer kind. Whenever there is a heat transfer involved, thermodynamics is on its home ground. The laws of thermodynamics relate changes in state of these systems to the various types of energy transactions and all the three laws have something to do with essentially this model of thermodynamics. So, here the energy transaction between two systems we will define as a thermodynamic interaction. A thermodynamic interaction is nothing but an energy transaction that means energy transfer, energy give and take between two systems. Here it is important although it is not very clear system A and B must be separated by a boundary. Usually this will be a common boundary between system A and B and all these interactions will take place across that boundary. So, our domain now be systems change of state means a process which is caused by some transaction and this state change will be related to the transaction, which is the interaction and the laws of thermodynamics which we are going to look at both the first law and the second law will relate change of state to a transaction. Since you have already studied thermodynamics, I am just giving you some form here. For example, the first law will give you something like delta E is q minus w. We have not yet defined any one of these terms properly, but just look at the form. On one side you have a change in property representing change in state, on the other side you have interaction or transactions. The second law also on one side you have a change in property, on the other side you have a function of interaction and the state of the system. It is the zeroth law which is different. Zeroth law has something to do with equilibrium with d q equals 0. It has something to do with transaction, but it has something to do with restricted transaction. So, this law is in a slightly different form, because we want no heat type of interaction. We have not defined any one of these terms. I am writing this here only to emphasize that the laws of thermodynamics relate change of state to transaction, except the zeroth law, which relates a property common to systems such that the heat interaction will be 0. Now, that brings us to the end of basic ideas and definitions.