 Welcome back. We are now going to analyze a Carnot cycle in detail. As we have seen a depiction of the Carnot cycle on the TV diagram will be something like this. We have a temperature at the higher level, we have a reservoir at that temperature and we have a lower temperature. Let us call the higher temperature T A, let us call the lower temperature T B and our cycle consists of four processes. Two processes say 4-1 and 2-3 are isothermal processes. 4-1 is a process in which heat is absorbed and 2-3 is a process in which heat is rejected. The remaining two processes are adiabatic processes in which no heat transfer takes place. But you will notice that work may be done in any of the four processes. Since our aim is to determine an expression of this cycle under the case of reversibility, we will assume that all processes are reversible, that is a requirement. Then we will assume that the working fluid is an ideal gas with constant C p, C v. And we will assume for modeling this that it is executed in a simple cylinder piston arrangement. Now let us look at how we are going to implement these four processes. We will first look at process 1-2, then 2-3, then 3-4 and then 4-1. Let us first look at process 1-2. Let me say that our cylinder piston arrangement is this. Since this process is going to be an adiabatic process, we will assume that the full system, all parts of the cylinder as well as the piston are well insulated indicating that whatever is inside, I will just show this by dotted lines, but I will not repeat dotted lines each time just to conserve some time. This is our system, ideal gas with constant specific heats. And the process 1-2 is an adiabatic process in which the state changes from state 1 to state 2 and it is an adiabatic expansion process. So the initial volume which is say v1 increases to its nu and larger value v2. How does this look like on the T-V diagram? Let us say this is our higher temperature, this is our lower temperature. Let us say T-A and T-P. Let us say state 1 is somewhere here and we will have a reversible adiabatic expansion from 1 to 2, state 2 will be somewhere here. After completing the description, we will come back to this and analyze it. Now let us look at the second process, process 2-3. This is an isothermal process in which heat will be rejected by the system. So let us again sketch the cylinder piston diagram. And now our piston is at the initial volume for this process v2. Piston is insulated, the cylinder is also insulated. But a part of the cylinder, the so called the head of the cylinder is not insulated. It is in excellent thermal contact with a reservoir at the lower temperature T-P. Some heat will be absorbed, the heat absorption will be a negative number. Let us call it Q2-3. And although the reservoir is at T-B, since the process is that of heat rejection and the state changes from 2 to 3 during an isothermal process as the piston moves in. It is an isothermal compression with heat rejection. The final volume becomes say v3. Let us now check the T-V diagram, the isotherm at T-A, the isotherm at T-B. This process 1 to 2 something which we have already seen. Now we execute an isothermal compression process from 2 to 3 like this. Since it is a heat rejection process, it is required, this is state 3, it is required that the temperature at 2 or 3, they are equal, this line 2 to 3 must be at a temperature slightly higher than T-B. But since we want it to be a reversible process, we will assume that T2 equals T3 that is necessary because it is an isothermal process equals T-B. Actually it will be T-B plus some small delta T but we will say that in the limiting case for a reversible process or analyzing this reversible process, we will neglect that negligible temperature difference. Unless we neglect that, we cannot claim this to be a reversible process. So two of the four processes have now been explained. Let us now go to the third process. We are now going to look at process 3, 2, 4 which again is going to be an adiabatic process. Let me sketch first the cylinder piston. Adiabatic process that means the piston will be well insulated, the cylinder all parts of it coming in contact with our system will also be well insulated, the piston will move in, the initial volume will be V3 and the final volume after adiabatic compression will be V4. The state of this system will go from 3 to 4. How will it look like on the T-V diagram? Isotherm at T-A, isotherm at T-B. We have already executed 1 to 2 and 2 to 3. Now we execute this adiabatic compression from 3 to 4. At 4 the temperature is T-A or just slightly less than T-A. Things will be clear when we look at the next, the fourth process. So we have now looked at three of the four processes in a Carnot cycle. Now coming to the final process, this is process 4-1 which is an isothermal process and process of expansion. So the system sketch, we have our cylinder piston initially at volume V4. The piston is insulated, part of the cylinder is insulated but because it will be absorbed from the high temperature reservoir, we have here a reservoir at T-A. Heat will be absorbed as the piston expands from its initial state at volume V4 to its final state at volume V1. Heat absorbed is say Q4-1 and the state changes from 4 to 1. When we come to the T-V diagram, these are the two isotherms at T-A and T-B respectively. We have executed three processes, 1 to 2 adiabatic, 2 to 3 isothermal, 3 to 4 adiabatic. Now we are executing the final process 4 to 1 which is an isothermal process. Again we should make it clear that since heat is absorbed during this process, the temperature at T-4 and T-1 should be slightly less than T-A for heat to be transferred from the reservoir to our system. However because we want everything to be reversible here, we will assume that T-4 which is equal to T-1 because it is an isothermal process equals T-A. In practice it will have to be slightly less than T-A since we are saying that it is going to be an exactly reversible cycle, we will neglect that small temperature difference. So this way we have looked at all the four processes in the Carnot cycle and now we will go back to each one of these and analyze that in some detail. Thank you.