 Welcome back. Before we go over to exercises, there is a small thing that I would like you to understand and appreciate. We will visit this and this will be used later when we discuss property relations. Let us consider a closed system containing a fluid and let it execute some quasi-static process. Let me sketch the process first on the PV diagram and let the process be shown like this from 1 to 2. And then let me show the same process plotted again on a PS diagram and let perhaps it will look something like this. All these processes are, it is the same process actually. The process is quasi-static, means on the PV diagram it can be represented by a continuous line. So, can it be on the TS diagram? And because it is a nicely defined continuous curve, we can determine the area under this curve on the PV diagram. Let me call it APV. Similarly, because the process is quasi-static and we can define the area properly, let this area on the TS diagram be computed and let me call this area APS. The question is what do these areas represent? Remember that this area represents integral PV from state 1 to state 2 and hence this area APV should equal the expansion work done by the system. What about the area ATS? This area equals integral TDS from state 1 to state 2. What does second law say about this? Second law tells us that DS must be greater than or equal to dq by T and hence TDS must be greater than or equal to dq and hence the area under this curve ATS is greater than or equal to the heat transferred to the system during this process. So, one area represents the expansion work. The other area does not directly represent the heat transfer but it can be greater than or at most equal to the heat absorbed by the system. And again we are encountering our second law inequality, the greater than or equal to here and the moment we see that one should note that this equality will hold only when the process is reversible. We should remember this. We will use this again a few videos later for property relations. Thank you.