 Let me take a few questions. Jabalpur, over to you. Good morning. My first question is, what is the reference of 0 degree Kelvin? My first question is, what is the reference point of 0 Kelvin? And my second question is, if I am the student of first year or second year, how will you define entropy? Over to you sir. Your first question was about 0 Kelvin. Get used to it. Forgot the reflexes over the weekend. About 0 Kelvin, 0 Kelvin is not defined. The, our thermodynamic temperature scales, remember thermodynamic temperature you could have many scales, including Kelvin scale just one for a single reference point. And for Kelvin scale, we know it is triple point of water. So, we do not have to define 0 K and it is not defined. However, there is already a discussion on Moodle also on this line. Do participate in that, where approachability of 0 K etcetera has been discussed. The second question was, how do you define S to a student in the first and second year? We define it precisely the way we have defined it during this course. First, emphasize before we come to second law, emphasize that energy also is defined as a difference. So, in a similar way we define entropy also as a difference. And we say that the show them this analogy delta E is defined as say minus integral 1 to 2. This change in energy between two states, the work done by an adiabatic process. And here we select any adiabatic process. First law says that for any adiabatic process, this work done will be independent of the path. So, we do not have to define the path. We select any suitable path. Only requirement is that it should be an adiabatic process. In a similar fashion, note this similarity delta S 1 2 is defined as 1 to 2 integral of d cube by t. Just the way we had adiabatic as the constraint here, reversible as a constraint here. And here any reversible process. So, we can say the first law which defines energy is our understanding of the behavior of adiabatic processes. The second law which defines changes in entropy is our understanding of the way reversible processes behave. And the second law tells you the derivations from the second law tell you that this integral will be independent of the path for any reversible process. This is the way a student who has done 12th standard calculus plus a bit more math in first year engineering can understand. We have had the teaching of thermodynamics in the four year B. Tech program right from the, we have had it at various stages from second year, second semester, second year, first semester, even in first year, second semester. And we have had absolutely no difficulty in making them understand this. Over to you. Thank you sir. Panvel, good morning. Over to you. Area under the TDS diagram, integration of TDS greater than or equal to cube. So, you have given the homework for checking this equality or greater than sign. So, in most of the books I found that it is given is equal to cube. Can you elaborate it sir? Thank you. This was the question I think which was discussed. I think sometime on Saturday. Again, let me sketch that. We have a quasi-static process on a P V diagram. What is that this area under this curve? And we said area under this curve is integral P D V and which is W expansion. No doubt about it. Now, let us take a process and we say that this also is quasi-static. Because it is quasi-static, we can sketch it as a continuous curve. Remember that a continuous curve in state space means only a quasi-static process. It need not be a reversible process. The question that arises is this. This is if this was A under the P V curve. Let this be A under the T S curve. Now, remember that our second law says that delta S or let us take in a differential form. D S is greater than or equal to D cube by T. That is our entropy principle or entropy relation. T is always positive. So, we end up with T D S is greater than or equal to D cube. Now, integrate both sides, left hand side as well as right hand side. The integral of T D S will be higher than or equal to the integral of D cube. And integral of T D S is nothing but area under the T S diagram of a quasi-static curve, quasi-static process which will be greater than or equal to cube. That means, even if you have an adiabatic process, it is possible for the process to have an area higher than that. That means, if you have an adiabatic process, the area can be 0 like this. Area can be positive. It can go like this. Area can be as much positive as it feels like. So, remember this comes out of the basic idea of second law or the entropy relation. Good morning, Dr. Brahmara. Any questions? Over to you. Yes, sir. There is one question regarding entropy, sir. I am handing out the mic to the participant. Good morning, sir. This is Janardhan. And my question is like what is the meaning of the word entropy? It can be dictionary meaning or general meaning. And what does it physically means? It is like if we say heat, we can get a feel of that. When we say entropy, how can we feel that? Physical explanation of that. The question is, what is the meaning of entropy and how do you explain it and how do you feel it? Remember that when it comes to feel, perhaps the only thermodynamic variable which we feel is the temperature because of the three thermodynamic properties which basic thermodynamic properties which we have defined T, E and S. Only the temperature is defined at some sort of a level. You know the label on isotherm and each isotherm can be considered as a level. Whereas, energy is defined as delta E entropy is also defined as a delta S. So, for this there is no direct feel. And that also means you will notice that there is no direct measurement also. And this is true not only of the thermal energy that we are talking about. This is true also of the measurement of other energy components. You know gravitational potential energy is not directly measured as energy. It is measured in terms of the level difference or height difference. At something comes down in a height, you can measure the work required to bring it down or work required to raise it up. Similarly, our electricity energy meter, it keeps continuously track of voltage as well as current and integrates that out to give you the actually what it measures is interaction. It does not measure delta E. Delta E is derived from it. So, one should be always conscious of the fact that of the three basic thermodynamic properties, temperature, energy and entropy. Temperature is the only one which is something like a level and we have a feel for it. Whereas, energy and entropy are first defined as differences and we do not have a feel for it. And that translates into the fact that there is no direct measurement for this. So, that should be emphasized because people think that kinetic energy can be directly measured. Kinetic energy is not directly measured. You measure the velocity of a particle or a body, linear velocity or angular velocity whatever it is and use a formula to determine the kinetic energy. If you try to measure the kinetic energy, actually you are measuring, you are creating a change of state from high kinetic energy to low kinetic energy and that energy change for example, breaking a vehicle that is an interaction and that interaction is being measured. Direct measurement of energy or energy differences is not possible. And as I have said earlier maybe a junior school boy or a junior high school boy may find it difficult to understand what entropy is. Energy for some reason is easily understandable and that is why we introduce it in early high school. I think quite often it is introduced is our ability to do work because reduction in energy as we have seen is the work done by a system provided there is no heat transfer. And because of that perhaps in school we keep the heat transfer separate from work transfer that is why we talk only of heat, we do not talk of thermodynamics. Thermodynamics properly should be learnt only when some calculus is learnt. So, over to you Brahmara. What is the dictionary meaning of entropic? When you say work we can tell that some body is moving from one place to other place some distance. But physically the entropy what is that? See for entropy we should not and I do not try to give a very simple explanation. It is a very useful property which allows us to determine whether a proposed process is a possible process or an impossible process. Students and even school kids understand that there is something called time, there is something called before and after there is only a direction in which many processes take place. You just tell them that entropy tells us the direction whether the proposed direction of a process is a possible or an impossible process. And remember that if you take an adiabatic system and look at its two states then all that we say is that state with the higher entropy will be the later state in time state with a lower entropy will be the before state or the earlier state in time. Tanjavur over to you, over to you Nirma at Amdabad. Sir, my question is can we calculate the entropy of any system entropy produce? I am talking about the entropy of any system absolute entropy over to you. I think I have said so far that entropy is defined only as a difference. So, there is for us there is no such thing as an absolute value of entropy. You may go into textbooks of material science and you know solid state physics and things like that. There they have a so called third law of thermodynamics where they say that the entropy of a perfect crystal at 0 Kelvin is 0, but there are two problems with this. The first problem is thermodynamics should not and basic thermodynamics does not depend on the properties of any material and should not. If a basic law of nature should be independent of any particular material. So, the moment you talk of something called a perfect crystal you are not remaining in the domain of proper thermodynamics. And second thing even if you accept a perfect crystal as something you know God given even then if you really look at it that also is a just a definition that let us define that to be 0. If you define it to be a positive number or a negative number absolutely nothing goes wrong because finally everything comes down to the fact that it is the entropy difference which is important as mechanical engineers we should never ever think up of absolute value of entropy over to you. Thank you sir over and out.