 Welcome back. Before studying the details of the second law of thermodynamics, let us look at some history pertaining to the second law of thermodynamics. Perhaps the most important name for us is Carnot. French engineer, his job was to extract water and move materials out of mines. So he used to handle pumps which were driven by engines. The engines were running on steam, coal, was consumed as a fuel and Carnot started looking at the so-called efficiency of those engines. Because an inefficient engine means for the same amount of work to be done, more fuel is needed. So it costs money. So he was always interested in improving the efficiency of engines and started thinking about what should be done to improve that efficiency. And is there an ideal engine which would have the highest efficiency? His thought processes led to what we call today the Carnot theorem. We will derive it as a corollary of the second law of thermodynamics. But historically perhaps this was the first process of thinking about what later became the second law of thermodynamics. He started looking at the various aspects of engines and he said that if I reduce friction, if I reduce leakages, then finally I will reach a situation where I will have a most efficient engine. And his thing led to the idea that a reversible engine will be the most efficient engine. This was one thought process which began the development of the second law of thermodynamics. And even today we will consider the behavior of engines. We will define an engine properly as one of the basic ideas in the second law of thermodynamics. We will apply it later to non-engine processes. We will apply it in a reasonably general way. But the idea of second law will be extracted out of so called behavior of engines. Then came Clausius. He linked temperatures with heat flow. He said that look, heat cannot flow from a system at a lower temperature to another system at a comparatively higher temperature. The Carnot's idea led to the maximum possible efficiency of an engine. Whereas Clausius idea, we will for the time being neglect the fact that we have not yet formally defined what is a lower temperature and what is a higher temperature. The Clausius statement or Clausius thinking gave us one aspect of second law which says something cannot happen. The possibility, impossibility brought in by the Clausius way of thinking about the second law of thermodynamics. The ideas of Carnot regarding engines were further developed by Kelvin and still further by Planck. And Kelvin and Planck, they came up with one simple statement of the second law of thermodynamics. In simple words, we will formalize it later. It says that the efficiency of engine can never be 100%. That means if you have an engine which produces power and it only absorbs heat and converts it completely into power, they say this is not possible. So, notice again, this is a possibility, impossibility type of statement. Another statement that we will note is that of Carrot Theodori, a mathematician physicist. And his is more basic thermodynamics, but purely in the domain of mathematics, calculus, differential calculus and so on. In a simple way, he says that if we have a thermodynamic system, let us show it for example on a PV diagram or some two properties x2, x1. Just for illustration, I am considering a two dimensional system. Let us say that we have a state here of a system. Let me show it by a point P. In Carrot Theodori, it says that if you restrict yourself to a diabetic processes, that means processes in which only work interaction takes place. Then consider this state in equilibrium. Around this, there are other states and these are states, all states here are in equilibrium, states that cannot be reached by quasi-static adiabatic processes. Quasi-static to indicate that even this state, initial state and the state which you are trying to reach must be states of thermodynamic equilibrium. Whereas there will be other states which can be reached. So this is a statement regarding what happens with adiabatic processes. Adiabatic processes, when you start from some initial state, will take you to only a restrictive set of states. There are other states which you cannot reach purely by adiabatic processes. Our next discussion will be to which one of these statements do we take as a primary statement. Thank you.