 Welcome back, while ago we looked at the various aspects of the second law as thought about by Carnot, Kelvin and Planck, Caratheo-Dory and Clausius. Of these four possible channels of attack or four possible statements of the second law of thermodynamics, we will now select one as our basic statement and proceed from there. We will not look at the Caratheo-Dory statement because that is mathematically too involved. It is not easy for us engineers to absorb it. The Clausius statement is considered a weaker statement of the four because it talks of a lower temperature and a higher temperature and we have not yet defined in a proper thermodynamic sense what is a lower temperature and what is a higher temperature. The Roth law tells us that look there are different temperature levels. We can provide labels for them, one label for each isotherm and we call that temperature. But the scales of temperatures, the numbers we give them are arbitrary. It so happens that most of the scales of temperatures which we use give boiling water at say one atmospheric pressure at a higher temperature value than freezing water at one atmospheric pressure say for example 0 degree Celsius and 100 degree Celsius. But these are the numbers which we have decided. Nothing would have prevented us from providing a higher temperature to the boiling point and a still higher temperature to the freezing point. But tradition and convention dictates that all temperature scales go in one direction. But thermodynamically we have not yet been able to define any proper hierarchy of temperature. That leaves the Carnot thinking and the Kelvin Planck thinking. The Carnot statement of the second law where you talk about the maximum possible efficiency requires thinking about an idealized engine, the so called reversible engine. Whereas the Kelvin Planck statement does not talk about any such thing. And that is why we will consider the Kelvin Planck statement to be the basic statement of the second law of thermodynamics. We will formalize it and we will proceed with the derivations pertaining to the second law of thermodynamics. We will define many terms en route to make the analysis simple and the derivations understandable. We will be able to use plosius way of thinking to indicate that there is a hierarchy of temperatures which we can arrange from higher levels to lower levels. Again higher and lower will be arbitrary but the fact that a hierarchy of temperature exist will be demonstrated using the second law of thermodynamics. The Carnot way of thinking will be demonstrated as a proof of the Carnot theorem after defining what we mean by a reversible process and a reversible engine. And finally when we define entropy and a final form of the second law of thermodynamics we will also be able to appreciate the Carrot Theodoris statement. We will be able to show that from a given state of equilibrium in the state space of a thermodynamic system there will be states where we will not be able to reach using adiabatic processes. Whereas on the other hand there will be states which we will be able to reach using only adiabatic processes. So let us come back and now let us look at the Kelvin plant statement of the second law of thermodynamics. We will call this simply Kp or Kp statement. In its basic simplest form the Kp statements considers a system which executes only cyclic processes. Actually it should not have no net change of state. That means either the change of state should not be there or cyclic process and this system executes a small process in which some amount of work DW is done. It has to be positive. That is the work has to be delivered by this system or done by the system on some other system. And other interaction is the appropriate amount of heat absorption. So by first law we have DQ equals DE plus DW because there is no change of state or a cyclic process is executed. This is 0. So we should have DQ equal to DW. And since DW is dictated to be positive, DQ also is dictated to be positive. Now what this system is doing is without undergoing any change it is absorbing certain amount of heat and converting it completely into work. This is complete conversion of heat into work using a system which undergoes no change of state or which executes only cyclic processes. The Kelvin-Plank statement says that this is not possible. If you are doing according to our convention a positive amount of work and that means if you are converting completely this heat absorbed into the work done by the system Kelvin and Plank in their statement of the second law say, no, this is just not possible. However this does not exclude the possibility that a system without no, without any change of state will absorb some amount of work that is DW being negative and reject some amount of heat to some other system. That is possible. But as shown here heat absorption from some other system and work done on some other system without a change in state of the system involved is impossible. That is the Kelvin-Plank statement of the second law of thermodynamics. Thank you.