 Welcome back. In this course so far we have learnt 3 objectives very specific to thermodynamics. The first one was a diabetic. We know what it means. The second one was reversible. We have defined it very meticulously. The third one was isentropic. Isentropic means at the same entropy. An isentropic pair of states means two states of a system which have the same entropy. An isentropic line means in the state space a locus any state on that will have the same entropy similar to an isobaric line or an isothermal line. It is possible that many of us are confused over this, over these three. What is the distinctness between these three? I will now make an attempt to reduce or possibly remove that confusion. Let us write the expression which we have derived linking ds to dsp. Let me write it as ds is dq by t plus dsp. This is change in entropy. This is related to heat flow and this is entropy produced. Notice that this tells us that change in entropy is partly related to heat flow and partly is produced. Now let us make a sort of a table but your columns are important. Rows are important. Do not have to give any meaning to the row. Let us begin with the middle column that pertaining to dq by t. We know that dq by t for some processes could be 0. Such a process we will call an adiabatic process. It is possible that during a process the system absorbs heat in which case this could be greater than 0. We do not have any special thermodynamic name for it but if a system absorbs heat maybe one could call it perhaps an endothermic process. It is possible that during a process the system rejects heat in which case dq will be less than 0 and dq by t will also be less than 0. Again you may call such a process an exothermic process but in thermodynamics we do not use these terms quite often endothermic and exothermic. So you notice that when it comes to dq by t term that term can be 0. It can be positive. It can be negative. If it is 0 then we will call that process an adiabatic process. Now let us come to the left column the one pertaining to change in entropy. It is possible that for a process the change in entropy is 0. In that case we may call that process an isentropic process. It is possible that for a process the change in entropy could be greater than 0 or it is possible that the change in entropy is less than 0. Nothing special about it. It all depends on what is the final state and what is the initial state. During our illustrations and exercises we will see a number of such examples. So when it comes to change in entropy we know that all 3 options are possible. It could be 0, it could be positive, it could be negative. Entropy produced is special. It is possible that it is 0 in which case ds is dq by t and that is possible only for a reversible process. So if ds be 0 we will call that process reversible. It is possible that it is greater than 0. If it is greater than 0 ds is greater than dq by t it is an irreversible process. What about the third option? Can it be less than 0? No, less than 0 is not possible because in that case it would be an impossible process. The second law tells us that this is just not possible. So here we just have 2 options. Now what is the consequence of this? Notice that it is possible for a process to be isentropic. That only means this term is 0. The first term is 0 on the left hand side. But on the right hand side these 2 terms need not individually be 0. It is possible that dq by t is less than 0 but dsp is greater than 0. Equal and opposite in sign so your ds is 0. That means you can have an isentropic process which is neither adiabatic nor reversible. Similarly consider a process which is adiabatic. It only means that dq by t is 0. It does not mean that dsp and ds are 0. It is possible that dq by t is 0 but dsp is positive and so is ds. And in that case we have a process which is adiabatic but which is neither isentropic nor reversible. The third option is also possible. Let us consider a situation where the entropy produced is 0. Well this term is 0. dsp is 0. That only means that ds is equal to dq by t. Neither of them need be 0. It is possible that a system absorbs it during a reversible process in which case ds will be positive. The entropy will increase. It is possible that during a reversible process the system rejects it in which case the change in entropy will be negative. Entropy will reduce. But we have an illustration and we have a number of illustrations where we have a reversible process which is neither isentropic nor adiabatic. So we should realize that the 3 adjectives isentropic, adiabatic and reversible. These 3 mean 3 different things. We must appreciate their independent definitions. They are related to each other but not very strongly. If you say a process is isentropic that does not mean that it is adiabatic. That does not mean that it is reversible. So an isentropic process need not be adiabatic, need not be reversible. Similarly an adiabatic process need not be isentropic, need not be reversible. And a reversible process need not be adiabatic, need not be isentropic. So these 3 are 3 independent entities in that sense. However going back to our relation ds is related to dq plus dsp. So if you decide to make any 2 of these 3 terms 0, the third will have to be 0. For example if you make ds 0 and dq 0, dsp has to be 0. If you make dq 0 and dsp also 0 that means ds also is 0. So what does it mean that although these 3 are 3 sort of independent characteristics, you decide that you have 2 of them then the third automatically comes. So if you have a process which is isentropic and adiabatic it will be reversible. You have no choice. Similarly if a process is isentropic and reversible it has to be adiabatic. There is no choice. And the process which is adiabatic and reversible must be isentropic. There is no choice. So either you must have these adjectives each one individually then the other 2 need not follow. But if you take any 2, the third automatically comes. So here you have a funny choice. You pick up any one, the other 2 will stay there. They won't follow you. But if you pick up 2, all 3 will then come together. So you either have just 1 or all 3. The choice of 2 out of 3 doesn't exist. Thank you.