 Welcome back. We have learned the principle of increase of entropy for any adiabatic process. In symbols it can be written down that for a small process, process element, process must be such that if it is adiabatic then the change in entropy must be greater than or equal to 0. Let us see the consequence of this, one consequence of this. Let us say that we have a system and I am sketching its state space say pv but could be any two properties x and y. Let us say that we have a state here and at that state the entropy is some S0 and we have not yet seen how to evaluate entropy, we will soon see how to do it but if we explore states around this, we will find that there is a locus of states which are all at the entropy S0. This is a locus of what is known as isentropic states, isobaric states are states which have the same pressure, isothermal states are states which have the same temperature. Similarly isentropic states are states which have the same entropy. Now this isentropic line at S equal to S0 sort of partitions the state space into two parts. One part where the entropy will be greater than S0 and another part is where the entropy is less than S0. And now according to this consequence of the second law if we execute an adiabatic process starting from this state say state 0 to begin with where we will reach the second law states that for an adiabatic process you must have a change in entropy which is greater than or equal to 0. Let us first look at greater than. So we may go to a state which has a higher entropy. So we can go here, here, here, here, anywhere. We can go anywhere in these directions and hence we have a zone here let us say and of course this is not the limit but even beyond this say this zone is the zone of states accessible or reachable from state 0 using some adiabatic process. However what about this zone? This zone the entropy is less than S0. So if you execute a process like this the change in entropy will be negative and second law forbids that and hence here we have the zone of states not reachable from state 0 using an adiabatic or using any adiabatic process and this precisely is the Karatheodori's form of the second law. For us it is not a primary form we started with the Kelvin-Planck statement of the second law as our basic statement and as a consequence one of the consequences was what Karatheodori proposed. Karatheodori turned it around he started with this statement as the basic statement of the second law of thermodynamics and derived everything else including the stuff which we have derived. Now in this limiting case it is possible that we want to remain exactly on this line the isentropic line in which case we will be executing a process which is adiabatic which is isentropic and because we will be satisfying this equality it will also be isentropic. So shown by green arrow what you see is a process which is all three together adiabatic isentropic as well as reversible. We will soon see the finer differences between these three adjectives. Thank you.