 Welcome back. Let us now see how to evaluate the entropy difference between two states of a system. We have defined entropy, we have seen its use, we have derived adjectives like isentropic, we have appreciated that, we have linked it with others. Now let us look at the situation where given two states we have to evaluate the entropy difference between the two. And remember always that entropy is defined as a differential or a difference. So absolute values are not of much use to us. Our definition of entropy change in a differential form is ds is dq by T for a reversible process element. And that means if we have two states one and two we should have after integration s2 minus s1 is integral of dq by T from state 1 to state 2 over a reversible process. And we should note that dq by T for a reversible process element is an exact differential. So this integral will be independent of the path. So this is for any reversible process. And what we do is execute a reversible process. How do we execute a reversible process? For this reversible process what is required is we have seen this earlier when we implemented the Carnot cycle is that the process must be quasi-static. Because then we know that it went through a certain set of states and we will be able to trace it back. Only two way modes of work if there is a heat transfer the difference delta T between system and surroundings must be negligible in principle 0. Similarly quasi-static expansion etcetera means if there is an expansion the pressure difference between the system and the neighboring system must be 0. No dissipative components. And not only our system but all systems involved must execute reversible processes. If we do this then we will be able to implement a reversible process and then integrate dq by T over such a process and we get S2 by S1. Now the question is which reversible process linking two states of a given system there could be more than one. In which case all that we do is we say any reversible process we will select one according to our convenience. For example if we have a simple compressible system or a fluid system a typical pair of variables would be PV for us to plot the state space. And let us say that this is state 1 and this is state 2. And now I am going to show processes which I claim to be reversible. One possibility is you take a process which is like this. Now although this is a possible process perhaps reversible if it is a reversible it is a candidate process for evaluation of entropy. But the variation of P and V is not uniform. Integration may not be easy or straightforward. But nothing prevents us to decide on a process or a set of processes starting from one ending at two which are convenient to work with. For example we could consider a isobaric line from P and a constant volume line from V and we can decide that perhaps 1, a, 2 this constant pressure followed by constant volume. This could be one possibility. Another possibility is take a constant volume line from 1, a constant pressure line from 2 and decide that we will go first along the constant volume line 1b and then go along the constant pressure line b2. The choice is ours. If we are very savvy at complex integration select a path. Otherwise it is best to do by the least complex path. Nothing prevents you from taking a very scenic route like this. It is perfectly okay to do this but it is only more cumbersome to evaluate this. If you have really selected a reversible path and done your integration properly then the result would be the same and the change in entropy S2-S1 will be represented by that expression which is the integral from 1 to 2 of dq by t over a reversible process. Thank you.