 Welcome back. We are now going to see the first use of the property entropy and for that we go back to the Clausius inequality, the full inequality part. Let us consider a process. I am not qualifying this process by saying that it is quasi-static or reversible or anything. Let me sketch the process as a general process between state 1 to state 2. Let me just sketch it as this process. So when I say process 1, 2, this is the process that I am going to talk about. Now let me complete and create a cycle by connecting 2 and 1 by a reversible process. So 1 to 2, 1 dash dash 2 is a process, any process from 1 to 2 whereas 2A1 is some reversible process. So it can be executed as 2A1, it can also be executed as 1A2 in the reversed form. Now we note that 1 to 2 followed by 2A1 is a cycle. But since the 1 to 2 part we do not know in any detail, it is not qualified as reversible, it need not be a reversible cycle. Hence for this cycle, the Clausius inequality would apply in its general form, 1, 2 back to A1. Let us split this as integral of dQ by T from 1 to 2. This is over the process 1, 2 as shown in the figure plus 2A1. But we notice that this part pertains to a reversible process. I should write this as reversible. And then we note that this is related to the entropy difference between state 2 and state 1. The second part, it is a reversible process starting from 2 ending at 1. So this is going to be S1 minus S2. This is definition of entropy. And combining this with the previous relation, we will get integral 1 to 2 dQ by T plus S1 minus S2 is less than or equal to 0. Now let me do one thing. Let me transpose S1 minus S2 to the right hand side. I will get integral 1 to 2 dQ by T is less than or equal to S2 minus S1. And flipping the two sides, I will get S2 minus S1 is greater than or at most equal to integral 1 to 2 dQ by T. This relation is known as the entropy inequality or quite often called the entropy principle. It says that the change in entropy for any process must always exceed or at most be equal to this integral dQ by T over the process if we are able to evaluate it. And remember as always that this equal to sign pertains to the reversible case. If the process is reversible, then this equality will hold. If the process is adiabatic, we will have dQ equals 0 throughout the process and hence we will get S2 minus S1 to be greater than or equal to 0. This is known as the principle of increase of entropy for an adiabatic process. Notice that this principle of increase of entropy pertains only to an adiabatic process. We should never forget the fact that it is conditional. It is for an adiabatic process and that in general in a process the entropy may increase or decrease. It will definitely increase or it will definitely not decrease if it is an adiabatic process. Again here we should remember that this equality pertains to a reversible process. That means if it is an adiabatic process and if it is a reversible process, then the change in entropy over that process will be 0. Thank you.