 So, let us discuss about entropy today. So, I am going to introduce this concept once I will discuss little bit about the heat engine. So, let us visualize what happens in the heat engine first. At a higher temperature T1, the system absorbs heat let us say. The heat absorbs absorbed is Q1 and then it gives away heat Q2 to a lower temperature. This is what happens and you are extracting some work out of it. The efficiency if you remember is 1 minus T2 by T1. So, you can see that efficiency of the heat engine depends only on the temperature. So, it does not depend on how much heat you are taking away from this temperature T1. And it also tells you that if same amount of heat Q1 if you are able to extract at a higher temperature let us say T1 becomes T1 dash and if T1 dash is more than T1 you will be able to extract more work or the efficiency will be higher. So, it in a way says that if you get Q1 at higher temperature this heat can be easily converted into work. And if same Q1 is taken at let us say lower temperature then your efficiency will be also lower. So, the quality of heat which are getting at higher temperature is more. This is what in a way it tells. So, the entire concept of entropy can be thought as an outcome of this only. So, basically entropy is a quantification of how much is the randomness of the system. So, if one has to quantify the entropy it will be heat absorbed divided by temperature if it is happening at constant temperature. So, let us discuss this what it is and then we will talk in detail about it. This is basically change in entropy sorry. So, if you are absorbing Q amount of heat at a temperature T increase in entropy will be Q by T. Now, if T is lower then increase in entropy will be higher. So, whatever heat you are absorbing most amount of that gets utilized as to increase the entropy of the system and lesser amount of heat is utilized to give the work. So, because the entropy change will be higher if you get same amount of heat at a lower temperature it is not useful. More useful heat will be when you get the same heat at a higher temperature because of that the change in entropy of the system will be lower. So, this is the reason why entropy is defined as heat absorbed divided by at what temperature heat is absorbed. Now, if temperature is not constant then I can say that small change in entropy is small amount of heat absorbed divided by temperature. It assumes that if you absorb very small amount of heat temperature does not change suddenly. So, total change in entropy will be integral of this. It will be integral and it will be from initial point to the final point. Had the temperature been constant temperature would have come out of this integral and you would have got the same result. But now temperature is not constant so it will remain inside only. One more thing you need to understand here is that increase or change in entropy is a state function. So, this is the basic quantification of the entropy. Now, let us talk about what are the implication of it or how the second law of thermodynamics puts restriction on what should be the change in entropy. So, basically second law of thermodynamics can be stated in terms of entropy also. So, according to second law of entropy according to a second law of entropy the for a closed system for a closed system change in entropy should be greater than 0. This gives a direction to any process. So, basically spontaneously if some process happens it will happen in such a way that the systems if it is closed the entropy of that system will always increase. So, basically it gives a direction to every process. Example could be you are let us say you have water in a glass. So, if you spill water if if the water which is placed on a vertical this thing if you make it horizontal all the water will come out. So, basically what is happening is that the randomness has increased. So, this will happen spontaneously the water will spill out spontaneously. But now water will not go back in the ordered state and you will not get this thing again back spontaneously. You need to do some work on it. So, this is a spontaneous process. Similarly, when you have let us say you you have a cloth let us say a towel is there which is wet and you have placed it in a room like this. After some time you will see that the after few hours you will see that the towel has become dry. So, what happens is that the water on a towel will evaporate and this is a spontaneous process. Why it is evaporating? Because when it is evaporating the liquid is converting into the vapor and naturally the randomness of vapors molecules is more than the randomness of liquids molecule. So, this happens spontaneously but spontaneously the vapor will not again condense on the towel. So, this tells us that in which direction the process will move. Because conservation of energy will not enable us to find out in which direction the process will move. Example could be that if suppose liquid converts to vapor and because of that it let us say it absorbs Q amount of heat. Then similarly automatically it will not happen that vapor condense to liquid and heat is released even though according to conservation of energy nothing is invalid but then this process will not happen. So, because the entropy changes negative of the isolated system. So, in an isolated or closed system any process will happen in such a way that the entropy should always increase. Let us take another example you have a hot object let us say temperature is T H fine and you have a colder object let us say temperature is T C and they are connected by a rod. Let us say they are connected by a rod like this. So, slowly and slowly the heat will get transferred from hotter temperature and to the colder temperature and this system of hot object and cold object together you can say they are forming a closed system. Let us see the individual entropy change and then we will see the entire systems entropy change how it is varying. So, for let us say this is object 1 and this is object 2. So, for object 1 the entropy change will be equal to whatever heat is given to the colder object divided by the temperature of the hot object. So, you can say that this is the integral of this this is for the 1. Now, roughly you can say that this is equal to the total amount of heat that is given away divided by some temperature let us say temperature T 1 which is the average temperature of the hot object. What happens is that the temperature of the hot object keeps on changing. So, basically T 1 will be lying between the hot temperature and the final temperature is let us say T F. Final temperature is a temperature of both the objects when the heat transfer is stopped. Now, the entropy of the object 1 is like this and then if you talk about entropy of object 2 change in entropy sorry it will be integral of d cube by T. Now, this can be roughly written as heat which is absorbed divided by temperature T 2 where T 2 is between the final temperature and whatever was a colder temperature. Isn't it? Now, according to sign convention since hotter object is losing the heat I have to put a minus sign over here. The amount of heat released by the hotter object is equal to the amount of heat absorbed by the colder object. So, this will be positive only. So, total entropy change will be equal to Q divided by T 2 minus Q divided by T 1. This can be written as Q times 1 by T 2 minus 1 by T 1. Now, you can see that clearly T 1 is more than T 2. Isn't it? Because T 1 is lying between higher temperature and the final temperature and T 2 is basically lying between the final temperature and the colder temperature. I will reverse it actually. T 2 is lying between the final temperature and the it is higher than the colder temperature and lesser than the final temperature. And here T 1 is basically higher than the final temperature but lesser than the hotter temperature. So, basically T 1 is greater than the final temperature whereas T 2 is less than the final temperature. So, that is the reason why 1 by T 2 is more than 1 by T 1 and hence delta S total is greater than 0 for this particular system. So, here you can see that even in the heat transfer when the temperature of the hotter when one object which is at higher temperature releases heat to the colder object. The change in entropy will be greater than 0 only when heat from hotter object goes to the colder object. So, spontaneously only this is possible. It is not possible that heat from the colder object goes to the hotter object. Then change in entropy total will be less than 0 and that will be against the second law of thermodynamics. See second law of thermodynamics has many statements. There are Kelvin Planck statement, there is Clausius statement and this particular discussion of second law of thermodynamics we are having is in terms of entropy. Now at times the system is not isolated. So, you will not be able to enclose boundary of a system but then whatever process happens if you enclose the system and its entire surrounding then it will become universe. So, system plus surrounding will always gives you universe and is universe an isolated system? Yes, universe is an isolated system because universe does not interact with anything else, nothing else is outside the universe and since universe is an isolated system and hence change in entropy of the system plus change in entropy of the surrounding which is change in entropy of the universe has to be greater than 0. So, whatever happens in the universe should lead to increase in entropy of the universe. If entropy of the universe is not increasing in a particular process that process is not possible. So, this is a brief discussion on the entropy and at times you will see that in a graphical type of questions sometime you will see the plot between let us say entropy and temperature. Let us say on x axis there is entropy and y axis there is temperature and for a reversible process you will see it is in line like this. So, this line represents isentropic process. This is an isentropic process or you can say a reversible adiabatic process where the heat exchange is 0. So, change in entropy is 0 and this represents isothermal process which is constant temperature horizontal line. So, like this you can see the plot and if you see a line like this and if you find out the area under this what it will be equal to. So, according to the definition of entropy ds is basically dq by t. So, dq will be equal to tds. So, area of tds curve is integral of tds which is nothing but heat exchanged delta q. All right. So, like this you should be able to play around with the concept of entropy and I hope the concept of entropy is very clear now and you will be able to attempt the questions. In case you feel any difficulties there or you are not able to get a particular problem, please feel free to get in touch. You can write in the comments or you can directly get in touch with us. Thank you.