 Yes. Ready? Shall we start now? Yes. So next is, so we had discussed entropy, we had discussed enthalpy in detail earlier only. So next we have second law of thermodynamics, thermodynamics, okay. That is slot, okay. So we have different, different statements for this second law of thermodynamics. The first one we have Clausius statement, basically different, different way to represent it. All these statements you should know, Clausius statement. It says it is impossible to construct, impossible to construct a machine, construct a machine with, with 100% efficiency, basically 100% efficiency is not possible, okay. This also means, this also means that complete conversion of, of heat into work, into work is not possible, right. And on the basis of this statement only, we have another form of second law of thermodynamics and it says, it is impossible, it is impossible to convert heat into work, heat into work without compensation, heat into work without compensation, right, means you have to do some change into the system, then only it is possible. If equal amount of heat, you know, if you want to convert that heat into work, you have to do some compensation, otherwise complete conversion is not possible, next. It also states that, it also states that, that the entropy of the universe, of the universe increases, increases in a spontaneous process, in a spontaneous process and remains unchanged, remains unchanged at equilibrium. It is second law of thermodynamics, all these statement, no, all these statements are second law of thermodynamics only, basically this statement, the first one is given by a scientist called Clausius. So we call it Clausius statement, such name we do not have here, just you should know this. It does not. It also states that, the entropy of the universe increases in a spontaneous process and remains unchanged at equilibrium. So mathematically what we can write, delta S of the universe, it keeps on, it is kept on increasing, greater than zero. And we know delta S universe means delta S total basically. So it is delta S of system plus delta S of surroundings, system and surroundings. Okay. Once again. Yeah. So universe and property keeps on increasing. That also we say one statement of this, that the entropy of the universe keeps on increasing. Right. So this is the mathematical statement we have at equilibrium, what we can write equilibrium we can write delta S of universe is equals to delta S of system plus delta S of surrounding, which is equals to zero. This is at equilibrium, right. For reversible process we have seen this, this relation already. Reversible process, the expression of entropy change, it is DQ by T. Already we have discussed it, right. The definition of entropy is the same. And if the process is irreversible, irreversible, we know the entropy change is greater than DQ by T. So if you combine these two statement, it gives DS is greater equal to DQ by, this is the combined statement or we say it is a mathematical statement of second law of thermodynamics, statement of SL40, second law of thermodynamics. What is this statement for second law of thermodynamics? You should know. At equilibrium, it is equal, whatever the change in entropy, first of all, the change suppose that equilibrium system entropy decreases with the same amount the surroundings entropy increases. So in terms, if you add the two, it will be zero. The change will be zero. Delta has to change the entropy of the universe or total entropy change at equilibrium would be zero. You can also say that at equilibrium, the magnitude of entropy change for system and surroundings will be equal, but they are of opposite nature. Means what? If system entropy increases by some value, with the same value, the surroundings entropy decreases. Hence the sum is zero. Okay. Now you see this. See we had started all this discussion with spontaneity, that is spontaneous process, right? For spontaneity, the condition is what we discussed. We discussed two conditions are there. First is the enthalpy should be less than zero, exothermic, this is what we see. And the second one was what? What is the second one? Tell me the second one. Anyone? What is the second factor for any process to possibly? Delta has greater than zero, that's not. Second factor is randomness. That's what I said. No. That randomness will increase, right? Remember that endothermic examples, those processes were taking place because of they are going towards the more randomness, okay? If you go back and check the relation over there, okay, H2O liquid converts into H2O gas. So gas will have more entropy than liquid. You go back and check, H2O liquid convert into H2O gas, wait a second, you see this. This reaction we were discussing, it was endothermic, it was endothermic, right? Why this reaction was taking place? Because it is going towards more randomness, you see, solid and liquid, liquid is more random than solid. Liquid to gas, gas is more random than liquid. All these are solids, solids and one gas is there. For all these reactions, you see, entropy is increasing if you're going towards the right and hence the process was taking place. Randomness was increasing. The second factor was randomness. First was enthalpy, second was randomness, right? These two factors we have for the spontaneity, is it clear now? Yes, these two factors we were discussing for spontaneity, either delta H should be less than 0 exothermic process or randomness should increase. So whenever you need to judge any process, whether it is, you know, spontaneous or not, you need to think of exothermic like, sorry, enthalpy change and the randomness. Randomness means entropy you need to check. This enthalpy and entropy, two factors you need to calculate in order to find out the spontaneity of any process. So later on what we did, because both are temperature dependent process, this and this both are temperature dependent process. So later on what we did, we thought that instead of, you know, finding instead of considering two factors that is enthalpy and entropy and find out the spontaneity of any process, why don't we club these two factors and we'll give a new thermodynamic term. And based on that single thermodynamic term, the new thermodynamic term, we can say the given process is spontaneous or not, correct? So with this thought process, what they have done, they have defined again a new thermodynamic term that is Gibbs free energy, Gibbs free energy represented by G. So what is the use of this Gibbs free energy? They have defined this just in order to, you know, understand whether the process is spontaneous or not, like just based on one term, yes. So what they did, they clubbed the two term enthalpy and entropy and they have given a new thermodynamic term, okay, statement for this. What is Gibbs free energy write down? It is, it is the thermodynamic quantity, thermodynamic quantity of a system, of a system. And it is, and it is the, or this is equals to equals to the amount of useful work done terms you must keep in mind, I'm writing on useful work done, amount of useful work done by the system, by the system. Basically what we say, this useful work done is nothing but the non expansion work done, non PV work. In this the pressure volume is not involved, non PV work. Like suppose you have a chair over here, you take this chair and put it somewhere else, right, from the bedroom to hall, if you put it a chair, you have done some work, right? This work is non useful work, non expansion work, right? This is the work we have over here. So if I take a chair from here and keep it somewhere else, I have done some work. This work equals to the decrease in my Gibbs free energy, right? I have a pen over here, I keep this pen, I take this pen from here and I keep it somewhere else. So I have done some work, right? This work is done at the cost of my Gibbs free energy, right? So what we can say, the useful work done, useful work done is equals to the decrease in, in Gibbs free energy, useful work done is equals to the decrease in Gibbs free energy of the system. So if you have done some useful work, your Gibbs free energy decreases. Oh wait, wait Praku, I will come to that point one by one, okay? Okay? So this is what the meaning of it, right? What is useful work done? So it is the work done equals to the decrease in Gibbs free energy of the system, right? That is what the physical significance of Gibbs free energy. You do some work, you, you do some work at the cost of your Gibbs free energy, right? That is the physical significance of it. Mathematically how it is defined, did you copy all of you, did you copy this? Mathematically how it is defined? The mathematical definition of Gibbs free energy is, it is G is equals to H minus T s, where s is the entropy, T is the temperature, H is the enthalpy and G is Gibbs free energy, okay? So like I said, instead of, you know, calculating or, no, understanding this enthalpy and entropy and then we will say whether the process is spontaneous or not, we have clubbed the two terms with the help of temperature and given a new thermodynamic term which is delta G and on the basis of this only delta G or Gibbs free energy, we can say that the process is spontaneous or not. What is the condition of spontaneity, we will see that, but we don't have to judge now what is enthalpy, what is entropy, because instead of these two, we have single term that is Gibbs free energy here, okay? So delta G, the change in Gibbs free energy, we can write delta H minus T delta s at a given temperature, this equation we call it as Gibbs-Hemholz equation, H E L M H O L T Z equation, copy the zombie, okay? So we will see the condition of spontaneity now, okay? We will see the condition of spontaneity, what should be the value of G Gibbs free energy so that the process would be spontaneous, right now, right on here, condition of spontaneity. Generally what happens, any reaction takes place at a constant temperature and pressure, so that is what we are assuming, what we are assuming our assumption is constant temperature and pressure, constant temperature and pressure, now suppose at this condition, I am assuming again Q amount of heat, Q amount of heat is given by the system to the surroundings, system is giving heat, right? System is giving heat, what is delta s total, obviously delta s total, we know it is greater than zero always, right? But we can also write this as delta s, because second law we know entropy keeps on increasing, right? Delta s total will be greater than zero and this we can write delta s of system plus delta s of surroundings, okay? Now see system is losing heat, what Q amount, so what we can write minus Q of the system and the amount of heat releases by the system equals to the amount of heat gained by the surrounding, minus Q system is equals to plus Q surrounding, right? And since we have the constant pressure here, so at constant pressure, the heat exchange is nothing but the enthalpy change, delta h of the system, can we write this? Yes or no? Is it clear this expression? Yes guys, respond quickly, right? Whenever the heat is given by the system, so minus Q of system is equals to the surroundings will take equal amount of heat, so plus Q for the surroundings and since we have constant pressure, so heat exchange of the system is nothing but the enthalpy change of the system, because we know heat, enthalpy is nothing but the heat content of the system at constant pressure, yes, okay? So what is the entropy change of the surroundings? Can we write this as plus Q surrounding by T, yes, whatever heat surrounding will take that divided by the temperature at which the process is taking place, that is the entropy change, standard definition we have, okay? But this Q surrounding is equals to what? Delta h of the system, but here I forgot to mention this negative sign, because Q system is delta h system, minus Q system is minus h delta h system, okay, same thing. So we can write delta s of surroundings is equals to minus delta h of the system divided by T. You see, we have enthalpy of system and entropy of surroundings, take care of this, okay? It is surrounding here, it is system here. Now this I will substitute in this expression, in this expression. So what we get here, you see, delta s of the system and delta s of surrounding equals to minus delta h of the system by T, you will understand why I have done this change over here, you will get it. So could you see here, this expression if you take, I will see it when I just you simplify this, you will get minus of delta h of the system, minus T delta s of the system, isn't it? Yes or no, right? And what is this expression, delta h minus T delta s, what is this expression? So I will write down T this side, T delta s total, okay? So this expression is nothing but the change in gifts free energy. So can we write this as minus delta g of the system right hand side, right? Isn't it, correct? So what is the expression you get here, you see? The expression we get here is the change in gifts free energy of the system is equals to minus T into the total change in entropy, correct? We know this delta s total is always positive, we know this fact, delta s total is always positive for spontaneous process, for spontaneous process. So for any process to be spontaneous, the delta g of the system should be less than 0. This is the condition of the spontaneity we have. So instead of calculating enthalpy and entropy, we'll simply find out the change in gifts free energy. If it is coming out to be negative, that is less than 0, it means the process is said to be an spontaneous process. Is it clear? Yeah, I'll go back, let me know once you're done, yeah. So this is the condition we have. So what happens here, from where did we get this condition? We know this fact that for spontaneous process, for spontaneous process, delta s total is greater than 0, which leads to delta g less than 0 of the system, right? For non-spontaneous process, it is opposite. For non-spontaneous process, delta s total is less than 0, so delta g is positive. When delta g is positive, then the process won't occur in forward direction, but it may go in backward direction, right? So right on forward direction, processes won't go, process does not occur in forward direction, but may occur in backward direction, right down here. You just copy this one important information I need to share with you. Those who all takes bio classes, right? Those who all takes bio classes, for coming week, this week and the coming week, you will have bio classes on Wednesday. Okay, so this is this arrangement we have for this change we have for just for the next, for the coming two classes, okay, next two classes. And then after that, you'll have the same schedule Monday and Friday. Okay, so tomorrow you all have a biology class from 4 to 7.30, correct? So all those who takes bio classes, please keep this in mind and take note of it. Tomorrow 4 to 7.30, okay, done this. See at equilibrium, no, Friday you do not have, you have a one class only in a week that is for three and a half hour, okay, for this two week, tomorrow and the next week classes, okay? And then you will have the normal schedule after 10th of December, okay? So Friday, guys, you do not have any class on Friday, only one class tomorrow and one class on next Wednesday, next week, Wednesday, for three and a half hour. Are you lagging behind the syllabus, biology? See this, at equilibrium, we have delta S total equals to zero. There's no change in entropy, is equals to zero. Hence, delta G is equals to zero also, at equilibrium. Now you see, yes, now the next thing you see, the role of temperature in spontaneity, role of temperature in spontaneity. We know the relation of delta G is equals to delta H minus T delta S. We just need to check whether delta G is negative positive or zero. Accordingly, we can say it is spontaneous or non-spontaneous. Two processes we have possible, either we have exothermic or we have endothermic, exothermic or endothermic. So in exothermic process, you see, we know delta H is what? Delta H is negative, exothermic process, delta H is negative. So this term is negative, right? You see here, we have delta H minus T delta S, delta G. Now listen to me carefully, you can write down a bit later. This delta H is negative already, right? It is negative. If T delta S is positive, then this is positive. One negative sign already, we have means delta G is negative in this case. Yes or no? For exothermic process, this means for exothermic process, if T delta S is positive, then the process will be spontaneous at all temperature, whatever temperature you take. If it is positive, it is spontaneous. The process will be spontaneous at all temperature. Clear? Did you understand this, all of you? Condition, you must understand. You will get questions on this only. Like this only, you will get questions, okay? I am taking this condition. I don't know whether it is positive or negative, but what happens if it is positive? We'll see the next condition also. If T delta S is negative, then what happens? Tell me, did you get it? Second condition is, if T delta S is negative, you see this. The expression is delta G is equals to delta H minus T delta S. Since the process is exothermic, so delta H is negative. T delta S, I am assuming it is a negative here. So obviously this negative, this negative becomes positive. Correct? So for condition for delta G to be negative is what? For delta G to be negative, the condition is what? The magnitude of delta H should be more than the magnitude of delta T delta S. Is it right? So this condition can be achieved. Obviously this entropy, you need to decrease. This condition can be achieved. Can be achieved by decreasing or lowering temperature. Decreasing temperature. So basically, if T delta S is negative, then the process will be spontaneous at lower temperature. At higher temperature, it's possible that T delta S becomes more than delta H, and hence it becomes non-linear, right? Yes, done, understood. OK, now you see the second condition we have when the process is endothermic. Endothermic process delta H is greater than 0, positive. So you see here, delta G is equals to delta H minus T delta S. Delta H is positive, this is positive. If T delta S is also positive, if T delta S is greater than 0, so for the condition for this to be spontaneous is what? The magnitude of delta H should be less than the magnitude of T delta S. And this condition we can achieve by increasing temperature, because as temperature increases and property increases and this condition can be, is possible. If T delta S is negative, then if T delta S is negative, then the process will never be spontaneous. Copy? Yeah, so one more relation we'll see here for today, and this is almost done. Standard free energy change. Write down, it is the free energy change for a process at a standard condition, basically. The standard condition is 298 Kelvin and 1 atmospheric pressure. And one more thing here, condition must be standard in which the reactants and products, the reactants and products are in their standard state. Standard state, OK, are in their standard state. So at the standard state, the Gibbs free energy is written as delta G naught. This dot means it is at the standard state. So all the term will be in their standard state, H naught T delta S naught. This is a relation at standard state. And this is standard free energy change. We have a relation here, that is delta G is equals to delta G naught plus RT ln Q. This terms, a little bit, you will understand in chemical equilibrium because it is applicable for reversible reaction. This relation, OK. Q is the, have you done chemical equilibrium in school? Q is the reaction quotient, OK. Q is the reaction quotient. Little bit, I'll tell you. This formula, you just memorize it. We'll discuss this later in chemical equilibrium. Delta G is the free energy change, Gibbs free energy change. This is the Gibbs free energy change at standard state. Gas constant, temperature. Q is the reaction quotient. What is reaction quotient? I'll tell you. This is, first of all, valid for reversible reaction. A gives B. So reaction quotient, Q is equals to the concentration of B divided by concentration of A. At any time, T, which is not equals to T equilibrium, means you can take the ratio of product and reactant at any time, but that time should not be equal to the T equilibrium. Just you keep this in mind. Q is product by reactant, that is it. Concentration of product by concentration of reactant, that is Q. But not the equilibrium concentration. Just one thing you have to keep in mind. Usually, I take up this chapter after equilibrium, chemical equilibrium and ionic equilibrium. Thermodynamics is, for me, it is the last chapter of your grade 11 physical chemistry. But since they have taken this up in the school, so I have taken it earlier. So this thing, you will understand in chemical equilibrium, which is the next chapter we have. So what is Q? Reaction quotient, concentration of product by concentration of reactant, valid only in reversible reaction. This concentration must not be equilibrium concentration. If T is equals to T equilibrium, means once the equilibrium is achieved, then this Q becomes, reaction quotient becomes Kc. What is Kc? Kc is the equilibrium constant. Equilibrium constant. This is also nothing but the ratio of the concentration. So Kc, how do we define? Again, it is the concentration of product by concentration of reactant. But the difference here, it is what? That this concentration is the concentration at equilibrium. This is the only difference here. So when the equilibrium is achieved, Q becomes Kc. If not, then Q is Q only. That is reaction quotient. Clear? Yes, tell me. Now I am taking the equilibrium condition at equilibrium. What we can write? Delta G is equals to 0, and Q becomes Kc. So what is delta G0? Minus 2.303 RT log Kc. This is the expression we have. ln, we convert into log 2.303, we multiply. This is the expression we get. So what is Kc? That is equilibrium constant. This equals to, we can also write this as, e to the power minus delta G by RT. This also we can write. If you take ln over there, both relation is true. This is also true. This is also true. So if you draw a graph, last thing, between K and delta G0, delta G0, it is an exponential graph. The graph goes like this. Exponential graph, the graph goes like this. You see here, if delta G0 becomes 0, what is the value of Kc, could you tell me? Delta G0 equals to 0. What is the value of Kc? 1, right? Suppose this is 0. This value is 0. Delta G0 is 0 over here. This side, it is positive. And this side, it is negative. Left side of this. So corresponding to this 0 value of delta G, this value is 1, right? Means if you have delta G less than 0, then value of Kc should be always greater than 1. So for spontaneous process, what we can write, here you see, for spontaneous process, we know delta G0 is less than 0. Means we have, no. On the left side of this point, 0. And whenever you come to this side, Kc value will be more than 1, if you look at the graph. So Kc is greater than 1. This is the condition we have for this point. End it out typing, guys, quickly. Did you understand this? This is a big chapter, right? So I haven't taken so much numericals today. Only one we have done. I will share the notes, the PDF with you, the assignment, that you must solve. We have done the first part of this chapter. Second part is thermochemistry, which will start next class and we'll finish it up. So assignment you must solve. You will understand what all formula and concepts we have discussed. Most probably next class, we'll solve some questions also before starting the second part of it, that is thermochemistry. Understood all of you? Please type in quickly. Yes, OK. See you in the next class. I will share the assignment in some time. Can solve those assignments. Yeah, bye. Take care. Thank you.