 Hello and welcome to lecture 12 of this lecture series on Introduction to Aerospace Propulsion. We have been over the last several lectures understanding some basic concepts of thermodynamics and we have already gotten introduced to the zeroth law, the first law and the second law of thermodynamics. And we shall continue our journey in understanding thermodynamics and basic concepts of thermodynamics because as I have mentioned several times that thermodynamics is a very fundamental subject that forms an important aspect of analysis of engineering systems which involve heat and work. And as aerospace engineers we are always interested in trying to maximize the performance of for example, an aircraft and or an engine and for that matter. And so in order that we understand how in order that we can improve the efficiency of many of these systems it is important for us to understand the basic concepts or the basic principles underlying the performance or the operation of these engineering systems. So in the last lecture we were discussing about the second law of thermodynamics and entropy as a consequence of the second law of thermodynamics. So today we shall discuss little further about entropy and also we shall explore what is the third law of thermodynamics which is again a consequence of entropy. So what we shall discuss in today's lecture are the following. So we shall begin our lecture today with discussion on entropy change for a system as well as we shall discuss about what is known as entropy generation. Then we shall discuss about increase of entropy principle and then we shall derive two equations which are very important equations which shall help us in determining entropy change for a given process and these are the T d s that is temperature differential change in entropy equations T d s equations. Then we shall derive expressions for entropy change in liquids and solids as well as entropy change for ideal gases. Subsequently we shall be discussing about the third law of thermodynamics and absolute entropy and then we shall talk about entropy and energy transfer what is the significance of entropy and energy transfer of a certain process and towards the end of the lecture we shall discuss about what is known as entropy balance. So these are some of the aspects as you can see they are all related to entropy and I think I mentioned in the last lecture that entropy is a very basic concept and obviously a very important concept in the understanding of performance of systems and entropy is one parameter which helps us in identifying whether a certain process is feasible or not. So in today's lecture we shall try to look at how we can use entropy to analyze a certain system and a certain process and how entropy helps us in understanding whether a certain process is possible or not or how is it that we can improve the performance of a certain system. So we will begin our lecture here today with discussion about entropy change as well as entropy generation for a certain system. Now in the last lecture if you recall we had discussed about the Clausius statement. So Clausius statement was basically of the Clausius theorem which states that the cyclic integral of d q by t should be greater than or equal to 0. So in the last lecture we were discussing about the Clausius inequality. The Clausius inequality is basically a statement which states that or you can actually derive it for any process which basically states that the cyclic integral of d q by t is less than or equal to 0. So we shall take this a little further and find out that how you can generalize it for a certain process and if you recall I had mentioned that Clausius inequality is valid for any process whether it is reversible or irreversible and so on and so that equality of cyclic integral d q by t is valid only if the process is reversible. For all other processes it is the inequality which holds. So let us take a look at a certain process which is what I have represented here. Now in this process which is plotted in terms of some coordinates x and y which could be pressure volume temperature entropy or so on. Let us look at 2 different processes here which occur from state 1 to state 2. So the first process let us say is from state 1 to state 2 it is it could be either a reversible process or it could be any reversible process and as the system goes from state 2 to state 1 it is an internally reversible process. So here we have a cycle which consists of 2 processes 1 2 which is which could be any process a general process reversible or it could be irreversible and process 2 1 is an internally reversible process. So as I mentioned about Clausius inequality the cyclic integral of d q by t for this particular cycle should be less than or equal to 0 or if you want to split the cyclic integral we have integral 1 to 2 d q by t which is for the general process plus integral 2 to 1 for d q by t for the internally reversible process. So this according to the Clausius inequality should be less than or equal to 0. So this second integral that we see here is applicable for an internally reversible process and so in the last lecture I had also mentioned that for an internally reversible process that integral d q by t should be equal to the change in entropy. So integral 1 to 2 d q by t plus s 2 minus s 1 or s 1 minus s 2 as in this case should be less than or equal to 0 because the final state is s 1 for the second process or we can express this as s 2 minus s 1 is greater than or equal to integral 1 to 2 d q by t or in general terms d s is greater than or equal to delta q by t. So here we have an expression which states that the change in entropy for any process will always be greater than or equal to d q by t. So this equality sign that you see here will be valid only if the process is internally reversible for all other processes the inequality sign will be valid. So d q by t which is the ratio of the change in heat transfer to the temperature at which the heat transfer is occurring is always less than or equal to the increase or change in entropy. So d s is greater than or equal to delta q by t is an expression which is valid for all processes and if you consider an internally reversible process then it is the equality which is valid that is d s change in entropy will be equal to d q by t and for all other processes it is the inequality which is valid. So for all processes in general we can write that the change in entropy will be greater than or equal to d q by t. So this is a general expression which is valid for any process whether it is a reversible process or it is an irreversible process and so on. And so as a consequence of this we can see that for an irreversible process what happens to this increase in entropy that we see that across any process if you have a d q by t the d s is always greater than d q by t. So which means that that is there is a certain amount of additional entropy which is which is getting formed as the process proceeds. So we will understand now that what is this additional entropy that we are talking about. So we will very soon name this as what is known as the entropy generation. So entropy change during an irreversible process especially if it is a closed system is always greater than the integral of d q by t which is evaluated for that particular process. So the limiting case of this is a reversible process. A reversible process is during a reversible process this the equality sign will be valid that is d s will be equal to d q by t. So this equality is valid only if the process is a reversible process. Now I mentioned that this d q by t the temperature that we talk about in this d q by t is basically referring to the temperature at the boundary where this differential heat is getting transferred between the system and the surroundings. So the temperature that we refer to in d q by t is basically the temperature at the boundary that is at the boundary where the heat transfer the differential heat transfer delta q or d q is transferred between the system and the surroundings. So d q by t is basically valid for that particular process where entropy the heat transfer takes place between the system boundaries and the surroundings. Now, as regards the inequality sign, now for an irreversible process the entropy change is always greater than or is always greater than the entropy transfer. It means that there is always certain amount of entropy which is getting generated or getting created during an irreversible process and this is primarily because of the irreversibilities in a process. We have already discussed about irreversibilities that can take place in the last lecture like irreversibility due to friction, irreversibility due to heat transfer between finite temperature and so on. So, all these irreversibilities put together or one or more of these irreversibilities might occur during a certain process and it is these irreversibilities that lead to an additional creation or generation of entropy. So, this generation of entropy which takes place during a process is known as entropy generation and it is usually denoted by a symbol as subscript gen which means entropy generation and so for any real life processes we will always have or if there is some amount of irreversibilities as we have already discussed and so irreversibilities always accompany or an irreversibility in a process will always be accompanied by some amount of entropy generation which is the reason why for an irreversible process there is always a certain amount of entropy generation and that is the reason for the inequality that delta S will be greater than delta Q by T. So, this inequality is what leads to the generation of entropy. So, to express it in the form of an equation delta S is that is delta S of the system is equal to S 2 minus S 1 that is change in entropy which is equal to integral 1 to 2 d Q by T plus term which is the entropy generation S gen. So, entropy generation is always a positive quantity for irreversible processes and it can become 0 only if the process is reversible which means that for all real life problems or for all real life processes which are irreversible in nature there is always a certain amount of entropy generation coming as part of the process itself. And the value of this entropy generation depends upon the process itself and it is not a property of a system. So, it is very important to understand here that entropy generation is not a point function it depends upon the type of process the nature of the process and therefore, it is a path function it depends upon how the process takes place. And if you look at an isolated system for example, an isolated system is one which has no interaction between the system and the surroundings. And if it which means that it has to be an adiabatic closed system then the heat transfer is 0. We know that across an adiabatic process across an adiabatic system there is no heat transfer. So, heat transfer being 0 the delta S that is the change in entropy for the isolated system is greater than or equal to 0. And so for an isolated system which we shall look at little later as well that there is always a certain amount of entropy generation that accompanies the process itself. So, when we consider the entropy generation during a certain process it is that for all real life processes that we are familiar with there is always a certain amount of entropy that is generated during the process. And as I mentioned that this entropy generation depends upon the nature of the process itself it is definitely not dependent on the initial and final state alone. So, entropy generation being a function of the nature of the process it definitely qualifies to be called as a path function and it depends upon the nature of the process. So, all the real life processes will involve certain amount of creation of entropy and it is important for us to understand that entropy generation is accompanied in or is a byproduct of any real life process. And so which means that for any real life processes which we are which we encounter on a day to day basis there is always a certain amount of entropy increase or entropy generation that should be part of all the real life processes which means that there is always a certain amount of entropy which is getting generated. So, if you look at the whole universe as an isolated system then the entropy of an isolated system will always increase and only in the case of reversible process will remain constant. So, this means that there is always a certain increase in the entropy of an isolated system. So, universe as a whole constitutes an isolated system and so there which means that there is always a continuous increase in the entropy of the universe and this is basically known as the increase of entropy principle. So, increase of entropy principle is valid for all irreversible processes the only limiting case is that of a reversible process which obviously is an idealized process wherein the entropy remains a constant. So, in the absence of any heat transfer entropy change is basically only due to irreversibility is because of friction or surface tension and other effects. So, all these irreversibility is basically lead to entropy change if there is no heat transfer and the effect of irreversibility is always to increase the entropy. So, irreversibility is will always cause an increase in entropy. So, the entropy of an isolated system as we have just seen it increases or only the limiting case of this is that entropy can be constant the change of entropy can be constant only for a reversible process. For an isolated system the entropy if the system consist of irreversible processes will always increase and if you consider the whole universe as an isolated system this means that the entropy of the universe is continuously increasing and because we come across so many irreversible processes. In fact, all the processes that we are aware of are irreversible because of the presence of irreversibilities and therefore, there is an entropy generation associated with any irreversible process. So, this means that the entropy the change in entropy of an irreversible process always increases if the universe is to be considered as an isolated system entropy of the universe is continuously increasing and this is what is known as the increase of entropy principle. Now, if you look at a process where there is no heat transfer it means that the only reason for increase of entropy during this particular process would be other irreversibilities like friction or surface tension and so on. So, in the absence of heat transfer during a certain process entropy increases due to the presence of other irreversibilities which accompany normal day to day processes. So, increase of entropy principle basically states that if you consider an isolated system because of the presence of irreversibilities within the isolated system the change in entropy is always greater than 0 or there is always an increase in entropy during such processes. Now, as I mentioned that because if you can actually consider the whole universe as an isolated system which is basically not interacting with any other system the entropy as per the increase of entropy principle it would mean that the entropy of the universe is continuously increasing and during a reversible process we have seen that there is no change in entropy or the entropy remains a constant during a reversible process. So, there is no increase in entropy associated with a reversible process, but as all the real life processes are irreversible in nature there is always a certain amount of entropy that is generated during these processes. So, a consequence of the entropy principle is that entropy of an isolated system will always increase, but this does not mean that entropy of a system cannot decrease. Well entropy of a system can definitely decrease, but it has to be compensated by a corresponding increase in entropy during some other part of the system interaction with the surroundings. In fact, the increase in entropy during that particular interaction would be greater than the decrease in entropy of that particular system and entropy generation basically is what is being implied by the increase of entropy principle that it cannot be negative and. So, it means that though entropy change can be negative during a certain process entropy generation can never be a positive quantity. So, there is always an entropy generation associated with all irreversible or real life processes. So, increase of entropy principle implies that you can always have certain processes wherein there is certain decrease in entropy locally, but there has to be a corresponding increase. In fact, a greater increase in entropy elsewhere, so that there is a net increase in entropy during that particular process and. So, to summarize this entropy generation or increase in entropy principle basically increase in entropy principle states that entropy generation or S gen is greater than 0 for irreversible processes. Entropy generation S gen will be equal to 0 for reversible processes and entropy generation less than 0 implies that that particular process is impossible or infeasible. So, entropy generation less than 0 implies the infeasibility of a particular process. Entropy generation equal to 0 is basically valid only for reversible processes and entropy generation greater than 0 is what is valid for all real life processes or irreversible processes. And so, if you consider a system and its surroundings put together you can actually form an isolated system by considering part of the surroundings which are close to the system. So, system plus the immediate surroundings can actually be considered or approximated as an isolated system. So, for such a system entropy generation is equal to the net change in entropy which is basically equal to change in entropy of the system plus change in entropy of the surroundings can be greater than or equal to 0 this is as per the increase in entropy principle. So, let us look at what are the consequences of increase in entropy principle basically entropy principle states that processes can occur only in a certain direction it cannot occur in any arbitrary direction it can occur only in a direction which leads to an increase in the entropy generation. So, processes must always proceed in that direction where the entropy generation is greater than or equal to 0 where the equality is valid only for reversible process. So, it means that as a consequence of the increase of entropy principle there is always an entropy generation which accompanies any reversible process. And another interesting aspect is that unlike energy entropy is not a conserved property which means that there is nothing like a conservation of entropy principle because entropy can be generated, but obviously it cannot be destroyed for real life processes. So, there is always a creation or generation of entropy unlike energy which is a conserved quantity you cannot create energy you can only transfer energy from one form to another entropy is something which is generated. And the conservation of entropy is valid in strict sense only for idealized reversible processes and for all actual processes there is an increase continuous increase in entropy associated with irreversible processes. So, unlike energy conservation of energy principle there is nothing like conservation of entropy principle because entropy is not a conserved quantity it does not well it can actually be created during all actual or irreversible processes. Now, so let us look at some example of applying increase of entropy principle to a group of systems. So, what is shown here enclosed within the walls of this particular system are several subsystems. So, let us say this is an isolated system what is shown by this bounding box here this isolates this particular system from the rest of the surroundings making it an isolated system. So, this isolated system comprises of several subsystems which are named as 1 2 3 4 and so on up to n. So, there are n number of subsystems which constitute this isolated system. So, the net change in entropy of this entire system this isolated system will be equal to the net change in entropy of these individual systems. So, which means that delta s total that is the entropy change of the entire isolated system will be equal to the summation i equal to 1 to n delta s of the individual systems and each of them well the total enthalpy or total entropy of the particular isolated system will be greater than 0. Even though you may have certain systems within the isolated system which may have entropy decrease, but that will be compensated by an even more increase in entropy elsewhere and as a consequence of this delta s of this particular isolated system will be always greater than 0. This is again as a consequence of the increase of entropy principle. Now, so we have been looking at entropy and increase of entropy principle as applied to isolated systems reversible processes irreversible processes and so on. And so what we shall do now is to try and derive expressions for calculating entropy for different processes. We shall derive expressions for entropy change for liquids and solids as well as entropy change for ideal gases. So, before we do that we need to understand or be familiar with what are known as T d s expressions or T d s equations where T is the temperature d s is change in entropy. Now, T d s equations form the basis for deriving expressions for entropy change in solids and liquids as well as for ideal gases. Now, to derive T d s equations we will have to go to the first law of thermodynamics apply that for a particular system and then express the internal energy and enthalpy in terms of the corresponding properties of a particular system. And so we can actually derive expressions in terms of the product of temperature and the change in entropy. So, from the first law as we are aware that delta q minus delta w is equal to d u. So, let us say the process is internally reversible. So, delta q internally reversible process minus delta w internally reversible out that is it means that work output is equal to d u. Now, for an internally reversible process we are aware that delta q internally reversible is equal to T d s because d s is d q by T for internally reversible processes. Similarly, the work output delta w is equal to p d v. So, if you substitute these in the first equation in the first law equation we get T d s is equal to d u plus p d v or per unit mass it can be expressed as T times d s which is in small s which means entropy per unit mass is equal to change in internal energy per unit mass d u plus p times d v which is v is the specific volume. So, this is known as the first T d s equation. So, T d s equal to d u plus p d v is the first T d s equation. Similarly, we can derive what is known as the second T d s equation that is if we substitute instead of internal energy we have enthalpy and enthalpy as we know is u plus p v. And so d h will be equal to d u plus p d v plus v d p and so you can get an expression in terms of d u is equal to d h minus v d p. So, that we will substitute in this first law expression and then we can derive what is known as the second T d s equation. So, let us do that here. So, as enthalpy is a combination property h is equal to u plus p v d h is equal to d u plus p d v plus v d p and since we have already derived the first T d s equation d s is equal to d u plus p d v. So, we can substitute for d u that is internal energy in terms of enthalpy and therefore, we get T d s is equal to d h minus v d p and this is known as the second T d s equation. So, the first T d s equation is in terms of the internal energy pressure and specific volume. The second T d s equation is in terms of enthalpy specific volume and the pressure. So, T d s is equal to d u plus p d v is the first T d s equation and T d s is equal to d h minus v d p is the second T d s equation. And as you can see both the T d s equations are in terms of properties of a system. First equation is in terms of internal energy pressure and volume. Second equation is in terms of enthalpy volume well specific volume and pressure which means that since T d s equations are themselves property relations they are again independent of the nature of the processes. And therefore, it does not matter what type of process we are looking at T d s equations are valid for all these processes and therefore, they are valid for both reversible irreversible processes as well as for closed systems and open systems. So, T d s expressions or T d s equations are general equations which can be used or which are valid for any processes irrespective of whether they are reversible irreversible open systems or closed systems. What we shall do now is to derive expressions for the entropy change for liquid solids as one component and separately for entropy change of ideal gases. Now, we are considering liquids and solids in one group because of one property that liquids both liquids and solids can be approximated or considered as incompressible. Now, when since they are incompressible there is no change in the specific volume d v will be equal to 0. And so we will use that property in deriving expression for change in entropy for liquids and solids. So, if you look at liquids and solids we know that the change in specific volume is 0 because we can approximate liquids and solids as incompressible substances. Now, since d v is equal to 0 we have change in entropy d s is equal to d u by T this is again coming from the T d s equations this T d s was d u plus p d v and d v is equal to 0. And therefore, T d s is equal to d u or d s is equal to d u by T which is again equal to C d T by T. And for liquids and solids the specific heat at pressure constant pressure and specific heat at constant volume are the same and the C p is equal to C v which is equal to C. And therefore, d u is equal to C d T therefore, if you want to integrate entropy change for a process s 2 minus s 1 will be equal to integral 1 to 2 C of T because C is a function of temperature d T by T. And in most of the common applications we would assume an average specific heat between temperatures T 1 and T 2. And so this can be approximated as C average log T 2 by T 1 where C average is the average specific heat for this particular process between the temperatures T 1 and T 2. Therefore, entropy change which involves liquids and solids will be during a particular process is equal to the product of the average specific heat during that process multiplied by log of T 2 by T 1 which is again in kilo joules per kilogram kelvin because it is entropy per unit mass. So, this is the entropy change for a process which involves liquids and solids. Now, what about ideal gases? Now, let us also look at entropy change for ideal gases. Now, for ideal gases we have already seen that change in internal energy that is d u is equal to C v d T. And we can express the pressure in terms of temperature and specific volume as p is equal to R T by v. So, from the T d s equations T d s is d u plus p d v. So, we substitute for d u and p here to get d s is equal to C v d T by T plus R times d v by v which is coming from the ideal gas equation that is the state equation as well as d u is equal to C v d T. Now, if you want to integrate this for a process we get the net change in entropy during that particular process. And so, s 2 minus s 1 will be equal to integral C v of T which is specific heat at constant volume which is again a function of temperature multiplied by d T by T plus R times log of v 2 by v 1. So, entropy change for a process involving an ideal gas will be s 2 minus s 1 is equal to integral C v d T by T plus R log v 2 by v 1 which again we will simplify as if you are to assume that C v if you assume an average value of C v then we get C v times log T 2 by T 1 minus R plus R times log v 2 by v 1. Now, let us also derive an expression for the specific heat at constant pressure. So, for an ideal gas again the change in enthalpy d h is equal to C p d T and v is equal to R T by p. So, again if you use the T d s equations the second T d s equation we get T d s was d h minus v d p therefore, s 2 minus s 1 is equal to integral 1 to 2 C p of T that is C p is a function of T d T by T minus R log p 2 by p 1. So, these two expressions that is the first equation which we derived for entropy in terms of specific heat at constant volume. And the second equation is in terms of specific heat at constant pressure both of these equations are primarily valid for ideal gases. Now, as we have done for solids and liquids as well here again we can assume an average value of C p and average value of C v for the range of temperatures for which we are calculating the change in entropy. Then we substitute C p of T as C p average and C v of T as C v average where these average parameters are averaged over the range of temperatures for which this particular process has been carried out. So, C p average and C p average refers to the average specific heats at constant pressure and constant volume during that given process. So, this is how we can actually calculate the change in entropy associated with the process involving liquids and solids as well as change in entropy for processes involving ideal gases. Now, what we shall look at next is what is known as the third law of thermodynamics. Now, before we understand the third law of thermodynamics we need to also be familiar with what is known as the Boltzmann's equation. Now, as we have as I mentioned a few times in the last lecture as well as in today's lecture that entropy is sometimes viewed or is often viewed as a measure of the molecular disorder or molecular randomness. So, as a system becomes more disordered the position of the molecules become less predicted or predictable and therefore, the entropy increases. So, if you were to apply this for different states of a system like liquid solids and gases we know that in the case of a gas it is the number of molecules in a given area in a given volume is much more rarefied than in solids or in liquids. And therefore, as a system changes its phase from solid to liquid to gas the entropy corresponding entropy of that system also increases because the randomness associated with the molecular order motion is the highest in the gaseous phase as compared to solids or in the liquid phase. So, as a system moves from solid to liquid to gaseous phase the entropy associated with that particular system also increases. So, Boltzmann basically expressed entropy in terms of the probability associated with a particular molecule as well as a certain constant which we now call as the Boltzmann's constant. So, Boltzmann basically related the entropy of a particular process to the total number of molecules the probability of the total number of molecules in a particular state which is known as the thermodynamic probability P and so the expression in terms of entropy in terms of the probability times a constant constant is referred to as the Boltzmann's expression or Boltzmann's equation. So, the Boltzmann's expression or equation is basically expressed as the entropy S is equal to k times log of P where k is a constant which we now know as the Boltzmann's constant which is 1.3806 into 10 raise to minus 23 joules per Kelvin and P is basically the probability or the thermodynamic probability which is basically the total number of possible microscopic states of a particular system the probability associated with that and so that is known as the thermodynamic probability. So, S is equal to k times log of P is the Boltzmann's equation. So, Boltzmann basically stated that entropy is proportional to this particular probability and the proportionality constant is the Boltzmann's constant which is 1.3806 into 10 raise to minus 23 joules per Kelvin. So, this is the famous Boltzmann's equation and interestingly Boltzmann wanted this equation to be engraved on his tomb and it is still there on his tomb the Boltzmann's equation has been engraved on his tomb or his resting place. So, from a microscopic point of view if you look at the Boltzmann's equation the entropy of a system increases with the molecular randomness or uncertainty and so if you look at a system in different states like in solids liquids or gases the probability molecular probability is the lowest as you look at a gaseous phase and correspondingly the entropy associated with that particular gaseous phase is the highest. So, if you look at the third law of thermodynamics which is again a consequence of the Boltzmann's equation the entropy of a pure crystalline substance will become 0 only at temperature of 0 Kelvin which is the absolute 0 temperature. So, third law of thermodynamics states that an entropy associated with a particular system or a process can become 0 which is primarily true for a pure crystalline substance it can become 0 only at absolute 0 temperature because at absolute 0 temperature there is no uncertainty about the state of the molecules at that instant. So, when you have 0 Kelvin temperature when the state when the state of the pure crystalline substance is at absolute 0 temperature that is 0 Kelvin there is no uncertainty about the state of the molecules at that instant. So, because there is no uncertainty about the state of the molecules the entropy becomes 0 at that particular instant that is at absolute 0, which means that at any other temperature you will always have a certain amount of entropy associated with a particular system. So, this particular entropy that we refer to is known as the absolute entropy. So, the entropy of a particular system at absolute 0 temperature is the absolute entropy. And so, obviously that should be the reference state for calculating entropy for any process or any particular system. But, as we have already discussed we it is impossible for us to achieve absolute 0 temperature or we have not at least been able to do that so far. And so, how do you calculate the absolute entropy of a particular process well it will be it is obviously, impossible to determine the entropy at its absolute state. But, that does not really matter because as engineers we are only interested in change in entropy of a particular process. We are not worried about the absolute entropy of a particular system in a particular state. And therefore, we only are worried about changes in entropy and usually entropy is calculated with reference to certain reference temperature which need not necessarily be absolute 0. So, pure crystalline substance as we have seen for the as per consequence of the third law of thermodynamics is one where the entropy becomes 0. So, a pure crystalline substance at absolute 0 has 0 entropy and therefore, there is it is basically in a perfect state of equilibrium. And therefore, its entropy is 0 at absolute 0. Now, we have already discussed about energy transfer. We have mentioned that energy transfer can take place in different forms of work heat and mass. And entropy is unlike energy there is also a certain amount of entropy transfer which takes place along with work. Now, work is basically an organized form of energy and therefore, work is free of disorder or randomness and therefore, it is free of entropy which means that there is no entropy transfer associated with energy transfer as work. So, that is if you are considering in a process which involves energy transfer as work there is basically no entropy transfer associated with that particular process. Now, we have already seen that as a consequence of the first law of thermodynamics the quantity of energy is always preserved or conserved during an actual process that is known as the conservation of energy principle. But, there is always a decrease in quality which is as a consequence of the second law of thermodynamics that during a certain process there is always a decrease in quality of the energy associated with that process. Now, let us look at this example there are two examples here. One is considering a racing of a weight by shaft movement. So, if you rotate this particular shaft by applying a certain work that leads to racing of this particular weight against gravity. Now, it is possible if as I mentioned that the entropy associated with work is 0 then you might wonder that it should be possible for you to regain that work which you have spent in racing this weight and that is perfectly possible because if you now leave that or drop the weight from this height then that will lead to generation of work output or shaft work output which you had spent in racing this weight and this is the reason why there is no entropy associated with a work transfer process. Well, if you look at the other hand on the other hand here there is definitely a work done on the system you may wonder that work is there is no entropy change associated with work transfer process. So, there should be no change in entropy during this process as well which is not really true here because if you do work on the system which consists of a gas the work done gets dissipated in the form of heat heating of the gas and so it is not just work work is getting transferred into heat. And since work is getting transferred into heat heat is a low grade energy and therefore there is an entropy associated with heat though there is no entropy associated with work which is a high grade energy because it is getting transferred or degraded into a low grade energy as heat it is not possible to get back the work after the work has been done on the system in the second case. In the first case on the other hand work was not transferred or converted into heat and therefore there was no degradation of energy associated with that work and so it was possible to recover the amount of work done by let us say dropping the weight it will basically get back the work that was spent whereas on the second case that is second example work was transferred or converted into heat which is a low grade energy and there is an entropy associated with that and so you cannot transfer or convert heat into work directly as we have discussed earlier and that requires certain special devices which are known as heat engines. So, entropy basically is associated with certain forms of work interaction energy interactions work is one form of energy interaction to which there is no entropy associated with that. So, there is always certain amount of increase in entropy associated with a decrease in quality. So, in the second example that we just discussed there is work getting transferred into heat there is a decrease in quality of the energy and therefore there has to be an increase in entropy during that process and heat is a form of disorganized form of energy and there is always increase in entropy associated with heat. So, processes can occur only in that direction which leads to increase in overall entropy or molecular disorder of a system. So, in some sense I mentioned that increase of entropy principle also states that there is increase in entropy of the whole universe. Well, this means that the entire universe is getting more and more chaotic day by day that is because entropy can be equated or can be compared to that of disorder of a particular system and since the entropy of the universe is increasing this also should mean that the amount of chaos or the disorder of the universe is also increasing day by day. So, there is whole universe is getting more and more chaotic day by day as per the increase in entropy principle. Now, let us look at another example of heat transfer or entropy transfer here we have hot body which is transferring heat to a cold body. Now, since there is heat transfer from the system from the hot body the entropy of this hot body decreases and heat is transferred to the cold body and therefore, entropy of the cold body increases. So, as we have also discussed that entropy is not a conserved quantity it means that entropy decrease of the hot body is not equal to entropy increase of the cold body. In fact, the entropy increase of the cold body will be higher than the entropy decrease of the hot body and therefore, there is a net increase in the entropy of this process basically because it involves the heat transfer and there is always entropy associated with the heat transfer process unlike work and if you had considered these two different bodies interacting through work interaction the entropy change would have been 0 because there is no entropy change associated with work because work happens to be a high grade energy and which has lesser disorder in it and so entropy associated with work is always equal to 0. Now, as I mentioned work happens to be an entropy free energy interaction, but obviously in day to day life we will always have processes which involve besides work interaction it may also have heat interaction. So, heat interactions between the system and surroundings are inevitable and that means that there is always a certain amount of entropy which is possible during any actual or irreversible processes. However, if the process involves only work interaction obviously, the entropy associated with that would be 0. Now, let us look at what happens if entropy and basically what happens to entropy and energy when you look at closed systems and open systems. So, if you look at closed systems energy as we have discussed is transferred by both heat and work and however, there is no entropy associated with work and so for closed systems the only mechanism for transfer or of entropy is by heat. So, in closed systems entropy is transferred only by heat and during work interaction on the other hand there is only energy interaction and during heat transfer there is both energy as well as entropy transfer across the system boundaries. If you look at an open system on the other hand entropy is transferred through heat as well as mass flow again in the case of open systems there is no entropy associated with work and so entropy transfer in open systems occurs through two modes it could be either heat or it could be through mass flow. On the other hand for closed systems entropy transfer takes place only through heat there is no entropy associated with work. So, that leads us to what is known as the entropy balance. So, if you want to look at what is the entropy net change in entropy associated with the process whether it is a closed system or an open system what is the entropy balance associated with that. So, entropy balance is basically looking at what is the amount of entropy net change in entropy associated with the particular process. So, if you consider this equation that stated here S in minus S out is basically the net entropy transfer by heat and mass which means that this is basically for an open system plus the entropy generation should be equal to the change in entropy of the system. So, net change in entropy of a system will be equal to the sum of the net entropy transfer which could be either by heat and or mass plus the entropy generation. So, you can also express this in a rate form. So, rate of net entropy transfer by heat and mass plus the rate of entropy generation will be equal to rate of change of entropy of the system. So, net change in entropy will be equal to sum of two parameters one is the entropy transfer which could be by heat and mass and the entropy generation. So, let us recap what we had discussed during this lecture today. We had basically started the lecture with discussion on entropy change of a system and entropy generation. We had discussed that during a certain process during an irreversible process there is always a certain entropy which is created or generated during the process. And so, entropy generation can never be less than 0 it can be in the limiting case become equal to 0 for reversible processes, but for all irreversible processes entropy generation will be greater than 0. And then we discussed about what is known as the increase in entropy principle which states that entropy of an isolated system will continuously increase. And so, if you consider the whole universe as an isolated system entropy of the universe is continuously increasing. So, that is the increase in entropy principle subsequently we derived what are the T D S equations that is product of temperature and change in entropy equations for in terms of change in internal energy d u and change in enthalpy d h. And using this as a basis we have derived equations for calculating entropy change in processes involving solids and liquids as well as in processes involving ideal gases. And then we discussed about entropy change for an isolated system and leading towards what is known as the third law of thermodynamics which was also something which Boltzmann's equation stated and which basically states that entropy of a pure crystalline substance at absolute 0 temperature is equal to 0. And so that entropy which is associated with this particular state is known as the absolute entropy. And then we discussed about entropy transfer and energy transfer we discussed that the entropy associated with work transfer is 0 whereas, for all other energy interactions there is a certain amount of entropy that is associated and which is what leads to certain amount of entropy generation. And towards the end of the lecture we were discussing about entropy balance which was net change in entropy of system is equal to the change in entropy transfer due to either heat and or mass plus the entropy generation. So, this is what we had discussed in today's lecture and what we shall discuss in the next lecture is that we shall solve certain problems we shall basically have a tutorial session we will solve problems related to first law of thermodynamics applied for closed and open systems. We shall also solve problems associated with heat engines refrigerators and heat pumps. So, this we shall take up during the next lecture that would be lecture 13.