 We now move on to the second half of the course and having completed our discussion of first law of thermodynamics both for our system as well as a control volume, we are now ready to discuss second law of thermodynamics. But as I mentioned during the introduction, one of the most important things that we should do first is motivate the need for a second law. In other words, what was deficient in the analysis that we have done so far using first law? What aspects have been absent and how do we account for that? So that provides the motivation for second law. And we already noted this point that heat supplied during a cyclic process cannot be entirely converted into work. We saw that when you supply heat to a system, we are actually supplying energy to the internal energy of the working substance, which is a disordered mode. And when we supply energy to a disordered mode and try to run a cyclic process, then all of the heat cannot be converted to work. If it is run as a single process, then we can convert all of the heat into work. But if you want to run it as a cyclic process, we saw that because we are supplying heat to a disordered energy mode of the system, it cannot all be converted to work. Now, the question that naturally arose in the minds of earlier, I mean engineers who are dealing with this during the earlier times was, is it possible to continuously improve our device to a level where it is like an ideal device? And would it then be possible to convert all of the heat into work? And our discussion here makes it clear that it has nothing to do with the actual state of the device because whenever we supply heat to a system, we can always supply only to the internal energy or disordered mode. That has nothing to do with whether the device is in a good running condition or not. If the device is not in a good running condition, that will only make matters worse. But that is not the fundamental reason why we are not able to convert all of the heat into work. So, this realization came to engineers who are looking at this in the beginning. And so, they saw that even if you make the device ideal, it was clear that not all of the heat can be converted to work. So, there seemed to be a fundamental limitation in how much of the heat can be converted to work. Now, the next question, logical question that arises then is, if we have an ideal device, how much of the heat will that device be able to convert to work? So, then the corresponding amount for the actual device will be even less. So, that was the question that naturally arose when engineers were looking at this. And so, these are questions that we will answer when we discuss second law of thermodynamics. So, that is one very important aspect that second law of thermodynamics addresses. So, what is the maximum performance possible, which would be that of an ideal device. And then we can actually calculate the performance of real life devices. The second important question that second law would address is the directionality of spontaneous processes. There are many processes in nature which are spontaneous. For example, heat always flows from higher temperature to lower temperature and air at high pressure stored in a vessel preferentially escapes from the vessel into the ambient. The reverse processes do not take place spontaneously. We have to do something to make them happen. Although from an energy perspective, probably both are equally possible. There is no preferential direction in first law. In fact, if you look at first law, even for the first bulletin item that we talked about, heat supplied during a cyclic process, how much of it can be converted. So, if you look at first law for a cyclic process, you may recall that the first law reads like this. So, there is nothing in this statement that precludes all of the heat from being converted to work. So, as long as the energy balance is correct, first law does not preclude all of the heat from being converted to work. Similarly, first law does not really have a way of telling the directionality of processes in which direction is the process most likely to occur. Because it has only energy balance and nothing more than that. So, that is a limitation that first law has. Whereas, second law would be able to tell which in which direction process will take place and that determines whether the process is spontaneous or not. So, these are aspects that we will look at as we go through this discussion. So, the first question that we are going to try to answer using second law is this. For engines that operate in a cycle and convert heat to work, what is the highest allowed efficiency? In other words, I have an ideal engine and what is the efficiency for such an engine? Of course, we will formally define efficiency and we are going to formally define a heat engine next. These things need to be formalized so that there is no ambiguity or gaps in our understanding as we look at much more complicated devices. So, a heat engine is continuously operating, please replace this with is. So, a heat engine is a continuously operating thermodynamic system which has heat and work interactions with the surroundings. Continuously operating would refer to a cyclic process because any other process would be a discrete process. It will happen and then it will stop. Continuously operating implies that the device operates forever which would not be possible if it were not operating in a cyclical manner. So, unless it operates in a cyclical manner, no operation can be continuous and forever. So, a heat engine is a continuously operating thermodynamic system. What is that? Here also we are saying it is a thermodynamic system which means no mass can come in or go out into the system and it has heat and work interactions with the surroundings. Let us look at a couple of examples of heat engines and then try to understand this definition better. The first one that we will look at is the so-called Rankine cycle which is a direct heat engine. We have already mentioned this earlier, a direct heat engine is one which is power producing. So, the net power from such an engine is positive. This is the simplest form of the Rankine cycle and this is what is typically used in coal fired thermal power plants. So, basically heat is added in a boiler. So, water is the working substance here and water goes through these cyclic processes. It circulates in this loop that is shown like this. So, it goes through these states as it goes through this loop. Notice that the loop is fully closed. So, the water that executes these processes in this loop is the thermodynamic system that we are looking at. So, we add heat to the water in the boiler, its temperature is increased, then goes through the turbine and executes the process. So, let us start with state one. So, at state one, the water is actually in a superheated state, superheated steam. So, it is actually superheated steam. It then expands through the turbine and it comes out as a typically as a saturated mixture at low pressure and a low temperature. It then enters the condenser where it rejects heat to the ambient and exits the condenser as a saturated liquid at low pressure and low temperature. There is no, we neglect any pressure drop in the condenser. So, it leaves the condenser as a saturated liquid at the same temperature and the same pressure. So, this is then pumped in the pump to high pressure compressed liquid. So, this compressed liquid is then taken to the boiler where heat is added and as a result, it comes out as superheated steam and the process is repeated again and again. So, this can be a continuously running device and the system that we are looking at is this loop which encloses the water. So, this qualifies as a direct heat engine. In fact, if you look at whatever is inside the red box. So, this is the, so, this is a system continuously operating thermodynamic system which has heat and work interactions with the surroundings. So, these are heat interactions, these are work interactions. So, whatever is inside, it is a continuously operating thermodynamic system and because the net power is positive, we call this a direct heat engine. So, the second example of heat engine that we will look at is gas turbine engine that operates in the so-called Brayton cycle. Here air is the working substance and air actually executes a cyclic process in this loop. So, air is contained in this loop and it flows through like this. So, air is the working substance and let us see what happens here. So, typically at state 1, the air is at maybe ambient pressure not necessary, but it is at ambient pressure and ambient temperature. The air is then compressed in a compressor and comes out at high pressure and higher temperature not necessarily high temperature, but higher temperature. So, we then take the air to the combustor where heat is added to the air typically by burning a fuel which is which can be a liquid fuel or natural gas or it is not cold, but it can be any other fuel. So, typically heat is added to the air here and when it comes out, it comes out at the same pressure which is high and it also comes out at a high temperature. So, now it is at high pressure and high temperature. So, it then expands in the turbine produces work. A part of the power that is produced by the turbine is utilized to run the compressor as you can see from this arrangement and so the net power that comes out is actually positive which is why this is also categorized as a direct heat engine. So, after expansion in the turbine, it comes out at a low pressure and a lower temperature. It is then taken to the cooler which is nothing but a heat exchanger where it is cooled down to ambient pressure which is the low pressure that we are talking about. So, ambient pressure and ambient temperature and the cycle is repeated. So, the thermodynamic system is the loop which encloses the air here and you can see that this operates continuously. So, in fact, if I look at whatever is inside the red box that is a thermodynamic system which is continuously operating and in this case since the net power is positive, it is a direct heat engine. So, this is the thermodynamic system that we are talking about. What is that? This system operates continuously and it has heat and work interaction with the surroundings. The next example that we will see is a reverse heat engine. So, this is the cycle that refrigerant in a domestic refrigerator or air conditioner executes. Here we supply power to the cycle so that it is a reverse heat engine, that is why it is called a reverse heat engine. Let us see what happens here. So, here refrigerant typically something like R134A although that is banned today, we can since those are the tables that we are using, we will assume it to be R134A. So, today much better environmentally friendly refrigerants are used in domestic refrigerators. So, typically a refrigerant, so let us be politically correct and say that the working substance is a refrigerant. So, the refrigerant executes a cyclic process 1234 and the loop that contains the refrigerant is a thermodynamic system that we are looking at. So, you can see here that at the end of the evaporator, so the refrigerant is typically a saturated vapor at low temperature, low pressure and this is compressed in the compressor here to a superheated stage, high pressure, high temperature. Now, when I say high temperature that is relative to the refrigerated temperature, typically the evaporator in a refrigerator may be at a temperature of 3 degrees Celsius or 4 degrees Celsius. So, this temperature here at the end of the compression would be more like 70, 80 degrees Celsius or so, depending on the size of the refrigerator. So, it is then taken to a condenser where it loses heat to the ambient. So, when it comes out, it actually comes out as a saturated liquid typically at the same pressure which is the higher pressure that we high pressure that we talked about, there is no pressure loss in the in the condenser. So, it comes out at high pressure and at the same temperature, but as a saturated liquid, I am sorry at a lower temperature, lower temperature as a saturated liquid. So, it is then taken to a throttling valve. We looked at the fundamental working principle of a throttling valve before. So, basically we accomplish a change of stage without any change in enthalpy or kinetic energy and potential energy changes. So, basically we go from a high pressure, higher temperature state to a low pressure, lower temperature state. So, when it comes out, it is at low pressure and low temperature and typically it is a saturated mixture. So, this low pressure, low temperature, saturated mixture then enters the refrigerator compartment which is also called the evaporator. So, whatever is kept inside may be at let us say room temperature. Let us say we have taken a bottle of water or a bottle of juice or something else and kept it inside the refrigerator. So, that will be at a higher temperature and so this low pressure, low temperature refrigerator then picks up the heat from the refrigerator compartment and then the cyclic process is repeated. So, the thermodynamic system is the loop which contains the refrigerant and as you can see here it executes a cyclic process 1, 2, 3, 4. In fact, whatever is inside the red box is our system which is continuously operating and which has heat and work interaction with the surroundings. Since we are supplying power to this, this is a reverse heat engine. So, the three examples that we looked at, two belonging to the direct heat engine category and one this one belonging to the reverse heat engine category or legitimate heat engines. And the important aspect of heat engine is that it must be continuously operating and it must be a thermodynamic system. There will be heat and work interactions of this system with the surroundings. So, what we can actually do is for the purpose of second law analysis, whatever is inside these red boxes that we have identified, whatever is inside is actually immaterial. All we are once we establish that it is a heat engine, the details inside of how actually or what actually happens is immaterial. We look at it as a system. So, we take one cycle. So, remember here it is operating continuously. So, we have said Q H dot which is in units of watts as you know or W X dot in or W X dot out which is also power in units of watts. So, we look at one cycle that this system executes which means we will no longer have power or mass flow rate, we will only have work in joules. And we say that during one cycle or during each cycle, so much heat is supplied, so much heat is rejected, so much work comes out of the cycle and so much work is put inside the cycle. That is what we will say. So, here also so much heat is supplied during a cycle, so much heat is rejected during a cycle, so much work is generated during the cycle. One cycle. Similarly, here during one cycle so much heat is absorbed in the cycle, so much heat is rejected, so much work is supplied to the cycle for a reverse engine. So, we will ignore all the inner details. These are not pertinent for our analysis. You may actually look at the inner details in a course like applied thermodynamics perhaps or more certainly in a course on refrigeration and air conditioning. And for these things, you will look at the inner details in a course on power plant engineering for instance, but not for a higher level thermodynamics course. So, as you can see here, this is the heat engine. So, we have encapsulated what was in the red box inside this. Inside this we could have we could have water executing a ranked in cycle or air executing a bread in cycle, the details are in material. So, this is a heat engine which is a continuously operating thermodynamic system. And it has the following heat interactions and work interactions with the surroundings. So, here this is a let us call this, this is a direct heat engine and this is a reverse heat engine. Again it is a continuously operating thermodynamic system with heat and work interactions. So, this is what was inside the red box in the case of a vapor compression cycle. So, we supply work and a certain amount of heat is removed from a low temperature refrigerator space and rejected to the ambient typically. So, this is all we need to know. So, we have encapsulated what was in the red box in each one of this circle for a direct engine and for a reverse engine. Now, let us try to define performance matrix for these two engines. So, for a direct engine, the performance metric is efficiency. So, this is efficiency and efficiency is defined as effect sort divided by effort input. So, here what we want is work from the direct engine and we are supplying heat to the engine. By burning a fuel, a fuel we are supplying heat to the engine. So, we may write this as W net. We may also be supplying work in some parts of the cycle. So, the network is what we are actually looking for that is the effect that is sought. So, network divided by heat that is supplied that is the efficiency of the engine. Now, if the device operates in a cyclic process, as we say a direct heat engine operates in a cyclic process. So, if you apply first law to this engine, notice that the net heat is Q H minus Q C that should be equal to the network that comes out W same is applicable here also. So, W net divided by Q H is this and I can replace W net in case it is a cyclic process W net equal to Q H minus Q C and we can then write it like this. So, W net equal to Q H minus Q C only for a cyclic process very, very important. If it is a heat engine, then it has to execute a cyclic process and the efficiency for the heat engine is like this. So, by definition eta lies between 0 and 1. So, the question that we asked at the beginning of this module, what is the maximum possible efficiency for a heat engine which takes heat and converts it to work. So, what we are trying to ascertain is what is eta max? If the engine were ideal, what would be its efficiency? Now, in the case of a reverse engine, two different performance metrics may be defined. The example that we have been seeing is that of a domestic refrigerator. In this case, what we want is for every watt of electricity that we supply, we want to remove as much heat from the refrigerator compartment as possible. In other words, we want to maintain low temperature in the refrigerator by spending as little power as possible. That is what we ideally want. So, we want to maximize Q C dot. So, the effect sort is Q C dot in this case. Now, in colder countries, the reverse heat engine is also used for a different purpose. So, this actually is a refrigerator or air conditioner. We can also have something called a heat pump. So, let us look at this. So, if this reverse heat engine operates as a refrigerator, then the effect sort is Q C. We want to maximize Q C for a given W. Now, as I said in colder countries, heat pump is used during winter times. In the case of a heat pump, what is done is it takes heat from the cold ambient and then puts it inside a dwelling which is maintained at a comfortable temperature. So, this would be the dwelling or house, which we want to maintain let us say at 30 degree Celsius. So, this could be the ambient at say minus 10 degree Celsius. So, heat pump takes in power, moves heat from the ambient which is at a low temperature and puts the heat in a dwelling which is maintained at a comfortable temperature. So, here what we want to maximize is Q H. We want to spend as little power as possible in trying to maintain the dwelling at a comfortable temperature, which means Q H is the effect that is sought. So, in the case of a refrigerator, Q C is the effect that is sought and in the case of a heat pump, Q H is the effect that is being sought. So, accordingly we have two different performance metrics, one for the refrigerator, one for the heat pump. So, for the refrigerator, since the effect sought is Q C, we may write it like this and if it is a heat engine, which means it executes a cyclic process, once again W may be written as Q H minus Q C. Here, we have written it by taking into account the fact that Q H is negative and in fact, the way we have written this, I am sorry, the way we have written this is we have not used the sign convention. What we are saying here is Q C is being supplied. So, Q C is positive, Q H is being rejected. So, Q H is negative and W is actually being supplied. So, W is negative, but by looking at this device, we can easily say that W in this case also will be equal to Q H minus Q C. If I look at it in terms of numbers, this typically would have been a negative number. This would have been a positive number. This would have been a negative number, which means that this sign would have become plus. So, if I multiply both sides by minus 1, then I get W, which is now a positive number and so this sign would have become positive and this again becomes negative. That is what we have done. So, all the quantities that are going in here are positive numbers. The sign has been taken into account when we write it like this. So, all these quantities are positive numbers. In the case of heat pump, the effect saw out is actually Q H. So, we can actually write for reverse heat engine, we can actually write COP like this and COP, notice that COP varies between 0 and infinity. So, this part of the definition is applicable only if it is a reverse heat engine and again only true only for a reverse heat engine. Since by definition, a heat engine executes a cyclic process. What we will do in the next class is look at two statements of second law of thermodynamics, which actually tell you what the maximum efficiency cannot be. This does not say what the maximum efficiency can be. It actually says what the maximum efficiency cannot be. So, that gives us an idea of what the upper bound is not. So, then we know that the actual value has to be something less than this and then we will see what that value is. We will take this up in the next lecture.