 Good morning everyone, we are now into our day number 9. Now, we are entering that part of thermodynamics which now we can say applications. In fact, if you are a real pure thermodynamics is at heart, you will say well open systems is also an application, but for mechanical engineers open systems are so common and so important compared to closed systems that well we can say that it is basic thermodynamics. For mechanical engineers one of the most important or very very common applications is in power plants that is use natural resources to create energy, useful energy or in refrigeration plants where you want to extract thermal energy from a system so as to either reduce its temperature or to maintain it at a low temperature. And this is done by devices which almost invariably work in a cycle. These are engines, refrigerators, may be a few other names are used and that is why it is considered appropriate that cycle analysis or at least the basic cycle analysis be taught as a part of the thermodynamics course and wherever you have the course long enough that is usually done. In many places we find that a 3 hour a week course over approximately 13 or 14 weeks is not sufficient to include everything in thermodynamics including cycles. We have found it difficult to do cycles in such a course provided all other aspects which were discussed so far are included. Whereas, if you have a 4 hour a week course then introduction to cycles, at least the basic introduction to cycles can be included. There are some models in which you dilute the basic part of thermodynamics. For example, do not put emphasis on the rigorous derivations of the second law or do not spend time on the second law for open systems or the property relations or detailed discussions of properties of steam and van der Waals gases in which case may be by deleting some part of the basic thermodynamics you can introduce cycles. Anyway, the local model is best left to yourself although I feel that whatever we have studied so far in the first 12 topics will be taught and then we will have this introduction to cycles either in the basic thermodynamics course or in a follow up course. So, when it comes to cycles, we first look at why cycles? On the very first day I said that one of the jobs of a mechanical engineer is to create machines of various kinds. One of these machines or some of these machines will take natural resources deliver useful power and the power does many things including produce machines control them operate them power also does something for us. Finally, what we want is a comfortable life we want that we be transported from one place to another place without taking marathon walks every day. We should be able to go up and down tall buildings without walking up steps. In a very hot climate, we want to sleep and work in an environment which is cool and comfortable. So, part of the comfortable life means providing refrigeration. So, that we can enjoy our you know chilled fruit juices and ice creams maybe we do not want to go to the market every day. So, we want refrigeration to preserve our food either raw or cooked over a long time and we want air conditioning so that we do not sweat just while sitting at our desks. So, when it the job of a mechanical engineer is to do machines which will convert natural resources to power and also provide refrigeration or air conditioning, but by cycles. So, remember we want to use these machines again and again we do not want these machines to be consumed. For example, if you want to cool something you can bring somewhere from somewhere a slab of ice, but once the ice made soft you have to hunt for another slab of ice. We do not want to do that we want a machine which will use a natural resources and keep on producing power for us and for that reasons such machines must be working in some cycle. Machines must be cyclic devices because we want to may use them again and again. And then brings us to the thermodynamic scheme the two type of machines which we have will be the engine type of machines and the refrigeration type of machines. Here R means refrigerator and not reversible and usually when we show on our thermodynamic scale T 1 will be higher than T 2. In fact, although this is the thermodynamic scheme it is necessary for us to show it on a scale of temperature and show in that the ambient temperature, environment temperature. We know that natural resources quite often come in the type materials known as fuels. We need not go into detail. Natural resources can be water at a height which is potential energy it can be wind which is kinetic energy of a fluid. It can also be you know naturally available chemical compounds like coal, natural gas, crude oil which can release the energy they have in thermal form by the process of combustion. And this energy will be released that is sufficiently high temperature at say some source temperature. And we know from our second law of thermodynamics that we must reject heat for an engine to work. So a schematic would be something like this. It absorbs heat at a rate Q dot 1 rejects heat at a rate Q dot 2 and produces W dot 2. The question is where is this Q dot 2 to be rejected? And we need a system large enough which will continue absorbing this Q dot 2 without really complaining about it. And one such system is the environment. And that is why the lower temperature of our engine will have to be the environment temperature or slightly higher than that. It puts a limit on engines. Refrigerators do two type of jobs. One type of job is the traditional refrigerator where we have a system which is to be maintained at a temperature T naught below the environment temperature. Although when one can say that one can insulate this perfectly perfect insulation is never possible. So even if you create a system at a temperature T naught the temperature will slowly rise as time goes. Not only that quite often you will put in warm stuff inside and you would have to extract heat to cool it down to temperature T naught. In either case either because of warm stuff kept in or leakages from the environment there will be a heat flow into this system. And to maintain the state of the system we have to extract that heat from this system at some rate Q dot 2. Since we must reject it to some other system and naturally an available system is environment and we must be able to reject it at a temperature equal to or slightly higher than that. This is what we get as our basic idea of a refrigerator. But sometimes we also use refrigerators for some other purposes. For example you may have an oven and you may have a incubator and you have to maintain it at a temperature higher than the environment temperature. It can be done by two ways take a fuel and directly burn it and use it but there is another way of doing it and that is by using a modified refrigerator. Actually it is a refrigerator itself thermodynamically but we call it a heat pump. It will supply heat to this system which is to be maintained at a high temperature Q dot 1. It will absorb some work W and it will take in heat from some system environment is available as a large system. It will absorb heat from the environment at a temperature at or slightly below the environment temperature because it has to absorb and provide this. So this is the three type of cyclic devices actually two type. This is the refrigeration class of devices and this is the engine class of devices. And using thermodynamics we have already decided on certain basic things. For example using the second law of thermodynamics we can say what should be the maximum efficiency of the engine or for a given Q dot how much W dot is to be provided. Let us look at first some absolute basic parameters and then let us look at the implementation. We will come to more performance parameters later. Remember when we talk of an engine the most important parameter is going to be the efficiency. When it comes to refrigerator there are two possibilities. If it is used as a refrigerator as a refrigerator we are interested in extracting this heat and this is what we have to pay for. So we decide on a parameter known as the coefficient of performance and it is defined as Q dot 2 divided by W dot. But if you use the same refrigerator as a heat pump it is a very similar machine. But now what we are interested in is supplying this heat to the high temperature system at T 1 whereas this is the power is what we have to pay for. We define our coefficient of performance as Q dot 1 by the power. There is a small definition change or a difference in definition between the two. And once you remember that engines which work on thermal energy will have the source at a temperature higher than the ambient the sink at a temperature very near the ambient or slightly higher. Refrigerator will have the refrigerated space at a temperature much below ambient. They will reject heat at a temperature near the ambient or at the ambient temperature or slightly higher. Heat pumps will supply heat to a system above the ambient and they will absorb heat from the ambient and the ambient temperature will slightly below it. And all these three devices work on cycles. So the next thing we do is we talk about classification of cycles. Now in classification of cycles remember that cycles when we talk in mechanical engineering thermodynamics. Cycles bridge thermodynamics on one side and the implementation on the other side. Thermodynamics we will only be talking about the working fluids at systems and processes. Whereas in implementation we will be talking about equipment and machinery. So when you talk about cycles you must be talking of all four cycles bridge this gap. When you talk about cycles we will be talking about the fluids which are used in the cycles. We will be talking about processes as saying that this is approximately a constant pressure process or a constant volume process or an isentropic process or an isothermal process. But we will also be talking of an equipment. We will be talking of a boiler, a turbine, a pump, a condenser, a heat exchanger and so on. So when you classify cycles, our classification will depend on fluids, processes, equipment, machinery and all that. And there are various types of classification. Whatever I say will never be complete because you can always look at cycles in different way, in different aspects and classify them as such. Perhaps the first type of classification is what we have seen is power cycles and refrigeration cycles. You can say refrigeration and heat pumping cycles. They are essentially the same type of cycles. Implementation is different. That is the first classification or first type of classification. Some of you will complain that I am classifying classification but that is bound to happen when you talk about the second type of classification is based on the working fluid. We have gas cycles and we have vapour cycles. Gas cycles are the cycles in which during the operation there is no change of phase involved. Since a change of phase is never expected, the word gas is appropriate. In a vapour cycle change of phase, particularly condensation and boiling are essential for the working of this cycle. So one process or at least one process in which the working fluid condenses, vapour of the fluid condenses becomes liquid and another process or processes in which the liquid working fluid becomes vapour is essential for the working of these cycles. Examples, our Brayton cycle, our IC engine cycles and some refrigeration cycles are gas cycles. Our gas turbine cycle on which our jet engines work is a gas cycle. Whereas most of our household refrigeration and air conditioned plant work on a vapour cycle. We know there is a condenser there and there is an evaporator in all refrigerators. For power plants working on steam, we have a boiler which boils the fluid. We have a condenser which condenses it. So these are vapour cycles. One characteristic of particularly from the thermodynamic analysis point of view one should note is because this is a gas, one can do what is known as a standard analysis in which we can assume that the gas is approximately an ideal gas with constant specific heats. And this and some other assumption lead us to deriving efficiency in terms of some simple parameters like pressure ratios, volume ratios and things like that, algebraic equations. All of you would remember that the efficiency of an IC engine cycle, the auto cycle is 1 minus 1 divided by rv raise to gamma minus 1. Efficiency in sum of simply two parameters. First parameter is gamma that is a parameter because we have assumed the working fluid to be an ideal gas with constant specific heats. And the other parameter is rv, a geometric parameter the so called volumetric compression and this is a standard analysis and ideal analysis, idealized analysis which gives us a cold closed form relation between efficiency and some geometric and operating parameter, simple geometric and operating parameter. That is not true for vapour cycles. Standard analysis I should not say x, I should simply say not possible. Not possible simply because the equation of state for a vapour can never be approximated by a simple relation. But simple relation will be too crude for any reason. And hence we cannot have a closed form equation, the efficiency needs to be computed for each case. And we have seen this even in our thermodynamic studies so far. When we saw it problems using first law, second law, whenever the problem involved a gas, we will say assume air to be an ideal gas with constant specific heats and then we obtain analytical solution. We will say the work done will be this, the heat transferred will be this, the process equation will be this like this pv raise to gamma is constant for an isentropic adiabatic process of air assuming it to be an ideal gas. But when it comes to steam, we do not have any such thing for every case we have to go back to the steam table, read the values, do the calculations and then provide the interaction. So just the way problems or exercises with steam had to be worked out in every case, whereas exercises with a gas gaseous system assuming into an ideal gas, you could derive formula and just substitute in the formula that same distinction exist between gas cycles and vapour cycles. When you come to detail, we will realize that because vapour can be selected to have a large latent heat like that of water, vapour cycles quite often tend to be more compact than gas cycles. And then when it comes to a question of scale, you will notice that if you want to produce just kilowatts of power or a few megawatts of power, you can use gas cycles. But if you want to produce hundreds of megawatts of power or thousands of megawatts of power, it will essentially be vapour cycles which you will be using because of their large latent heat that means you can add a large amount of energy without significantly changing the temperature they tend to be compact. So remember that vapour cycles tend to be generally more compact than gas cycles usually, let us say often. But because a condensation and vapourization is involved, a vapour cycle will definitely be a more complex cycle than a gas cycle. The third classification that we talk about is a classification based on the type of equipment. Remember that the engine or refrigerator will execute a cycle. So there will be processes in which one process in which pressure increases, another process in which pressure decreases, one or more processes in which temperature increases and temperature decreases. And similarly there will be a process in which a vapourization takes place, there will be another process in which condensation takes place if the cycle is a vapour cycle. So when you take a cycle, although in a general case on some diagram say PV diagram the cycle will be shown, we have shown cycles like this but in actual case it will be made up of some this thing saying this is a constant pressure process, this is a constant entropy process, this could be a constant temperature process, this could be a constant volume process something like that. So cycle can usually be separated into a few typically four or more distinct processes. The classification based on type of equipment is a single equipment cycle or a multi equipment cycle. Here all processes take place in a single system, a single geometric system. Here each process has a piece of equipment, its own equipment associated with it. For example you take our petrol engine or any IC engine for that matter. There is one cylinder piston which does the job of everything, taking in the fluid, compressing it, burning it, expanding it, exhausting it. This is an example of a single equipment cycle. Whereas you take our household refrigerator all of us know that it has four major components, a compressor, a condenser, a throttling device and an evaporator. Similarly a steam power plant will have a boiler, a turbine, a condenser and a pump. So you take either a refrigerator, let us take the household refrigerator. You have a compressor, you have a condenser, you have a throttling device and you have the evaporator. Each one essentially doing one process. Compressor does the process of increasing the pressure, condenser does the process of condensation, throttling device does the process of decreasing the pressure, evaporator as the name says converts it, working fluid back into vapor. So each process has a specialized equipment associated with it and there are ducts used, connect one piece of equipment to another piece of equipment. Because of this, although a multi-equipment cycle like this and you can sketch such a block diagram for a steam plant and maybe for a gas turbine plant. Although multi-equipment cycle looks more complicated, remember that technically this would be an easier thing to do because you have this one equipment specialized for one job. Whereas in an IC engine, the same cylinder piston arrangement will have to do all the tasks associated with the cycle. Because of this, again multi-equipment plant tend to be more compact and hence are attractive for very large capacities. Quite often they also tend to be more efficient because each piece of equipment is specialized in the certain type of job. Condenser does not have to do the job of compression, the throttling valve does not have to do the job of condensing the liquid or evaporating it. There may be some evaporation associated with the throttling valve, but its major contribution is in reducing the pressure. So this was the third type of classification, the fourth type of classification and mind you, this 1, 2, 3, 4, 5, there is nothing, no, there is no special order in this. I am just mentioning them as they come to my mind. The fourth type of classification is an open cycle and a closed cycle. Maybe I should discuss the closed cycle first and then we will discuss the open cycle. A closed cycle is one in which the working fluid always remains within the confines of the equipment as a sealed system. In fact the sealed unit is a name given to the heart of the equipment quite often in household refrigerator or a small air conditioning system. This is an illustration of a closed cycle. Although in a refrigerator there are these 4 pieces of equipment, a properly working refrigerator and a well maintained refrigerator will see to it that the refrigerator never comes out of any of these 4 pieces of equipment. It will go from one piece to another piece, but it remains where it is inside that full piece of equipment. Same thing in a steam power plant, the steam may get converted into liquid, get pumped back into the boiler, gets converted to steam, expands in a turbine, but remains within the confines of the power plant. Such a cycle is a closed cycle. An open cycle is one in which we depend on nature to execute at least one process. I am not writing that. So in this case the working fluid comes out of the piece of equipment, goes back to nature and we collect a similar working fluid or whatever is available in nature into our system. Illustrations of this are our IC engines or what is known as air cycle refrigeration or even the evaporative refrigeration that you have in dry hot climates where you have so called desert cooler. That is some sort of air water vapor cycle refrigeration. It is an open cycle in the sense you do not circulate the same working fluid. Whatever is cooled after it is used is thrown away means it leaks out of our chamber. You get in fresh air, humidify it, cool it and use it. In IC engine you take air and fuel, burn it, produce power and throw it out of the exhaust. So this is an illustration. These are illustrations even our desert cooler is an illustration of an open cycle. Many of our gas cycles particularly producing power and which use air as their major working fluid will be open cycles because air is available in plenty in nature. So we do not have to do the job of decontaminating the exhaust gases, purifying it. We just throw the exhaust gases out into nature and say nature you do the job and give me fresh air back. There are some vapor cycles which are also open cycles. For example the steam locomotive. The steam locomotive uses a vapor cycle. It takes water, it boils it, it pumps it into the boiler, it boils it, it expands it through an engine. For some reason again compactness and small power we do not have a turbine in a steam engine. We have a steam engine that is a reciprocating steam engine and after that the steam is thrown out into the nature and that is why the steam locomotive needs every few hundred kilometers the water as well as the fuel to be replenished. The fuel has a high density so the replenishment of fuel is not that frequent but the replenishment of water is reasonably frequent and nowadays we do not have steam locomotives being used in India. They are used only as you know vintage devices at a few places. But earlier at almost every station or every other station something like an elephant's trunk, an inverted u-tube with a flexible outlet pipe was very with scene. You see it even at a few places once in a while and those were for replenishing water in the steam locomotive. So these are illustrations of open cycles whereas our household refrigerators, steam power plants etcetera these are typically closed cycles. The last classification at least which I am going to mention now and I leave it as an exercise to see whether there are other types of classification. A pertain to power plants. Notice that most of our power plants which we will be talking about in thermodynamics are thermal power plants for which the basic schematic of the 2 T heat engine is the proper schematic although it is very simplified it is a proper schematic. Now the question is where does that q 1 come q dot 1 come from? If you look at the natural possibilities we have solar energy, we have say what are known as fossil fuels, we may have other type of fuels may not be really called fossil say artificial fuels or bio fuels, we may have nuclear fuels. Now out of these a solar energy usually for power plants will be concentrated and then it will be absorbed whereas fossil fuels and other fuels will have to be put through a process of combustion q dot is absorbed. And this combustion makes the energy available in the form of q dot. Nuclear fuels may be there will be some sort of concentration or preparation but typically we have power plants undergoing fission. No power plant has been set up undergoing fusion and this fission releases energy. Now what happens is this process of combustion when you look at it is fuel plus air, air is used as an oxygen part of it gives you products of combustion the chemical products of combustion plus energy and this energy forms our q dot 1. And this process can be implemented in two different ways and that gives us this fifth classification for power plants restricted only to power plants as internal combustion versus external combustion. And the idea is this in under internal combustion the process of fuel plus oxidant that is air providing you products and releasing heat takes place within the working fluid directly. So, you can show a schematic as the working fluid you have air plus fuel at a low temperature combustion takes place inside the some chamber in the we have products at high temperature. Heat release is the process of combustion is taking place here there is no process of heat transfer involved. Whereas, when it comes to external combustion you have typically a chamber in which air and fuel is mixed it is five continued it is not six it is five continued this pertains to power plants. This is the preliminary part of five the five really starts from this slide. So, we have air and fuel burning producing. So, combustion takes place in a combustion chamber may be called a combustion chamber may be called a furnace. And there is a process of heat transfer which makes it available to the working fluid which then goes from a lower temperature to a higher temperature or from the liquid state to the vapors. Such a heat transfer process is not involved in the internal combustion scheme of things because the combustion takes place within the working fluid itself. Whereas, here the combustion takes place outside the working fluid and the process of heat transfer is involved. Now, because of this because of internal combustion these plants tend to be more compact, but although they are compact this internal combustion can be managed only at a low scale. So, when it comes to large sizes of power plants internal combustion has its weakness. So, that is why the internal combustion engines usually are restricted to smaller capacities if they are if they are of the single equipment kind typically reciprocating because the cycle has to be complete. They will be restricted to may be kilo watts hundreds of kilo watts may be a few mega watts if they are of the turbine kind the gas turbine kind they will be restricted to few tens of mega watts that is their typical scale. External combustion on the other hand can go up to 100 and 1000 mega watts if this is not so compact. And now notice that because the external combustion scheme does not change the composition of the working fluid it is possible for the external combustion cycle to be a closed cycle. Whereas, remember that in case of internal combustion because the working fluid it itself takes part in the product in the process of combustion the composition changes you have air and fuel to begin with and you have products at high temperature which come out. So, consequently the cycle cannot really be completed if it is closed once air changes its composition to product you cannot burn more fuel in it and because of that internal combustion cycles will always be open cycles. We do not have an illustration where an internal combustion cycle is a closed cycle. Now that brings us to the tentative end of classification I will leave it to you to extend this or modify this because there is nothing this is not like a law of thermodynamics. So, it is not as precise as that this is our understanding of the way we try to look at cycles. Now let us come to implementation of cycles see it is very easy for us in thermodynamics to sketch a say p v state space and say that let us execute a constant pressure process let us execute an isothermal process let us execute a constant volume process may be another constant volume process let us execute an isentropic process and we can create a cycle all that it needs is sketch it properly. For example, this is a constant pressure process this is a isothermal process this is a constant volume process this is another constant pressure process this is an isentropic process it is very easy for us to sketch it and analyze it and talk all sorts of parameters about this. But the question is how do we set up equipment equipment we call individual piece of equipment collection of equipment will be a plant. So, you have a piece of equipment you have a collection of equipment finally, a complete plant to execute these processes if you look up what is possible the following things seem to be reasonably possible without much difficulty. One thing which is possible is a constant volume process in a closed system seal something in a cylinder piston arrangement sees the piston that is lock it at one place whatever process takes place is a constant volume process. The second process which is reasonably possible is an adiabatic expansion compression process this can be done in a closed system using a cylinder piston arrangement provided we our system is well insulated and we do it reasonably quickly enough. So, that when we transfer to or from the system is small because perfect insulation is never possible this can also be done in an open system with a very designed turbine or a turbo compressor. The third thing which to seems to be reasonably easily possible is isobaric heating cooling and that too in an open system because a simple thing is you provide a duct in which your fluid goes in fluid comes out and you provide a diameter large enough. So, that any pressure drop is small compared to the system pressure and you provide a hot fluid outside or a cold fluid outside. So, that you have the required heat transfer into or away from the system this is what we do in heaters boilers condensers heat exchangers. But remember it is an open system and the isobaric is managed by providing sufficient area so that there will be some pressure drop but that will be a small pressure drop and if you see most of our equipment will have processes which are one or more of these isobaric adiabatic and constant volume. If it is constant volume it will always be in a closed system adiabatic is possible both in a closed system and open system whereas isobaric heating cooling is possible in an open system. One thing we know is that our best cycle the most efficient cycle is a 2 t cycle the Carnot cycle type and the two processes there are adiabatic reversible so isentropic. So, that perhaps we can implement but there are two processes which are isothermal heating cooling seems to be not in the normal scheme of things but we will see soon come to that and that is where our vapour as a working fluid will help us. So, in implementation if we say that the best cycle is Carnot then remember the Carnot cycle on the T s diagram looks like a rectangle. Let us consider a Carnot cycle. So, let us consider a Carnot cycle for an engine and on the P V diagram you have isotherms and two isentrops this is looks like a very stretched and even in that the two processes which are isothermal will be difficult to implement the two processes which are isentropic are not that difficult to implement. So, this brings us to the idea that from this point of view can we modify the Carnot cycle in some way. So, that we do not lose the efficiency because that is the highest one or we do not lose any significant efficiency but the cycle becomes easier to implement and when we come to implementation let us bring in some part of item 3 of 13 that when we create our cycles it is not just the efficiency that we are going to look at. We are going to look at a few other parameters and hence before we complete let me say that there are apart from efficiency or coefficient of performance there are certain parameters of performance which we are going to look at. I will talk about this from the point of view of the engine but you can always refresh them from the point of view of turbine. The first parameter is going to be the efficiency eta for refrigeration it will be the coefficient of performance. This should be higher the better that is what we want that is good for us but apart from that there are certain other parameters. One parameter which we tend to neglect but which is important what is known as the work ratio. Now this is not talked about in thermodynamics and you will find many textbooks in thermodynamics show an engine something like this. You show an energy balance stream they show an engine like this but instead of arrows they show a big channel coming in part of that getting converted to work and the remaining part going into the heat rejection system. So they show this as q 1 or q dot 1 they show this as q dot 2 and they show this as w. The problem here is student get an impression that part of q dot 1 is directly converted to w and when you do this this idea of work ratio gets hidden. Remember a cycle is a closed process and since there are pressure differences and temperature differences in a cycle part of the cycle would require that we expand the working fluid part of the cycle we require that we compress the working fluid. So although here we are looking at just the w net and thermodynamically we do not have to split w net into any part when we really look at the actual inner working cycle. Part of the cycle will be producing positive amount of work part of the cycle will be absorbing work so producing negative amount of work the algebraic sum of this or the numerical difference of this will be providing you the net work output. And this is important because it is possible let us consider a cycle which takes in 100 watt of q dot 1 rejects 60 watt as q dot 2 and produces 40 watt if you want bigger scale write kilo watt or mega watt 40 watt of w dot net. Now this w dot net is made up of two components a positive component and a negative component this is the expansion work during the cycle this is the compressor work during the cycle or compression work during the cycle. And the efficiency says that the efficiency is 40 watt divided by 100 watt so efficiency is 0.4 no doubt about it it is 0.4. But now let us consider two engines again efficiency 0.4 power output 40 watt but one engine produces 40 watt by producing say 60 watt in the expansion and consuming 20 watt in compression to complete the cycle. Another engine again produces a net power of 40 watt but instead of 60 watt it produces 1060 watt and it consumes 1020 watt which one is a better engine is it engine A or is it engine B. You can discuss it but I propose that engine A is better because only 30 percent of what the expansion process produces is consumed back by the engine and the remaining 60 percent or one third is consumed two thirds is provided to the outside world. Here we say the engine produces a large amount of power but most of it is consumed only a small fraction is made available to the outside world. Now look at the actual implementation in thermodynamics we look at the ideal world. In the ideal world we have no friction no leaks. In real world we will have some friction some leaks. So when you say W dot positive and make part of it available for completing the compression. Here 60 watts is produced and we say 20 watt consume 40 watt given out but when you really implement because of friction and other mechanical overheads 60 watt which is produced not all can be pumped back 60 watt by the time it comes out it may be a few watts would be gone say let us say 5 percent is gone. So instead of 60 watt you get 57 watt and here may be 5 percent more has to be given as a technical bribe. So here instead of 20 watt what you really have to provide is 21 watt. So instead of 40 watt now you will get 57 minus 21 something like 36 watt a 10 percent reduction here. Now see what that 5 percent does 5 percent here means more than 50 watt will be lost. So you will get something like just about a kilo watt but here instead of 1020 watt here the compression process will need 1070 watt just the 5 percent axis here and there and you will find that with a small amount of technical frictional and other overheads this type of machine B will fail to work and that is why the ratio of this W dot minus to W dot plus is important and that is what we define as W R work ratio and here the smaller and that brings us to a situation where this type of a diagram needs to be modified this is not the correct idea and if you look at the way the industry keeps track of its energy flow and material flow they have this idea of what is known as a Sankey diagram. Here anything which is balanced may be money may be people may be manoeuvres may be water flow may be air flow or may be energy flow it is shown in terms of a diagram in which each channel is proportional to the unit and this diagram proportional to the flow and this diagram shown here is a Sankey diagram. For example, an engine with a 40 percent efficiency will be shown like this 100 units coming here say 100 watt 40 watts going here 60 watts going here. So, the width here will be proportional to 100 width here will be proportional to 60 width here will be proportional to 40 but as I said this does not look at the work ratio. So, this is not a good representation what we should show it is something like this in our case let us say that we have 100 units coming in finally, what goes out is 40 units but there is a 40 units is made up of a W plus which is say 60 units and W minus which is say 20 units. So, the W minus will be an internal channel showing 20 units and we can show it like this. So, now this is 100 watts which is Q dot 1 going out 40 watts which is W dot net heat rejection is 60 watt that is Q dot 2 but inside there is a stream which is 20 watts which is being plowed back as work. So, out here I have something like 120 watt and what your this is the complete Sankey diagram and you can make it as complicated as you feel like and it shows the W plus it shows the W minus this is the W minus and it gives you a much better value. So, this is the idea of the energy balance those who have done energy balance for IC engines should rephrase and re draw this diagram for that particular thing and impress it on the students that the W minus is also important as we go ahead we will see the W plus and W minus for various cycles. So, the second parameter which we have seen is the work ratio the first one was efficiency second one was the work ratio. Now, beyond this the parameters become specific to the type of plant for example, for almost all plants we can have a parameter called specific output. Now, for power plant this is more suitable for a power plant but you can work it at specific power consumption for a refrigeration plant work it around. The idea is like this you have a cycle which produces certain W dot net but in the cycle there is a working fluid which is getting circulated. If it is a closed cycle it is getting circulated if it is an open cycle it is going through the cycle and going back to nature and it produces W dot net. This circulation rate let us say is m dot for the working fluid you can write m dot W f saying it is m dot of the working fluid. Then the specific output is W dot net divided by m dot working fluid the units will be this is kilo watt or mega watt this will be kilograms per second and if you convert it you can even convert it to kilo joule per kilogram or mega joules per kilogram or the electrical power people who supply electricity can convert it to kilogram hour kilo watt hour per kilogram where kilo watt hour is the commercial unit of power sold as electricity. Now what is the significance of this notice that m dot W f represents the amount of fluid circulated larger the amount of fluid circulated larger will be the size of the plant because you will need bigger boilers bigger ducts bigger turbines etcetera. So, for a given size of a plant for a given W dot net a smaller m dot W f means a larger specific output and that means it is a more compact plant. The higher W dot m f means a lower W sp for the same W dot net and it means a plant not so compact. So, this represents the compactness of a plant and here we have the higher the better.