 next topic and that is cycles. Now, we have a thermodynamic cycle. By thermodynamic cycle we mean what we have defined in our basic introduction. A cycle is nothing but a process in which the initial state is a final state. So, any process which can be represented even crudely as a closed loop on a state space that is a cycle and a cycle requires just one state of equilibrium. Just to assert that state one is state two. Two states which are not in equilibrium, we cannot say that they are the same because we do not know enough about every state. So, a simplest depiction on a cycle on any diagram P v or T s. The minimal depiction will be some state from there start off and come back to that state. You need not worry what happens in between. But for our purpose most of our cycle will be depicted using some quasi-static processes. So, we will have any number of points of equilibrium in between. Actual cycles may not be like this because a non-isentropic turbine we will say that look we need to know only inlet and exit states what happens in between and we do not really care. But this is about thermodynamic cycles and now on one side we have thermodynamic cycles, on the other side we have actual plant which is made up of pieces of equipment and we have in between technical cycles. Technical cycles are thermodynamic cycles as implemented in a plant. So, now we have cycles from thermodynamic. We have cycles technical considered for implementation and we have plant that is actual equipment. And when we now talk of cycles classify them we are actually in this domain. When we do cycle analysis we use the ideas of thermodynamic cycle but now what we mean are the cycles which are technical cycle which are executed in equipment which is part of a plant. So, when it comes to classification there are number of modes of classification. One type of classification is based on usage. First one is whether it is a power cycle or power plant or a refrigeration cycle which is for a refrigeration. Thermodynamically these are power producing cycles, these are power consuming cycles. For these cycles W dot would be greater than 0, for these cycles W dot would be less than 0. You can say these are normal or forward cycles, quite often these are known as reverse cycles. So, sometimes the same cycle can be used for example a sterling cycle can be used for power plant. Sterling cycle when implemented in the other way can be used as a refrigeration cycle. In fact, sterling cycle more implementations would be as refrigeration, refrigeration, heat pumping, carnos or cryogenic cycle. We will be using refrigeration meaning all refrigerators, heat pumps and cryogens. So, in one case you say sterling power cycle, the other case you can say sterling refrigeration cycle or the reversed sterling cycle. But you generally do not see people do not say that liquid nitrogen blast based on the reverse sterling cycle because moment is a liquid nitrogen plant it is known that it is a reverse sterling cycle and anyway there are many power plant implications of sterling cycle anyway. But, Brayton cycle generally used in gas turbines and jet engines. You can use a reverse Brayton cycle for refrigeration reasonably common for aircraft cabins and many other simple implementation. And if the pressure for greenhouse gases becomes extreme then Brayton cycle because it can use ambient air will become a rather attractive option. Only thing is it is not as thermodynamically efficient as is a vapor compression cycle for example. So, the reverse Brayton cycle is so common that we have the name joule cycle for it. Otherwise it is nothing but basically a reverse Brayton cycle. So, that is based on usage. The second classification is mainly for power plants. For power plants traditionally the energy which is supplied comes from combustion of a fuel. And when this happens we have a classification when combustion of a fuel is involved of what is known as an internal combustion or external combustion. And naturally because combustion may be involved for only for power plants no combustion in refrigeration cycle. This is only for power plant and that to certain type of power plant. For example, a solar power plant no combustion is involved. So, there is no point in calling it internal combustion or external combustion. In internal combustion the process of combustion is within working fluid. So, no heat transfer process is involved. This happens in our car. We put in fuel air it sucked in the combustion takes place within the engine. So, that is an internal combustion plant and the cycle is implemented as an internal combustion cycle. Car or a jet engine all these are internal combustion. In external combustion combustion in a fluid then there is a process of heat transfer to the working fluid of the cycle. So, there is a process of heat transfer involved. For example, over steam power plant you have a boiler a separate furnace. There are coils of water which absorb heat and become steam. Combustion does not place take place within the water or within the confinement of steam. So, that is an external combustion plant. It should be noted that because of this heat transfer to the working fluid because of the heat absorption there is no change in composition of the working fluid. Here there will be a change in composition. First one was based on classification on music. Second one was based on the type of combustion. The third one we look at is the type of equipment. And for this we have a single equipment plant and we have, see although we have shown on a TS diagram just some cycle. In actual practice this particular cycle is implemented as reasonably distinct processes. Some at constant pressure, some at reasonably constant entropy, some at constant volume and all that. In a single equipment cycle all processes in the same piece of equipment. Our car engine is a typical example. The same cylinder piston arrangement does the job of everything. Sucking in the fluid, compressing it, burning it, expanding it, throwing it out, everything. Whereas a multi-equipment plant is different equipment for different processes and fluid flows from one to the other. So, such cycles can be shown as block diagrams. One piece of equipment, second, third, fourth and fluid goes. One could be pump, one could be boiler, one could be turbine, what could be condenser. So, our power plants, household refrigerators, these are, you know household refrigerator is a typical example of a multi-equipment plant. You have the evaporator, you have the condenser, you have the compressor. Three pieces of equipment very easily seen by everyone, except that condenser these days is integrated with the body so it is not so easily seen. But simple models of refrigerators still have a proper black-pented condenser coil. The capillary tube is hidden somewhere so unless you really hunt it out you cannot hunt it out. You are air-conditioner, multi-equipment. Then a closed cycle for an open cycle. A cycle is said to be closed when the working fluid sort of sealed in and except for leakage which have to be taken care of. There is no interaction of the fluid directly with the environment. Nothing comes out, nothing goes in. So, one typical example is our household refrigerator, air-conditioners, steam power plants. All these are closed cycles. An open cycle on the other hand is the working fluid is taken in known as intake or induction or inflow and the working fluid is then thrown out and that means that at least one process is left to nature to work out. Illustration, IC engines, all our car engines, jet engines, air breathing engines as they say. You take in air, you take in fuel, you throw out the exhaust. Let nature worry about what to do with that. Naturally internal combustion cycles will have to be open cycles because you are changing the characteristic of the working fluid. You cannot go on using it again and again. So, you have to throw it out and let nature worry about how to give you fresh air out of the exhaust. Cloth cycle, steam power plant. But that does not mean all steam power plants are cloth cycles. Our steam locomotive is an illustration of an open cycle steam power plant. It takes in water. You have to continuously feed it water. That is why electric engines have essentially an infinitely long range. Diesel engines have a much longer range because diesel is a very compact fuel. Steam engines have a much shorter range because periodically you have to supply coal which is a huge bulk and also water because water is a working fluid and the locomotive does not have a condenser. It throws out the steam which comes out of the engine part. Those will also be open cycles. Even partial recovery will make it open because to work the cycle you have to keep on feeding the working fluid at some end and there the recovery is not there because perhaps it is not economical or technically easy to recover or maybe it gets contaminated. But if it does not get contaminated goes only through heat exchangers maybe you can recover it. In this case it will be and finally the fifth classification is the type of working fluid giving you a gas cycle for a vapor cycle. Unlike the second classification external combustion, internal combustion see the first is applicable to power plant refrigerators that makes a classification. Out of then this internal combustion, external combustion is applicable only to power plants whereas type of equipment, single equipment, multi equipment is applicable to both power plants as well as refrigerators and closed cycle, open cycle applicable to both power plants as well as refrigerators. Similarly gas cycle and vapor cycle is applicable to both power plants and refrigerators. In a gas cycle the working fluid is a gas. No change of phase is involved of any kind. Here the working fluid is typically in two states liquid and vapor and hence condensation and evaporation or boiling are essential part of the operation of the cycle whereas no change of phase is involved here. Now from a student point of view there is an advantage. Here for example in this case the gas in a simple situation can be assumed to be an ideal gas with constant Cp Cv. In which case we have simple equations to worry about and it is possible to do what we call quite often a standard analysis assuming the working fluid to be an ideal gas and you get neat expressions for efficiency at some function of P1 P2 or T1 T2. Simple expression just substitute them in a calculator within half a minute you have the answer for efficiency and many other parameters. Whereas here because a vapor is involved and condensation evaporation is involved there is no simple equation of state whether it is water for power plants or any refrigerator for any refrigerant for refrigeration plant. So every case will have to be worked out. So we have a formula for the efficiency of a standard auto cycle formula for the efficiency of the standard Brayton cycle but we do not have the formula for the efficiency of a standard ranking cycle or the COP of a standard vapor compression cycle of any kind. So no simple EOS so we have to work out each case. See when you teach cycles in thermodynamics once you realize that cycles are one major link between thermodynamics and further engineering and hence when you come to cycles you must spend time in explaining what a cycle is and the different classifications of cycles. Show them at this time pictures of various equipment and their cycles so that their interest immediately let them realize that the thermodynamics one of the direct implementations is in analyzing power plants and refrigerators and the link is through thermodynamic cycles. So coming back to this thermodynamic cycles, technical cycles which are implemented in plant there is a link between these two. We will analyze thermodynamic cycles they are implemented as technical cycles in appropriate plant and you will notice that some classifications pertain to these cycles as well as these thermodynamic cycles. Some classifications pertain only to these cycles and the plant. For example when it comes to open cycle and closed cycle it has nothing to do with thermodynamic cycle. Thermodynamics is let nature cool it it is a constant pressure cooling process but when it comes to actual implementation there is no piece of equipment executing that cycle. Now the next thing you do is talk about performance parameters. There are performance parameters which some provide you the goodness of the plant. These parameters are known as efficiency or coefficient of performance for refrigerators. Then there are certain parameters which talk about compactness of a plant. These are usually some specific output or specific refrigeration effect. There are some parameters which talk of the size for the capacity. Here we talk about the power output in case of refrigeration we talk what is known as the tonnage. And then there are these are the parameters which almost everybody will be talking about. But then there are other parameters which are of some of them will be economic, some of them will be purely thermodynamic. We will talk only about one of these. For example other parameters directly or indirectly related to these are work ratio in some cases, mean effective pressure. See the size and capacity is essentially a scale small plant or big plant. When it comes to real thermodynamic size and capacity does not matter. We analyze a 1 megawatt steam plant and a 2000 megawatt steam plant using the same principle, same paper, same pencil. So that is a minor parameter. We are going to look at efficiency and the compactness and then we will look at the work ratio. Efficiency is invariably defined is for power plant or engines. And this is simply our schematic diagram would be we have an engine producing some output W dot, some heat rejected. This would be the typical nomenclature rather than Q dot 1, Q dot 2. This would be the environment temperature T naught. This would be some supply temperature T sum. Efficiency will be defined as W dot net divided by Q dot supply and naturally higher the better. That is simply Q dot supply depends on how much fuel you have. Power output is what we want. Fuel is what we pay for. If you are a power plant engineer, any type of power plant, you will generate power and sell it. So this is the revenue department and this is the purchase department. You have to buy fuel. You should be able to generate more revenue with the least amount of fuel. So higher is this ratio, better. Then when it comes to refrigeration and heat pumping plants, there is a coefficient of performance. And here there is a small difference. A refrigerator plant will do the following. You have an environment T naught and you want a T refrigerated space to be maintained less than T naught. You cannot have perfect insulation. So from the environment there will be some energy leaking into it. In between you will put something at room temperature and into it and say cool it or put water into it and freeze it. So either to take care of this leak into it or to cool the temperature or reduce the energy of the stuff which is put in it, we will have to extract heat out. That heat which is extracted is known as the refrigeration effect. And naturally our second law tells us that you just cannot throw it out at a temperature higher than or equal to environment. You cannot throw it at a temperature less than environment because you just cannot do it. You must be setting, sending it out to the environment and wherever you do heat transfer must be possible. So temperature must be above the environment, at least by a small amount. And you cannot do this unless you provide a W dot, supply a W dot. This is the equipment known as the refrigerator. What you need is Q dot R. It is what you want. What you have to pay for is Q dot supply. Q dot R, if it is good then your refrigerator will keep things very cold, produce lots of ice. If Q dot supply is bad it will consume more energy, your electricity bill will go up. You want your room to become comfortable with your air conditioner, but your bill should not go up. So this is the ratio that you are provided. Coefficient of performance is what we want divided by what we pay for. It is a dimensionless ratio, but unlike efficiency which the second law says should be less than or equal to 1, this can have a value less than 1 equal to 1 greater than 1. That is why it is called coefficient of performance. And out here your W dot net is usually denoted in terms of megawatt, kilowatt, maybe gigawatt for big fans. Although this can be in compatible units to give you a ratio, quite often Q dot R is measured in tons of refrigeration and the conversion factor is 1 ton of refrigeration, 3.5 kilowatt. Tell them that this is an approximate number. Historically the value may be slightly different, but for our purpose remember that 1 ton is about 3.5 kilowatt that is to remember. Let them read some book to find out the history, what it was meant initially by 1 ton of refrigeration. Do not tell them stories about that short term 9 from 0 degrees C to 0 degrees C. Let them read something on their own, they will find it out on the internet in a. W dot net is measured in kilowatt and hence quite often C O P may be written in terms of tons of refrigeration plus kilowatt. It is a dimensionless number, but now it has a unit. We talk of energy efficiency of engine as 30 percent, 40 percent, but when it comes to an air conditioner the supplier may say that look it provides you 1 ton per kilowatt or a more efficient one will provide you may be 1.2 ton per kilowatt that means it provides you this much of refrigeration effect consumes this much power. And there are other units BTU per kilowatt hour or kilo joule per kilowatt hour whatever they are all dimensionless numbers only units are different. So, do not ever insist that C O P must be given to you as a pure number it may have a unit associated with it, but the unit should be such that it should be a dimensionless unit. But if somebody asks you what is the C O P you should give him a pure number meaning it is kilowatt per kilowatt or ton per ton. This is for refrigerators when it comes to heat pump it is the same reversed cycle which does pumping of heat, but here the job is to keep a space at a temperature T higher than T naught and then you say that rather than directly heating up the job of a heat pump is to take heat from the environment and supply the required amount and run it as a essentially as a refrigerator. So, looking at it it is a reversed cycle takes it from a lower temperature dumps it at a higher temperature, but here we are interested in the refrigeration effect the amount of heat extracted from that low temperature system. Here we are interested in the amount of heat pumped and hence the C O P here is defined in a slightly different way instead of Q dot R by W dot supplied this is the definition of C O P here, this is the definition of C O P. The denominator remains W dot supplied the numerator now is the amount of heat supplied and why do we need to supply this heat because there could be some heat losses to the surrounding you cannot have perfect insulation or you may keep something there and expect it to be heated up by absorbing heat. So, this is the heat pump load heat pumping load not refrigeration effect that divided by heat supplied C O. So, these are the three parameters and you must spend time in explaining them the differences and similarities between the two particularly the differences between the C O P for a refrigerator and C O P for a heat pump and take this opportunity to tell them what is a turn off refrigeration means at least approximate. Then the something about compactness and size see whatever plant we have it has a working fluid and whatever we do the working fluid usually flows from one equipment to another this could be a power plant this could be a refrigeration plant does not matter M dot working fluid. Now, we may have a given capacity of the plant for example, you take a power plant it produces some W dot net and we can compare two plants one from company A another from company B both producing 1000 megawatt. So, they will be different differences and one company will say that look for 1000 megawatt we need to circulate steam 800 kg per second another company says we need to circulate steam 900 kg per second both may have the same efficiency but the fluid circulation rate is different and hence we define a parameter which is known as there are two parameters defined one is the specific output which is W dot net M dot working fluid and the other one is the reciprocal of it M dot working fluid divided by W dot net the unit here will be kilowatt per kg per second or megawatt per kg per second or it could be kilo joule per kg here it could be the other way round kg per second per kilowatt per megawatt per kg per kilo this is known as specific output this does not have a name but in steam plant this is known as the steam rate or specific steam rate and what is the effect if specific output is higher that means for the same working fluid flow rate I take more output from the plant or looking at the other way for a given output I need to circulate less amount of fluid this fluid is not consumed it is only circulated but if you need less fluid to be circulated that means you have smaller sizes of equipment smaller duct smaller duct sizes smaller boiler sizes and hence something which has a smaller steam rate or a higher specific output will be a more compact plant it has nothing to do with efficiency it has something to do with compactness of the plant similarly your refrigeration plant once in a while something leaks out okay particularly from the split air conditioners because these are not sealed system there are ducts there are flanges there are connectors so something leaks out and you have to fill in now suppose you have two such split end air conditioners both of 5 tons but once you fill in one requires more filling one requires less filling the one with less filling is naturally more compact works with less fluid may be circulates less fluid so this is something to do with compactness and size and this is what the technical name should be specific output or steam rate or working fluid rate steam rate is a very common in steam power plant so going to our parameters compactness size capacity is a scale so we have now these are the parameters which we talk about and these are specific to certain type of engine for example work ratio can be applied to engines and is usually applied to engines but usually is applied to but can be applied to refrigerators also you will find that many text books show an engine you supplied you rejected w net q dot supply w dot this is a very simple schematic but in many text books you will notice that it is shown like this what is called a Sankey diagram q dot supplied w dot net q dot is applied w dot net q dot is it really so is it like a highway one lane going there and other lane going here it is not so because we know that to keep the plant working there are certain internal exchanges which are not seen from outside so show them something like this you show them that look this network comes out but this networks come comes out from a work which is flowing inside the system something like this you show maybe I will do it on a bigger diagram on the next page you say that look this is the heat which is supplied I will show it horizontally I have a larger part of it is definitely rejected no doubt but it is not that the remaining becomes work this becomes work no doubt this is supplied but during working much more work is created and is recirculated within the system like this so there is a positive work flow in the system there is a negative work flow which is fed back and network goes out and you can show them this on a PV diagram and also on a TS diagram for example they generally have an idea of the Carnot cycle on a PV diagram and Carnot cycle on a TS diagram so show a Carnot like cycle on the PV diagram these are the four processes let me say A B C and show the whole thing on a TS diagram. On a TS diagram the Carnot cycle would simply be a rectangle A B you ask them what is the area under the curve A B for A B C on the TS diagram what does it represent q dot supply for q supply what does this area represent heat rejected so this area represents the W net which is q supplied minus q rejected so the ratio of W net to q supplied is the efficiency and you can say the ratio of q rejected to q supplied is the say the heat transfer ratio and efficiency higher the better heat transfer ratio lower the better because heat transfer ratio is nothing but 1 minus efficiency. Now you ask them what is the area under the curve A B C this area work of expansion what is the area under the curve C D A work of compression what is this area in between this is network A B C D this you say is work of expansion which I call W plus magnitude this I call work of compression which I call W minus by magnitude so that W plus minus W minus is W net but do we call W net by W plus as the efficiency it is not the efficiency in fact W plus W minus have nothing to do with efficiency but now consider two engines with different ratios W minus W plus this what we call the work ratio what is the significance if there are two engines with a work ratio of 0.9 and another work ratio of 0.2 which one would you prefer 0.2 why less overheads that means well in either case suppose I am supplying 100 kilo joules my efficiency is 50% I am taking out 50 kilo joules of work but to take out 50 kilo joules of work internally I may be doing 500 kilo joules of less than 0.5 right. So this work ratio is better and for us this is lower means better this is usually not worried about in thermodynamics because this has nothing to do with thermodynamics and this is useful because when we start discussing cycles the first question which comes up is if Carnot cycle is the best why not use Carnot cycle it turns out give them an example and it is there in the illustration a Carnot cycle has one of the worst work ratios and hence we get attracted towards Sterling cycle Erikson cycle which are modifications of Carnot cycle. Then there is another parameter which comes into operation and which is the mean effective pressure this has something to do with reciprocating machine either power plant kind or the refrigeration kind we can give an illustration of power plant you say your car engine everybody knows that your car every student may not own but I think every student or his or her family owns at least one two wheeler these days most probably all students have a two wheeler these days and everybody talks of a 100 cc engine 200 cc engine typically in that range what does this 100 and 200 mean they say it is a displacement it means that you have a cylinder piston arrangement in which if you take the piston from one extreme end to another extreme end the amount of volume which is swept which is displacement is that V which you talk of V displacement VD technical name is a displacement volume and then you say that one cycle of working would take the piston from one end to other end and back at least once in some old engines it could be completed in one back and forth most of the modern engines it is implemented that you do it twice some cranky engineer in Kochi has implemented it by doing it thrice six stroke engine and I am sure there are other possibility now you say the work done per cycle and by this cycle I mean the technical cycle not the thermodynamic cycle of just going back and forth and at this time tell them that this movement is known as a stroke and this movement is known as a stroke a stroke one way the stroke another way and if your thermodynamic cycle is completed within two strokes it has it does require an even number of strokes right you have to come back to the original state then you say that it is a two stroke cycle if it is completed in four strokes it is a four stroke cycle during cycle analysis rather than straight away go into diagrams and formula it is worth spending a few hours explaining all this this way you are making the life simpler for people who will teach them IC engines and steam turbines provided they realize that the students already know this and just revise this quickly and go ahead otherwise they will bore the students so you determine the work done per cycle let us call it let me say network done per cycle is Wc now if I assume because this is moving by PD if I say that let me assume that this is done in one stroke of the piston what should be the pressure that should be acting on that stroke that pressure we call the mean effective pressure the displacement volume or you may call it stroke volume sometimes this is also known as Vs for stroke volume for engines the mean effective pressure would be the work done per cycle per unit stroke volume because work per done per cycle is mean effective pressure multiplied by the stroke volume at this stage there is no need to split it into break mean effective pressure and indicated mean effective pressure we are looking common thermo dynamic point that we can come when it comes to IC engines and similarly you say for an engine this will be the work done per cycle so multiply this by the number of cycles per second and you will get the power output of the engine you can even set up a small problem based on that for for example you tell them that our household refrigerator also as a compressor it consumes power so work consume per cycle if you calculate and divide it by the stroke volume you will get the mean effective pressure for that compressor for any reciprocating machine you take a reciprocating compressor you use that small pump for filling air into your foot ball or basket ball or even bicycle tire you can determine the mean effective pressure for that how much is the work done per cycle divided by the stroke volume which is a geometric feature find out the area of the piston how much does the piston move from one end to the other you have the stroke volume you get the mean effective pressure once you do this after this it is our routine formula but tell them this and the next more in next most important thing to tell them I will put this if you want in the final version is why not carno cycle in fact if you go through the exercises the first two exercises 8.18.2 now I will call it CA1 and CA2 are essentially this the characteristic of a carno cycle and its modifications the sterling cycle sterling and Ericsson cycle in the carno cycle I have asked you to determine efficiency all state points of course all state points come first only then you calculate the efficiency oh temperatures are given so efficiency comes straight away work ratio work done per cycle mean heat supplied per cycle and mean effective pressure for a carno cycle you will notice that although the volumetric compression ratio is 20 so the actual pressure will be 20 multiplied by 360 bar maximum pressure the work ratio is so near one that the mean effective pressure is pretty small mean effective pressure should be high because in a given volume you are doing more work so a higher mean effective pressure means a more compact machine either a more compact engine or a more compact compressor tell them that why did I write about mean effective pressure here it should be the higher the better so efficiency should be high mean effective pressure if it is a reciprocating machine should be high specific output should be high or specific working fluid flow rate should be low work ratio should be low it should not be near one.