Next parameter, mainly for power plants, this is specific fuel consumption. This is for power plants and tells us that if this is our power plant, it produces W dot net. Since it is taking fuel, you will take an m dot air and you will also provide sufficient amount of fuel. I should say sufficient amount of fuel to produce Q dot 1 and appropriate amount of air to provide complete and proper combustion. Then specific fuel consumption is the amount of fuel needed for unit power output. Units of this will typically be Kg per kilo watt or mega watt or you can have it is Kg per kilo joule or Kg per kilo watt hour. Then depending on the plant, there are some other measures. For example, one question was asked, let me go to the next thing. I am not consuming any papers here. What was that five? This is appropriate only for certain kind of machines, particularly machines of the machines which are single equipment and which are the reciprocating type, mean effective pressure. The way the specific fuel consumption is for power plants, there is no fuel consumed in the refrigeration plant. Mean effective pressure can be used for power plants, can be used for refrigeration plants, but it is for machines which use a cylinder piston scheme. Now let us first look at the power plant, a power producing device that is an engine. Now what happens? Here we get into some geometric details. Let us say that you have a machine which works in cycle by moving a piston back and forth and this displacement or movement of the piston is known as a stroke and this volume which is displaced by the piston is known as the stroke volume. Let us say it is an engine and let us have a simple model in which we say that during one stroke a uniform pressure Pm acts on this piston. Then what will be the work done per stroke? Work done per stroke will be Pm multiplied by Vs where Vs is the stroke volume. So this is work done or I should say net work done per stroke and we say that if there are n dot cycle is the cyclic rate that is number of such strokes in which work done per unit time then the power output blue dot net is Pm into Vs into number of cycles per unit time or the cyclic rate. This equation defines Pm the mean effective pressure. I can work it around and write it as Pm equals W dot net divided by stroke volume into n dot. Now see this represents the speed of the engine. The stroke volume represents the size of the engine and this represents the output of the engine. So although Pm has units of pressure notice that it represents the power output per unit stroke volume that for a given size and per unit speed and naturally an engine naturally remember that the speed of the engine will usually be restricted because of some mechanical considerations lubrication dynamics of the cylinder, piston, slider, crank, crankshaft all those mechanical devices they will dictate also the rate at which you can properly open and close valves. So n dot cycle is within a narrow range whereas size is something which we can design and if you want a higher output we can have a higher size. But if a machine has a higher Pm that means for a given Vs it can produce more power output. So here Pm is the higher the better the Pm represents the compactness of a machine. A machine which produces the same output at the same cyclic speed if it has a higher Pm it will have a lower Vs that means it will be a more compact machine. And here I am talking of output if you talk of consumption then the same thing is true of refrigeration plants. Now here I have to use some technical terms whenever you implement a cycle unfortunately I will be talking about power cycle but again as I am saying again and again you can use this for refrigeration cycles also. When you work an engine there is a thermodynamic cycle being executed and using the laws of thermodynamics we get a W dot net. This we can say is thermodynamic power as dictated by the laws of thermodynamics. But this is the power produced by our system which is the working fluid. The working fluid delivers this much net power to the mechanism of the engine. But the mechanism has to overcome friction may be the mechanism has to take care of some devices to make the engine run safely, make the engine run smoothly and take care of some lubrication and some control purposes. So there will be some power consumption let me say by local I mean pertaining to the engine itself and what we will get is the net power to the outside word I will say this is the delivered power. So whenever we talk of an engine when we buy an engine we are interested in the net or delivered power. This thermodynamic power quite often it said to be the power developed by the engine this is the power delivered by the engine and particularly when it comes to the power plant and particularly when it comes to IC engine this power is known as break power and this power is known as indicated power why indicated that we will talk about later and why break because traditionally a break type dynamometer was used to measure this and indicated power because traditionally a piece of equipment known as an indicator is used to determine this power. Now because break power and indicated power will generally be different because there is some local power consumption this may be conscious consumption for running some auxiliaries or control circuits or some safety circuits but it could also be power which needs to be consumed to overcome friction lubrication and such stuff. And now you will notice that because we have a separate BP and a separate IP whenever this W dot net turns up in your mean effective pressure definition or the specific fuel consumption definition or the specific output definition or even the efficiency definition. We have to be careful in classifying it for example efficiency if it is based on break power say W dot net thermodynamics W dot net delivered this will be known as break efficiency because this is based on sorry this will be known as indicated efficiency because it is based on IP whereas the delivered power is BP this will be known as the break efficiency. Similarly, when it is specific fuel consumption this will be known as indicated specific fuel consumption this will be known as the break specific fuel consumption indicating it is specific fuel consumption based on the break power. Similarly, when it comes to the mean effective pressure technically quite often known as MEP this will be indicated mean effective pressure and this will be break mean effective and so on. Now we come to again the implementation we say that look the processes which we could implement where easily easy implementation was possible for these kinds of processes the constant volume process in a closed system adiabatic process expansion compression in a closed or open system or isobaric heating cooling in an open system and we looked at the parameters like efficiency work ratio mean effective pressure and so on. So, let us look at the let us evaluate our traditional Carnot cycle using a gas as a working fluid and we have sketched the T s diagram let me sketch the PV diagram unfortunately no Carnot diagram on the PV plane is ever drawn to scale and that is why even if you try to draw it crudely you will be able to you will be showing it as a crooked non-linear or curvy linear parallelogram working between two temperature levels T 1 and T 2 and two isentropic at s 1 and s 2. The problem that arises is although efficiency of this is maximum for a given T 1 and T 2 when it comes to other parameters you will find and I recommend that you sketch the Carnot cycle using air as the working fluid and sketch it to scale take T 2 to be say 300 Kelvin near our room temperature. Take T 1 at say 900 Kelvin not very high but good enough we expect an efficiency of 67 percent 66.66 percent with this. But now when you actually sketch it recommendation sketch this to scale now remember that assume that your engine is of a certain size and of a certain volume and so T 2 and V 2 gives you P 2 this is P minimum. Let us say the P minimum is 1 atmosphere and that will give you the amount of mass in the Carnot engine. Now we have decided that T 1 is 900 K we decide the maximum pressure that we can have because the cylinder will have to be made strong enough to handle that pressure. Let us say the higher pressure is 50 bar then you know the temperature you know the pressure you know the mass you can determine what this volume is. So you can plot the all the things you will notice that the Carnot cycle is a curvilinear parallelogram but it does not look anywhere like this. It looks so thin that I cannot properly sketch it on this diagram I have plotted it and if I find that plot I will put it upon Moodle and you will be surprised to know that the work ratio for a Carnot cycle is almost equal to 1 it is of the order of 0.95, 96, 98 of that order. That means a significant part of the work produced during the expansion process is governed is consumed back in the compressor process. It is a very thin parallelogram and because of that we can show that the PM is very very low and because the PM is very low you will find that the Carnot cycle with a gas as a working fluid is never implemented in practice. Carnot cycle as defined in textbooks is never implemented in practice but then what is implemented? Modifications of Carnot cycle are implemented. Now remember the attraction of a Carnot cycle is that it is a 2T cycle heat absorption at one temperature, heat rejection at one temperature but the Carnot cycle if you say is a TSTS cycle one process in which temperature is maintained constant second process in which entropy is constant, third process in which temperature is constant again at some other value, fourth process in which entropy is constant at some other value. For it to be a 2T engine it is necessary for us not to change this isothermal heat absorption and heat rejection processes but we can change this isentropic processes and when you change these isentropic processes two things happen. First thing you are modifying the cycle but remember that if you want the modified cycle to have a Carnot efficiency of 1 minus T2 by T1 two things are necessary. First it should be a 2T cycle that we are not changing because we have one constant temperature process and another constant temperature process but when you replace these two constant entropy processes by say constant volume or constant pressure processes you will notice that a reversible constant volume process and a reversible constant temperature process will not be an adiabatic process that means the working fluid will need to be supplied heat or from the working fluid we will need to absorb heat extract heat as we execute those processes. So it does not remain a 2T cycle if you directly do it but we overcome that hindrance by using an internal heat exchanger. I will show you the scheme. If you replace this S by two constant pressure processes you end up with a cycle and of course with an internal heat exchanger we end up with a cycle which is known as the sterling cycle and if you replace these by its two constant volume processes and internal heat exchange is managed by heat exchanger you end up with what is known as the Ericsson cycle. Let me go to the next page and sketch a big TS diagram actually on this smooth tablet it is difficult for me to sketch straight lines. Let us say we are sketching horizontal lines seem okay vertical lines are bad. Let us say this is T1 this is T2 the S is long just because I want to show the three cycles next to each other. The Carnot cycle will be like this heat absorption at T1 heat rejection at T2 and these are isentropic so these are adiabatic process. Now when you take the Ericsson cycle you have heat absorption at T1 no doubt you have heat rejection at Q2 no doubt but you need to absorb heat during this constant volume constant pressure process because it is reversible constant pressure process. Similarly you need to reject heat during this constant pressure process because it is a reversible isobaric process and for this you will have to absorb heat at temperatures other than T1. So what is done is we say that look whenever the working fluid reduces its temperature below T1 that heat is being extracted and it is stored somewhere and is made available to the same working fluid when it starts heating up. So we set up an internal heat exchanger so called a regenerator to do this and that way we change our Carnot cycle to the Ericsson cycle. Similarly if instead of two constant pressure processes you take two constant volume processes the constant volume process lines would be slightly steeper although they do not seem to be very steep here than the constant pressure processes on the TAs diagram and again you have Q1 Q2 and an internal heat exchanger known as a regenerator to see to it that even the sterling cycle remains a 2T heat engine. So with this heat exchanger with the ideal internal heat exchanger each one of this is a 2T heat engine so the efficiency of each one of them will be 1 minus T2 by T1. Now with this modification we still retain the 2T characteristic of the modified Carnot cycle but we need an ideal heat exchanger internal to it than ideal regenerator. We will maintain the Carnot efficiency but now the question is do we really improve the work ratio? It turns out that the work ratio is improved but not very tremendously and the problem of implementing with a gas an isothermal process where you have to do work transfer as well as heat transfer together still remains and because of this of these three cycles you will find that if at all any cycle is implemented and that is the sterling cycle. The sterling cycle is not really implemented as an engine although attempts are being made and there are some working engines working on the sterling cycle but for refrigerators particularly for cryogenic refrigerators the sterling cycle is considered a very good option. So the basic sterling cycle or its modifications are the devices by which we do all our very low temperature refrigeration known as cryogenic refrigeration. But remember that whether you take the Carnot cycle whether you take the Eriksen cycle or whether you take the sterling cycle we end up with the situation that our heat absorption has to be under isothermal conditions heat rejection also has to be under isothermal conditions and hence these become difficult to implement it with an ideal gas or even any gas as a working fluid. And I will first take a few questions and then go over to our cycles discussions. I have hands raised from VNIT, Nagpur then KJ Somaeya Mumbai. VNIT, Nagpur do you have any questions? Over to you. Hello, why the whole lake do not get freeze till up close depth? Why the only upper layer of lake gets frozen? Okay I am taking over I understood the question. Your question was why is it that the lake, lake gets frozen only on the surface and not all over. The reason there are many reasons for this each contributing to some extent. First thing remember that the inside the earth it is always warm. If you go down a few meters the temperature is the mean annual average temperature which depending on the location. For example, you take a place like Delhi minimum ambient temperature of the order of may be 5 degree C maximum ambient temperature of the order of 45 degree C. So, it is reasonable to assume that if you go down something like 45 meters the mean temperature in the earth will be of the order of 20 degree C. Consequently the lake any lake is usually exposed to reasonable warmth at its depth. And when it freezes it freezes because the ambient air temperature goes down and that is it loses heat from the surface. And once a thin layer of ice forms remember ice and water may have almost the same order of magnitude of thermal conductivity. But through ice the heat transfer is only by conduction whereas if it were fluid by natural convection or may be by surface wave some sort of if not forced induced convection it will be well mixed. All these things combined to give you a layer of ice below which water will remain. And that is and but the layer of ice can be pretty thick in fact sometimes vehicles can be driven over it. So, may be that is the reason lakes get frozen only on the surface and not at the depths over to you. Over and out. K. J. Somaia over to you. Yes sir. Good afternoon sir. My question is the dual cycle is a modified form of this diesel cycle whether it is used for operational cycle for the diesel engine over to you sir. We will be discussing this during our lecture in the afternoon over to you. Okay sir thank you sir. Ph. G. Coimbatore over to you. Good afternoon sir. This is a question regarding the figure you drew in the morning's class. You stated the relation between engine refrigerator and heat pump by drawing the temperature limits sir. You had a three temperature limits one is environment temperature another one is lower than the environment another one higher than the environment. And considering the case of engine it is rejecting heat to the T environment but you showed that it is slightly higher than T environment. Can you please explain thank you over. Let me explain I think this is the figure that you are talking about I showed a this is the temperature axis and I sketch this as the environment temperature and remember that an engine rejects heat to the ambient a refrigerator also rejects heat to the ambient but a heat pump absorbs heat from the ambient. And remember that a heat transfer will not take place unless there is a small temperature difference in the ambient direction. So if you have an engine it takes in heat from the T source when it rejects there has to be a small delta T. And hence the heat rejection temperature to a small extent will have to be higher than that of the ambient. Similarly when you have a refrigerator taking in heat from some cold space at T naught it rejects it to the ambient. So I should really show it like this a delta T above the ambient. Whereas for a heat pump it rejects heat to the T let us say hot space absorbs work. Since it absorbs heat from the ambient it will have to be at a temperature slightly lower than the ambient. These delta T's which I have shown here should be as small as possible because that is better from a thermodynamic point of view over to you. Thank you sir over. That brings us to the end of this quick interaction after lunch. Let me now go over to my tablet and continue from where I left off. In the morning we looked at various parameters, classification, etc. And then we said that the modification of the Carnot cycle we looked at two modifications the Ericsson type modification and the Sterling type modification. The question was raised as to whether it is right that Ericsson is two isothermals and two constant pressures and Sterling is two isothermals and two isometric or isochoric constant volume lines that is right. One thing you should remember is the following. Carnot is T S T S, heat addition in this T, heat rejection in the other T. If you take Ericsson it is T P T P again heat addition in the two isothermal processes and these two reversible processes whereas to be a heat exchange between these two processes. Similarly, Sterling it is T V T P again heat absorption and heat rejection in the two isothermal processes and these two reversible isometric or constant volume processes have to exchange heat internally with each other using a heat exchanger. That is necessary because ideally all processes in these cycles have to be reversible. Then we notice that the real problem with these cycles is the Q 1 and Q 2 at constant temperature. That is the issue. That is very difficult to implement in practice using a gas whereas heating at constant pressure is easy to do. So perhaps for a gas the easiest cycle is the cycle in which Q 1 and Q 2 would be constant pressure processes because these are easy to implement and the remaining two processes would be isentropic processes. We know that isentropic processes can be implemented reasonably easily in either an open system or a closed system. That brings us to the next cycle and also remember that constant pressure process is easy to implement in an open system whereas constant volume heating and constant volume cooling may be implemented in a closed process. These modifications that heat addition and heat rejection could be at constant volume and constant pressure processes whereas the other two processes could be isentropic. Give us rise to two or more cycles. The most important of them are Brayton, Otto and Dez. The fourth one is sometimes called an Atkinson cycle but it is not really used in practice. It is a good approximation for some type of cycle. So that brings us to the Brayton cycle. The Brayton cycle is a PSPS cycle. So the heat addition would be here, heat rejection would be in the next isobaric process and since the isobaric processes are reasonably easily established under open system conditions, the Brayton system cycle is almost always implemented as a multi equipment cycle and this is the basis for all gas turbines and jet engines of all kinds. The T-S diagram of the cycle looks like this. It works between a higher pressure and the lower pressure limit. Wherever you have, it is always a lower temperature limit and a higher temperature limit. T low, T high and again a P low and a P high. You start with the lower temperature and lower pressure gas usually at ambient conditions and compress it ideally adiabatic reversible, so isentropic to the higher pressure you go from 0.1 to 0.2. Then from 2 to 3 at the higher pressure you have the process isobaric heat addition. So you can say 1 to 2 is this process, 2 to 3 is this process at constant pressure. Then expand it isentropically, reversibly isentropically, so adiabatically you come to state 4 that would be this process and cool it from 4 to 1 that completing the fourth process. The actual implementation needs to be shown because it is a multi equipment cycle needs to be shown in a block diagram. Compressor, heat absorber, cooler 1, 2, 3, 4. Show directions of flow, show compressor, heater, cooler, turbine. You will have a W dot turbine, you will have power absorbed by the compressor, W dot C, Q dot 1, heat absorbed by the heater, Q dot 2, heat rejected by the cooler. And at this stage before talking about the open brick cycle, make them understand that this is not a constant temperature cycle. So although it works between a higher temperature T H and a lower temperature T L, it is not really a 2 T heat engine because during heat absorption the temperature rises from 2 to 3 along this process and during heat rejection it lowers itself from or it gets lowered from 4 to 1. Consequently, we do not expect the Carnot efficiency to be obtained here, but we can do a standard analysis of the Baton cycle. In standard analysis what we do, we assume the working fluid to be an ideal gas with constant C p, C v. All processes are ideal. As prescribed constant volume, constant entropy etcetera, quasi-static and here we do not have to say, but internal combustion if any is replaced by let me say external heating and if necessary we assume that it is a closed cycle. This is not a strong assumption, we do not really need to make it. And the standard analysis all of us are familiar with is found in any textbook and show that the standard analysis of the, call this the standard efficiency of a Brayton cycle will turn out to be 1 divided by 1 over R p raise to gamma minus 1 by gamma and bring to their attention two properties 1 gamma is the ratio sorry not 1.4. It is the ratio of C p by C v that is the characteristic of the fluid and R p is the pressure ratio or the compression ratio of the Brayton cycle and that is p higher divided by 1 over R p lower. And at this stage you can give exercises on determining the specific output and all that. It is necessary at this stage to show them that the actual Brayton cycle quite often known as the gas turbine cycle is essentially the same cycle, but the block diagram differs. We have the compressor, but the compressor takes in ambient air at 1 instead of a heater you have a combustion chamber in which certain amount of fuel is also injected, it burns and up to here you have compressed air. Now, you have a gas that is products of combustion and hence the turbine which follows is known as the gas turbine and now this gas is exhausted at 4 this is 3 this is 2. Again you have a w dot t coming out w dot c going in and w dot net will be w dot t minus w dot. So, this is the first modification that we have studied of the Carnot cycle and it is a p s p s type of modification. So, first show them the T s diagram then emphasize that it has to be a multi equipment cycle. So, show the block diagram then do a standard analysis derive the efficiency and then show them the actual block diagram of a gas turbine cycle and say that here we have air, here we have air, but now here what you have is gas that is a gas turbine. Exhaust of combustion chamber and this is again the same gas which gets exhausted and because this gas has a different composition than the fresh air which is taken in, this is an open cycle. Now, if we see the Brayton cycle as a p s p s cycle another possibility is to consider a modification of the cycle which would be V s V s cycle. This V s V s cycle is traditionally known as the Otto cycle and the basic thermodynamics of the cycle will look like this. First thing you should remember is that heat is absorbed and rejected in the constant volume process. So, the Otto cycle will essentially be a cycle in a single equipment because a closed system is needed for constant volume processes and it is implemented in a cylinder piston arrangement and when you have a cylinder piston arrangement and expansion and constant volume processes it is possible to show this properly on a p v diagram. We will show it both on a T s diagram as well as the p v diagram. On the T s diagram we will now have two constant volume processes, a lower volume and a higher volume and we will have a isentropic compression, we will have constant volume heat absorption, we will have an isentropic expansion and a constant volume heat rejection 1, 2, 3, 4. So, the highest temperature point is at T 3, the lowest temperature point is T 1. No T 1, T 2, T 3, T 4, the lowest point is T 1. This is the lower volume, this is the higher volume. On the p v diagram it will look like this. There is a volume at which heat is added, there is a volume at which heat is rejected. So, this is V h, this is V l this is pressure and let us say we start at 1 and we make an isentropic compression 1 to 2, no heat is added. Then at during a constant volume process 2 to 3 heat is added and then 3 to 4 during another isentropic process expansion takes place and 4 to 1 is the constant volume heat rejection. So, you can show here this is Q 1, this is Q 2 and out here also this will be Q 1 and this will be Q 2. Thermodynamically, we do not have to do anything more for the basic explanation of the Otto cycle and you can show here this is the constant volume heat addition. So, this will be 2 to 3 expansion 3 to 4 heat rejection 4 to 1 and compression again 1 to 2. That way the cycle is completed and again you can do a standard analysis of the Otto cycle and show it to them that the standard efficiency of an Otto cycle as an expression very similar to that of a Brayton cycle exponent is different. And again bring it to their attention that one property of the fluid gamma is included in the right hand side. The second property is R v the volumetric ratio volumetric compression ratio which is defined as v higher divided by v lower. Now, at this stage students will ask and I have already been asked how this constant volume heat rejection takes place quickly and how this constant volume heat absorption that too quickly is created or implemented. So, at this stage it is necessary for us to explain to them the implementation of the Otto cycle. Now because we have a cylinder piston arrangement and a mechanism of the cylinder the piston the connecting rod sometimes a piston rod then the connecting rod then what they call the Gajan ping the crank the crankshaft and all that the problem becomes remains not only that of thermodynamics, but also that of mechanics. Add to that we need to have valves for that open cycle for taking in the charge and throwing out the products and the description becomes really complicated. You will have to bring in the idea of a 4 stroke machine at this time there is no need to confuse them with 2 stroke and 4 stroke. Tell them that there is a 2 stroke implementation, but explain to them at the basic level essentially of the 4 stroke. So, here you talk about all the details of mechanism you talk about the top dead center you talk about the bottom dead center you talk about stroke length you talk about the bore diameter and then you talk about clearance volume V C you talk about stroke volume V S and so on. And you talk about valves and how they are managed open closing that you can talk about the cam there is enough detail that one can worry about. In a thermodynamics course it is not worth spending time may be if you have a power point or an audio visual or a movie which you can show or a cut out model if you have in the lab that explains a lot. It is not worth spending in a thermodynamic course you have to spend about hour 2 hours in just explaining these technical details and since there is no basic principle involved only implementation is involved this is best left to the students themselves. But what we should emphasize that is that the real implementation of auto cycle as in a petrol engine you tell them the following is that it is an open cycle it is an internal combustion cycle. In fact that you this we can do right in the beginning when we come to Brayton cycle the standard Brayton cycle here it is shown as an external combustion cycle whereas the real implementation of the Brayton cycle is an internal combustion cycle. Similarly, the standard scheme of the auto cycle is the standard analysis means external combustion and closed cycle whereas the real implementation of the auto cycle is internal combustion cycle. Then you say that the working fluid to begin with is a mixture of air come petrol vapor and in early days this air and petrol vapor mixture was created using a mixing device called carburetor. Nowadays the petrol vapor is sprayed or injected into the air stream before it enters the cylinder. Then you say that because of this it is internal combustion so it begins as a mixture of air and petrol vapor the process of combustion is triggered by a spark and then you say after that the working fluid is our exhaust gas which is nothing but product of combustion. And then at this stage it is necessary to tell them that we are actually not the heating process. It is not really implemented it is a constant volume remember that the heating process is by combustion triggered by the spark and because it is a premixed and already preheated because we have already compressed it. If it is a premixed air fuel mixture everything is already in the vapor form so the combustion is very fast. So fast that the movement of piston which is near TDC at that time can be neglected because it is very fast the delta T for combustion is so small that the movement of piston can be neglected. Hence the process can be approximated as a constant volume mind you it is not executed as a constant volume process it is approximated as a constant volume process. And if you want you can show them that the real process if say this is the ambient pressure and you start with the clearance volume this is the stroke volume V s plus V c then the actual process of combustion does not really take place like this it takes place something like this. There is a small movement of the piston but for a quick calculation and modeling it can be neglected. But if you use an indicator you can really trace this curvature of the PV diagram. Similarly the second question arises is how is the heat rejected at constant volume and there the explanation is heat is not rejected at constant volume. As the piston approaches this is the bottom dead center this is the top dead center. When the piston approaches the exhaust sorry the bottom dead center somewhere near here the exhaust valve opens and when the exhaust valve opens the high pressures in high pressure gas in the cylinder is suddenly exposed to the ambient of course through the exhaust valve the exhaust duct the silencer and may be any other piece of equipment you have. But the fact remains that the high pressure gas not very high pressure but reasonably high pressure gas suddenly find itself into a in a situation of free expansion and left to itself this will create a gunshot like sound what is known as a report a very sharp very uncomfortable sound and that is why all the petrol engines and all IC engines have a silencer or a muffler in that exhaust line. Good job is to reduce this effect of this sudden pressure reduction sudden expansion and reduce the noise so that the people surrounding that engine nearby they do not come to any harm their ears do not come to any harm. If you find that your car engine does not have a silencer or if the silencer has rusted and corroded off you will find this noise coming from the engine those of you who have a motorcycle can do a simple experiment remove the silencer and then just try to start the motorcycle the sound will be so horrible that you will never touch the motorcycle without a silencer again. The same thing is true of a car in fact any car which has a leaky silencer will immediately be known and heard by everybody else as a problem car. So when the exhaust valve opens the pressure suddenly drops and then in the final stroke the whatever is remain is thrown out at this stage you can show them an actual indicated diagram and show them that during the exhaust stroke the pressure will be slightly higher and during the induction stroke the pressure will be slightly lower exaggerate this and show them that the actual indicator diagram of an auto cycle will have a positive work loop and will also have a negative work loop and then at this stage it is good to tell them that the mean height of this diagram positive added and negative subtracted from the positive is the mean effective pressure of the cycle. Now that comes that brings us to the end of the basic auto cycle then comes the question immediately a student will ask what is the diesel cycle the thermodynamically the diesel cycle is a cycle in which heat is added in a constant pressure process that is this is the Q1 process expansion in a constant entropy expansion or almost constant entropy expansion heat rejection during a constant volume process and heat sorry compression again in a constant entropy process at this stage since we would have already talked about the mechanism of an auto cycle.


The Senate has called on the Inspector General of Police and Police Service Commission to investigate the Tarabah State Police Commissioner over the alleged abuse of human rights of 14 residents. The resolution followed the liberation on a motion by the Deputy Senate Minority Leader Emanu Poacha over the allegations of human rights abuses in the state. Poacha says that 14 persons have been in detention beyond what the constitution stipulates, even without a trial. Lawmakers noted that illegal detentions and abuse of power formed parts of reasons some Nigerians are against state police. Mr. President, the issue in question is a gross abuse of fundamental human rights of 14 of my constituents and the names I provided herewith. That Mr. President, the alleged offence though being made against them was said to be criminal assault or criminal force and mischief, which actually was a quarrel between them or exchange of unpleasant words between them and a younger brother of my governor. Though the alleged offence being made against them was criminal, but I yet to be proving it is common knowledge that the Nigerian constitution demands in the matter of this nature the suspect shall be charged to court within 24 hours. A member of the same political party with the sitting government in Tarabah State who has come to the floor of this Senate to alleged that the reason 14 of his constituents have been detained illegally was because they were alleged to have done something to the younger brother of the sitting governor, another PDP, you know, person. So we cannot sit here and say it is a PDP affair or it is because Tarabah State is led by PDP. This is a flagrant abuse of our constitution of our law and it must be addressed as so. These are issues that as presented here might require maybe further investigation if need be. But Mr. President, distinguished colleagues, permit me to say also that if this is true, it clearly shows one of the reasons why some people are opposed to, for example, the idea of police, we are a governor, we have our federal power to do and undo.


Oakland, it's as gorgeous as like the people and the style and the redwood trees. But it's also kind of grimy and has a hard edge to it. My grandfather had to leave.  So there was a lot of refugees. Oakland was the land of refugees. The man doesn't have us out, nobody has us out organized.   When the community here at Oakland chanted, I am Oscar Grant. It created a movement throughout this nation. My Oakland, we hella innovative, hella energetic, lively. We have been a black enclave and thus a manufacturer of culture. Who don't? I'm about to run this movement.


Hi, I'm Sally, I'm a third year PhD student at the Australian National University and I work on an enzyme called Rubisco. So enzymes are biological catalysts. They work to allow reactions to happen under biological conditions and a lot of different things affect how enzyme functions and how well it functions. Enzymes are biological catalysts, usually made of proteins that allow reactions to occur under biological conditions. A number of factors will affect the rate at which and how well enzymes work. And most enzymes are specifically adapted to work in a very limited range of conditions. Temperatures can have massive effects on enzymes. If you consider warm-blooded organisms like people, the cellular environment in which enzymes operate is constantly maintained at 37 degrees Celsius. For many enzymes, if they get too hot, the bonds that hold the proteins together in their secondary and tertiary structures break and the enzymes lose their shape. This is called denaturing and when that happens they can no longer perform chemical reactions. Chemical reactions in biology are still chemical reactions and this means that energy in the form of heat makes them go faster. At low temperatures there isn't much energy and things move slowly, reactions go more slowly. This means that for enzymes the fastest rate is usually an optimization between a temperature at which it's warm enough for the substrates and the enzyme to be moving about but cool enough that the enzyme still maintains its tertiary structure. And because most enzymes are made of proteins, they're sensitive to the same things that proteins are sensitive to. So proteins are made up of amino acids and each of the 20 amino acids differs by the side chains that those amino acids have and some of these side chains are sensitive to pH. They might change their shape or their charge at different pHs. This has a flow on effect to the rest of the protein and can result in differences in the way that protein functions. Enzyme activity can also be altered by the presence of other compounds in the solution it's working in. Competitive inhibition occurs when a substrate similar to substrate of the enzyme is added. This inhibitor also fits nicely into the active side of the protein. When the non-substrate substance is bound it prevents the substrate from binding and this reduces the rate of reaction. Non-competitive inhibition occurs when the inhibitor doesn't bind to the active site but to another part of the enzyme. When the inhibitor is bound the shape of the active site changes and the substrate can no longer bind. This reduces the rate of reaction. Inhibition doesn't only occur by the action of non-substrate substances though. In some cases the presence of large concentrations of the substrate or the product can result in inhibition of the enzyme. High concentrations of the product means that the product is more likely to re-bind to the active site than the substrate is. This means that the reactions occur less frequently and the rate of reaction slows. Processes of enzyme inhibition are important biological processes that are closely regulated within organisms. Rubiscoe is a really important enzyme in photosynthesis. It's the enzyme in plants that fixes carbon dioxide from the atmosphere beginning the process of converting carbon dioxide into sugars. It does this by fixing the CO2 to a sugar phosphate called RUBP. Because photosynthesis uses light from the sun it only occurs during the day. At night CA1P another sugar phosphate that binds the active site but doesn't bind CO2 binds to rubiscoe and this switches off the enzyme by competitive inhibition. It's then removed by another enzyme in the morning so that rubiscoe can start its work again. These processes of inhibition are important in regulating and maintaining enzyme activity in organisms.


My talk is like very nice, I have the ability to shorten my talk nicely if it's the amount of time I actually have. It'll still be nice to go hearing. I would just introduce you on behalf of Roy. Roy is not here. Hi, yeah, hi. So my name's Gene, I'm in the logic program, but I'm not normally in charge of this. Roy is the organizer for this semester, so I guess we have to... Where is he? He's, I don't know, somewhere over the rainbow. We are empty today to talk about impact minutes and... Is it recording? It's recording. I'll be in... I think so. I'm sorry about the food. Thanks for letting me speak first. I enjoy any opportunity I can get to bombard people with interesting point set topology. So today we're going to talk about the point set topology, caveats. Everything today is going to be house dwarf. Let's just remember what that means. If I give you two points, I can separate them by open sets that are also disjoint. That's the setting in which life is going to happen today. But we're interested not just in house dwarf spaces, we're interested in compact spaces. So let's remember, so X is compact. This is the same thing as finite subcover. Open cover is just some collection of open sets that covers the whole space. And then finite subcover that is hopefully clear. There's a lot of other things I could write down that are equivalent. Often what's really useful to work with is this definition. Every net has a convergence subnet. This is a sequence. I won't be using nets too heavily today, but just there is a sequence-like definition of compactness that does generalize to arbitrary spaces. And why do we like compactness? Compactness is really nice. It's much easier to work with. If we have a space that's not compact, we would often like to stick it inside some compact space that we can use the techniques that compact spaces allow us to use. Let's remember a few facts about what are the nice things about compact spaces that we want to use. Actually, maybe let me start off with some prototypical examples. The unit interval, compact space, I can look at any finite set with discrete topology. The other main thing we're going to do is if I have a lot of compact spaces, I can take arbitrary products. That's to take an office theorem. So in particular, what we're really going to be focusing on a lot today is taking the unit interval and raising it to some power. So here I is just some set to be huge. I could be ridiculously huge, but we're still going to get a nice compact space. Remember that the product topology of nice space is given by you can specify an open set on finitely many coordinates, and then you just have to take the whole thing. So if I have compact space, I can take products, and then the other sort of prototypical example we're going to work with is closed subspaces. What's actually kind of surprising is that the interval 0, 1, the ability to take arbitrary products and the ability to take closed subspaces, this is actually entirely general. We get every compact space that we could ever want out of this. And before I get into that, one more nice property. Every, so a nice, this is called a nice thing, nice thing, house store spaces. Though I don't have to specify house store because life is house store today. Spaces are normal. So let's remember what normal is by picture. Here's a space. Here is a closed, so here's a space x. Here's a closed subspace a. Here's another closed subspace b. a and b are disjoint.  I can stick b inside an open set v. And u and v are disjoint. And this is actually incredibly useful. This is really the driving engine between, like, as I prove a irisome petrization theorem. This is how you prove irisome's lemma. Irisome was kind of an important person. But yeah, if you look at the picture, normality is just kind of a more powerful version of house store. It's what's known as a separation axiom. Sometimes it's called T4. Today we're going to actually talk a lot about, not T4, but what's called T3.5. And to motivate that, I need to sort of tell you what the talk is about. Because we have to mention the second word, compactification. So, house store space, life is house store. A space, the image is dead. We could really think of, it's helpful to just think of y as being a subset of x by some shifty re-labeling you can actually do that. Also, if I omit this condition, I can just take the closure of the image and then obtain a compactification. Because we have this nice property, closed subspaces and compact spaces are compact. So the question we're attacking today is what spaces admit compactification? So, I'll just point this buzzword to space x is compactifiable, x admits a compactification. So what's a nice, let's think about what properties compactifiable spaces have to have from, what can we learn about it from the compactification? Well, compact spaces have normality. So that's going to immediately tell us from normality is what's known as completely regular. I'm going to define this, completely regular. So define and justify why we get complete regularity. We need to remember that normal spaces, there's actually stronger property that's equivalent to a normality. Not only can I separate a and b by open sets in a normal space, I can do so by a function. So let's remember what that means. There's some continuous function on x that's going to send a to the value zero and b to the value one. Not necessarily, I'm not requiring that a is the pre-image of zero or that b is the pre-image of one, but just that a is contained in the pre-image of zero. And that's certainly strong enough to imply normality as I've defined here. The equivalent, the hard bit is irisome's lemma, which as we've heard, irisome is an important guide. So when I take a compactification of x, I, let's say that I have a point. Let me draw a picture. So here's x. Here is the compactification. Actually, yeah, I'll call it compactification. Let's say that I have a in x and a, let's call it point p. And I also have a closed, let me actually draw this a little bit more suggestively, closed a, a subset of x. A is closed in x, but a is not necessarily closed over x prime. So this is why compactifiable spaces are not necessarily normal, because if I have disjoint closed sets and then I take their closure in the compactification, they might suddenly meet somewhere. But since I require p be a point, we're gonna be okay, the closure of a, maybe a prime, a prime might have some points over here, but a prime and p are suddenly disjoint. So what we've done is we can separate, or what we can do, I should say, I can separate a prime and p by a function, because I can do it over here. And this is exactly the property that is complete regularity. Let me write that down. A space complete regular, not containing the points, maybe I'll just say avoiding the point, can be separated by a function. So not just by open sets, but actually by a function. In the regular setting, those are not the same. Orison's lemma doesn't generalize to regular spaces. Point can be separated by a function. Alright, so what we've done so far, we have isolated a property that any space that admits a compactification must have. Any space that is compactifiable must be complete regular. What is actually, again, kind of surprising and not terribly hard, is that that's actually all that we need to require. Before I erase this, let's remember this guy right here. We're going to be taking product of unit intervals a lot in this proof. Completely regular space is compactifiable. So how are we going to prove it? This is one of those buzzwords I mentioned in my abstract. We're going to take the Galfan transform. So I'm just going to put that in parentheses here. Galfan transform. So I'm going to let c of x. This is not quite the traditional notation, but it's what I'm going to use. c of x denotes continuous 0, 1 value. So I mean any continuous function would be bounded, but I really want to fix the bounds of 0 and 1 form. So this is a box space that has lots of topologies, but I actually don't care about any of that. I'm going to regard this as just a really big set. And what did I say we can do with really big sets? We can put them in the exponent of 0, 1 and obtain a nice compact space. So I'm going to form the space 0, 1 to let c of x. This is just a nice, it's a very large space that's compact because it's just a product of 0, 1 by a lot of. And the compactification is going to be a closed subspace because what do we need to do? We need to cook up a compactification of x. I guess I should have said x is suppose x is compactifiable. We're going to construct a compactification. I suppose x is completely regular. Yeah, thank you. That's the direction of going. x is completely regular. The compactification is going to be a closed subspace of this guy. So what's the map? They're just the space of measures. The product is just the space of measures. Well these aren't necessarily measures. They're just 0, 1, 1. They're not linear necessarily. x doesn't necessarily have a linear structure on it. They're just all the continuous functions. They're bounded between these two. So define, the map is actually, once you write down this map it's really the only choice of map. It's really cool. So what is phi of some little x going to be? This is going to be... So the typical coordinate in this large product is some continuous function f. The value I'm going to put at that coordinate is nothing more than f of x. This is like the double tool. Yes, it's a very similar construction. And this is as f ranges over... Phi may not have dense image, but we're just going to take the closure of the image as our proposed compactification. So we need to prove, what do we need to prove? We need to prove that phi is an embedding. What I hope is clear immediately, phi is definitely continuous. And it's definitely injective. So the only tricky bit is showing that the images of closed sets are relatively closed. So to say that precisely what we need to do, we need to show... Once we show this, we will have that phi as an embedding. And to construct our closed set W, this is where complete regularity comes in. A is closed. So we're just going to pick functions separating A from every other point. So for every, I'll say p in x separates A and p. And I'm going to assume... Let's just set fp of A to always be 0. So then the point gets value 1, A always be 0. So it's W going to be... W is just going to be those functions, functions from c of x to 0, 0, 1. What do I want to demand? I'm going to demand that for every p, that's not very legible, that at coordinate f sub p, we take value 0. Then it's immediate that we've done what we set out to do. Because say that W certainly... We want to argue that this is the same as this. This certainly contains phi of A. If there were some other point, that can't happen because we separated it. At that point, r of fp would be 1, and that's not going to happen. So W doesn't depend on A at all? Oh no, W depends... Remember, we chose these functions. So that's going to depend, say, what coordinates we want to be 0. So that's actually... This is our first characterization of compactifiable spaces. And with almost enough time to actually attempt to do this, but probably not quite enough, I'm going to attempt the second characterization. Because what is sort of lacking in this proof is... Let's ask, what is the Gelfand transport? Which of these things is it? Is it like... I think it's... I think it's forming this space. I'm not entirely sure. I believe it's the step of forming this space, and perhaps this map also. Gelfand was heavily involved in this proof. It was like these sort of ideas are what go into the Gelfand-Nymark theorem. So if you're familiar with those things. So what is... What's deficient about this proof? Or what else could we hope to understand? Given a completely regular space, X, this proof constructs the same compactification. This is actually the beta-compactification of X. It's the largest, most general compactification of X. But say that I ask the question, given a compactifiable space, what compactifications can I form? This proof is not going to help us out. This spits out the same space every time. So it would be awesome if we could figure out some internal characterization of what compactifications of X look like. And that's what I'm going to attempt to do in 25 minutes. So I'm just going to morning now. My proofs might start getting pretty hand-wavy just due to the time constraint. But what we're going to do is take a brief diversion into the topic of uniform spaces. I'm going to define this completely generally for now. This is just a set. I have not to apologize it or anything. But I'm going to tell you what it means to put a uniformity.  It is a collection of subsets of X cross X. So think of this as the way to intuit this definition is to pretend that X actually is a topological space. Here's X, here's X, here's the diagonal. And U is going to look like around the diagonal. And this picture is going to be made formal by the next few bullets. So you have to satisfy the intersection over U and U of all U is actually equal to delta. Which is, I guess I should tell you that this is my notation for the diagonal. I am being more strict than the most general. I lied. I said I was being entirely general. But since life is house-dorfed today, I cooked this up in a way that's going to give us house-dorfed things later on. Normally it's just this intersection would contain equality. Fancy you to be closed under some nice closure properties. So I might just say this really quickly and say U is a filter. A quick reminder of what that is, that means it's closed under finite intersections and taking supersets. So it's a notion intuitively script U is a notion of neighborhood of the diagonal or contains a neighborhood of the diagonal. So we should demand that it be closed under finite intersections and supersets. Is that if I have something in script U, then U inverse is in script U where U inverse is just where I flipped the coordinates from members of U. U inverse is the trickiest but most important. And what 4 corresponds to is a kind of very weak version of the triangle of equality. So I'm going to write it given some U and U. So I'll just maybe do this. In the language of metric spaces, this says we can divide distance by 2. There it is. So given some guy in script U, I'm going to find a smaller guy in script U. How much smaller the subset? I have to explain this notation because it's actually horribly abusive. I do not mean v cross v. I mean e to the power of 2 r pairs so that there is another point in the set so that... So if I said this is like the triangle of equality performing a triangle, here's x, here's y, I'm saying this is roughly a distance U. I'm saying that there is some, quote-unquote, distance v and a point z so that this guy and this guy are at distance. So v squared are those points so that there is a z and x with x, z in v, z, y. So if you think about these, if you think about these subsets of the product as relations on the set, then this is just a composite of v with a sum. Yes, yes. That makes sense. That's exactly what we're doing. Is there any value in thinking of it that way? Not especially. In practice, you only need to dive down to things like... Because this is inductive, I can replace 2 with n and this action 4 will still hold. In practice, you only need to go down to 4 or so and you'll be able to prove anything you want to prove. That's mentioning that we want to think of this... We should have the intuition that x is actually a space and not just a set. And we're going to justify that intuition by cooking up a topology from a uniformity. Topology, uniformity. We're going to say all this kind of be informal tau of the uniformity. This is going to be the topology, topology. The typical neighborhood is going to be so that... Notice I did not say... I did not say the typical open neighborhood. These will typically not be open neighborhoods. But from a notion of neighborhood, you can recover a suitable notion of open neighborhood if you want to just work with open neighborhoods. And often, from now on, I'm going to be thinking topology first, uniformity second. So we can simplify our discussion a lot by always working with members of script U that are open and symmetric. And so often I'm going to make those assumptions implicitly. Before I go on, let's just get some examples out there. So uniformities are also uniform spaces in nature. Pro-typical example, metric spaces. Your typical uniformity are all points that are no further apart than epsilon. I guess I should say who are less than epsilon apart if we want to open. Here's kind of a fun example, which I like, but I won't go for it anyway. Any topological group has a very natural choice of uniform structure where I can say, your typical uniformity is going to look something like GH so that GH inverse is in V where V ranges over neighborhoods of the identity. I don't see, we have a lot of analysis people in here. So anytime you define a, I'll just say like normed spaces, or actually spaces whose topology are generated by any collection of norms, I'll just say spaces generated by norms, or even more generally I can replace norm with just pseudo metric. Both the topological vector spaces you work with in functional analysis have very nice uniformities either from 2 or from 3. There's going to be equivalent. And I guess what we're going to is, I'll write this definition here, a space is uniformizable. So after the topological space, it's uniformizable if the topology is the same one induced from some uniformity. Why did I take this 10 minute diversion into defining what uniform spaces are? So one of the key observations is that compact spaces are uniformizable. So let's try to prove that real fast. What I want to be is not bad. The proof is let u subset of x squared neighborhood have to check that this actually works and notably for 4 you have to use compactness to make it fly. But you can do it. And a nice remark which is also suggestive is that u has above uniformity. And so this is kind of suggestive because what it's saying is that somehow compact spaces do not have a lot of choice and they have no choice in what uniformity you have to take to generate that topology. And so this suggests that if you have a space that is merely compactifiable that maybe studying uniformities on it is a good way to study compactifications. And that's exactly what we're going to do except for the fact that we only have 7 minutes left. I should remark that and I've used it implicitly subspaces of uniform spaces are uniformizable just by you can take the subspace uniformity and so then compactifiable spaces by this result are uniformizable. You can imagine that if you have different compactifications of a space the uniform structure you get induced is going to look different depending on what compactification you started with. And while you would hope that the correspondence is exact it's not quite right. There are more uniformities than there are compactifications. But the good news is that every compactification is described by a uniformity. And I don't have enough time to what I was hoping to do was to actually build this smack going back and forth between uniformities and compactifications. But I'll just mumble something about it. Different thoughts, information. I'll just put this in quotes. And so what the information is is the construction runs via these things called near-altre filters. You define those based on your uniform space you get a nice compact house-door space out of it to compactify your uniform space. But I don't have time to run through that so I think I'm going to stop now. This is a question that doesn't relate to anything you said recently. You intrigued me because you said it earlier. You say you can construct any compact house-door space from taking arbitrary products and closed subspaces of the unit. Yes. How hard is that to prove? We did it. We proved it. Take the Gulfant transform of a compact space. I think it's up to you. I think it's up to you. Because you're taking the beta-compactification of a compact space so it's just the same space. Isn't it slick? Does this law spit still work in non-house-door spaces? In house-door spaces. I'm thinking algebraic varieties. I don't think compact spaces in the non-house-door setting are necessarily uniformizable. Because the whole contradiction that you get over here is you obtain a point because say that the way that this proof roughly runs is say that you have a failure of condition 4 in hoping that this is a uniform space. You use compactness to find a nice subnet of a suitably chosen net. You obtain a point, supposedly a pair of points. It's a point in X cross X. Supposedly in every element of your uniformity but not on the diagonal. And that's the whole source of your contradiction. So that contradiction goes out the window when you're not house-dwarf. I know embarrassingly little about what happens in the non-house-door setting. I have to ask the category's everything question. Okay. Do uniform uniform spaces form a category? Other morphisms? Oh yeah, uniform continuity. Okay, so, okay. Or I guess like uniformly continuous maps. Distinct compact spaces give rise to distinct uniform spaces. So if there's one... Distinct uniform spaces give you distinct compact spaces. Oh, so that's what I was trying to hint at but not quite. Compact spaces give you distinct uniformities. There are different uniformities that can give rise to the same compact space. I'll mumble a little bit more about this because it's actually not hard to say that any uniform space gives rise to a notion of a proximal space where what you do is you say that a is proximal to b if for every set in your uniformity I blow a up by v.  So I'm demanding for every epsilon that this be non-empty. And what matters in constructing the compactification is this proximalization. And there actually... there is a notion of proximal space and proximal continuity and that is... I guess it would have to be the same as the Seahouse. So I think my line of inquiry was like if this is not going to work it's not going to be what you think. Oh, absolutely. Because you go from uniform to proximal. Proximal is I think by this discussion naturally isomorphic to Seahouse. Then Seahouse... Yes, I think... I just... I smell... I don't know the right... I smell about 5.5. Yes, there's probably an injunction. I'll stop, I'll stop. Do you have any relationships on how nice the information could need to be or is it space to be metaphysical? Ooh, countably generated. Right, because if the diagonal is is gdelta and then you can't... Yeah, so it's... if and only if you have a countably generated uniformity. And then I guess this is a nice general remark is that given any uniformity any uniformity is... any uniform space has a topology generated by pseudo-metrics exactly because of that observation. And that's sort of a... that's a nice alternate characterization of what the uniform space is. It's any space whose topology and really what is... your prototypical pseudo-metric is just some function to the reals. You do assume compactness, man. You assume compactness, though. The compact plus countably generated uniformity is metrizable. Uh, no, no. Any uniform space. Any uniform space. Any uniform space is gdelta diagonal or metrizable. I'm afraid to see the U2 version. Oh, my god.


Erin you'd always said this is not a team that ever takes their foot off the gas But to start the road trip getting swept and to finish it with a winning record. What does it say about your group? I mean they're they're very resilient and and they're very hungry and You know, that's why I talk about sometimes, you know, you're gonna have a series where we get they get you or But I from a mindset standpoint I've never had reason to to be concerned with these guys and and what they're gonna bring for the next day for the next series and I think that's why I was confident going on to LA and coming up here and For us to take care of the business the way we did today after a tough start to this trip and finish off a really good West Coast Really says a lot about those guys out there judge and Sanchez added again today both with home runs What are their contraband contributions meant on this road trip? I mean huge, you know the Obviously we we rely on power a lot and and those are two, you know, huge bats there and You know, I thought I thought Sheffield threw the ball pretty well, but to be able to ding them there with Gary following Glaber's hit to kind of get us to get us a little bit of a cushion there and Set the tone and then we're able to kind of chip away and add on throughout the day to To make it a good day. It's like every number you've called this season has done a nice job in stepping up You mentioned that Luke Voight is expected back Friday, but in his absence Mike Ford has played pretty well another home run tonight.  No, we'll talk about it. But yeah 40s been been great for us and You know, it's really been a huge presence Hitting mostly at the bottom of our lineup and the power the strikes own control You know, he's a big reason why we we were able to win some games on this trip Pakistan just one hit but command didn't necessarily Seem like it was there with five walks. What did you see from him this afternoon? Yeah, I thought, you know, he had a quick first inning, but you know, I thought, you know Probably stuff wise maybe a tick down, you know I thought he was fine and then then obviously labored there a little bit in the middle middle later part of his outing where he You know struggled a little bit with the command and But you know the that's a sign there of what he's capable of, you know, even when he's not at his best, you know He's still able to limit them. I thought he threw a number of good cutters I thought, you know, his fastball up at times was really good today But you know, just obviously labored a little bit there in the fourth and fifth I think he's okay. Just got a little tight in the in the groin So You know want to be safe with that and hopefully it's something that's not a big deal. Will he have an MRI? I Don't know as of now. I just checked on him in the immediate after the game and and he seemed he didn't think it was a big deal He seemed fine, but We'll see what we what we need to do with it in the off day Around the third inning I was made aware He just said it was a little tight and then the fourth after his next at bat and played the field He came in and we checked on him again. He's like it's tight. I'm okay, but it's tight and I just We had a DD move in there and just thought it was it was the best thing to do Did he came through everything okay with the shoulder? Yeah, DD DD was good You


to the NPTEL session on supply chain digitization. This is a lecture in continuation of procurement strategies which is part of supply chain design and operation strategies. In the last session, we had discussed about what is meant by the Kralgic matrix and how it is used in defining supply portfolios and what is the use of supply portfolios. In this session, I will be picking up an example application in order to demonstrate what is the use of the Kralgic matrix. So, I am picking up a very simple example over here. It is the case of a bottling plant for soft drinks which is reviewing its procurement strategy for eight of the items that it has purchased in the last financial year and the data on purchase quantity and cost is available in the table. Before I show you the table, just a bit of understanding of what we mean by this. This is a plant level decision making that is going on and like I mentioned in the last session, an organization could look at procurement strategies at the facility level, for example the plant or at the organizational level. And here we are talking about bottling plant which is going to be a core part of creating the final product. So, it is going to be little bit downstream of the value chain when we consider the production of soft drinks. Bottling is an important and very popular process which is well documented and you will find a lot of videos which are also present that can help you understand how the bottling process looks like. I will not be explaining the bottling process in detail and I would encourage the viewers to look this up. In this example, I have taken eight items that are being procured and like I mentioned in the previous session, the organization could look at procurement of items or services and it could have many items that it procures as well. So, I have only taken eight representative items, there could be many other items that the bottling plant is going to procure in reality. So, this is in the true sense of the word a very hypothetical example that I have picked up. We have data which is present on the purchases based on the last financial year and it is not necessary that we have to consider only the previous financial year, we can look at past historical data for several years as well. And in this case, we have data available for the financial year which has completed, but it might not always be the case in which case the organization would need to look at what are the prices in the market and what quantity it is looking at procuring before it defines the procurement strategy. So, let us look at the example that we have. So, as this is a bottling plant for soft drinks, we are looking at the procurement of some items like plastic bottle which is going to be containing the soft drink, the procurement of syrup which is going to be fed into the bottle in the bottling process. The labels which are used for the bottles and I have mentioned label A and label B kind of indicating that perhaps there are multiple types of soft drinks that the bottling plant is looking at creating, cartons which are going to be used in order to hold the bottles when they are finally bottled and these will be used in order to transport the product to other places. As you can observe over here, the labels A and labels B will be placed on top of the bottle in order to identify which kind of product it is. The carton is going to be used in order to hold the items. So, this would be part of the labeling and packaging process that would happen after the production has been completed. Then we have paper standard let us say A4 size sheets of paper which are being used by the office. So, a bottling plant can also have a back office which is looking at different administrative activities. We are looking at another item which is the printer ink cartridge for A and B. So, there may be some specific information that needs to be printed on the labels. A part of the label might be printed and already delivered to the organization or to the bottling plant, but there may be some additional information. Let us say the date of bottling, the batch number and perhaps also the location and maybe other attributes which are very very specific to the product that is being made. It might not be possible for this to be obtained from the supplier in a ready made fashion that is a likelihood that is going to be there and hence this printing process would be carried out in house as a part of the labeling and packaging process. Then we have a printer ink cartridge which is used again by the office because you know for whatever work they are carrying out using the A4 size papers they might need to also use some ink. Now, this is typical products that are being procured and they are all consumed by the processes which are carried out at the bottling plant. Like I said it is only representative there could be many other items that are being procured. For example, if this is a fizzy drink that is being made you might also look at some gases that need to be pumped into the product as well. There may be other elements to the taste that need to be considered, flavors that need to be added which might have to be procured separately and added in the process. There could also be other consumables that are procured by the offices for supplies such as stationary supplies like pens, staplers and all of that. There could be many items that the company is going to procure for the bottling process. Hence, this is only a representative example of what could be procured. As we can observe these items are being used in various processes. Now, what we can observe is that each of these items is available in some standard pack sizes. If I were to purchase plastic bottles I would need to purchase it in a pack of 500. This would be what is available in the market and or what is being negotiated with the suppliers. So, over here 500 for the plastic bottle whereas, let us look at the syrup. The syrup is available only in quantities of one in a pack. It could be several gallons of syrup, several liters of syrup, it could be available as a barrel. It depends upon the nature of the product and hence this is helping us identify how much is being procured in a pack. Again, if you look at the labels A and B we can see that we are obtaining the same quantity in a pack for each of these labels. If I look at the carton it is showing here that we are going to procure in a pack only one carton. This need not be necessary you could get many cartons in a pack, but this may be the way that the company has been procuring from its supplier. If I look at the paper we are getting let us say 10 in a pack. It could be 10 reams of paper, a ream may consist of may be 400 or 500 or even 300 sheets of paper. So, this is 10 reams in a pack that you are procuring and if I were to consider the printer ink cartridge we are procuring one in a pack whether it is for the labeling and packaging process or whether it is for office supplies. So, this is the quantity that we are purchasing in a pack and this is the quantity that the bottling plant has purchased in terms of number of packs in the last financial year. If you can look at it we can observe that if you look at this information which is present we can see that the highest quantity which has been purchased in terms of number of packs is the cartons 30,000, but this is one in a pack hence we have purchased 30,000 cartons in the past whereas, if we actually look at the plastic bottles a little closely we can see that we are purchasing or 2000 packs, but there are 500 which are being purchased in a pack. So, this is definitely a larger number than what we are otherwise observing we would be in the same way we see here for label A you are procuring 500 packs and in a pack we are finding 2500 labels. So, this would be a large quantity that you are purchasing in comparison to just the cartons. So, we can observe these different things across what we have over here in terms of quantity and again if we look at the cost of purchase it is at the pack level. The most expensive in terms of the purchase at a pack level is the labels and it sounds a bit counterintuitive as to why labels which are just going to be pasted on the bottle are so expensive, but remember this is associated with a pack and a pack is having 2500 labels. So, this is this could be misleading if you were to just look at it from a pure unit cost perspective we also need to understand all of these attributes. Now, similarly we can see the syrup is quite expensive in comparison only one syrup costs 6300 it could be per barrel and this is quite expensive considering what you are procuring and this could be a very important element which is a part of your purchase. Now, while we can understand these aspects and attributes from this data that we have we can go one step further and find out what is the total purchase value that is procured and this is what it looks like. The total purchase value is highest for the labels as we can see here this is coming out to be 75 lakh rupees and this is followed by plastic bottles and syrup very closely. On the other hand if we see the total purchase value for office supplies is quite low just about 1000 rupees, so this is quite low in terms of contribution to the procurement value and if we were to consider the cartons over here as well as paper they are also within the range of a few lakhs not much and hence we can see these are low value purchases in comparison to the first 4 or 3 items as we have defined over here. In standard ABC analysis we would identify label A as an A item and perhaps the plastic bottle and syrup as B items may be extended to label B as well or we would identify the first 3 as A items and label B and carton as C items B items and then the last 3 as C items and this is a standard ABC analysis which is carried out, but this does not really help us much in the procurement strategy. It has helped us in identifying or classifying the items and it can help us understand how we should maintain the inventory policies for these items. How do we store higher value items might require higher material handling costs because of the value associated with it and we might also need to consider what kind of review policies we have for inventory control periodic review or continuous review, but beyond that these are internal processes it does not tell us much about the procurement strategy as such. So, we would want to understand a little bit more which is on the supply side is there any other information that we can gather on these items. So, one information or one piece of information that we have is how many suppliers are present in the market and what is the average distance of a supplier from the bottling plant. So, this brings in a little bit of more dimension to our problem right now and we can now start understanding not just from the total cost perspective, but also in terms of what is the exposure of the bottling plant to supply side risk. As we can observe here we have 1000 suppliers present for the plastic bottle, but just one supplier which is present for the printer ink cartridge. So, in terms of supply risk purely on the basis of number of suppliers we can see that you know the printer ink cartridge for labeling and packaging of the bottles is presenting higher supply risk because there is only one supplier present in the market who is going to give you this ink. So, this increases the supply risk which is present for this item although if we see the total value of purchase is not really very high in compare in comparison to the highest value purchases that we have carried out. Similarly, we can observe that items like carton and paper have large number of suppliers present in the market and it is natural to expect this because these are products which would be used by other offices. These would be used for the logistics and transportation processes of other companies as well other bottling plants apart from your own bottling plant other competitors. It would also be because cartons are also used for other products hence it is natural to expect a large supplier base for such kind of items. The same thing for the printer ink cartridge which is being used in the office whereas on the other hand the syrup is something which is going to define what is the kind of soft drink that you make. The technical specifications that you have provided for the syrup might be possible to be you know accepted for development for production only by a few suppliers and over here we have just two suppliers who may be capable of making this syrup. Similarly, we have just four suppliers who are available for printing these specific types of labels that you want. Again these labels might have some attributes and characteristics that are not present in other labels in the market may be the material of the label may be the ink used in the label may be the design that might only be possible with a few suppliers. So it is possible that this kind of a scenario exists for these items and lower supplier risk which is present with the number of suppliers here. Now let us look at the distance over here we can observe that we are having some of the suppliers for plastic bottles available very very close to the bottling plant. So we have large number of suppliers available very close to the bottling plant. So the supplier risk over here purely bases the distance is quite low which means if you have a shortage you can quickly get the items and it is further more low because there are several suppliers if you do not get it from one supplier you might be able to get it from another. Whereas if I were to consider the syrup the syrup is being procured from a very large distance perhaps an international procurement that is being carried out and as a result of this this presents high supply risk for the bottling plant. The similar case is observed with the printer ink cartridge which is used for labeling and packaging this is also present in a very far away location and presents high supply risk. Whereas if I were to consider paper it is being procured from a slightly far away supplier it is moderate risk but not at all high when compared to what we observe for the printer ink cartridges for A and B as well as the syrup. This is the information that we have in terms of the supply risk that we have as an exposure for the bottling plant and the purchase value that we have for the various items. We can create a cryologic matrix from this point onwards. One of the steps that we could do is to present a metric that represents the purchase value and a metric that represents supply risk that is a metric which represents profit impact and a metric which is going to represent supply risk. So, we can create a dimension in order to present the supply risk. One of the observations that you can make here is in case of number of suppliers higher number of suppliers presents low risk whereas, in the case of distance higher distance presents high risk. So, these are slightly in terms of what they represent there at odds with each other. So, we need to find a way to represent supply risk in a way that that is demonstrating both these attributes in the right fashion. What can we do? So, over here we have scaled the purchase value we have scaled the number of suppliers on a range. So, for purchase value I have taken a scale of 0 to 10 where 0 represents low impact in terms of profit and 10 represents high impact. And 0 would be present closer to the items which are having very low total purchase value. So, for example, here this has very low purchase value and 10 represents that which has very high purchase value which is here the maximum. So, you can see the profit impact we have scaled from 0 to 10. On the other hand for the supply side I have considered a scale slightly different 1 to 10 it will be preferable to have both the scales as 1 to 10 or 0 to 10 I have considered 1 to 10, but it would be preferable to have similar scales it does not impact our analysis too much. However, it would be preferable to select the same scale. In this particular case if I were to consider low risk for average distance I would scale this close to 10 and I would scale this close to you know 1 for the supply risk. In terms of number of suppliers I would scale this close to 1 and I would scale this close to 10 which means higher number of suppliers is low risk and lower number of suppliers is high risk. So, you can observe what is the scaling that has been carried out, printering cartridges in terms of number of suppliers presents low risk whereas, in terms of distance if we were to consider the printering cartridge A and B it represents high risk. It is also in terms of high risk we can observe the syrup is high risk in terms of the distance, but we still do not have a single metric for supply risk we do have a single metric for profit impact. So, what do we do? We can create a weighted supply risk metric for the supply side, we pick up a weight for the number of suppliers and a weight for the average distance of supplier from bottling plant and we apply those weights. So, over here this would be 0.8 into 5.502 plus 0.2 into 1 which will give me the weighted supply risk. This would be again scaled on 1 to 10 because this is also 1 to 10 and this is also 1 to 10 in terms of scaling hence it is quite useful to scale it with the help of weights. Why did I select 0.8 or why did I select 0.2 for the distance of the suppliers? I have picked up weights and this is left to the judgment of the company perhaps the company feels that the number of suppliers has a larger impact on the supplier risk rather than the distance and the distance is manageable, but let us say we are working in a terrain which is very very poor and the distance would then have a higher impact on the supply risk. So, the weights have to be chosen in the context of application I have chosen these weights and these weights can also be changed. So, when we consider this if we were to find the supplier risk which is weighted for the items we can see that the supplier risk is highest for the syrup at 9.996 followed by the printer in cartridge and the least supplier risk is observed for the printer in cartridge which is used in office and a low amount of supply risk is also observed for paper as well as plastic bottles. On the other hand if we can look at the profit impact which is scaled on 0 to 10 although I would prefer 1 to 10, but 0 to 10 is also fine for the context of explanation. We can see that the profit impact is highest for label A followed by the syrup and plastic bottles. Now, let us put these two dimensions together and position the items on the matrix. So, we have on the x axis the profit impact and on the y axis the supply risk where profit impact is going from 0 to 10 and the supply risk could be scaled from 1 to 10. Now, we can observe that the printer in cartridge is representing very low supply risk and low profit impact whereas, syrup and label A are representing high supply risk and high profit impact as well. So, let us see whether we can create a classification of the cryologic matrix for these items. So, over here let us say the bottling plant decides that any value of profit impact that is higher than 6 on the scale of 0 to 10 and any value of supply risk which is higher than 6 on a scale of 1 to 10 is going to be considered in the other quadrant. Then we are going to have the quadrants created basis that. So, this is going to look at look something like this and we can observe that printer in cartridge label B carton falls in bottleneck items, non-critical items represented by paper, printer in cartridge, plastic bottle represented as leverage item, syrup and label A represented as strategic items. So far so good we have carried out the classification based upon some amount of judgment and selection of matrix. What do we do next? So, we review what is our current procurement process? Our current procurement process can be reviewed for each of the items, plastic bottles which are leverage items. We have been procuring for the same supplier for last 5 years. For the syrup which is a strategic item we are procuring from same supplier for last 10 years, but we are negotiating the contract on a yearly basis. For label A which is a strategic item we are again choosing the supplier on a yearly basis by negotiating cost. Remember for label A and label B we did not have many suppliers as well. For label B which is a bottleneck item because of the low value it represents again the supplier is chosen on a yearly basis. For carton we are which is a bottleneck item again we are choosing it on yearly basis. For paper the supplier is chosen as per need basis, it is a non-critical item. For the printer in cartridge A and B the supplier has been awarded a contract for 3 years and then we are going for a new supplier. And for the printer in cartridge used in office it is a non-critical item and the supplier is being chosen currently as per need basis. This is the current state of procurement. So, the organization might want to think what can we do going forward. So, this is what could be a recommended strategy. For the plastic bottle which is actually a leverage item we can try to reduce cost because there are many suppliers available in the vicinity. We can encourage vendors to come through a competitive bidding process which can reduce the cost of procurement instead of depending on the same supplier. If I look at the syrup we have been dependent on the same supplier, we could explore a potential of joint venture or negotiate rates to lower the cost. Since there are only two suppliers for the syrup maybe we could explore other alternatives which can reduce the risk of supply, but this is not necessary. If the syrup is going to define what the product is it might be difficult to explore other alternatives. For label A and B you can observe that these two items are different categories altogether. The first supplier is chosen on a yearly basis in both cases. Maybe it would be better to offer a longer term contract to a few suppliers which can do two things. One is it can lower the cost over a long term. Strategic items would have the cost implications over here which can be reduced. And we can reduce the risk because we are going to consider distributing the procurement between few suppliers rather than depending upon one supplier every now and then. For cartons there are many suppliers who will be present. What we could do is we could empanel multiple suppliers and we can reduce the risk which is being presented as a nature of the supply risk that is there. Similarly for paper perhaps we might want to identify whether the purchase value is really justified and we could explore pay-per-view processes to reduce the cost impact. It is a non-critical item it does not you know really represent much risk. For the printer ink cartridges and B this is actually a bottleneck item. We could explore the takeover of the supplier or other alternatives to the ink cartridges with near supplier. What was happening is we were dependent only on one supplier or so, maybe we can explore whether we can move to other suppliers of regular ink which can help us streamline our processes better. And for the last case also it is in alignment with the fact that we are procuring paper. So, we could explore paper fee processes in the office to reduce the cost impact. So, these are the recommended actions. One thing that we need to really keep in mind is considering the kind of segmentation that we have carried out. It may be a good idea to have a continuous improvement approach focused on the development of the Kralljik metric and a matrix and the procurement strategy. We can review the nature of selection and scaling of matrix carefully. We can review the weightages which we give to the matrix. We can also bring in a lot of consensus on the matrix. Perhaps someone is not very happy that we are looking at just the number of suppliers and the you know the distance. Maybe there are other attributes of the product we need to consider. And we need to also understand whether the link between strategy and segmentation is working out well. Currently this is more user defined. So, we need to also carry out sufficient deliberation and research whether these strategies really work with the kind of segments that we have. Remember this is the Wattling plant which is looking at its supply portfolio. There may be some good best practices also available in the market carried out by other bottling plants that can help us identify what could be the better procurement strategies that can lower the risk and reduce the cost of procurement. So, with that I conclude the discussion on Kralljik matrix as applied in procurement strategy and development of portfolios for procurement. I hope this was useful and it can help you identify different ways to develop the procurement strategies going forward. So, thank you very much and I hope this was a useful session. Thank you.