 conversion right this is the you will take any one example take the auto cycle so called auto cycle this is the one on which your gasoline car still operate so I have P versus V what I have is a piston cylinder assembly piston moves up and down the normal procedure is for you to have two valves you can have now 16 valves or even 32 valves in a one is called an inlet valve this is the outlet valve these are the details that Carnot refused to get into they told him what is your engine he said I do not care really frustrated people back in when you are talking of thought experiments and abstract thinking in the universities now you take it for granted I mean every other Joker tells you do a thought experiment but you must realize that when Carnot did it first nobody ever thought that you could discuss a heat engine meaningfully without an actual engine but anyway this is just for concreteness there is a piston cylinder assembly this moves up and down these strokes are like this first you have at atmospheric pressure you have an intake stroke let us draw some figures this is clearance volume that is the when the cylinders in this cylinder reaches the top dead center this place is called top dead center TDC the cylinder is shaped in such a manner that you have actually a small dead volume there it is called clearance volume and for example one of the achievements of Japanese manufacturers is to reduce the clearance volume and show you the efficiency increases tremendously so there is a clearance volume this is a design specification you can make it as small as you are capable of it is it cannot be made zero but subject to that then from here you have you open the inlet valve keep the outlet valve close then the gas is taken in the air is taken in typically and the cylinder moves outward so the volume increases it moves to some point here so this is the inlet stroke stroke is simply movement of the piston stroke during which the air is taken in and then the valve is closed here the inlet valve is open the outlet valve is closed at this point you close both the valves then you have an adiabatic compression at this point in gasoline engine you have a spark plug spark is created across the spark plug I do not know how many of you have seen a spark plug spacing is we used to do it in it is about one tenth of a millimeter spacing or actually it can be up to a millimeter which is less much less usually a spark is actually you have a induction coil that generates very high voltage and a spark crosses this and that spark ignites the fuel at this stage this this air is actually a fuel air mixture nowadays what you have is an injection device that injects the fuel as well because it measures the fuel exactly normally in a normal in the classical engines and we still have a few of them those the air that comes in here comes in through a carburetor the word may go out of the dictionary soon so you may not even need to know it the carburetor what it does is measures the if you put your pedal to the metal then a lot of fuel will be taken in if you relax on the accelerator only a few drops of fuel be taken in that is actually controlled by a beautiful mechanism if you have seen any of the I think I am talking to you in a language of before you are born practically this actually till last 10 years ago there were carbureted engines even now you have carbureted engines the carburetor usually has a needle valve it is a very nice mechanism you have a valve that looks like this is a tank that contains the liquid and as this valve goes up and down the air flows over the sorry the air flows over the thing as this goes up and down you have exposure of the liquid the exposure of the liquid will vary I should make this narrower then the amount of fuel picked up by the air will depend on the surface area of the fuel so it will vary in drawing an upset picture you have to actually see the carburetor properly I will get picture anyway that is controlled so at this stage this is a fuel air mixture a small amount of fuel and air enough air to combust the fuel and normally you have excess here because you want to pressure the fuel is too precious so you want complete combustion so if you suddenly press the accelerator you often do not have enough air so you get a smell in the exhaust but anyway at this stage the sparking is done when sparking is done the in the auto engine the ignition is this is ignition stage so this is adiabatic compression then this is ignition the ignition is so rapid that the cylinder that comes up to the top does not move back during the time of ignition a time of ignition is really small so effectively it is constant volume ignition that is the characteristic of the auto cycle as far as thermodynamics is concerned this is where the reaction occurs reaction products have much lower internal energy than the product coming in so the difference appears as heat because no work is done delta q is equal to du in this process so the change in internal energy is what is supplied as heat normally you call it constant volume heat addition in the case of a diesel engine this actually is pressure is much higher and the ignition is supposed to be at constant pressure because as you inject the diesel it burns by spontaneous combustion and that takes longer than spark ignition so actually the piston moves back and the pressure is maintained incidentally this is what they will do when they tune a carburetor they can tune a carburetor for you to get better acceleration I mean they can tune the engine what they do is to say that this fuel intake I am sorry this ignition the spark ignition the spark will be ignited before the piston reaches the top dead center so that the ignition occurs exactly when the pressure is maximum it is measured in degrees because you have a dial on top which is turned they will say 5 degrees if you talk to these mechanics they are pretty clever guys they do not know exactly what is going on inside but he will tell you how much advance to keep and it is particularly effective in your motorcycles keeps a little more advance it will go my much better there is a big difference if you make it to if the advance ignition is too far in advance then before the piston reaches the top dead center it will be sent back so you lose some power in that process okay anyway you get to this you get ignition then you have adiabatic expansion this is adiabatic meaning it occurs in such a short time that there is no time for exchange of heat to this around and then this is simply cooling this is your radiator fluid if you have an old Volkswagen Beetle it does air cooling very effectively simply with more fins and then there is a exhaust stroke the inlet stroke and the exhaust stroke the exhaust stroke pushes out all the material inside this piston and actually nitrogen is the same part of the oxygen will be consumed replaced by carbon dioxide since fuel also has a bit of hydrogen you will have some water but if you ignore the inlet and the outlet strokes and simply look at this cycle it is a close cycle if you pretend instead of change in composition change in composition does not really change the specific heats significantly so it is air plus whatever or just call it here with a certain specific heat that goes through a cycle and here you have heat addition that is instead of the reaction that produces a change in internal energy that gives you the heat we just call it heat addition in this heat addition and here it is heat removal so effectively you have an adiabatic compression followed by heat addition at constant volume and then you have an expansion so this expansion will give you work on this diagram you will calculate work as PDV so the area under this curve is the work done by the system the area under this curve is the work done on the system because you have to compress it which is why we always have an electric motor to get the whole thing started you crank the motor it compresses it first once this heat addition occurs then there is enough energy then it goes out here and then it can keep so the net work done is this area under that curve is the net work done in the cycle so this volume here we will call these various points by name call this a we will start here a b c and d a b c d is your cycle this volume is called the stroke volume simply measured by the pi d squared by 4 into the length of the it is the volume swept by the piston in a moment the quantity of interest is how much heat do you add here we write this in terms of q in actual fact it is a reaction occurring where I said told you internal energy of the products is less than the internal energy of the reactants and therefore you get net heat added to the system but we calculated in terms of heat added and work done the heat added divided by the calorific value of the fuel will give you the amount of fuel consumed so effectively per fuel consumption what is the amount of work you can do what is the mileage you get so this is the one that I want to analyze this is the original cycle proposed by auto so what you do is in order to do the analysis I will write a b all the equations are given on this is a close system delta q-delta w that is it as far as I am concerned so the stroke a b I am going to ignore the inlet and outlet strokes as cancelling one another I do not have to consider them at all I pretend that here I start at a pretend instead of fuel ignition I pretend heat addition and I pretend here that there is heat removal which is actually is true I remove it very quickly a b is an adiabatic system so delta q is 0 so delta w is equal to du if I assume ideal gas I do not have to there is actually thermodynamic charts for this which you can use but if you assume ideal gas you are talking of CV DT then I have BC or I will write W itself WAB so I can integrate this WAB is simply CV into T2 TB-TA see if CV is constant you use an average value of CV otherwise you have to strictly a function of temperature but for all practical purposes in engineering we use average values of CV to the integration then I have BC sorry here BC is simply constant volume heat addition it is actually not heat addition as I told you it is simply a reaction occurring the carbon will go to carbon dioxide the hydrogen in the fuel will go to water in the change in internal energy is equal to the heat added so again if you like delta q is actually equal to du or heat addition is simply integral of again CV into TC-TB the conditions at a are known the pressure at the intake is known it is usually atmospheric this can be when you have a supercharged engine all you do is have a compressor and increase the ways this level you can show you that gives you better more power per cycle but at the cost of more fuel it is not doesn't make it more efficient but you get so initial that kick you can get by supercharging your engine putting compressor in the outlet compressing the inlet gas and sending it in inlet air and sending it in then CD CD is again an adiabatic process you have WCD there is a minus sign here because du is minus delta W this is minus then WCD is exactly like here I can simply write it down this is CV into TD-TC because TD is less than PC this will turn out to be positive that will turn out to be negative and ask one is DA this is again Q this is QBC QDA is exactly like this CV into TA-TD so what I am looking at this I am interested in this W net by QBC because QDA is simply heat lost to the environment I get nothing from it but QBC is what I supply that is my fuel so remember QBC by calorific value of fuel will give me mass of fuel if I want work done per unit fuel consumption I will essentially have to calculate W net W net is essentially WCD-WAB by QBC so you get PC-TD- we have WAB-TB-TA I have taken the minus sign out by switching divided by QBC is TC-TB so this is 1-TD-TA by TC-TB so this is your efficiency all you need to do is calculate the temperatures and you can calculate these temperatures very easily because TA is known TA and PA are known this is adiabatic you have your formula PV per gamma is constant so from here to here you know this volume so you can calculate the final pressure here so once you calculate the pressure your T is again PV is equal to RT then here again this temperature is known this temperature is not directly known unless you know the heat addition that depends on how much fuel you add so I can give you the fuel consumed you can multiply it by its calorific value and put in Q here so you can get this temperature actually backwards from this equation it is I know TB now I can calculate TC is equal to TB plus QBC by CV so I can calculate that temperature so I can calculate these conditions and then these conditions again this is an adiabatic expansion once I know these two I can calculate here because everywhere the volume is fixed it is fixed by the geometry of the system so when they say 1.3 liter engine we usually mean this is 1.3 liters BS if you have a BMW 6 5.3.0 5 is the series then 3.0 liters 3 liter engine and the compression ratio also determines the pressure from here to here depending on this ratio you get higher or lower pressures and if you look at this clearance volume it has physically a bad influence because at the end of the process when you compress it you have clear is you have gases at the end of this process at this pressure and at this volume so when you expand it out this gas remains when you finally expand it out that gas remains in the system and so it occupies space much more at atmospheric pressure it occupies more space than it would before so essentially it represents a loss because you have the spent fuel air mixture that still occupying the space inside the cylinder so clearance volume represents loss what we can do is work this out in terms of geometric specifications as far as possible you get all the variables in terms of geometric specifications we will do that so we will just calculate each of these temperatures then I can get these ratios ta I am wondering okay ta is known I should have done it in terms of okay I will leave ta as it is tb what is the formula it is pv power gamma is equal to constant pv is equal to RT n is constant here the number of moles is constant so I want vt relationship that is all so instead of p I write by v power gamma minus 1 so tb power gamma minus 1 is equal to constant right so tb if I am writing in terms of ta tb is simply ta into va by vb to the power gamma minus 1 va vb are geometric specifications I give you the cylinder dimensions then I have given you all the data for va and then similarly I suppose I should have kept pc comes out in terms of heat addition okay I will try and use this equation rather than this so I have got tb in terms of ta similarly td is equal to tc into the same ratio vc vd are the same ratio as va and vb so tc vc is vb by va to the power gamma minus 1 va by vb so I will write everything in terms of tc here or this is td that is efficiency is equal to if I pull out a td this will become tc by td which is va by vb we will call va by vb as r it is a geometric specification so I have td into tc is r to the power gamma minus 1 minus 1 minus ta into tb by ta is va by I want vb by va so minus tb I will pull out this tb into 1 minus ta is a smaller one it is vb by va now va by vb is r so this is correct what I wrote is right first ta into r to the power gamma minus 1 divided by tc minus tb you are you manipulating this equation or this one this one okay what do you want okay ta in terms of tb that is already written right here you want ta I have written that ta is tb into r to the power gamma minus 1 I have written that but ta is tb into vb by va so 1 by r to the power gamma minus 1 right that this equation I have written ta then r right okay 1 by r to the power gamma minus 1 comes out you are now doing this equation okay td minus ta yeah so you got yeah thanks so it has equal to 1 minus td and ta is tb minus tc minus tb into 1 by r raised to the power gamma minus 1 divided by tc minus tb yeah thanks so you have efficiency equal to 1 by I am sorry 1 minus 1 by r to the power gamma minus 1 r is what you have control over because you are building this so your r is actually vs plus vc this is stroke volume this is clearance volume if you want I will call this vcl to make it clear because we have another vc by v clearance clearance volume is the dead volume if you like when the piston is at the top so this ratio is in your control actual practice what happens is that these things are rounded off it does not happen exactly like this because the actual stroke the valve has to close it takes some finite time so on but if you look at the whole process it is sort of controlled if you are talking of 3000 rpm you got one explosion about for every rotation of the crankshaft of the wheel not the wheel the crankshaft because in the wheel is geared but for every rotation of the crankshaft you have two explosions and you are talking of 5000 rpm you are talking of 2000 controlled explosions per minute so that is how your vehicle runs your vehicle runs through a series of controlled explosions every time you have if you are burning you have a small explosions all contained the other cycle that one can discuss incidentally the Carnot efficiency the efficiency here is 1 minus 1 by r to the power gamma minus 1 of course the other way of changing this is to use a fluid that has a different gamma but other than air anything else you use you are going to pay heavily so there is no point in trying unfortunately air and oxygen have the same gamma otherwise you can try purifying using oxygen but in any case does not make sense so this is the only thing the Carnot efficiency is you have to take the highest temperature as the source and the lowest temperature is the sink equivalent Carnot efficiency so will be 1 minus the lowest would be Ta by Tc so do you have an expression for Ta by Tc 1 minus Ta by Tc would be written in terms of Ta by Tb into Tb by Tc you do not like Tb by Tc suppose I do not have choice this is 1 minus Ta by Tb is 1 by r to the power gamma minus 1 again into Tb by Tc so Tb by Tc is less than 1 and therefore your Carnot efficiency is greater than efficiency that you get from the Otto cycle analysis directly the diesel cycle is actually similar except that you have two parameters for control you have a Vs and a Vc again the same construction you have the exhaust stroke and the inlet stroke what you have is a compression adiabatic compression at this stage the fuel is now added by injection and you cut off the fuel injection at some point and then it goes like this so here it is constant pressure heat addition the word heat addition is used to denote the change in internal energy that occurs during combustion so you have the same ABCD usually these pressures are much higher so the diesel engine has to the block has to be much heavier in order to withstand that pressure and there is a cutoff ratio here this ratio of the volume here C this is clearance Vc by Vs plus Vcl is defined as a cutoff ratio Rc it is the time at which you cut off your diesel that depends on how much you press your pedal and you can show this is just a lot of algebra you can show that it is always less than this for Rc when the Rc is equal to this when this is equal to 1 by what did we call this V clearance by Vs is that what we called R yeah so when it is equal to R you will find that the efficiency is same as an auto engine so in general the efficiency of a diesel engine is less than the efficiency of an auto engine for the same on a actually there is an air standard cycle table from which you take thermodynamic properties so you can actually calculate the you can take the non-idealities into account because you are doing this ideal gas analysis here at this point it can be an ideal gas but the higher pressures it would not be an ideal gas some departures from ideal gas these have been computed and you can read it from a standard cycle the other thing I wanted to say was in the terms of the pH diagram here you do not actually have a pH diagram for a case like this because it is not a pure substance but if you treat it as air or if you treat it as a single substance again air is a mixture but if you treat it as single substance you are always talking about the critical point so you are really looking at this region all you have is you are starting at some you are working between two pressures there is a P1 or P high and a P low and you are working within two adiabatic processes so you can start at P low at some temperature and you have an isentropic process it goes up to P high and then you have heat addition at constant volume so how will you represent it on this diagram when you do is go along a constant volume line and this is isentropic this is V is equal to constant along the constant volume line you have a heat addition that means temperature how will I draw this diagram I have these lines this is T1 this is T2 T2 less than T1 I have compression from low pressure some this is where I start let us say this is A from here I have I go to the higher pressure I think I should draw this a little lower getting outside the board otherwise I go to this pressure this is B from there I have a constant volume line which is a different slope this is the constant entropy line you have seen that the constant volume lines have a different slope lower slope so I have some heat addition so I will go up to this point C and then come back along an adiabatic this is D so A then B B to C this is B this is C here and then D this heat addition is what you have to know you have to know how much heat is added during the process so you have to add the internal energy there and move along that line to the new point essentially I would not give it to you in the form of a chart I mean the form of a graph it will be given to you in the form of a table and then there are variations of these that have been discovered through history but really the auto and the diesel are the ones that have remained the simplest and easiest to operate what I will do is I will for the sake of completeness I will discuss refrigeration very briefly on the although you have done this because this is called vapor compression refrigeration which is what you would have done on the pH diagram and then I want to discuss later absorption refrigeration which is what is used on large scale this is work to heat conversion devices here you are talking of two phases what you do is take let us say pure vapor could be free on now you have non fluorohydro carbons for this thing but you have pure vapor which you compress along and adiabatic I work between two pressures again I have a b this is adiabatic compression from a to b from b I cool it to saturated liquid then I carry through an isenthalpic process this is called throttling so you bring it down to a point d where you get a mixture of liquid and vapor and then whatever liquid there is you evaporate here this is actually I will call this condensation and I will call this evaporation evaporation requires that you take heat from the surroundings Q e here you add heat when you give up heat when you condense a fluid the latent heat is given up to the surroundings just happens that you give up heat at a higher temperature and you absorb heat at a lower temperature since you are interested in the extent of cooling the coefficient of performance for such a cycle is the amount of cooling that you produce which is Q e which is h a minus write this down Q e by w this is where the work is this this process for this isobaric process the total heat that is removed is h a minus h d and the amount of work done for an adiabatic system for flow systems per unit mass flowing through the system it is a difference in enthalpy so by h b minus h a it is called the coefficient of performance so if I give you the chart for the fluid it is absolutely trivial for you to calculate this you must have done this calculation this is vapor compression what we look at this mixtures where you do absorption refrigeration you find that for large scale absorption refrigeration is much better here you have a compressor with moving parts there you do not have the same what you do is absorb the gas in a liquid and you take away the gas in a liquid to different temperature you find that this you can use this difference in solubilities and the enthalpy of dissolution to do the calculation to extract some refrigeration out of it.