 Now let us proceed further, we have completed in our scheme of things, we have completed zeroth law of thermodynamics, we have ended up with the concept of temperature and that is what zeroth law ends up with, it ends up with the concept of temperature as labels on isotherms, how to label them, whether to label them by numbers or by names, if names, names of what, we use color as an illustration but you could use anything else. But we have a feeling at the back of our mind that look, colors are few but we will have a large number of distinct isotherms, we know already, so naturally we cannot have gray, gray, blue, blue, blue, green, such combinations we would not have and hence numbers are better because we have a more or less continuous and any wide range of it. Now we will go to a part of thermodynamics in which not real thermodynamics is involved. So in the, in this section, thermometer and in the properties of fluid, let me start off by saying that no new fundamental principles of thermodynamics will be involved, the new principle we will come across only when we come to second law. So what we are going to do now is apply whatever we have learned so far, particularly zeroth law to proper measurement of temperature and see what the consequences are because zeroth law does not tell us how to measure temperature but we have realized that temperature is a useful quantity. Many people have set up methods by formally assigning values to isotopes and that science is known as thermometry. So for us, thermometry is nothing but methods assigning, I should say numerical, there are different methods, different approaches, so we have different assignment procedures and the first definition here is a thermometer is a reference system used for thermometer. So our classical Celsius thermometer, centigrade thermometer as it was known as, mercury in glass thermometer. So that standard uniform capillary with a bulb of mercury at the end, uniformly graduated was our thermometer, while doing this, remember zeroth law does not tell us what is the higher temperature which is the lower temperature but we human beings have a feeling of what is hot, fire was hot, we know what is cold, water is cold, ice is cold, water is cold, ice is cooler still, boiling water is hotter than normal water. Some vague idea that steam and water, may be steam is hotter, may be it is not, all these ideas existed earlier before phase rule and other things came into picture. So let us look at the historical development of thermometer and we will essentially look at the mercury in glass thermometer, a few others then gas thermometer and then we will more or less end this by talking about the ideal gas thermometer which will bring us to ideal gas equation of state. And again mind you, till we start our discussion of the second law of thermometer, no new basic principle of thermodynamics is involved, after zeroth law. So going further we will look at the mercury in glass thermometer, realize that the mercury in glass thermometer is a rudimentary system, there is no two way work mode associated with, you cannot do stirrer work, there is no electrical work, there is no expansion contraction work nothing, even stirrer work does not exist, there is no work mode one way or two way associated with it, if you try to work with it it will break, that means it does not remain a thermometer anymore, we do not want to destroy a system. So there is one variable of state, one property by which the state is defined and that is the length of the thread of mercury in the capillary. So if it has a property called temperature, the temperature must be directly related to the length of mercury thread in the capillary. So that is the basic idea, I will just show a very crude depiction. So length of capillary, let us say this is some, if the capillary mercury is up to here, this is L. Now we have to map L to some temperature values and because we have a idea of what is hot, what is cold, the psychological feeling is whatever is hot must have a higher temperature, whatever is cold must have a lower temperature. Just our traditional feeling nothing to do with thermodynamics, actually this is so much ingrained in it that all those different people who have Celsius, Fahrenheit, Rankine, Romer, Kelvin, who came up with temperature scales, none of them dare to propose a temperature scale in which ice would have a higher temperature than steam because people would have laughed at it. It is only for that reason that all temperature scales have temperature of boiling water higher than temperature of freezing water. So that is the first part of our field that hotter stuff will have a higher temperature. But zeroth law hasn't yet told us what is hot and what is, it will never tell us, it is only the second law which will allow us to formalize what is a higher temperature and what is a lower temperature. So what did Celsius do? Is the Celsius scale or sea scale as a, it talked of two fixed points, reference points. For this two different systems were used, one fixed point was what was called as the steam point. Here you have a system at one atmosphere defined as 1 0 1 3 2 5 Pascal, so that is a primitive measurement, one atmosphere and equilibrium between water and its vapor which we generally know as steam. Because this was a simple enough system, water and its vapor maintain it at one atmosphere and bring the state in such a way that you have both liquid as well as vapor in equilibrium. This is known as the steam point. This was given the arbitrary number 100 units degree C, this was defined to be, let us define the isotherm corresponding to this with the label 100 degree Celsius. Earlier it was 100 degree centigrade, last few decades we call it 100 degree Celsius. Nothing about degree Celsius, that degree has that old idea which many of you have written, degree of hotness, there is no degree of hotness involved here, it is just a nomenclature. System 2 is what is known as ice point. This is again at one atmosphere and equilibrium between ice plus water. But here there is a problem, this is air saturated water because later on we will notice that at so called 0 degree C which this is defined to be, we cannot have an equilibrium between ice and pure water, pure ice and pure water that will exist only from 0.1 degree C on this. So if at one atmosphere pressure, if you want equilibrium between ice and water that is air saturated water that was known as 0 degree C. This was defined in such a way because in the simple physics labs which existed at that time, this was reasonably easy to make although it was not very precise. This was decided to be 0 degree C and what was later done was using this, bring this in thermal equilibrium with the steam point that means create a system at steam point, put this thermometer in it, maintain the system at steam point, wait till the thermometer also comes in thermal equilibrium with that system at steam point. Note the length of the thread, call it L1 that is one marking, you have graduated the thermometer at 100 degree C and make that mark known as 100 degree C, mark it as 100 degree C. Then do the same thing by using the same thermometer at the ice point means create the ice point in a system, put your thermometer in it or let it interact with that system across a diathermic partition, wait till thermal equilibrium is reached and maintain the system still at ice point. When thermal equilibrium is reached, the state of this system will be such that the thread is at L2, mark that as 0 degree C. Then comes the assumption that our thread is uniform in bore and the expansion coefficient linear or volumetric expansion coefficient of mercury is also uniform and then we define by an interpolation law, the temperature of our system with mercury thread at L will be equal to going back, proportionate between L minus L2 and L1 minus L2. So this will be equal to, I think it will turn out to be L minus L2 divided by L1 minus L2 multiplied by 100 because L1 minus L2 defines 100 degree C temperature range, this in degree C and this was defined to be, this was the definition of the Celsius scale. So what does this mean in thermodynamic language, we simply say we do not measure our own body temperature in Celsius, we talk of Fahrenheit which is another similar scale. But we say my temperature is 37 degree Celsius, what does it mean? It means that if I have a Celsius thermometer and if I bring it to a state where it is showing 37 C that means it is 37% above the ice point towards the steam point and if I bring it in contact with me across a diathermal partition, there will be no heat interaction between me and that thermometer, that is what it means. And that means by our thermodynamic definition me and that thermometer with the thread at that point are isothermal systems, so they will have the same temperature level, since the temperature level there is 37 Celsius, my temperature level is also 37 Celsius. But if you try to tell you to a doctor, he will send you to a mental asylum, so be careful. But as good students of thermodynamics we should understand this, this is a very long winded way of saying it, but that is what it really means when I say that my temperature is 37 degree Celsius. Now this also means that on the centigrade scale, the temperature of ice point need not be measured, it is defined at 0 degree Celsius, temperature of steam point need not be measured, it is defined as 108 degree Celsius. These are the calibration points, this is a minor issue but we will come to this again when we talk about the ideal gas thermometer and then the later on the thermodynamic scale. Now similar to this is the Fahrenheit scale, Fahrenheit scale was funny, he wanted to measure lower temperatures, so in his lab he could create a temperature lower than the ice point temperature, if you put a Celsius scale that thread will go much below the 0 degree sea line. I think what he did was he discovered a iso, not isotropic, allotropic mixture of water and ammonium chloride, found out the minimal boiling point of that, called that is 0 degree Fahrenheit. When he measured his own body temperature, maybe he did not realize that it changes from morning to evening and all that and called it 96 degree Fahrenheit and interpolated linearly between the two. It later on turned out that both these fixed points were of no real use because they were very difficult to reproduce, this was later on standardized as ice point being at 32 Fahrenheit and steam point being at 212 Fahrenheit. The original fixed points were forgotten but the basic idea is the same thing mercury in glass thermometer. Now y100, y32 and 212 that is rather arbitrary and so long as we did not worry about really low temperatures and really high temperatures mercury in glass thermometers were good enough. But people soon realized that we cannot go below something like minus 40 Celsius because mercury freezes at something like 39 or 41 degree C. Similarly mercury boiling point is about 350 or 360 degree C, so it is no good going beyond 320, 330 because the vapor pressure of mercury will increase and the thermometer will crack. But slowly people started using steam at higher pressure, they started measuring the temperature of fire and there was no way of measuring the temperatures. So they needed a system by which temperatures could be measured over a wide range going to say minus 100 Celsius, minus 200 Celsius. Physicists and engineers were always trying to obtain lower and lower temperatures, trying to hunt out this very limit. On the other hand they found material melting at higher and higher temperatures, those melted materials boiling at still higher temperatures using arc furnaces and concentrating solar rays, they could go to very, very high temperature but there was no formal way of being able to measure those. So people started using resistance thermometers, platinum resistance thermometer. But platinum also makes and at very low temperature platinum resistance thermometer loses its sensitivity. Some property of some system which varies at different, for different isotherms it has different values is used. So finally just to extend range people found that gas thermometers are very useful because they realize that there are gases like hydrogen, helium which they found that they just could not liquefy in the temperature range in which they could liquefy up. Hydrogen liquefies at something like minus 250 Celsius, helium gets liquefied at approximately minus 269 Celsius and upper limit they remain in the gaseous form for quiet some value. So the range of applicability of gas thermometer if we could set up one was very wide and hence gas thermometer was the next thing. But remember that unlike a mercury in glass thermometer which has only one property because it is a rudimentary system, a system containing a gas is a simple compressible system. So it has two properties to define its state. Pressure and volume are the most convenient ones. So once you have two properties you have a problem how do you link temperature to two properties. So since gas will have two significant properties, pressure and volume we started off with a situation where we have a constant volume gas thermometer and then we have a constant pressure gas thermometer and all that thing done was like this. All that you do is you have a cylinder piston arrangement in which you have some gas fixed in leak proof piston. You measure the pressure, you measure the volume. If you fix the piston then you end up with constant volume then temperature will be mapped only to the pressure. You can decide that the pressure relates directly to temperature by means of some empirical relation. Just the way Celsius said let it be linearly interpolated so you can define it. Or for the constant pressure what you do is you have a leak proof but ideally frictionless piston. So P is maintained constant by exposing it to a system with a uniform pressure and that you measure V. So here it is constant P. And temperature is related to volume and then it was discovered that at reasonably low densities unless you really have a high pressure. It was noticed that if you start looking at the Celsius temperature of this gas, the Celsius temperature is more or less linearly varying with pressure. The Celsius temperature was linearly varying with volume approximately. And then came the great Boyle. What did Boyle's do? What was Boyle's law? How do we remember Boyle's law? Or how do our students remember Boyle's law? At constant temperature what happens? P into V is constant for a constant temperature. Let us rephrase it. Boyle's law says that it is an approximate empirical law that if you have a closed system, containing a gas which does not liquefy, then what he did was he plotted isotherms for different values of temperature. So these are different isotherms. And then he noticed that any given isotherm is approximately represented by P V equal to constant. This is different for different isotherms. That is what he discovered. Well, in our language because all isothermal states have the same temperature, we can say that if you fix a temperature constant that means you are restricting yourself to some set of a particular set of isothermal states that will be approximately represented by P V equals constant. Then he also found that this approximation is good low pressure, high temperature and that means at low density. It is very good at low pressure and higher temperatures. That means high volumes for the same mass, that means low density. And hence one could imagine a fluid which would have its isotherms representable exactly by P V equals constant, no approximate. What do we call such a fluid? What do we call such a fluid which obeys Boyle's law exactly all through its cases? An ideal gas. So let us define an ideal gas is a fluid or a gas whatever you want obeys Boyle's law all over its state. Definition. Do we find that any gas is an ideal gas? No, there is no gas will obey Boyle's law all over its state space. But there are gases which are better in obeying this. For example, hydrogen is a good approximation, very wide range. Helium is a still better approximation, very wide range of pressures, volumes, densities where it obeys Boyle's law. Or you take any gas so long as you work at very, very low pressures near vacuum it obeys Boyle's law. So ideal gas is an approximation and it is as good or as bad an approximation is that of a reversible process or a quasi-static process. But it is a useful approximation, it is an ideal. We can approach that ideal using gases like hydrogen and helium and otherwise any gas but at low pressures and low densities. Do not pack it up, have it at low pressures and it will be a very good approximation for an ideal gas. Now, for an ideal gas any isotherm is represented by an ideal by a fixed value of P into V. You take isotherm A. If the value of P V it is a 1 atmosphere meter. Then if you have a pressure of 2 atmosphere volume will be half a meter. If you have a pressure of 0.5 atmosphere volume will be 2 meters and all these states will be isothermal so can be labelled with the same temperature. But you take a different state where for the same mass initially when I said volume of 1 atmosphere and 1 meter cube let me say 2 atmosphere and 1 meter cube. Then the temperature will be different but 1 atmosphere 2 meter cube because the P V product is the same. The temperature will be the same as 1 atmosphere 1 meter cube. So for an ideal gas each isotherm is a distinct rectangular hyperbola P V equals constant where this constant will differ for each isotherm. So now the idea is cannot we use that constant as a measure of temperature. We should be able to because if we find 2 states find out their P V products if they are equal same temperature. Find out what that temperature is by determining that constant. Then you find some other state where P V product is the same constant we will say oh that will also have the same temperature. So in principle we can use this constant as a measure of temperature or the P V product itself as a measure of temperature. That idea gives us the idea of an ideal gas thermometer. Now if you look at the old thermometry text books from here they talk of a 2 fixed point method of ideal gas thermometer, single fixed point method let us not go into it. We realize only one thing that for any gas ideal or otherwise we can never have for a closed system volume infinite and hence pressure 0. Nor can we have pressure infinite and volume 0 it is impossible to compress it to 0 volume. Consequently our P V product will never be 0. We are assured of that mathematically not equal to 0. So a simple way a simple method is to consider that the product is product P V itself multiplied by some constant represents our temperature. So one way of defining is define a reference state, reference say system define a reference T for this call it T naught, reference state say naught rather than a or b let me say reference state naught. And then for example we can define T as T by T naught is P V divided by T V divided by T V naught. This would be one method of defining it. There are other methods this is a ratio method you could have a linear method but because we know that P V can never be 0 a ratio method is okay. We are sure that in the denominator we will not not P V naught P V naught or P naught V naught in the denominator okay. And again there is certain amount of arbitrariness because we are free to decide what the reference system is what the state 0 of that reference system is and we are free to define what the reference temperature T naught should be. So I can define see warm water it has been taken away warm water is my favorite so that could be my reference state and I may say something like 1050 that is my favorite number that could be it is reference temperature and I would have a ideal gas thermometer based on the Gaitonde scale of ideal gas thermometer. Somebody may like ice cream Amul ice cream of some flavor Amul vanilla ice cream as bought from some particular shop that could be your reference system before it melts what is it is temperature that could be your reference state and you may call it you cannot call it 0 then we will have problem so you can say T0 is my 100 for that and you could have your own Amul ice cream temperature scale based on ideal gas thermometer. So this is just to impress on you that arbitrariness is involved and arbitrariness is not good then each one of us will start speaking in a different language and we will just not be able to communicate with you. So what we have is the ideal gas Kelvin scale to which we now turn our attention Kelvin scale ideal gas here the reference system is a system containing water plus steam plus ice as appropriate reference state the so called triple point what do we mean by triple point from the high school may know what is triple point and again link this up with the phase rule the phase rule says that number of phases plus the number of degrees of freedom is number of components plus 2 here there is only one component the right hand side is 3 number of degrees of freedom is the number of variables from the pressure temperature pair that you can independently vary but if the right hand side is 3 and number of phases is 3 the number of degrees of freedom is 0 that means you cannot vary pressure you cannot vary temperature they have fixed values that is the triple point then all three phases are together your pressure is fixed your temperature is fixed here pressure is of no use to us but the temperature is of importance yes sir yes in physical chemistry lab you can create a triple point without much difficulty all that you need you have to experiment a lot because it is the only the amount of mass which is in your control put it in a sealed thing put it in a refrigerator and you can demonstrate triple point I have seen it being demonstrated in the thermodynamics lab of chemical engineering there was one professor Kutcher maybe that apparatus still exists one could demonstrate not only for water but for many organic fluids the triple point the vapor liquid equilibrium and also the critical point if our water the critical point is very high in pressure and temperature but for many other organic fluids it is only a few bars and maybe even 100 125 okay if you look up some oldish text books take for example a book by Lee Sears engineering thermodynamics published in 30s or 40s it will have actual pictures of these otherwise one should be able to hunt them out now on the internet anything is available it is a bit difficult critical point is very difficult to create because 220 bar pressure is no joke but triple point is not very difficult to create okay thank you sir. So triple point is fixed P and fixed T fixed state in state space fixed P is something we are not interested but fixed T is something we are really interested in so that gives us the reference state so this is reference system this is the reference state 0 we also have to define T0 reference temperature and T0 we will soon see why this funny figure is used this is 273.16 K definition I will explain why this particular clear figure was used in a few minutes let us complete the discussion and then the temperature of any system T was defined as as earlier so on the ideal gas Kelvin scale how do I measure my temperature I create a system containing an ideal gas first I bring it in thermal equilibrium with a system containing triple point of water that means this system should have simultaneously some water some ice and some vapour in equilibrium with each other bring this ideal gas in thermal equilibrium with that measure its P measure its V we do not care what PV individually are we are interested in the PV product then bring that system in thermal equilibrium with me I should hold it in my hand wait long enough so that there is no more thermal interaction and then measure the PV of that and then apply this and I will end up with T may be as 310 Kelvin since I am a human being and I am reasonably Hela and Halti will not be more than 1 degree Kelvin on either side of 310 Kelvin this is the definition of the ideal gas Kelvin scale it is based on the triple point of water it is based on the definition that the triple point of water has temperature of 273.16 k and it is defined using this interpolation law again it is arbitrary in the sense that the triple point is an arbitrary decision we have selected thermodynamics has not dictated again the value 273.16 we have selected why I will explain later and this it is one of the simplest interpolation routine now the reason before you ask me why such odd thing the reason for decision of 1, 2 and 3 is as follows the Kelvin scale was established the Celsius scale and its relations like Fahrenheit etc. But particularly the Celsius scale was well established so people wanted a scale which would align itself well with Celsius temperature for example we are comfortable for medicinal purposes or even in America they still talk of daily temperatures in Fahrenheit but even a school kid can convert from Fahrenheit to Celsius because all you have to do is do one multiplication and one addition or subtraction right from Fahrenheit subtract 32 divide by 1.8 and from Celsius multiply by 1.8 add 32 simple enough but if you say you have to take a sine function and then some inverse logarithm or exponential something then people will get scared right. So a simple rule should exist preferably between the Celsius temperature and Kelvin temperature if we define the Kelvin temperature this way it turns out that ice point I will put triple point and steam point on the Kelvin scale this is 273.16 Kelvin and putting it in block because it turns out to be exact by definition on the Celsius I would say old I will tell you what is old and new. Ice point was exactly 0 degrees C steam point was exactly 100 degrees C again in block means exact and the triple point turned out to be 0.01 degrees C I am not putting it in blocks means it was almost exactly but not defined to be on the Kelvin point this turned out to be 373.15 Kelvin this turned out to be 273.15 giving you T in Kelvin of a system to be approximately equal to T in Celsius of the same system plus 273.15 this is for the old Celsius and this was a very simple conversion factor to Celsius at 273.15 you get the Kelvin temperature and to Kelvin subtract 273.15 and you get the Celsius temperature it was for this reason that 273.16 for the triple point of water was selected. Now the question is when we do exact measurement and remember physicists and chemists they are particularly physicists they are mad after as exact a measurement as possible they will go after measuring the gravitational pull of earth to 7 decimal places they want to know what is the variation in the standard kilogram apparently it is varying for some reason in one part per billion per year or something speed of light they want to measure it to as accurately as possible. So something like this an approximate link between Kelvin and Celsius is something which makes them uncomforted. So what they did was they want to get rid of this approximation. So they said this old Celsius let us be forgetting so we define the current Celsius I will just call it current but not continue with it the current Celsius temperature is defined as temperature on Kelvin minus 273.15 definition. So that there are no two independent definitions of temperature today our Celsius scale is defined in terms of Kelvin scale the Kelvin scale is defined using ideal gas demand and because of this on the current Celsius scale what is exact this is 0.01 degree C this is exact is this 100 degree C yes it is 100 degree C almost exact but not definable anymore as 100 degree similarly the ice point is 0 degree C not exactly not defined as 0 degree C as earlier but to an excellent approximation it is 0 degree C to a very small fraction of a degree 0.000 something yes sir. So instead of selecting triple point as reference state that is we have selected 273 what will happen if suppose if I select 200 all that will happen is this will become 200 this will become something may be 340 this will become something like 155. So instead of such a simple relation you will have a Fahrenheit to Celsius type of relation there will be some factor here and this will be some different value there will be a multiplication involved along with a addition and the advantage of this is much of our data particularly specific heat data which is so many kilo joule per kilogram per degree Celsius now a difference of 1 degree Celsius is also a difference of one Kelvin. So all our specific heat data all that in the denominator degree C you replace it by Kelvin that is it no change takes place. Is it by trial and error 273.16 it is by derivation you say let that I think somebody would propose that scale we will let that be some x what should x be so that the temperature difference on Kelvin scale between steam point and ice point should be 100 and then x turned out to be 273.16 that is how it was arrived in a way it is trial and error but trial and error is not necessary because it is a simple equation you can solve for an unknown. Sir Kelvin scale we have defined that T upon T 0 is equal to P V upon P V 0. So for the particular system that should be behave like a ideal gas only. Yes the if you see Kelvin scale is for an ideal gas the reference system is this but our thermometer is a system containing an ideal gas. When you want to measure the temperature of other system than the ideal gas. So I am it is a thermometer I measured my temperature using that ideal gas thermometer I gave an illustration there is hot water in this how do I measure it is temperature by thermometer I can use a mercury in glass but I can always use an ice the Kelvin thermometer ideal gas I will create a cylinder piston arrangement containing an ideal gas create another system say this is my system containing triple point put it in thermal contact with this see to it that it is in thermal equilibrium that means both of them have isothermal state same temperature measure the P V 0 product then put it in contact with this open it and put it in thermal contact measure the P V product the ratio of this P V to that P V 0 is the ratio of T to T 0 P V 0 is measured P V is measured and T 0 is defined as 273.16 the only unknown is T which I solve for it will turn out to be if it is drinkable I hope it is it is not more than 44 or 45 Celsius. So 273.14 273.15 plus 45 whatever it comes to it will come to 316 or 317 that is the temperature of that in Kelvin. Now Kelvin temperature is very useful for all thermodynamic calculations and all data but traditionally we have been very comfortable with Celsius and that is the reason why we have redefined Celsius in terms of Kelvin so that there is no confusion there is only one definition everything else is in terms of that. Sir it is our understanding may be misunderstanding that the Kelvin scale has been devised on the basis of the internal energy like 0 internal energy is 0 Kelvin. We have not talked about where the internal energy is 0 because energy any form and internal energy is no exception to it is always with respect to some data and the first law has defined internal energy or energy only in terms of a difference only differences in energy of any kind are significant we may think that kinetic energy is 0 when the velocity is 0 but then the question comes velocity is 0 in which frame of reference and we have enough illustrations of a person standing on the platform and a person standing in the train. All molecular activity becomes 0. Did we talk of any molecule so far? No. Our thing is a continuum system so do not bring in molecule. At 0 Kelvin the product PV is it becomes 0 because. If you reach 0 Kelvin the product PV will be 0 I agree. So, in that case how this product will be 0 means how to interpret this that volume will be 0. We will come to that after the second law because currently the Kelvin scale the ideal gas Kelvin scale is absolutely arbitrary it has no thermodynamic basis it is only after the second law using the second law of thermodynamics will be having a proper thermodynamic basis for measurement of temperature thermodynamic basis for assigning temperature and there we will have a thermodynamic Kelvin scale unfortunately the word Kelvin is used either way but immediately after that we will be able to show that the thermodynamic Kelvin scale and the ideal gas Kelvin scale are numerically the same at least ideal gas Kelvin scale we are able to in a physics laboratory create because we can have a small system containing a gas at very low pressures which will behave as exactly as you need as an ideal gas but the Kelvin thermodynamic scales requires a reversible engine to be executed which is nowhere near possibility of execution. It is excellent as a thermodynamic definition it is horrible as a practical definition. The ideal gas Kelvin scale is good enough even for a practical definition it can be approximated the thermodynamic measurement of temperature cannot even be approximated but we define that we have already defined an ideal gas scale we will show that the two are numerically equivalent and that way we will provide a thermodynamic basis for the temperature measured on the ideal gas Kelvin scale and say that because they are equivalent although we have measured it on an ideal gas scale they are the thermodynamic temperature okay but we need at least one more day which one as he is asking no he said 0 Kelvin he was talking about 0 Kelvin you are talking about 0 Kelvin not on 0 Celsius there is nothing special about 0 Celsius no it is an assigned value you asked you asked a good question that now that we have Celsius temperature defined as triple point must be 0.01 degree C and Kelvin temperature defined as at triple point to 73.16 K that means that on the current Celsius scale and on the Kelvin scale temperature of the triple point a system which is properly created as the triple point of water system the temperature will never be measured if tomorrow you have a entrepreneur friend who comes with a very jazzy thermometer and said I measured the triple point of water's temperature and my thermometer indicated it to be 0.01 degree C you say okay you did not measure it all that you demonstrated is that your thermometer is displaying proper temperature because the temperature of that system has to be 0.01 degree C if tomorrow he measures it as 0.02 degree C he cannot publish a paper saying all the earlier data was wrong people will say your thermometer is useless better get it calibrated so that it shows 0.01 degree C for the triple point of water that has been taken yes it is taken so that is why what I showed here the block and here are defined temperatures earlier for Celsius 0 and 100 were defined temperatures today they are not but this 273.16 is accidentally so good that the real boiling point of water is 100 point I think 302 or something like that nobody worries about that similarly the ice point is almost exactly 0 degree C no steam table will show it as 0.01 if at all it is shown it will be 0.01 even 2 decimals which is the maximum temperatures are tabulated to it is 0.00 degree C and steam point is 0.00 but it is not mathematically exact mathematically exact numbers are triple point 0.01 degree C you put any number of zeroes after that they have to be all zeroes yes sir is there any specific reason why we are not using degree for Kelvin okay that is because the earlier thing was that temperature has something to do with degree of hotness that degree of hotness came with degree Celsius degree Fahrenheit okay with Kelvin it was realized that there is no such thing as degree of hotness and hence when it came to Kelvin consciously that degree was dropped now the question is when you come to Celsius why do we continue with degree Celsius but when we say scientists will say my temperature is 100 sorry 37 Celsius it is not correct to say 37 degree Celsius but it is okay to say when we write it we write it degree Celsius because C is already used as the unit symbol for Coulomb so if we use C as a symbol for the Celsius temperature there will be confusion you will have to see what you are talking about okay so better write degree C so tomorrow you choose something which is say kilo joule per C divided by C you know that you are talking about some thermal effect if it is degree C whereas we will be talking about some electrical effect because that charge is transferred again some work will be done so kilo joule per Coulomb may also be a useful entity somewhere so just to remove that confusion in symbolism we continue with degree C yes madam for this Kelvin scale we have taken the reference system as water, steam and ice at triple point at triple point the reference state is triple point so that T naught which we have arrived at as 273.15 16 16 1 6 1 6 is it not the product of P naught and V naught measured at that point no no it is only see I have not said what is the mass of that ideal gas system it could be large or small if you have a large system or if you have at a reasonably high pressure and higher volume your PV naught will be large but correspondingly your PV will also be large it is totally arbitrary it is totally arbitrary in fact one of the reasons for telling all this and discussing is to impress on you what Brahmara said that yes it is arbitrary we are doing it for convenience and hence by convention we are following yes madam in one of the heat and mass transfer question sir to calculate q we use the formula del T by k no del T by resistance that is in conduction no but that is heat transfer no sir in that question paper it was given the temperature difference as 5 degree centigrade okay so what our students did they added plus 273 and they calculated the value see that that is funny the question that when you say temperature difference of 5 degree C the temperature difference is 5 degree C the temperature difference is also 5 Kelvin because when it comes to temperature differences a delta T in degree C is also the same delta T in Kelvin in fact this 273.16 has been arrived to keep that so what the students did was not right it is wrong sir but in the question paper they instead of degree C they are given just to the numerical value then it would have been. See in the in the I will tell you I will tell you the confusion that happens and the confusion exists even in thermodynamics soon after this we will define a quantity called specific heat the unit of that will be joule per kilogram temperature difference which can be represented either as degree C or Kelvin okay but this joule per kg degree C or joule per kg K if that C or K degree C or K represents the presence of a temperature difference later on we will have entropy okay so that will also be kilo joule per kg Kelvin but there that Kelvin represents temperature itself so for entropy we cannot make it degree C because that is temperature itself whereas here it is DT or delta T so for specific heat whether it is Kelvin or C does not matter because it represents DT or delta T whereas in entropy it is it matters because it is absolute temperature itself so it is Kelvin nothing else when it comes to proper thermodynamics and entropy is a proper thermodynamic entity no replacement of Kelvin Kelvin has to be Kelvin period but when it comes to specific heat it is something some D something by DT so it is a derivative so it is a slope so the absolute value at the origin does not matter sir unit of R that is universal gas constant is joule per kg Kelvin or joule per kg degree Celsius which is correct no there it is Kelvin Kelvin because R is associated with T yes but R is also CP minus CV no that is a relation that is a relation we will come to that why it come and R is CP minus CV under very restricted conditions it is not a general thermodynamics now remember that we have defined where did it go we have defined ideal gas as a fluid which obeys Boyle's law all over its state space we know it is an idealization but we also know that it is a good idealization it can be approximated reasonably well at least for thermometry purposes but then it turns out that for engineering purposes physicists and chemists may not be happy but engineers are happy because for a large number of gases including air which is a mixture of gases over a reasonably wide range of pressures and temperature the behavior can be well approximated as an ideal gas and hence ideal gas the model of an ideal gas is a useful model to be used given by engineers for handling gases in a reasonably wide range of pressure and temperature.