 VLE is something which is all pervading in the background so far as distillation is concerned and more so with reference to experimentation or experimental determination of VLE. It has been going on for almost more than a century or even before that in crude form but over the last 50 years let us put it this way a lot of data has been generated by different people for their own purposes as well as some as an organized effort to generate VLE data and then model it to get theoretical and fundamental understanding or insight into what is all this about equilibrium between vapor and liquid which ultimately governs or limits what you can do with distillation. So from that point of view so far as experimental part of vapor liquid equilibrium is concerned it is almost unlimited the scope is unlimited and the kind of efforts that have been put into by people are also very vast both in terms of conceptualization and design of equilibrium cells as well as efforts to make the measurements as accurate and dependable as well as reproducible as possible. I have done my own post graduation work in the field of vapor liquid equilibrium and since those days my interest or primary love has been for thermodynamics in general but lately the efforts have been more on modeling and simulation rather than experimentation but I did continue after I joined the MS University the main limitation of course for me has been the funding that is now required to carry out the kind of experimentation and sophistication that is required. So the limited efforts which we have done at MS University are in the form of our collaboration with IPCL then he did some VLE data generation to design some of their own separation and combined reaction separation processes particularly with reference to acrylics manufacture. With this a bit of introduction so to say myself as well as the field of VLE I would begin with my presentation. To introduce VLE experimentation we can have a broader look out at why VLE. So we know that VLE data is needed for number one reliable design and simulation of distillation particularly and other separations where vapor or gas mixture and liquid is contacted and second is the insight that scientists as well as some engineers want to get into this behavior so that you can predict it without going in for experimentation and that is in the form of development of models for phase equilibrium. So these are the two major fields for which we require VLE data. The data that we generate or predict or estimate is used in the form of isobaric temperature liquid composition vapor composition or isothermal pressure liquid composition and vapor composition data. Out of this of course what is of primary interest in distillation design simulation etc is the isobaric data the boiling point data so to say and therefore that is of primary interest in which lot of people have worked both in terms of experimentation as well as prediction or estimation of VLE data. Usually from experimental determination point of view or measurements point of view the VLE data is usually available as primarily the isobaric TXY data because it is easier to operate your VLE steel by fixing your pressure and then go on measuring your boiling points rather than the other way round and therefore that is the primary data that is available. The other data that we have need for and also is getting generated is the isothermal PXY data. So these are the two main forms of data which are made available by VLE experimentation. Let us look at the tasks which VLE experimentation or an experimenter has to do in totality. There are two primary tasks which we can relate to one is task number one to generate the liquid and vapor phases in equilibrium with each other which is primary because that is what you want to measure and one should do this by keeping fixed value of temperature and fixed value of pressure which is also to be measured. So at fixed and sensed values of temperature and pressure you want to generate a liquid and vapor which are in contact with each other long enough so that they are in equilibrium with each other that is the first primary data. If we look at this generation of vapor and liquid in equilibrium with each other from the fundamental thermodynamic point of view then the real theoretical true equilibrium will exist only if your system is supposed to be isolated. We know from thermodynamic point of view open, closed and isolated are the three systems. Only the isolated system in any manner not necessarily only in vapor and liquid but any system for it to reach equilibrium ultimately it should be an isolated system. And therefore although we have said that the first task is to generate vapor and liquid which are in equilibrium with each other which are in true equilibrium with each other. We have to ensure as far as possible that the system is isolated there is no exchange either of mass or energy between the system containing your two phases vapor and liquid and anything which is outside. But at the same time we can also have a look at why do we need VLE data. In majority of situations as we know in this case for example we need it for designing distillations. These distillation column also are not going to operate as isolated system they are going to operate as steady state flow systems may be or back systems. So either of these two do not fall under the isolated system category. And therefore since the operation is also not in an isolated system or our interest ultimately from use of VLE point of view is not in case of an isolated system we may as well make some concessions and not let the system being isolated from which we want to measure what is the vapor liquid equilibrium. And therefore here there is this question of isolated true equilibrium system and a steady state dynamic equilibrium system. We have to see from experimentation point of view what we want whether we want to go in for this kind of system or whether we want to go in for this kind of system. The other task is of course once you get all these things in place we must know what their numerical values are and therefore we must be able to measure the temperature pressure and the composition of liquid and vapor not necessarily always sometimes we let go one of the phases say vapor and measure only the composition of liquid. So therefore that is the minimum measurement sensing recording and measuring that we have to do the temperature the pressure and the liquid. Here there is some kind of if I may say so we can bring in the principle of uncertainty. We want the equilibrium to be true equilibrium so that theoretically true temperature pressure liquid and vapor compositions are established but at the same time we also want to know their values. So while measuring we may disturb the actual equilibrium which may exist and therefore in totality taking these two tasks, task one as well as task two together gives us something which is a compromise between the two and that is where most of the efforts and such a wide variety of efforts by different people lies what do you want to achieve? You want to achieve best accuracy of measurement and at the locations where it exists or whether you want to get the true equilibrium values. The other problem associated with this is of course the time element involved the effort not in terms of only money but also in terms of time that is required so far as generation of the vapor liquid equilibrium data is concerned. The second point that I have indirectly said is the sampling and analysis of the liquid and vapor for composition it is here that majority of the problem comes in. So far as knowing the exact equilibrium values of X and Y that is the liquid composition and the vapor composition during sampling there are so many difficulties which may give you a sample which may not be the true liquid or vapor equilibrium sample that we desire. Having said all that people have and we have to continue doing generating the data. So let us have a look at what is a general idea of the VLE setup that we can have or what are the components of a general VLE setup? There are four important plus the fifth one which I would put it because that really gives a lot of it is an important factor that we put it this way. You may be able to get all these four but the fifth one is something which probably luck can get you that. The first one of course is the VLE still or the sale as it is alternatively known. The most common names to the heart of the VLE experimental setup given is either a still or a sale, so VLE still or a VLE sale. Then of course the control system because as we have already said we want to maintain temperature, we want to maintain pressure, we also want to maintain certain state of matter so far as the different vapor and liquid is concerned and their compositions and therefore control system is therefore one of the very important and crucial component of the VLE experimental setup. Then you require the analysis instrument or methods for composition and a lot different type of ancillary apparatus or systems for this and this two components of the system to work properly and to ensure that nothing else creates any problem in the equilibrium compositions with reference to purity as well as the balance between vapor and liquid compositions. So for that therefore there are a lot of ancillary apparatus as well as ancillary systems which we the fifth one is as I have said a willing worker, lot of data generated so far even today has lot of manual component in it. You can replace a willing worker with a willing servant in the form of automation why I have written this fifth is that now there is a lot of trend towards going in for automation. So some companies have even come out with complete VLE setup automated VLE setups where the human element or manual element involved is very least and therefore that is where why I have and probably I will talk or rather only refer to one study by a group which has attempted this automation to bring in automation so far as generation of VLE data is concerned. So that is the fifth one as I said this is the heart of the system this is the environment which is necessary for the system and this is something which always stays in the background you cannot work you cannot achieve these two without this that is the fourth one ancillary apparatus or system. Once we have this broad idea about what is the experimental setup required for VLE automation let us have a look at the experimental techniques or experimental methods which one can talk about or broadly speaking divide all the efforts that people have put in so far into. There are many ways of even looking at this one can look at the experimental techniques from the viewpoint of the method and this is given by one of the most famous and important book or a monogram by Raal and Moolbauer which talks a lot almost 50% of the book is I think if you have the notes I have given the reference of that book also almost 50% of that book is devoted to experimental techniques that is measurement of the VLE generation. So from their point of view the different techniques can be classified into these five one is the dynamic method which may be recelculating dynamic method or a flow dynamic method second is static method these two methods are actually directly related to what I discussed as the true thermodynamic equilibrium component and the steady state dynamic equilibrium component. So that gives us these two different type of methods automatically there are what he has separated as semi micro techniques which are really part of the static methods majority of them unless one devices methods which require very small quantity of material as well as small dimensions of the element that is the steel which falls under the recirculation time otherwise this semi micro techniques have been evolved on their own because of their importance particularly dealing with chemicals which are very costly or which are which cannot be handled in large quantities because of other difficulties. Then special techniques for measuring what in thermodynamics is known as infinite dilution activity coefficients this is one method of avoiding getting experimental determination of compositions throughout the range from 0 percent to 100 percent of a particular component. If we can obtain data only on the very dilute region but a very precise and accurate data then that can be used from thermodynamic relationships to generate or estimate the complete data or alternatively this IDAC is now important from pollution point of view and therefore this technique has been referred to separately as IDAC measurements of course it also requires special experimental techniques as well as special experimental setups for measuring that those infinite dilution activity coefficients something which is easier to visualize and probably think that easiest to do is to determine the dew point and the bubble point methods dew point and bubble point of systems and therefore those methods which measure either dew point or bubble point of a given mixture they are referred to as dew point and bubble point methods they are relatively simple because one of the most the greatest advantage of these methods is you do not have to take any sample and measure its composition that is the one greatest advantage for these methods which we have. Let us have a look at the other way of looking at what are all these different techniques of VLE data generation if we look at it from the apparatus or equipment point of view that is the heart of the system that is VLE steel or VLE cell then again we can group them into five different dynamic VLE cell ebuleometer I have kept this separate although many times this is part of what is dynamic VLE steel then you have what is called as static VLE cell not steel because the operation of steel and a cell is quite different from each other and therefore these are referred to as cell whereas these are referred to as steel then you have the flow through cell and finally again the same thing what I discussed in the previous classification as dew point and bubble point techniques from the very name this dynamic means there will be some movement of material inside and it is quite likely that it may do something as exchange with surrounding right and therefore that is quite likely whether you want it or not this dynamic steel or method will always have something to do with surrounding and therefore we have to be careful about that as compared to that the static cell VLE usually is at least physically isolated and therefore does not or has minimum interaction with the surrounding but at the same time there are some disadvantages of this as well as some disadvantages of this probably we will go along as we go along we will see so let us see some details of these from the based on the equipment or apparatus what we have here the dynamic VLE steel approach can be depicted conceptually with the help of this I hope it is visible properly this in the very brief tells you what it will consist of the dynamic VLE steel there is this heart of the matter as I said the place where vapor and liquid are going to be present you may start with a liquid so you will take a liquid but generate vapor inside or it is quite possible that you will start with both liquid and vapor separately and then bring them here and mix them so that is where you have this usually since vapor will be generated from liquid which is taken in you will have a heat source which will therefore generate vapor from liquid which usually is a superheated mixture of this once you separate it as is written here in the separation chamber or separator the vapor is taken to a mixing chamber where it condenses first and then mixes with the distillation or the distillate already getting collected right this mixing chamber also refers to something which may be physically not present in the actual equipment which we see but the distillate which is generated from the vapor that distillate is mixed back or recirculated with the liquid which is boiling and therefore this so called mixing chamber may be bringing about mixing of the distillate with the liquid which is already getting boiled and therefore this mixing chamber is where actual the heat source will supply heat to this is only therefore this will show us only the flow that will take place in mixing it is preferable that there is a separate location of mixing of distillate and liquid and a separate location for generation of vapor from the liquid but this is very difficult to achieve in practice and therefore as we will maybe see later on the difficulty or inaccuracy that crops in so far as many really stills are concerned is this simultaneous mixing and heating at same location can generate problem due to heat being absorbed by the distillate directly before it gets mixed with the liquid this can give rise to a generation of vapor which is not really in equilibrium with the mixed liquid but is in equilibrium with the distillate which is coming in and that is where if you see the books majority of modifications of the original vapor liquid stills which people have come in has been done so so far as design of equilibrium stills are concerned their effort is partly directed towards removing this difficulty that there should preferably a separate mixing chamber and then the mixed liquid only should receive heat and get vaporized and therefore the vapor is in equilibrium with the liquid which is left behind and then you sample them so that is where this is now as is shown here vapor is also separately shown to be moving or circulating liquid is also shown to be moving and circulating but in reality all the liquid VLE stills do not have this provision therefore broadly they can be classified into two types of VLE stills dynamic stills one is one those stills which have only vapor recirculation and therefore there is no liquid which is getting circulated liquid is steady in one particular location of the still vapor gets evolved gets condensed and comes back to the same liquid at the same location from where it is getting vaporized there are some where the design also has provision for circulating liquid so liquid is getting boiled at one location it is then taken to another location where liquid and vapor separate from each other so that the actual equilibrium is established at the location where vapor and liquid are separated from each other and therefore the measurement should be at that location these things will become clear to you but what I am trying to say is only this that either only vapor recirculating or vapor and liquid recirculating are the two major types of stills VLE stills that generally are used so far as dynamic stills are concerned and then of course you have this requirement of pressure control and pressure measurement so this is about the dynamic VLE still from applications and other features point of view these are some of them for example as I said many designs have come in that means this particular dynamic VLE still is the one which is at a mature stage of progress important parts of the VLE still therefore are the following one is boiler where heat is given to the liquid and vapor is generated the other one is cotrel pump which may or may not be present in some of the stills the purpose of this so-called cotrel pump is nothing but make the liquid circulate through the VLE still so if you want a VLE still in which liquid is also getting circulated then the most common method adopted is to generate or is to put in a cotrel pump this cotrel pump is not a mechanized pump but something which exists due to simple heat absorption by the liquid if you provide a very small constriction like if I may say so calendria of a evaporator or crystallizer what happens there is vapor is generated at different locations where heat is governed but heat is not taken up by all the liquid and therefore at different locations bubbles of the vapor are generated if you provide the flow cross section area very small then the vapor occupies the complete cross section and there is a there are slugs of liquid separated by bubbles this is what cotrel pump is supposed to do so that is where vapor vapor bubbles are generated separated by liquid slugs since they are vapor vapor bubbles they will move up and carry along with them the liquid that that kind of pump is called a cotrel pump so that is the function of the cotrel pump for circulating the liquid then there is a third component possible if these two are enough then you do not have this that is a vapor and liquid contactor but if these two are not enough or this is not present for example cotrel pump is not present you are not provided for it then you must have these two locations the boiler as well as a separate vapor and liquid contactor it is here that the task number one namely generating the vapor and liquid in equilibrium with each other will be generated so the you in some designs you have a vapor and liquid contactor separate totally different locations from either boiler or cotrel pump it is quite possible that in some designs all the three boiler cotrel pump as well as vapor and liquid contactor is present then of course you must bring them back because it is the same material which is getting present nothing is coming in and nothing is going out because it is still and therefore you have the recycle loops for both condensate and or liquid that is liquid recycle loop may not be present but condensate recycle loop is always present something which I have specially mentioned here although it is apparently not significant is what is called as drop counter this feature has to be present inside a VLE steel because it is an indirect measure of how much heat or energy is being supplied whether that will result into overheating or providing less energy for true equilibrium to exist that is your heat supply must be just enough to take care of whatever changes which are taking place including the possible loss which may occur loss of course is partly prevented by insulating providing vacuum jacket etc etc but whatever is present inside what is happening inside for that you require just the right rate of heat input in for which the apparent indication is what is the rate of condensate generation and therefore this so-called drop counter is a small design feature static part of the equilibrium cell or dynamic cell which is present which gives you an indication of what is the rate of condensate formation which means what is the rate of evaporation from the system probably in one of the images that I will project I will show you what this drop counter is and then you have to provide for sampling ports for the vapor and liquid which is generated vapor of course is not taken out as vapor but is taken out as condensate in majority of these dynamic cells and therefore both of them you have to provide sampling for liquid system rather than vapor and liquid. Majority of data generation so far of course has been up to one atmosphere because that is the range of pressure of interest for distillation as the major operation in which this is used and therefore lot of systems have been put into place majority of them have been glass VLE steels and they are very common so far as pressures up to one atmosphere is concerned there are also many steel and other material VLE steels available fabricated by different people and used at much higher pressure including up to 40 to 50 atmospheres but they are relatively rare as compared to the glass apparatus that we have these are some of the names which are associated with it you will find them their designs or details of this in any of these books. Othmer is the most the oldest steel that we have Gillespie, Jones, Erasunis and Raal I think what you would have seen if it has it was shown already by it was Raal apparatus that you must have seen. Majority of the designs which are being used today are based on this what is called as Erasunis steel Raal apparatus which I am referring to is also a modified Erasunis apparatus but yes as I said this is the oldest and therefore you will find hundreds of modifications of the Othmer steel you could call even these also as modifications of that because Othmer was the oldest or the earliest or the pioneer so far as Viennese steel are concerned. I have as I said earlier made spatial mention of Ibilometer if not for anything else for the reason that this is the simplest equipment and therefore the cheapest equipment that you can have it is also easiest to handle because it requires minimum processes to take place inside the VLE steel and therefore this is something which can be used when you do not have or you cannot depend on any estimation of VLE data must carry out some experimentation but do not want to spend time energy and effort on VLE. This is the easiest way out for those experimenters who want to generate VLE data but do it with minimum efforts and therefore Ibilometer is one of the most important equipment to be used. It is also part of a major setup of VLE equipment as we will see later on. We are looking at the step before that that is to generate the boiling point vapor pressure data. So Ibilometer is the equipment suggested for pure component boiling point vapor pressure data. You need not go beyond that why for the simple reason that since you will be taking a pure component there is no difference between the vapor and the liquid so far as composition is concerned. Both of them are pure components and therefore what you are trying to find out is only very precise boiling point temperature by maintaining a very accurate constant pressure in the cell that is all that you have to do and for that Ibilometer is the ideal equipment so far as this is concerned. So far as VLE is concerned Ibilometer is adapted to finding out say boiling point of a given mixture or vapor pressure of a given mixture. So it is a question of we are using the equipment which is primarily enough for a pure component VLE measurement because boiling point vapor pressure is nothing but pure component VLE for a mixture and therefore usually Ibilometers are used widely for binary mixtures particularly to find out boiling point. It is because of this reason that the data that you get from Ibilometer will have one limitation. In Ibilometer because your purpose is not really to get any sample of vapor or liquid out and analyze it we do not need to do that even for a mixture but then what will you get for a mixture what you will get will be or should be whatever composition that you use to feed the Ibilometer for that particular composition you will get what is the equilibrium pressure if you maintain a temperature or if you maintain the pressure you will get the boiling point. So what will you generate will be actually only P versus X or T versus X data because you are not taking out any sample. If required you can take the sample and only to confirm that the sample of the liquid that you get is same composition of that is same as what you have fed because the design of Ibilometer ensures that the volume occupied by vapor is so small that the liquid which is there present in the equipment does not undergo any major change of composition from the feed. So although part of the liquid has been vaporized the moles of vapor generated are insignificant as compared to the total moles present and therefore the composition of the liquid is same as what is fed and therefore if you know it you do not need to take a sample and measure it and therefore this gives that is the reason why this gives a very quicker method of generating VLE data but it is not complete data maybe I would not have occasion later on to say anything about it therefore there is one limitation so far as VLE data is concerned. Whenever we generate VLE data by experimentation we know that usually we test it against consistency test right thermodynamic consistency test based on Gibbs-Duhem equation are usually applied to any experimental data which you generate for vapor liquid equilibrium and therefore that kind of test or that kind of consistency test cannot be applied to data generated from Ibilometry that is one major limitation. So if you are a stickler from thermodynamic consistency point of view then you will not use Ibilometer as your equipment because it does not lend itself to thermodynamic consistency check for the VLE data generated whereas other stills will provide you with usually both vapor as well as liquid compositions and therefore you can use the thermodynamic consistency test for those kind of data. Other stills also have sometimes some designs have problem which we will probably see later. This has provision for recirculation of both vapor as well as liquid in other words therefore cotrel pump is an inherent part of every Ibilometer. No sampling for composition determination is necessary as I have already indicated and therefore can rapidly generate pure component vapor pressure data as well as isothermal Px data for mixtures. I have already said it can also generate Tx but what is preferred is this rather than Tx data because for Tx data you have to maintain a constant pressure whereas it is easier the equipment is small and therefore it is possible to have a thermostated environment to maintain the temperature and then you find out only the pressure at which your mixture boils. One variation of this Ibilometer is a two stage or what is called as differential Ibilometer. It measures both boiling as well as condensation temperatures as I said in case of pure component they are both same but for a mixture they can be different why because liquid and vapor are at their bubble point and dew point which are quite different if you take temperatures since the pressure will be maintained throughout and therefore you can measure both the boiling point of the liquid and condensation temperature. So therefore you have to provide two locations Ibilometer has to be modified two locations where temperature is measured at one location liquid should be boiling generating vapor at the other location vapor should be condensing generating liquid. This again of course can have the recirculation of both the liquid as well as vapor particular use or importance of this differential Ibilometer is in the generation of infinite dilution activity coefficient data. So if you see that Rall's book you will find a host of designs available for this differential Ibilometers in fact to be more precise with exact dimensions given for the complete equipment for the differential Ibilometer for generation of infinite dilution activity coefficients data. So if you see yourself doing something here then probably you can refer to that book and get designs with exact dimensions to get Ibilometer fabricated. Two names probably one Svito Slavsky is the oldest again as like Othmer Svito Slavsky is the person who first got this made and used it there is a design modification given by Thomas both of them Svito Slavsky does not exist in Rall's book so you will find some other book giving it but Thomas design is given in the Rall's book. So these are the two major type of Ibilometers that you will have. Next is the static VLE cell this is popular for isothermal high pressure VLE studies it is not that other studies cannot be done but major application of static VLE cell particularly for systems like this are for isothermal measurements and high pressure measurements so far as vapor liquid is concerned. In this case there is no need for sampling the vapor phase particularly if you are operating it at low pressure if you are operating it at high pressure then the vapor phase also has to be sampled the reason is same as what you have in Ibilometer. The amount of vapor present or the vapor space present in this still is so small as compared to the amount of liquid present is that that does not create any appreciable change in the liquid composition and therefore you do not need to sample it. So there is no need for sampling the vapor phase but complete degassing is necessary this is something which is quite different or absent in the dynamic VLE still by degassing we mean any liquid as we know under storage will absorb lot of gases in its environment and they will be present here in this particular cell because usually there will not be any so called boiling of the equipment of the liquid and therefore recirculation of the system you will not have or rather the vapor space being very small will be therefore concentrated with the inert gases which are previously dissolved in the liquid but are now released inside the cell and therefore before you charge your liquid inside the cell or preferably after you charge the liquid in the cell and then actually start measurement of the system or isolate the system you must ensure that all the dissolved gases must be separated because that will the amount of vapor is so small that even small amount of inert gases entering the vapor space will change the equilibrium drastically because of the relative amounts of inert gas and the actual component present in the vapor space and therefore degassing is a very important and essential feature of every static cell equipment that we have. It can also be used for idax as I have already mentioned here micro static cell requires very small amount but this cell as same as what I said as static VLE cell. In fact two Indian authors I forget the name one of them is Ray they have also proposed a design in which there are micro drop VLE cells the amount required is in the form of drop which can then measure the VLE vapor liquid equilibrium cell. So there is one design of so called micro static cell is also in the form of micro drop these are some of the good designs which are given in some of the books. So for a static VLE cell is concerned probably I will take one example of this bit later. Next is flow through apparatus that is you do not have recirculation but only one passage through the apparatus. As we see here therefore you have two different pumps pumping the two different components assuming that we are handling a binary which are pumped through to a mixer. So they will mix here maybe they will get heat or they would have already got heat here before they are pumped or during their pumping and then this mixer will provide provision for the liquid and vapor to separate and also to exchange matter that is mass transfer will occur they will reach equilibrium and then you have a separator so that they separate into a vapor separate vapor and separate liquid which are then taken out. Since this is a flow through apparatus although I have not shown it all these are the arrows can be taken as the flow out of these two. So you allow them to separate into vapor and liquid and then the vapor and liquid are flowing out you can then sample them from the two streams which are going out from here and here and analyze them. Again here you have this both temperature and pressure maintenance as well as measurement provision here. Temperature is not measured here where they are mixed but temperature has to be measured here where they are actually separating for the reason that I said earlier it has to be the same location where they are in equilibrium with each other. So this is ideally suited for temperature sensitive and reactive components because too much of exposure to high temperature or longer time is not required then for flow through equipment. The amount of mixture which you have can be quite high and therefore sampling can become easier as compared to some of the other designs but at the same time since larger quantity of materials will be required you will have a problem if the components are expensive and therefore this is not suitable for expensive type of components. The last is what we have already said as dew point and bubble point apparatus. It can be either a pressure measurement at dew point and bubble point or it can be temperature measurement at dew point and bubble point. Again one advantage of this is that you do not require to sample and analyze either a gas or a liquid mixture because in fact what you are doing is you are taking the whole system as a single phase. If you are trying to find out the dew point then what you are starting with will be a vapor mixture and just at the appearance of dew you want to know the composition, temperature, pressure etc. Since the dew will appear with negligible quantity of liquid and therefore moles contained in it will be negligible the composition of the vapor is same as what you have taken as the feed and therefore composition measurement need not be done. What you have to do is maintain pressure, find out temperature or maintain temperature and find out pressure. So that is how it is done but in reality how this is done because how do you know whether it is a rather a dew point has reached and a bubble point has reached. One of the ways is you can do it visually, have yourself, look at it and find out whether haze appears, that is dew appears or whether the last droplet of the liquid has vaporized so you get a bubble point or something like that. So that is what rather the first bubble appears from liquid so bubble point. That is of course very inaccurate method of doing it and therefore the actual measurement is quite different. The actual measurement is in the form of volume how that varies as a result of controlled pressure change. In other words this is nothing but a typical PVT data generation. You fix the temperature, change the pressure at known different values and go on finding out what is the volume. One of the ways of doing this will be do not actually measure the volume, you calibrate your equipment and knowing the position of the piston for example as can be shown here. Knowing the position of the piston you know what is the volume enclosed inside the equipment. You just find out the pressure for fixed value of volume that you have and therefore PV is what the data that you actually measure. But then how do you find out that the bubble point or dew point is reached, it is indicated by sharp breaks. In fact if we assume that the change between P and V is almost linear and it will be as I have not shown it but as you can see in some of the books the actual experimental plots of P versus V they are all linear except that you have three different linear parts of the graph of P versus V. One below the bubble point, another above the dew point and the other way round and one in between the bubble and dew point and therefore you will find a sharp break at two locations bubble point and the dew point that is how you measure it. In addition to that there is one more thermodynamic data that you get here automatically and that is the liquid molar volume of the system. You take different naturally what does it mean, it means that you have to repeat the experiment, what kind of experiment will it be, it will be an isothermal experiment. You maintain the temperature change P or change V and find out P, you have to repeat this at number of temperatures. So what you will get will be at different temperatures and corresponding pressure what is the liquid molar volume data. This is extremely useful if not anything else in some of the thermodynamic consistency tests also just as what is called as excess enthalpy or volume mixing enthalpy data is required. Mixing volume data is also required in some of the thermodynamic consistency tests.