 Good morning all of you. We begin our day 3 essentially where we left off yesterday. Yesterday we looked at properties of fluid particularly we looked at an ideal gas then a general gas but then saw it some problems essentially using ideal gas as a working fluid. Today we will continue and today's plan is to complete properties of fluids introduction to steam tables etc. We will essentially go fast through this because I think this is a part in which you will reasonably be comfortable with there is no new principle involved. There are only some slippery parts in the steam tables which all of us know are slippery we will take care of that. Then we will go to the second law of thermodynamics and 3 p.m. when we complete our thing today we expect to have completed properties of fluids the second law and maybe some problem solving using second law so that tomorrow morning we will be ready for property relations. Now yesterday when we concluded we now have a reasonable grass of compressible systems simple usually but if it is an electrolyte we know how to handle it. In this a general gas and we had a model of an ideal gas in all this we essentially considered that the fluid would be in a single phase typically the gaseous phase but when we come to a real fluid for example water it exist in 3 phases a part of it is a liquid phase part of it is a solid phase. So today we are going to first see how do we handle in a simplified manner liquids and solids and then we will move on to a discussion of the steam tables that means properties of what I will generally call steam but later on we will use a technical name for this and we will see the introduction of steam before we go to second law and I will rest a while and allow professor Van Darker to deal with you and with the second law. For a gas any gas we know that there is a relationship between p, v and t the equation of state the second relationship we know is the requirement that you must be specified as a function of say 2 variables t, v or something like that t, v, t, p similarly for h and later on we will need a specification even for the entropy. For an ideal gas we have very simple relations for this what is the difference between a gas and a liquid and a solid from a point of view of thermodynamics where we consider these to be simple compressible systems. System containing a gas is a simple compressible system so is a system containing a liquid so is a system containing a solid. If things we are not considering open systems then if it is a closed system it does not really matter whether the material inside is able to flow or not flow. So from that point of view when we consider a closed system whether it is a gas in it or a liquid in it or a solid in it basically it does not matter. So if we look at it from the state space point of view the differences would be something like this I am showing p, v diagrams if you have a gas we know that a typical isotherm this is my habit if I show a property with a circle surrounding it near a line or a locus or a surface that means that say surface representing a constant value of that property. So tomorrow iso isentropic lines will be shown with lines similarly for p, v etc. So this is typically what happens for a gas for an ideal gas it will be a rectangular hyperbola for other gases it will be not a rectangular hyperbola for a liquid when you increase the pressure the volume hardly decreases. So if you start with a volume like this and increase the pressure the isotherm for a liquid will be something like this as you pressure increases volume reduces slightly very slightly. In fact what I have shown here could even be an exaggeration for a solid it is still sharper is a constant volume lines solid will go almost like this. So if we consider compressibility of a fluid as the rate at which pressure increases pressure has to increase to provide a certain decrease in value then the sorry let me put it the other way the compressibility is the change in volume for a certain rise in pressure it is pretty large for gas and it is pretty low for a liquid and perhaps still lower for a solid that is the major difference we look at when we consider the difference between a gas a liquid and a solid but that does not mean that liquids and solids are not incompressible we have their bulk modulus or bulk compressibility is available to us but those values are much much smaller than that of a gas smaller to such an extent that quite often as a very good approximation a liquid and a solid within reasonable ranges of pressure not pressures where you go to thousands of bars but pressures of a few tens of bar may be a hundred bar they can be considered essentially incompressible and when you come to the steam tables you would notice that hardly any steam table will have a reasonably extensive property tabulation of the liquid zone below saturated liquid state what we call subcooled liquid water or compressed liquid water there will hardly be any tabulation because it is considered that that is a very that is an approximate zone of incompressible liquid and you will use the reader or the user will use certain approximations to take care of it so that brings us to the topic of the incompressible liquid or the incompressible solid the same model is applicable in either case mind you just the way ideal gas is an approximation it is a good model for many real gases in a reasonable range of pressures and temperatures the incompressible liquid or solid is also a good model for real life liquids and solids again over a reasonably narrow range of pressures how narrow that depends on what that liquid and solid is but typically this is a few tens of a problem bars not generally more than a hundred bar definitely it may not be valid when you go to thousands of bars and if you want to see how experiments were done at thousands of bars and look at the work of Pw Bridgeman I talked about him two days ago his book physics of high pressures is considered a classic and all that he did was okay you are measuring specific heat at a near room temperature and near ambient pressures he would measure the same specific heat and properties conductivities at very high pressures very high pressure means he is talking of thousands of bars so that type of experiments he has done anyway now our model is going to be for a general fluid you have one two way work mode and that is why this becomes a simple compressible system but when you have an incompressible liquid or solid does this work mode exist when you say incompressible you change pressure volume does not change so no expansion or compression work possible why because the density does not density or specific volume is independent of P it could be a function of temperature but it definitely is not a function of pressure in particular we can write rho could be a function of temperature or v could be a function of temperature and rho is not a function of temperature and pressure pressure cancels out for a general fluid this will be true for an incompressible thing there is no effect of pressure that means what we discussed yesterday the incompressible liquid or solid is a fluid with 0 two way modes of work now when some system has 0 two way modes of work how many properties do we need to describe the state of the system one property hence only one property describe state and naturally the most convenient property here would be temperature illustration is our mercury in glass thermometer and some such thing there could be something but the most convenient property is temperature because that links all systems so that means all basic properties would be functions of temperature and temperature only that means rho will be a function of temperature u will be a function of temperature s will be a function of temperature temperature only and pressure in particular pressure does not have an effect one exception I can always define a property containing a pressure and in that case I cannot get away with the effect of pressure so for example this the exception is we have defined H to be u plus pv for an incompressible liquid u is a function only of temperature agree p exist v is a function only of temperature and because of this presence of p directly here H will be a function of temperature as well as pressure in fact it will be linearly varying with pressure so this exception should be noted and we will come back to this in open systems when we have a simple pumping problems I am discussing this because I think most of our steam tables do not have the compressed liquid or the school liquid zone tabulated and we will have to use this approximation whenever we need properties in that zone at least at low pressures up to a few tens of bars if you want more than that then you better go to a big fat steam table the ACME steam table or one of those standard steam tables or use the formulation to compute the properties out is that clear now after these preliminaries we come to our favorite topic that is steam tables now steam tables is the end part but what do they tabulate they tabulate the properties of water at a range of at various pressures temperatures etc. Now the question is what do we mean by water here which water and which phases before that what type of water by the time students come to you they already know that there is something called light water and heavy water so which water are we talking about no we are talking about what is known as the ordinary water substance now water substance is the name given to what we call water in any of its phases generally if we see a solid we do not call it water we call it ice if we see liquid we call it water if we see vapor we call it steam water substance is the name given to all these 3 phases together so that we do not have to use 3 different words for the 3 phases so water substance is the name given also to the solid phase also to the liquid phase and also to the vapor phase where the normal name would be ice water and steam so when you if we say steam tables then why are saturated liquid properties listed here if we say water tables steam property should not be listed so the technical name is water substance indicating any one of these 3 phases having said that we will not be using the word substance quite often and as required we will be using water steam so long as we understand what we are talking about now what does this word ordinary mean we know that water exist in 2 different variations the light water and heavy water if we take the mean concentration of water on earth that means take sea water remove all everything except H2O D2O from it you will find that the concentration of D2O or abundance of D2O natural abundance of D2O is of the order of 70 ppm and it is very difficult to remove that of course D2O by itself is a very precious liquid so there are plants which use D2O as a working fluid many nuclear plants and hence extracting D2O from this 70 ppm availability is a big industry by itself these are strategic plants but nobody makes an effort to remove D2O from water and give us pure drinking water H2O only nobody does that that 70 ppm D2O has been there for ages and we are all comfortable with it so we use for drinking purposes household purposes and also for industrial purposes the naturally available mixture of H2O and D2O so the naturally available mixture of H2O and D2O is known as ordinary water substance so although your thing stays steam and other tables first thing these are not just steam tables these are tables listing the properties of the water substance this is a small steam table it may not have ice oh it has ice so it has all the three phases but then it should be tables of ordinary water substance ordinary because it guarantee nothing says about whether it is H2O or D2O naturally occurring mixture of H2O and D2O. Now at after saving this the next thing we should tell the student is that there are three phases solid ice liquid water and gaseous for vapor steam at this stage a student will ask what is the difference between a gas and a vapor what can be the answer isothermal compression you mean that would simply mean that any vapor below its critical temperature will be called vapor above that it will be called gas right that there is no proper definition of what is a vapor and a gas they are you know interchangeable except that we consider air to be a gas but we can liquefy air okay just by not by isothermal compression but we can liquefy air. So the use is relative if in during our calculation it is likely that it will condense by whatever mean then we tend to call it a vapor otherwise we may call it a gas but there is absolutely nothing wrong in replacing vapor by a gas and gas by a vapor they are the same phases we will not make any distinction between them however there is a very special thing whenever a vapor is in contact with its liquid part in equilibrium or otherwise we will talk of the liquid phase and the vapor phase there is nothing wrong in calling it a liquid phase and the gas phase in fact our subscript for the vapor phase will be g our subscript for the liquid phase will be F and that is the symbolism used in this steam table and many other steam tables. So a liquid a fluid is a general thing anything which flows with a fluid so both liquids and gases or liquids vapors gases are all fluids but we will be using vapor and gas interchangeable but in particular we tend to use vapor when its liquid is also nearby otherwise we are free to use gas there is no restriction there is nothing wrong in any place by replacing the word vapor by gas or gas by a vapor remember that now the moment there are three phases we should talk if we have not already talked about the phase rule and you should start by showing the what is known as the phase diagram of water when I say water hence forth I will generally mean ordinary water substance the phase diagram is usually shown on PT coordinates and we should show a triple point show the three phases show this point as the triple point show this point as the critical point and you tell the students that you take any substance pure substance no mixture of one gas and another gas the phase diagram will be something similar to this in nature the slopes will be different instead of this solid liquid line sloping inclining towards the left it may incline towards the right in many substances many systems but show it to this then tell them that the triple point is the point where all three phases are together in equilibrium and that means the phase rule says that P is fixed at P triple point T is fixed at T triple point and that is one of the reasons why the triple point temperature is used as a reference temperature for some reason the triple point pressure although being a naturally fixed value is not used as a reference pressure at least not yet perhaps because it is too low triple point of water we are fortunate in having it very near 0 Celsius but the triple point pressure is almost very very low it is good vacuum nowadays we have got much better vacuum but otherwise it requires really good vacuum then you also say that this solid liquid interface bring it to the notice that any point on this represents the melting point of that fluid at that pressure and remind them that we have notice that it is turning slightly towards the left indicating that at higher pressures the melting point decreases slightly that all of them know at the melting point of water decreases as pressure increases the boiling point of water increases as pressure increases the boiling points are represented by this you can show one line saying this is one atmosphere and if that is one atmosphere this will be 100 in degree C you can even say that the triple point will be at 0.01 degree C in the triple point pressure is something you can read off from the steam table 0.006112 bar this is approximately 0.0061 in bar pressure except for one atmosphere otherwise will be in bar and this point is approximately 0 degree C this you can show tell them they are all comfortable with this because this is the data which they have then you tell them that look at the boiling point as pressure decreases the boiling point decreases reaching the triple point temperature at the triple point pressure as pressure increases the boiling point increases but as the pressure increases the difference between the liquid and vapor as indicated by the difference between densities remember when liquid boils the liquid as well as its vapor will have the same pressure same temperature the densities will be different that is why we call them two phases. So this density goes on decreasing and there is a funny point known as the critical point at which the density difference vanishes this it takes the student a bit to appreciate this but tell them that look the liquid phase and the vapor phase are not significantly different from each other. So if the density difference is made to vanish the difference essentially vanishes and hence beyond this pressure critical pressure there is no difference between a liquid and a vapor both of them can simply be called fluids and we will call that as supercritical steam or supercritical water substance if somebody asks you whether it is a liquid or whether it is a vapor is it the distinction does not exist at supercritical pressures at this stage may be it will be a good if we take some photographs of that critical point and what happens surrounding it one of our exercises after this will be to hunt out such photographs from the net if you show them the meniscus vanishes then they will be able to appreciate this yes sir. Sir there is general confusion between the terms evaporation and boiling. No difference from a thermodynamic point of view. From a heat transfer point of view when you consider rate usually you know if I put a few drops of water here they will slowly convert themselves into vapor that is such processes are usually called evaporation whereas if you put the bulk of that on a stove and you see vigorous action of liquid forming into vapor then that is called boiling otherwise from a thermodynamic point of view both evaporation and boiling mean the same thing unfortunately we have those two different names because evaporation is considered perhaps is the older one because that is the natural phenomena people would have noticed that you sprinkle water on stone and if the stone is in sun it evaporates and later on when they discovered the safe use of fire they would have discovered that they can bring water to boil initially I am sure there was the two phenomena were considered absolutely distinct and that is why perhaps two distinct words came up one evaporation and boiling but that brings us to the next fact that now let me change the color for some time during a process we can take a liquid or a system from our liquid state to a vapor state like this causing a change of phase this is what we just now called and discussed evaporation or boiling you can execute a process the other way this process is known as condensation similarly if you start with a solid and increase its temperature it will become a liquid this is the process of melting the reverse process is known as solidification similarly at low pressures below triple point they know solid will simply sublime into vapor they know the sublimation process dry ice and all that they have been told about and the reverse of that is considered depending on again two words sometimes condensation is used because a vapor is going into a non vapor phase sometimes solidification is used because the end result is a solid but at this time it is also necessary to tell them that a liquid can go into vapor not by increasing the temperature but by decreasing the pressure and a vapor can go into liquid not by reducing temperature but at the same temperature increasing the pressure this also is a possibility and that will also be liquid going to vapor will be boiling or evaporation vapor going into liquid will be condensation and this you may later on have to link when you come to applied thermodynamics and talk of sacrometry. Now at this point it is necessary to tell them that our steam tables a good steam table should have properties listed all over the state space right from significantly low pressures below triple point pressures to significantly high pressures and there are good tables which give you data almost from vacuum to something like 1000 bar and almost from something like minus 40 or minus 60 Celsius to something like 800 or almost 1000 Celsius. Good data is not available beyond 700 or 800 but tentative data is available definitely up to 800 may be up to 1000 same thing pressures up to 800 bar up to 500 600 bar definitely up to 800 and 1000 bars tentative and there are teams of people because water is such an important fluid there are teams of people all over the world who are measuring various keep on measuring various properties of water in a more and more precise way you can say it say industry by itself because water is so important for us not only domestically but also industry however most of the steam tables and our steam table is no exception will tabulate data from the triple point onwards in temperature triple point upwards in pressure. So, this is the zone of tabulation of steam tables yes sir sir I have one question why the specific internal energy and specific enthalpy entropy is negative at 0 or less than 0 degree centigrade that just because we have a reference state we will come to that in this they see when you come to internal energy or energy we have already said that the absolute values of energy do not matter our first law which defines energy defines itself as delta E. So, each and every component of energy including U is defined only as delta U. However, if you want to tabulate delta U our tables will be too thick because everything not T1 P1 to T2 P2 we will have to tabulate rather than do that we define a reference state and define a value of U at that reference state and the simplest reference value to be defined with 0. So, on one side of that reference state you will have positive value on the other side you will have negative value you should also tell them that in this steam table for example internal energy is tabulated but that is with respect to some reference state we will find out what that reference state is. But if I take I write a computer program and reprint this steam table with a constant added to all these values of U a fixed constant added or subtracted from all these values of U. If you do not like negative numbers find out what is the biggest negative number suppose it is something like minus 80 you add 100 to everything. So, you will see all positive numbers nothing below about 20 nowhere near 0 that is perfectly alright the data is not at all wrong all that you have done is you have shifted your reference point the figures remain the same only the origin had shifted in any calculation we will always be using delta U. So, between two states the data you calculated by the old table or the new table so long as it is the same it just does not matter. So, negative values of U H because H is U plus P V and S and any other derived properties just do not matter if you are uncomfortable with them just add a constant value to all of them and proceed but see to it that it is the same constant that is used everywhere for a given system. Now, at this stage you should after having shown this green one you would say since the process of boiling and evaporation are important much of the data is around this line liquid vapor line since steam is also important this data is also reasonably is available in reasonable detail. However, small steam tables like this occupying no more than 30 pages will generally leave this data alone and we will have to use an approximation to obtain that data. Fortunately for us this steam tables as it goes into newer and newer prints has added more and more data and hopefully in another few years it will have details of this also it has some details but not very great detail let us look at it. Now, I will sketch a part of the state space and I will start from P triple point P triple point is the origin and we will go up to critical point this is the liquid part this is the vapor part and this we know is the super critical part where the distinction between liquid and vapor vanishes some student will say sir you said this is the process of evaporation but cannot I go from here compress it then go into vapor and come back here and then go from liquid to vapor without physically seeing boiling or evaporation the answer is yes perfectly yes that is possible nothing wrong nobody would like to do that because significant compression and decompression will be involved that would be a waste of energy but yes in principle that is possible. Now, the boundary between liquid and vapor is of great significance to us and we know that say at one atmosphere this is 100 degrees C if you go to a higher pressure we know the higher temperature a pressure will be higher this is what we do in a pressure cooker and we now tell them that we now use some technical words for example if the one atmosphere pressure is one atmosphere the boiling point is 100 degrees C we look at this point and if we look at the state here what do we find if we look at the state here we will find only a liquid in it if we look at a state here we will find only a vapor in it if we look at a state here what do we find the word saturated has not yet been used. So, you say that any possibility exist if this is the point say I call it point q at point q you will have in your system some liquid and some vapor you say the liquid settles only because I have assumed the presence of a gravity if it is there is no gravity if you take it on a satellite it will be droplets of liquid in vapor or bubbles of vapor in a liquid depending on which occupies the larger volume visually what would be the amount of liquid and amount of vapor that we cannot say it could be a small bit of liquid and a large bit of vapor or a large bit of liquid and just a few bubbles of vapor that also is a possibility. So, the amount of liquid and vapor we cannot say but both the liquid and the vapor will have the same pressure and temperature the effect of gravity being neglected for the time being when we say this we understand now that in this situation liquid and vapor are in equilibrium with each other such a state where two phases are in equilibrium not just liquid and vapor could be solid and liquid or solid and vapor is known as a saturated state. Saturated state means two phases are in equilibrium with each other and you may link this up using phase rule saying two phases are in equilibrium. So, only one independent variable between P and T. So, if you change the temperature pressure will change if you change the pressure temperature will change yes they are also saturated but all three phases together. So, pressure cannot change temperature cannot change. So, you now talk about the line which we will now call the liquid vapor saturation line it starts from the triple point it ends at the critical point at this stage make them open their steam tables and bring their attention to table one can you see this. Now first thing you have to tell them is that there are some gross mistakes in this and the very first line here you ask them to erase it. It is a good idea to get a new copy and spike it of yourself. The title says saturated water and steam temperature from 0 degree C to critical point you should say triple point to critical point because saturated liquid and vapor water and steam cannot exist below triple point this mistake the authors are committing since ages. So, every time I get a new copy I have to erase it. So, you notice the first thing here is the triple point 0.01 degree C that is an exact value by definition but this is an experimentally measured pressure 0.006112 bar just look at the first two columns as the temperature increases the saturation pressure increases. Come in particular to the second page where you have a 100 degree C line at 100 degree C the saturation pressure is 1.01325 bar which is one atmosphere as you increase beyond 100 degree C the tabulation is a bit crude at 150 degree C you need a pressure of 4.758 bar. So in table 1 the first two columns provide you the link between so table 1 provides you for a given T1 the saturation pressure corresponding to T1. Now since P and T are directly linked to each other we can provide saturation pressure for a given temperature or we can provide for a given pressure the saturation temperature same information another way suppose this is P2 this is T sat corresponding to P2 it is a line. So, you can provide y as a function of x or x as a function of y in the first table you have round values of temperature and pressures are provided in column 2 if you go to the second table table 2 here the author has not made a mistake of showing something below the triple point he has correctly written triple point to critical point started with triple point why does that mistake remain table 1 we do not know table and one and table 2 are perfectly equivalent except that table 1 is for round values of temperature table 2 is for round values of pressure that is all you have to explain to them and table 2 for some reason is more extensive there are no significant jumps like this it is interesting to show them on page 2 the one atmosphere line 100 degrees C and bring their attention to the fact that as you increase the pressure below above one atmosphere you go to higher and higher pressures in particular at approximately 2 bar which is 2 atmosphere it is about 120.2 degrees. Now at this point it is good to tell them because all of them have seen pressure cookers and why do they use pressure cookers because at higher pressures the boiling inside takes place at higher temperatures and food gets cooked faster and difficult to cook foods can also be cooked because the temperature is higher. Typically the dead weight on the pressure cooker is equivalent to raising the pressure by one atmosphere so when a pressure cooker is operational and it starts disabling the inside the pressure inside it is approximately 2 atmosphere so the temperature inside it will be approximately 120 degrees C. If you can set up a small experiment with a thermocouple inside a pressure cooker that will be nice you can demonstrate. Then you should also tell them because they have a feel for the amount of time something gets cooked in a pressure cooker and outside the pressure cooker. A general rule of thumb is that all cooking reactions which are biochemical reactions typically speed up by a factor of 2 when the temperature goes up by 10 degrees C. Most of the biochemical reactions approximately will have a reaction rate doubling when the temperature goes up by 10 degrees C roughly. So when it goes up by 20 degrees C from 100 to about 120 the reaction will speed up by a factor of 4 twice for the first 10 degrees C twice for the next 10 degrees C. And hence something which gets cooked in one hour without the pressure cooker will typically get cooked in 15 minutes in a pressure cooker. Those who have handled pressure cookers and cooking will realize that this is roughly the ratio yes or no. Bring this to the attention of the students to make them realize that what they generally know if they have tried some cooking in pressure cooker themselves has a link here and also with the reaction rates of biochemical reactions. Yes you can further increase the question is can you increase it further. Yes for example you can increase it to say 5 bar come here and bring it to something like 150 degrees C. There are two disadvantages. One a technical disadvantage that your pressure cooker will become bulkier. Now it is a thick vessel then it will be a pressure vessel you will have to get certification from you know the inspector of explosives and get it certified by the compressed gas people. Thus now no certification is required except by the manufacturer that ISI stamp is good enough for its safety. And second thing is as you increase the temperature the reaction will take place faster but also the food may not be able to sustain that temperature. So we want the cooking reactions to speed up we do not want degeneration reaction to take place. So that is why I suppose in cooking 1 to 2 bar and 100 to 120 degrees C it is considered perhaps near optimal both from the technical point of view that is thickness of the pressure vessel and also from the speeding up. A speeding up of a factor of 4 I think is good enough. Nobody complains about it everybody is happy. Of course there are some people who say that you should not even speed up they cook rice and even meat at temperatures as low as 55-60 degrees C and it takes 12 hours for the rice to cook but then they claim that it tests excellent. So this is an illustration that even at 100 degrees C some degradation takes place. At 120 degrees C it will be slightly higher but perhaps we all tolerate it and at 150 degrees C may be the degradation in the quality of food will be reasonably significant. If everything becomes pulp we will not feel like eating it right although it may be palatable not palatable digestible. Then continue with table 2 because it is a very exhaustive table there are some points they should remember for example 1 bar roughly 100 degrees C 2 bar roughly 120 degrees C 5 bar roughly 150 another good point to remember is 40 bar is 250 degrees C. As engineers we should also develop some feel right. So if a boiler is at 40 bar saturation temperature will be 250 degrees C and then bring them to the end of this table which is at the bottom of page 10 and say that this table as well as the previous table table 1 ends at 221.2 bar and 374.15 Celsius why because that is the critical point critical point is 221.2 degree Celsius and the critical pressure sorry the other way around. Critical pressure is 2 there should be some automatic method of doing this if I touch my stylus here it should become 221.2 bar and this is 374.15 degree C. Yes the question is about the critical point come triple point. I am coming to that we have just talked to the student it is not good to confuse with everything in the table tell them first about the first two columns both of table 1 and table 2. Tell them that it is the same information one is for round values of temperature second one is for the round values of pressure otherwise it is the same information show that the triple point the critical point and the point corresponding to one atmosphere they have identical values in both the tables. Then come to this state you can even draw another figure you can even now draw two different things you can draw the P T diagram triple point to critical point and you can draw the P V diagram and you say that let us consider one pressure some pressure at this point on one side you have liquid on the other side you have vapor and if you have a system containing the vapor and the liquid there will be some vapor and there will be some liquid and this is the situation at this point both will be at the same pressure both will be at the same temperature and the pressure temperature will be linked by the saturation relationship provided in the first two columns of table 1 or table 2. Now the remaining columns list the properties of the liquid phase and properties of the vapor phase and you can show them that if instead of P T I consider the P V diagram liquid will be denser vapor will be lighter the specific volume of liquid will be lower specific volume of vapor will be higher. So, at the same pressure I will have a liquid and the vapor this is known as the saturated liquid symbol F the vapor phase is known as dry saturated vapor symbol G why dry saturated vapor why not gas free liquid that is convention the liquid properties are for that part of the liquid where there is not even a single bubble of vapor and the vapor properties are for that part of vapor in which for assuming that the vapor does not have a single droplet of liquid. So, that is why we say dry saturated vapor saturated means in equilibrium with the liquid dry means without any trace of liquid in itself. If there is a mixture of liquid and vapor some part of liquid part of vapor say in droplet form or bubble form we will call it wet vapor and then you show them that the remaining columns of table 2 for example, we have the pressure temperature perfectly ok. Now notice you have a specific volume of the liquid part specific volume of the vapor part saturated liquid dry saturated vapor not only specific volumes, but we also have specific thermal energy or specific internal energy for liquid specific internal energy for vapor. Also specific enthalpy of liquid specific enthalpy of vapor we have not yet talked about entropy, but consider it to be another property like internal energy and enthalpy and specific entropy for liquid specific entropy for vapor are also listed. If somebody asks sir what is this hfg and sfg you simply tell them that during calculations quite often we need this difference hg minus hf and just to ease our life the difference has already been computed and plotted both at sfg hfg and sfg. Make them calculate for a few and confirm that they are the same and you can tell them that if you delete this hfg column or delete this sfg column nothing goes wrong that information is there it is an additional information. In fact you can frankly say that if you delete the whole of enthalpy column nothing goes wrong because so long as the internal energy column is there pressure and volumes are there you can always calculate h as u plus pv or you can keep h and delete u then h minus pv you can calculate you also show them that at different values of pressure or different values of temperature you have different values of vf vg uf ug etc. So, that if I consider at different pressures you will get a trace like this for liquid trace like this for gas and show them that the curve closes at the critical point bring their attention to the last part of this table and show them that as you go higher and higher in pressures look at the volumes first they are different but the difference goes on decreasing specific volume of liquid increases specific volume of vapor decreases they become nearly equal and at critical point they are identical specific volume of liquid is specific volume of vapor density of liquid is density of vapor there is no distinction between the two and that is why the line ends there not only specific volume you notice that even the specific internal energy is the same because there is no distinction between the liquid phase and the vapor phase same thing about specific enthalpy and specific enthalpy entropy and that is why the differences become 0 it is very prominently typed there at 0 at this stage it is a good idea to make the students ask the students to read out a few values that way they feel comfortable and particularly they should read out the values at the critical point for specific volume and pressure you should not go away from this table without doing the following come to the triple point either on the pressure table or the temperature table and make them realize that the specific internal energy at triple point has a value 0 this is an assigned value because that is the reference point all other energies are calculated with respect to triple point saturated liquid which is assigned the value 0 similarly come to entropy tell them that just the way we have defined energy as a difference entropy will also be defined as a difference and hence we need a reference point for simplification of tabulation and that reference point is also the same but for enthalpy it will not be 0 because enthalpy at triple point will be internal energy at triple point for saturated liquid plus PV in the PV product is not 0 it is approximately 0.01 kilo joule per kilogram so that is right you can even encircle these two and say this value and this value are defined to be 0 reference value and using our thermometry triple point temperature 0.01 is also a defined value by definition today the triple point temperature is 0.01 degree C now at this stage somebody will say sir what about a state in which you have liquid and vapor together.