 So, now let me begin with the topic at hand today and the topic at hand today is properties of fluid. In the properties of fluids, we have looked just now at so far at gases, which we say are simple compressible systems or a system containing a gas is a simple compressible system. And in particular, we looked at a special kind of gas, an ideal gas. We looked at it for two reasons. One reason is it has a very simple set of isotherms, the equation of state is very simple. An ideal gas is obeys two laws, Boyle's law, which says that p v is a function only of temperature and we define the Kelvin scale. So, that we can write it as in a simple form p v equals r t and it also obeys Joule's law, which says that u is a function only of temperature. Then there are gases, which do not behave like an ideal gas. We have real gases for which none of this is valid. We will have a very complicated equation of state and then we have liquids like water, engine oil, mercury and all that. Gases and liquids can flow. So, we call these as fluids and then there are substances similar to liquids, but which cannot flow. These are solids like stone, rubber, metal, what have you. But all these materials are such that a thermodynamic system when you include them is likely to be a simple compressible. Of course, certain assumptions will be involved. For example, we will assume that the gas is not charged or the molecules of the gas are not dissociated because if they are charged or they are dissociated then we can do electrical work on them and then it would not remain a simple system. Similarly, a liquid it is expected that it is not a magnetic liquid or electrically conducting liquid like mercury or it is not a dielectric liquid because if it is so, then we can do electrical work or magnetic work on them and again it will not be a simple system. And the same thing is true of solid. We expect the solid to be not a charged solid or not a magnetized solid because in which case it will not remain a simple compressible system. So, whenever we have a gas a liquid and a solid under certain simple situations, we can consider them as forming a simple compressible system. But it is necessary for us to look at the basic difference between them although they are compressible system. Let me draw a huge p v diagram so that I can make things clear. And let us say that we consider two pressure levels say one at one bar and one at two bar. Let me write specific volume let me say I am taking 1 kg of that substance. If I take a gas typically the density is low the specific volume will be large. And if I compress it I will find that my volume for a gas from an initial state of one bar if I compress it isothermally I will end up with a final state at two bar where the reduction in volume will be of the order of 50 percent. This is what happens for a typical gas. A liquid typically has a much higher density than a gas. So, you take a liquid at one bar and try to compress it it does get compressed. But the reduction in volume is pretty small you can say this will be of the order of may be a few p p m say approximately 5 parts per million or 50 parts per million of that order very small not 50 percent 50 parts per million. So, this is typical of liquids for solids typically solids liquids have the same density. But let me show it slightly different for solids also when you compress it from one bar to two bar there will be a difference in volume difference in volume will be so small that is this is of the order of 1 to 5 p p m for a typical solid. So, this is the main difference between a solid a liquid and a gas. And we have equations of state for gas rather simple if you assume it to be an ideal gas we will have a very simple equation of state p v equals r t later on we will see more and more complex equations of state. For liquids the equations of state are still complex for solids they may turn out to be still complex. But whenever we have a system containing a liquid and a solid and we have it as a simple compressible system then we can say that solids and liquids are almost incompressible. And just the way we can say that many gases are almost ideal and continue using the ideal gas law for them. Quite often we can say that solids and liquids which are almost incompressible can be considered to be really incompressible. And in that case we will have a very simple method of managing their properties thermodynamically. When we come to the properties of water and steam in their state space there is a zone where we using some approximation like this we will come to that when we come to exploration of that part of the state space of steam. Now when we work as mechanical engineers there are two most important fluids for us one is air and another is water. But unlike air which quite often is always in the gaseous form we know air can be liquefied and we work with liquid oxygen, liquid nitrogen and other components of air. But usually we can get away by assuming air to be made up of a single component and remains always in the gaseous form not only that unless we go to very high temperature or very high pressures we can assume that air behaves almost like an ideal gas. And most of our engineering calculations and design of aircraft compressors is done routinely assuming air to be an ideal gas that is not true of water. Water we know is easily available in three forms or three phases solid which is known as ice, liquid for which we do not have any name water and gaseous or vapor form which we know as steam. The technical name for all these things together and to remove the confusion between water as a chemical compound and water as a liquid a proper thermodynamic name for this is water substance. Water substance means the chemical compound known as water either in its solid liquid or vapor form gaseous form. So, a water substance in the liquid form will be known as water, water substance in the solid form will be known as ice and in the vapor form will be known as steam. Now, if you talk to a high school student for a chemist you will say that look we generally write water as the chemical compound represented by the formula H 2 O. But we also have heavy water known as D 2 O. And if you take naturally occurring water it is a mixture of H 2 O and D 2 O the abundance of D 2 O is of the order of 70 p p m in naturally occurring water. Most of it is H 2 O, but D 2 O forms a small part and D 2 O is an important industrial fluid particularly useful for nuclear power generation using certain routes. We use it in India in a large number of our nuclear power plants and that has to be extracted by separating it out from this naturally occurring water. And when we talk about properties of water we must be very clear which water we are talking about. Are we talking about pure H 2 O? Are we talking about pure D 2 O? Or are we talking about the naturally occurring mixture of H 2 O and D 2 O? It turns out that the abundance or the fraction of D 2 O in naturally occurring water is so small that no effort is ever made to obtain pure H 2 O. So, all the water which flows through our pipes, falls as rains, fills our lakes and rivers which we drink this water contained in this bottle which I will drink sooth. All this is this naturally occurring mixture and this is what we call as ordinary water substance, ordinary water and in any of its phases it will be ordinary water substance. And when we now use the word water or steam or ice it is actually not H 2 O, but the ordinary water substance which is the naturally occurring mixture of H 2 O and D 2 O. And this is an important fluid unfortunately it is so complex occurs in all three forms that there is no simple equation of state. Of course, using a large amount of experimental data and very powerful computers people can use it. People have fitted a very complex equation of state, it requires something like over 200 parameters compared to that remember our ideal gas law P v equals R T uses just one parameter and that is R. And because there is no simple equation of state the properties are tabulated or they are graphically expressed. The advantage of a graphical expression is that you can see a large amount of information in a small space, but the resolution is poor not good for calculations. And hence for understanding we may look at it graphically, but for calculation we will be using the tabulated data. And that brings us to our steam properties as tabulated in the steam tables. Now, I will assume that all of you will have a copy of the steam tables available with us and we will soon start exploring that, but before we come to steam table let us appreciate the state space of water. Now, initially there may be some confusion because when I say water I may mean water in the form of this liquid water which we drink or I may mean the ordinary water substance which may mean water ice or steam as appropriate. But soon we will get over this confusion when I wrote here state space of water I actually mean state space of ordinary water substance. Since there are three phases the first projection we see is what is known as the phase diagram. The phase diagram is nothing but the projection of the state space on the pressure temperature plane. And if you look at the phase diagram for water that is for ordinary water substance you will find that the phase diagram looks like this. It is split into approximately three parts by approximately we will soon see. There is some sort of a crooked y there. There is one point from which three lines go out one goes south west one goes almost north slightly towards west one sort of ramps up slowly in a crooked fashion, but ends at a point. And the roughly three zones because this ends you can say this is one zone, but we will consider them to be two to begin with. Tell us that if the temperature is low enough you end up with the solid phase this is where ice exists. This is where the liquid water exists and this is the vapor phase where steam exists. So, this is plotted by doing an experiment you put say 1 kg or some amount of water in a cylinder piston arrangement. Pressurize it to a pressure p bring it to a temperature t and see what is inside. If you see ice note that you are here if you see water liquid note you are here if you see vapor you are here. So, you will go on point plotting solid points liquid points and vapor points. And you will see that there is a boundary between solid and liquid which you will plot that is the way this is plotted. There is one point at which all these three lines converge and that is known as the triple point. Now, why is this a unique point a question was asked what is the importance of this. Remember that whenever you have more than one phases or more than one components physical chemistry tells us that the phase rule is in operation. The phase rule defines a relation between the number of phases the number of degrees of freedom will come define this number of components. We will not go into the detail if you really want the detail we study books on physical chemistry or recommended book for those who want to get into the absolute detail of the phase rule is a book by Findlay F-I-N-D-L-A-Y title is the phase rule it is a very old classic somewhat readable somewhat not so easy to read. The number of phase a phase is a distinct part denoted by a density. If at the same pressure and temperature you find if you slightly change the state you end up with liquid if you slightly change the state you end up with vapor you have two distinct phases. So, the phase is a generic name for the solid liquid and vapor these are three phases they behave slightly differently liquid and vapors flow, but solid and liquid have their own volume vapors will generally tend to occupy any volume that you make available to it. Solids will have a surface liquids will have a meniscus vapor will not have a surface of their own their surfaces will be defined by either solids liquids or other boundaries in which they are confined. Component are distinct chemical species now although we say that ordinary water is a mixture of light water H2O and heavy water D2O. There are two issues here that the amount of heavy water is pretty small just 70 ppm and whenever we work in our domain of thermodynamics in power plants we never change that composition. So, our number of components when it comes to water is 1. So, the right hand side 1 plus 2 becomes 3 on the left hand side we have this degree of freedom this degree of freedom is the is the measure of the variables like pressure and temperature which we can change and still remain in the same phase. So, for example, out here we have single phase vapor. So, number of phases is 1 right hand side is 3. So, number of degrees of freedom is 2 that means if you are here then I can change my temperature slightly and I will still remain in the vapor domain I can change my pressure slightly and I will still remain in the vapor domain. So, I have freedom to move temperature to a higher or a lower value I have a freedom to move pressure to a higher and a lower value. So, I say that number of phases is 1 the degrees of freedom is 2 and that is what happens in this zone in this zone as well as in this zone. Now, let us look at the triple point this is a point where you may have a solid from one side liquid from one side and vapor for one side this is a point triple point is all three phases are in equilibrium together. That means at the triple point the number of phases is 3 since the right hand side is also 3 the number of degrees of freedom is 0. And what does number of freedom of degrees 0 means I have no choice of varying the pressure I have no choice of varying the temperature. So, for a given component the triple point will be defined by a unique value of pressure and a unique value of temperature. And experiments with water show that this is 0.01 degrees C temperature the pressure is 0.006 1 1 2 bar that is about the triple point. Now, let us come to these three lines these are known as the phase separation line interface lines or simply phase lines. Let me draw this clearly again on another page this has become slightly too much theta it is almost straight slightly in line solid liquid vapor. Now, let us look at a point here I have here liquid plus vapor in equilibrium. Now, there are two phases in equilibrium the right hand side is 3. So, the number of degrees of freedom is 1 that means out of pressure and temperature I can select only one it is like this if I select pressure. And if I want to change the pressure and still have this liquid and vapor in equilibrium I cannot independently choose temperature if I change pressure I must change the temperature also. That means given a pressure the temperature for this liquid vapor equilibrium will be fixed as well as given temperature the pressure will be fixed for this liquid vapor equilibrium. And that is why we have this as a line indicating that for a given pressure if you want liquid and vapor in equilibrium this should be the temperature. And for a given temperature if you want liquid and vapor in equilibrium this will be the pressure. So, that is the meaning of this degree of freedom 1. Now, some nomenclature these lines which are interface lines in our thermodynamic nomenclature these are known as saturation line. So, this line going from triple point it ends at a point known as the critical point we will come to that later is known as the liquid vapor saturation line. Similarly, this line from the triple point going upwards there is no real end to it inside separating the solid phase from the liquid phase is the solid liquid saturation line. And similarly this line going from the triple point towards the south west if I may say. So, separating the solid phase from the liquid phase is known as the solid vapor saturation. We will come to the critical point when we study the liquid vapor saturation line in some detail. Now, let us look at some processes we may have an initial state in any one of these three zones. The final state may remain in the same zone does not matter, but interesting things happen when the initial state is in one zone and the final state is in some other zone. For example, if I take a liquid and increase its temperature at a given pressure. So, that it makes a transition from the liquid zone to the vapor zone that means the system initially contains liquid then during the process it converts itself into vapor. This is the process of vaporization or evaporation or boiling. On the other hand so, from liquid to vapor is the process of evaporation. If you go back from vapor to liquid like this that will be a process of condensation from here to here it is a process of condensation. Similarly, if you start with a solid and increase its temperature and end up with a liquid you have a process of melting. If you start with a liquid and go over to the solid domain you have a process of solidification or sometimes we call it freezing. So, this is the process of melting the reverse of that is the process of freezing or solidification. Similarly, if you come in the in this zone where there is a solid vapor equilibrium line solid vapor saturation line. You can start with a solid and increase its temperature and you notice that the solid converts itself into a vapor form that is the process of sublimation and you can take a vapor at low enough pressure reduce its temperature make it become a solid make it into a solid. You have the process of either solidification sometimes it is also known as condensation or sometimes it is known as desublimation of a vapor. So, this is sublimation and this is solidification or condensation of a vapor into a solid. In our study of mechanical engineering and mostly in power plants and refrigeration plants and typical heating and cooling utilities. We generally do not deal with the solid part although we create ice. Ice being a solid does not flow it is good for you know cooling some stuff, but it is not good for it is not really that much useful as a flowing medium. So, our interest essentially lies in the liquid and vapor zone and hence most of the steam tables tabulate this part of the state space pressure from triple point to higher values and temperature from triple point temperature to higher values. Again one should notice and remember that the temperature of the triple point for ordinary water substance is 0.01 degree C. The pressure at the triple point is 0.6112 bar 0.6112 bar 0.6112 bar 0.00 I forgot those two. Now, let us look at the liquid vapor saturation line in more detail. Now, I am sketching I will start only from the triple point I will not show the other two lines and I will go up to the critical point. I have called it critical point, but we have not discussed it yet. First let us see let us open our steam tables. Can you give me the steam table from there? We have this steam table with you you should have it and you should open it up. What I am going to do is I have a scanned version of this and which I am going to look at. So, that both of us are at the same page first we have to find out this relationship between pressure and temperature. This line is the liquid vapor saturation line and the terminology is this relation between pressure and temperature is known as the saturation relation or the saturation line relation. If this is the temperature T, then the pressure corresponding to the saturation line is known as the saturation pressure at that temperature and if you take any pressure P the temperature at which this line exists will be known as the saturation temperature of that pressure. This information saturation temperature as a function of pressure and saturation pressure as a function of temperature is provided in the steam table in tables 1 and 2. So, first I request you to open your steam tables on page 3, page 3 table 1 look at the first two columns only just now first column is temperature the second column is pressure. The pressure is the saturation temperature saturation pressure corresponding to that temperature. Now, this is not my copy. So, there is do not blame me for this mistake here this is triple point with a single P not double P should be t r i p l e and now notice that in this copy the first line has been struck off and I would like you to strike off or erase or use white fluid or mark off the first line and why is that that is because the liquid vapor saturation line starts from the triple point which is 0.01 degree C. You cannot have liquid vapor saturation line existing at 0 degree C. So, the 0 degree C line is meaningless how has it been tabulated it is an illustration of garbage in garbage out you have a computer program which when given a pressure given a temperature gives you the saturation pressure you insert 0 degree C in it gives you some value and that is dumped in the first column. So, just first row. So, just erase and neglect the first line the saturation data starts with 0.01 bar 0 1 degree C saturation temperature. Notice that the corresponding saturation pressure is 0.006 1 1 2 bar and you will notice that as the temperature goes up the pressure also goes up at the end of the first page at 35 degree C it is 0.05628 bar go to the second page 1 point here you notice when the temperature is 100 degree C the pressure is 1.01325 bar which is 1 atmosphere and that should be so because 100 degree C is the standard boiling point of water at 100 degree C water will boil if the pressure is 1 atmosphere 1 atmosphere is 1.01325 bar. And after that the tabulation is a bit crude only about 50 degree C till you come to the last point which is 374.15 degree C a pressure of 221.2 bar this is the point at which the table ends why does it end there that we will see soon. Now, this is the table where you have temperature sorry pressure given temperature. So, given temperature the saturation pressure is found from table 1 this is the information about this line the liquid vapour saturation line. Now, we go to table 2 where the same information is provided with pressure as the independent variable in table 1 you would notice that temperatures have round values there are only two temperatures here which are not round values 1 is 0.01 degree C triple point. And the second one is the last point 374.15, but now you come to the next page which is table 2 the title of table 2 and table 1 are similar saturated water and steam table 1 says temperatures from triple point to critical point. And table 2 says pressures from triple point to critical point look at the first two columns they are slightly different instead of temperature and pressure now you have pressure and temperature. So, table 2 provides the same information, but the other way round given a pressure obtain the temperature this is table 2. And you will notice that table 2 is printed at a finer detail starts with the critical point sorry triple point 0.006 1 1 2 bar goes at reasonably round values of pressures. And you will notice that the triple point temperature is 0.01 degree C goes on over a number of pages notice here pressure of 1 bar slightly less than atmospheric the saturation temperature is 99.6 degree C go to 1 atmosphere 1.01325 bar a non round figure, but important because it is 1 atmosphere it is 100 degree C as it is expected to be. And you will find that this is in much more detail this is its third page fourth page up to 20 bar fifth page up to 70 bar sixth page ends at 221.2 bar where again the temperature is 374.15 degree C. So, the information in the first two columns of page 1 and page 2 is the same information tabulated in two different ways one is tabulated with temperature as the base round values of temperature the second one is tabulated with pressure as the base round values of pressure. Now, let us proceed we have said that around this line this is the liquid vapor interface zone. So, this is the liquid zone this is the vapor zone. So, suppose I take a state here I will see only liquid suppose I take a state here I will see only vapor, but suppose I take a state here exactly on this what do I see what happens is if you approach this state from the liquid zone you will end up with a liquid which with a slight rise in temperature will move into vapor. And if you start from this end you will end up with vapor which at a slight decrease in temperature will move into liquid I will I am not showing the origin indicating that I have taken a part in between, but this is pressure I am enlarging small part this is liquid vapor. And I am taking a point here and looking at the state here if I come from this side I get the limiting liquid state if I come from this side I will give a limiting vapor phase. And it is possible that because the two states will have the same pressure and same temperature if I enlarge this I will see a system containing liquid and vapor together. And you know we will always be under the influence of gravity however low. So, if you look at it the thing will look something like this you will have liquid and you will have vapor in equilibrium with each other. So, both of these will have the same pressure and same temperature the liquid will settle because of gravity, but let us neglect the small pressure difference because of the gravitational pressure gradient. If you neglect gravity then you will have a mixture of liquid bubbles in vapor liquid droplets in vapor mixed with vapor bubbles in liquid a very foamy type of a thing is what is going to happen if you really take it to a place where there is absolutely zero gravity. But what you have is liquid and vapor in equilibrium and that is what we mean by two phases together the pressure is the same temperature is the same, but the density here is different this is density of vapor and this is density of liquid and the denser part will settle under the influence of gravity. So, this is what is the scheme and now because there are two distinct densities there are two distinct phases. So, we have the limiting liquid phase and the limiting vapor phase the limiting liquid phase is known as saturated liquid and the vapor phase is known as dry saturated vapor. The technical meaning of these terms is the saturated liquid phase is the liquid phase which remains in equilibrium at the same pressure and temperature with its vapor phase saturated liquid is a liquid that remains in equilibrium with its vapor phase and dry saturated vapor is the corresponding vapor phase which remains in equilibrium with its liquid phase. The word dry is used to indicate that the vapor does not have even a speck of liquid inside it. This word dry or the adjective dry has come up from the fact that when you create the vapor from a liquid the vapor rises over the liquid and quite often droplets of the liquid are carried with the vapor. So, by dry saturated vapor we mean remove all those droplets have a vapor which is free of liquid that is why the adjective dry and the term dry saturated vapor. Since the densities are different properties other than pressure and temperature are all likely to be different. There is no guarantee that they are different the densities will definitely be different other properties are likely to be different and our steam table tabulates those properties. The nomenclature is let me use another page so that things are not cluttered. The saturated liquid state is denoted usually by the symbol f the dry saturated vapor state is denoted by the symbol. For example, the internal energy will be u f enthalpy h f specific volume v f specific entropy s f we have not yet defined it, but it is tabulated. So, we will look at the values similarly for the dry saturated vapor corresponding properties will be noted as u g h g v g and s g. Let us look at our table again and see those values and again you have a choice of either table 1 or table 2. Let us look at any one of them let us begin with table 1. Let us come to page 4 and let us say at 100 degree c let us look at the figures at 100 degree c the saturation pressure is 1.01325 bar that means when I go to the this thing if I select my temperature to be 100 degree c my pressure is 1.01325 bar and now let us look at the properties of the saturated liquid state and dry saturated vapor state at 100 degree c which means at 1.01325 bar and out here you will notice that the specific volume of the liquid I am rather away from the title I cannot bring it. It is here just about there 001044 meter cube per kilogram is the specific volume of the liquid 1.673 is the specific volume of the vapor meter cube per kilogram. Notice that the vapor occupies a much larger volume compared to the liquid. So, the liquid is very dense the vapor is very light. Now, you have the internal energy of the saturated liquid state uf 418.9 kilo joule per kilogram and internal energy of the dry saturated vapor state at 100 degree c. Similar you have enthalpy of the liquid state neglect this column for the time being enthalpy of the dry saturated vapor state and entropy of the saturated liquid state and entropy of the dry saturated vapor state. Again you will notice that for enthalpy between h f and h g there is a column which is h f g and for entropy between s f and h g there is a column which is s f g. These are these columns do not provide any additional information these columns h f g is defined as h f g is defined as h g minus h f and s f g is defined as h g minus h f and s f g is defined as s g minus s f. So, those differences are plotted here at any point you will notice that s g minus s f is h f g and s g minus h f g and s g minus s f is s f g. One could have plotted u f g and v f g, but it is not plotted may be the authors thought that we will come across h f g and s f g more often. But even if you drop these two columns the value of the steam table does not get reduced because that information can very easily be computed from the neighboring columns. And just the way you go down to say the pressure base table come to page 10 let us look at what happens at higher and higher pressures. Let us go to a pressure of 100 bar saturation temperature 311.1 degree c. Notice that the difference between the specific volumes of liquid and vapor has now reduced 001452 meter cube per kg and 0.180 meter cube per kg. You go to still higher pressures you go to 200 degree c 200 bar temperature 365.8 degree c pretty high. You will notice that the volume difference is still low 0.002036 and 0.00583 and you go to higher and higher pressures in corresponding higher and higher temperatures you will reach a point 221.2 degree c sorry 221.2 bar as the temperature is 374.15 degree c where you will find that the liquid specific volume and the vapor specific volume is the same 0.003155 degree c meter cube per kg. That means when you come to the critical point there is no distinction between the liquid phase and the vapor phase. And because of that you will notice that the saturation line ends at the critical point. As you approach the critical point the distinction between the liquid and the vapor reduces and at the critical point difference between liquid and vapor vanishes. So, they do not remain to distinct phases anymore and that is why this line ends at the critical point. Going back to our table notice that critical point is at 374.15 degree c, 221.2 bar pressure. The liquid specific volume and vapor specific volume are the same not only that you will notice that the specific internal energy of the liquid and vapor is also the same enthalpy of the liquid and vapor is also the same giving you hfg to be 0. And entropy also of the liquid and vapor is the same giving you hfg to be 0. I think it is just past 11. So, we break for t we will continue our discussion at 11.30.