 So, welcome back. So, after having decided that we are going to study water as fluid here, we will try to understand more about water now. So, the outline of this lecture would be to understand the phase diagram of water, features of phase diagram and the phase change processes that takes place from liquid to vapour, solid to liquid, solid to vapour, etc. Let us concentrate on phase diagram of water and what I show here is a phase diagram. Now I will show you this phase diagram in three dimensions, which actually will make us understand more things about phase transformations, phase changes, single phases, etc. So, this is an animation of a phase diagram on in three dimensions. We can see here that I can see pressure and volume in this direction. I can rotate this phase diagram like this. I can also zoom in and zoom out this phase diagram so that we can understand more and more about the diagram itself if you want to see something from close or from distance. So, we got both the facilities of rotating in this direction as well as in this direction. Let us now look at this three-dimensional phase diagram of water and what you see from here is we have got three axes, vertical pressure, this was volume and temperature. So, pressure volume temperature normally referred as PVT diagram also in three axes and if I show in this direction you can see in a pressure temperature axis one can read this phase diagram. What you can see from here is you can see there are three phases solid, liquid and vapor and you can also see that between solid to liquid you have got a phase transformation line. So, if I go from this direction and increase temperature you go from solid to liquid and if I go beyond that I can go from liquid to gaseous region also. Also what you can see from here I can go from liquid to vapor region from here and again this is a phase transition line. So, there is a phase transition line between solid to liquid and liquid to vapor region here and vapor I say beyond a critical point I normally call it as gas. This is what we call as sometimes superheated vapor also. Also what you can see from here is if the pressure is much less and the temperature is less the solid can get transformed into vapor directly and again there is a phase transition line over here. This is directly getting transformation solid phase transformation from solid to vapor region across this phase transition line. What you also see in this particular direction are the isotherms. You can see the temperature lines over here and you can see a temperature line that goes through a critical point and this temperature is called as critical temperature. Corresponding to this critical point the pressure is called as critical pressure and what you can also see is that beyond this critical point beyond this critical pressure there is no phase transition line from liquid to gaseous region. So, this transition from liquid to gaseous is not like what you see from solid to liquid or from liquid to vapor. During this liquid to vapor transition there is a latent heat is involved. In solid to liquid transition also latent is involved while from liquid to gas region which is above the critical point which is about the critical pressure here in this case there is no latent heat involved in this transition from liquid to gaseous region. There is no actual phase change the phases are so close that one cannot possibly notice the transition from liquid phase to gaseous phase in this region. Now, let us rotate these to see the diagram from this direction pressure volume. So, here you can see that if I transition from liquid to vapor region you can see the existence of dome here when my pressure is less than critical pressure. If the pressure is less than critical pressure the liquid can get phase the phase transition from liquid to vapor happens under this dome where you can see that there is a two phase mixture of liquid plus vapor exist. So, while having a phase transition from liquid to vapor region it goes through a two phase region and if the pressure is much less the solid can be transformed the phase transition can happen from solid to vapor region directly but that also happens after going a two phase region of solid plus vapor. It is noticeable that this happens when the pressure is less than critical pressure. So, this liquid plus vapor region is encountered when the pressure is less than critical pressure liquid goes through plus liquid to vapor region and then it enters the vapor region. Similarly, solid to vapor transition passes through a solid vapor region. If I come back to again this direction what you can see is an existence of triple point one can see that solid liquid and vapor are actually coexisting or all these three phases are in equilibrium at one point. I can show you that in two dimension in a better way but what you can see from here is a triple line. So, from this direction if I see I see existence of triple point but when I see in PV axis I see a triple line. The triple line has not much significance but triple point has a significance that it tells us that at given pressure and temperature condition all the three phases are in equilibrium and they coexist. Now, let us go to orthography projection of this figure. So, what you see here is a PT diagram now. You can see existence of solid liquid and vapor coexisting together. This is the PT diagram. We can see that solid liquid and vapor are coexist and this is a triple point. Similarly, if I show you PV diagram this is the PV diagram and again you see the same thing which I showed you earlier in a three-dimensional but from this direction. One can also see a VT diagram and again what you see is a dome in which two phase mixture exist when it gets transformed from liquid to vapor or the phase transition happens from liquid region to the vapor region. Similarly, you see at lower pressures what we can see from solid phase transformation into vapor going through a solid vapor two phase region. What you also notice is about the critical point about the critical pressure and critical temperature what you have is existence of gas. This can again be seen from PV diagram. Above this what you have is a existence of gas. Below that what you have is a vapor. I think VT diagram is a better. Below the critical point what you see is vapor and above the critical point what you see is presence of gas. We will refer mostly to the pressure and temperature diagram and sometimes pressure and volume diagram also. I will not be referring all the time to the three-dimensional diagram. The animation was made for understanding the phase transition but we will mostly refer to the pressure temperature diagram and pressure volume diagram. Thank you very much.