 Welcome to the third lecture of cryogenic engineering. I will just briefly take a overview of what my earlier lectures were. In the first lecture, we talked about what is cryogenics and we discussed various applications of cryogenics in space in superconducting in mechanical engineering and in medicine and thing like that. In the last lecture, which was the second lecture, we talked about different temperature scales and we also concluded from there that one can positively use Kelvin scale. It is for our benefit. We do not have to say every time minus 196 degree centigrade and we can always say 77 Kelvin using this temperature scale. We also talked about various cryogens. We talked about their properties and we talked about the importance of T s diagram that is temperature entropy diagram. We found that from the temperature entropy diagram, lot of things can be understood. We can understand what is the boiling point, what is the critical point, how the enthalpy is vary with temperature, how the entropy vary and how different pressures and temperatures vary and we discussed different cryogens and their properties in brief of Aragon, Ayr, Nitrogen and Neon. So, here we got a feel of various cryogens and what I am going to talk about today is cryogen-hydrogen. We talked about specialty of hydrogen that is ortho and para forms of hydrogen. What are these different forms? What is it all about? We will see in this lecture. Then helium is a very special gas, is a very very useful gas in cryogenic engineering and we will discuss the phase diagram of helium. What are different phases in helium? How do they coexist and things like that? In my last lecture, when I talked about cryogen, we had written one statement over there that hydrogen and helium are special cryogens and therefore, they will be dealt specially in a special lecture and this is this special lecture which we are going to talk about hydrogen and helium and in fact, we will continue about talking about helium in the next lecture also. Let us go up to hydrogen which has got its boiling point of 20 Kelvin. Hydrogen exists in diatomic form as hydrogen, everybody knows about this and these are the normal properties of hydrogen gas. What are its properties? It has got a normal boiling point of 20.27 Kelvin at 1 bar, 1 atmosphere. It has a normal freezing point of 13.95 Kelvin. It has a critical pressure of 1.315 MPa or around 13 bar pressure. It has a critical temperature of 33 Kelvin, 33.19 Kelvin to be exact. Now, it has got a density of 70.79 kg per meter cube and the latent heat is 443 kilojoule per kg when it gets converted from gas to liquid or from liquid to gas. These are very important properties and this means that I can use liquid hydrogen to give me cooling effect at 20 Kelvin around 20 Kelvin approximately or above. I cannot come below 20 Kelvin. If I were to come and use hydrogen at lower temperature than 20 Kelvin, then I have to remove the pressure over it. That means I have to go into vacuum to touch down lower and lower temperature and at 13 Kelvin, 13.95 Kelvin, liquid hydrogen will get converted to solid hydrogen. Now, this is the temperature entropy diagram of hydrogen. I always told you that all the mechanical engineer or all the cryogenic engineer first should refer to T s diagram to understand the different property variations with temperature. So, on the y axis what we have is a temperature and what x axis what you have got is a entropy. You may not be able to see properly. It is possible, but just have a look at different lines on this diagram. For example, you can see the dome over here. It means that inside this dome what you have is a two phase mixture that is liquid plus vapor. You can see all these lines which are coming from top to bottom. It means they are all isobaric line that is the pressure remaining constant and you can see all these curved lines. They are all isenthalpic line or the enthalpy remaining constant. Why I am stressing this point is when you go in the next lectures, when you go for liquefier and refrigeration, we will deal with these diagrams in every problem. We have to understand the property variation, enthalpy variation, entropy variation at every point and for that we will always have to refer to the T s diagram of different gases or different cryogens. So, here you can see a line which is at one bar and this is the temperature corresponding to the change of phase from gas to liquid or nothing but the boiling point of hydrogen which is one atmosphere pressure and 20.27 Kelvin as the temperature. Now, this is the critical point and the properties of critical point are 13.15 atmosphere and 33.19 Kelvin temperature. So, this is the critical temperature and this is the critical pressure. In addition to that I have just given data to understand density of vapor at one atmosphere in the saturated condition is 1.33 kg per meter cube and that of liquid is 70.79 kg per meter cube hydrogen. Now, some general information about hydrogen. It has three isotopes hydrogen, deuterium and tritium. Now, the relative percentage of existence of these three isotopes is 6421 for hydrogen and deuterium respectively. The atomic mass in this case all these things have got one proton in the nucleus and the number of neutrons will vary depending on what isotope we are talking about. For example, for hydrogen we have got zero-netron, for deuterium we have got one-netron and for tritium what we have is a two-netron. Now, this tritium is very, very rare substance, a very rare gas in comparison to what you see for hydrogen and deuterium. In addition to that the tritium gas is a radioactive gas and is unstable with a half life of 12.5 years. So, whenever we have to deal with tritium one has to very, very careful one has to worry about all its radioactivity and all the measures have to be taken to deal with this tritium. In fact, this is not normally used in commercial operations. What normally we will use is hydrogen of course and sometimes we can have deuterium as heavy water etcetera. We will come to that later. The relative ratio of existence of hydrogen as diatomic molecule that is hydrogen H2 and as hydrogen deuteride. Sometimes hydrogen is like H2 or HD, deuterium atom get combined to form hydrogen deuteride HD and the relative ratio is 3200 to 1. Now, the important part about hydrogen is it exists in two molecular forms that is ortho and para. So, we have got a ortho form and we have got a para form. This is very important and we will talk about this ortho and para forms of hydrogen in little bit details in the coming slides. So, what is this ortho and para hydrogen? Well before I really go into ortho and para etcetera I will talk about some third parameter called spin because from this definition of spin we understand what is ortho hydrogen and what is para hydrogen. So, what is this spin? This spin is defined as a rotation of a body about its own axis. We know the earth spins, we know a top while on the earth when it rotates it spins about its own axis. So, this is what I am talking about one hydrogen molecule and you have got two atoms of hydrogen together which means you have got two protons. So, hydrogen molecule has two protons and two electrons. These protons will be spinning all the time. The distinction between the two forms of hydrogen what we talked about as ortho hydrogen and para hydrogen is basically because of the direction of the spin of these protons. So, as I just said these two protons will have some spin and what is the direction of that spin will decide if it is a ortho hydrogen or if it is a para hydrogen. As soon as we talk about ortho and para lot of properties associated with the energy of hydrogen will get decided and we will talk about that in the next slide. The two protons possess a spin which gives angular momentum. Possibly I talked about this in MRI system also you got hydrogen molecule and this proton immediately gets aligned to the magnetic field because of this spin. Similarly, I am talking the same thing here the two proton possess a spin and this gives a angular momentum which will have a direction. So, here you can see two protons and you can see two clockwise directions over here which indicate the spin of these protons. If the nuclear spins are in same direction for both the protons what we call is it is a ortho hydrogen. That means, if both of them are in the same direction clockwise in this case this is nothing but ortho hydrogen. And if you see the next slide we have got two protons two atoms hydrogen together one has a spin in this direction one has a spin in the opposite direction. So, one is a clockwise and other one is a anticlockwise and this is what we call as a para hydrogen. So, essentially if the nuclear spins are in the opposite direction for both the protons it is para hydrogen. Both the spins are in the same direction we call it ortho hydrogen and when both the spins are in opposite direction we call it a para hydrogen. So, it is just a difference of spin of the protons which make it ortho or para. Now, what happens why are we studying all this? As soon as you start lowering the temperature of hydrogen gas this ortho will start getting converted to para. That means, the molecules which had the spin in the same direction will now have spins in opposite direction. So, with the decrease in the temperature the ortho hydrogen is getting converted to para hydrogen. So, what is happening as you lower the temperature the gas hydrogen we slowly start getting converted to liquid. And here when we start lowering the temperature or when we start liquefying the gas basically I want to reach down to 20 Kelvin from room temperature what will happen ortho hydrogen will get converted to para hydrogen. And how do they happen? What is the percentages of ortho and para is at 300 Kelvin I got 25 percent ortho and I got 25 percent para alright. And at 20 Kelvin after the whole conversion has taken place and equilibrium hydrogen has formed what I have is all the ortho almost all the ortho have got converted to para. So, para hydrogen at 20 Kelvin which is nothing but the boiling point of hydrogen the 75 25 ratio has got converted to almost 100 percent 0.179 ortho has remained there while para is 99.8 percent here. So, almost 100 percent ortho has got converted to para alright. Now, this is the clear distinction what exactly happens when you go on lowering the temperature of the gas from 300 Kelvin to 20 Kelvin here ortho gets converted to para. Now, this para form is a low energy form and therefore, heat is liberated during conversion this is a very important thing that ortho has got higher energy form while para is a low energy form. So, during this conversion the heat is liberated because ortho has higher energy while para has lower energy. So, during this transformation from ortho to para lot of heat gets liberated which means that this is basically exothermic reaction. So, conversion of ortho to para as one goes on lowering the temperature is basically going to result in the release of energy or there is lot of heat energy is involved over there. So, conversion of ortho to para form of hydrogen is an exothermic reaction and this conversion is a very slow process. This is the most important point again about this conversion just want to summarize as you go on lowering the temperature 75 25 ortho 75 25 ortho will get converted to para which is 0.179 and 99.8 percent respectively. This process of ortho to para conversion is a exothermic reaction and also this conversion is a very very slow process it does not happen fast it happens very very slow. It is very important for liquefaction that this ortho to para conversion takes place faster and it is also very important that this conversion is complete during liquefaction. What will happen? We will see later, but if I want to make this process of conversion very fast then what I have to do is I have to add catalyst to this reaction. So, in order to make this conversion faster catalysts are added there are different kinds of catalysts there are 3 or 4 types they have to added in correct quantity in order to convert the ortho hydrogen to para hydrogen as fast as possible or to make the reaction faster. So, I just said during liquefaction the heat of conversion causes evaporation of 70 percent of hydrogen originally liquefied. Now, this is the effect of this conversion from ortho to para what is happening during liquefaction the temperature is decreasing. What is happening because of the decrease in temperature the heat of conversion is getting evolved that is it is being an exothermic reaction lot of heat is being liberated and it is evaporates because of the effect of this heat release whatever liquid has got form it gets evaporated immediately. So, if I get liquid 70 percent of that liquid will get evaporated because of this conversion from ortho to para alright and this is very important constraint in liquefaction and storage of hydrogen. So, as I said the conversion is a very very slow process and if the conversion does not take place during liquefaction I will store in the form of liquid. In this liquid form this ortho will slowly get converted to para during this conversion from ortho to para lot of heat will get released and therefore lot of liquid will get evaporated. It means that we should ensure that during liquefaction all the conversion gets happen all the conversion happens during liquefaction only that means all the conversion from ortho hydrogen to para hydrogen happens during liquefaction only if that if that does not happen then whatever liquid you get at the end of liquefaction the ortho will get converted to para in the liquid form and therefore it will cause the evaporation of most of the liquid that is stored and this is very very typical of hydrogen this has to be taken care of. So, what we do we add catalyst during liquefaction as I just said the catalyst make this reaction faster and this will ensure that the whole conversion of ortho to para will take place during liquefaction only and whatever liquid has got form it will not get then evaporated. Now this is a graph which shows that depending on the initial ortho existence in the liquid how much amount of liquid will remain at the end of so much of storage time for example this talks about mass fraction remaining in ortho to para conversion progress and this is the storage time on the x axis. If I talk about this line for example I have got liquid and this liquid has got 60 percent ortho that means the whole conversion has not taken place during liquefaction the liquid which I have got is stored with 60 percent ortho in it what does it mean that after so many hours more than let us say around 1500 hours what remains here is only 0.35 percent whatever original was there only 35 percent of that remains all the rest is getting evaporated that means around 65 percent of the fluid has got evaporated completely. However if I compare this with this figure of 20 that means my liquid hydrogen which I have got had only 20 percent of ortho remaining in it that means 80 percent conversion had taken place it has got 20 percent ortho in it at the end of around 1500 hours what it will have is around 70 percent that means only 30 percent liquid has got evaporated during the conversion when the initial ortho existence was only about 20 percent. Now imagine if I got all the conversion taken place during liquefaction that means my line would almost be flat line over here if I just extrapolate this if I say that all the conversion has taken place during liquefaction only then over 1500 hours this line possibly could have been at 95 percent that means only 5 percent possibly would have got evaporated this shows the importance that the liquid hydrogen which I am storing should have no ortho content or as little ortho content as possible it means that all the ortho which was there should get converted into para and therefore all the ortho to para exothermic reaction would takes place during liquefaction only. So, this figure shows the fraction of liquid hydrogen evaporated due to ortho to para conversion which storage time this is very important and a big difference of hydrogen as compared to all other cryogens. Hence we should ensure that liquefaction of hydrogen should ensure complete conversion this is what I talked about I am sure this is clear to you. The second gas or the isotope of hydrogen is deuterium it has got one proton and one neutron and two deuterium atoms make one D2 which is called heavy hydrogen. So, you know D2O is heavy water and D2 is what we call as heavy hydrogen. Now, similar to hydrogen deuterium has got also ortho and para forms, but they are in different forms that means their percentages are different. The relative concentration of these two forms is a function of temperature again as what it is in normal hydrogen the normal deuterium has got two third ortho and one third para. So, 66 percent is in ortho and 33 percent in para at initial case as against 75 25 over there. As the temperature decreases for deuterium here the para D2 gets converted to ortho D2 as against ortho H2 get converted to para H2. So, it is opposite that all right this is just a point for comparison we are not going to talk about deuterium in detail, but I just wanted to show the comparison of deuterium behavior with that of hydrogen. So, what happens at 300 Kelvin you got 66.67 ortho and 33.33 percent of para at 20 Kelvin that means when whole thing has got converted to liquid deuterium what you have is almost all the para has got converted to ortho. So, you got 98 percent ortho and 1.998 percent para this is the point of difference between deuterium and hydrogen. Most of the physical properties of hydrogen and deuterium mildly depend on ortho and para composition. So, whatever be composition the physical properties do not depend so strongly on this ortho and para conversion. The different uses of hydrogen we have talked about it is used in cryogenic engine as a propellant as a fuel it is being considered as a fuel for automobile this is a very important liquid hydrogen as a fuel is a very popular and it is looked at as a fuel future fuel bypassing petrol and diesel. Cryocoolers working on a closed cycle sometimes use hydrogen as a working fluid. However, one should know that hydrogen has got some safety requirements hydrogen codes and standard should be followed to ensure safety while handling liquid hydrogen. These are different uses of hydrogen. The next gas is helium as I have explained to you about helium this is one of the very important gases as far as cryogenic engineering is considered. Why? Because it is a inert gas it is a non-reactive gas and it is got the lowest possible boiling point it is 4.2 Kelvin at one atmosphere. It means that this gas will remain in gaseous condition till 4.2 Kelvin. All other gases all other gases will get liquefied because their boiling points are above 4.2 Kelvin temperature and therefore, if I want to achieve temperatures very close to 4.2 Kelvin or below or in the range between let us say 50 Kelvin to 4.2 Kelvin I got no other option, but the only safe gas the inert gas is helium. Helium has got a tremendous importance in cryogenic engineering. The evidence of helium was first noted by Janssen during solar eclipse in 1868. It was discovered as a new line in the solar spectrum. So, the discovery of the gas only happened around 1868. In the year 1895 Ramsey discovered helium in uranium mineral called as clavite. So, this was discovery on the earth for the first time in 1895. So, you can understand that it is a gas of just 115 years old on the earth. Since in which in the year 1908 Cameralinguonus at Leiden University is liquefied helium using helium gas which you obtained by heating monazite sand procured from India. So, this is a Indian connection to the first helium liquefaction that happened in 1908 by Cameralinguonus at Leiden University in Netherlands alright. This is a good Indian connection of which I talked about earlier and also I told you about in year 2008 what we had is a centenary year of helium liquefaction. So, all the cryogenic engineers and physicists associated with low temperature research celebrated the year 2008 as a centenary year of helium liquefaction. Helium is an inert gas and exists in monoatomic state. These are the properties of normal helium. What are they? It has got a boiling point of 4.25 Kelvin. Normal freezing point it does not exist. Critical pressure it has got 0.227 MPa that is around 2.27 bar. Critical temperature 5.25 Kelvin. Liquid helium density is 124.8 kg per meter cube and the latent heat is around 20 kilo joule per kg, 20.28 kilo joule per kg is a very small latent heat. It means that with the smallest heat coming the liquid helium will get evaporated and so one has to be very careful in the usage of helium. Heat in leaks that happened when you use liquid helium. It is a very important parameter because the latent heat is the one which gives you the amount of cooling effect or refrigeration effect what you want at 4.2 Kelvin. Let us see the same properties on a TS diagram for helium. Here you can see the dome and this is 5 Kelvin which means that 5.2 is a critical point over here and what you can see is again the pressure lines, enthalpy lines and there are density lines also. On the x axis what you have is entropy. This is a 1 bar line what you see is a boiling point of helium which is 1 atmosphere and 4.2 Kelvin. This is a critical point and the critical coordinates are 2.27 atmosphere and 5.25 Kelvin. This information has to be known by all the cryogenic engineers. So, whenever I say helium or hydrogen or nitrogen one has to know the boiling points, one has to know what are the critical parameters associated with those cryogens. This is least expected from a cryogenic engineer because the choice of temperature, the choice of pressure one does one has to have this knowledge when we apply this cryogens for a specific application. Again the density for comparison sake, the density of vapor at 1 atmosphere in saturated condition for helium is 16.87 kg per meter cube and for liquid it is 124.8 kg per meter cube. Helium in 1920 Aston discovered another isotope of helium which is helium 3 in addition to helium 4. Now this isotope of helium which is helium 3 is also very important in cryogenics because this is what we use in dilution refrigerator in order to reach temperatures below 1 Kelvin and therefore, this aspect will be covered in the next lecture and this is a very important and its discovery happened in 1920. Helium exists at 2 isotopes, helium 4 which has got 2 protons and 2 neutrons and helium 3 what we just talked about as 2 protons and 1 neutron and that is why we call it helium 3 and helium 4 respectively. The percentage of helium 3 is very very small 1.3 into 10 to the power minus 4 percent so mostly whenever we get we get helium gas it is helium 4 only alright. So, this terminologies are used quite frequently in helium which is helium 4 and helium 3 and in further we find helium 1 and helium 2 these are very different ways of putting helium in very different contexts. So, one has to get used to talking helium 4 and helium 3 when I say helium 4 it is a normal helium when I say helium 3 it is the isotope of helium 4. So, the isotope is helium 4 which is relative percentage wise almost 100 percent is helium 4 of course there is helium 3 and the relative percentage is very small. This also means that the cost of helium 3 is very very high very very high as compared to helium 4 I will not be able to tell you exact cost of helium 3 because we could never buy that in India. However, this cost will be possibly 100 times more than that of helium 4. So, it is a very costly and therefore, its usage has to be really properly justified. Now, what is important about helium is its phase diagram this is the one of the most important aspect of helium. This try to understand this because I am going slow and trying to explain as much as I can on this diagram. If I want to understand about helium phase diagram what I have is a pressure and temperature. I am plotting pressure and temperature here and what you see is a saturated vapor line vapor pressure line basically. So, at 5.25 Kelvin what you have is a critical temperature corresponding to that what the pressure would be critical pressure. So, you got a critical pressure and critical temperature below this would be what we get is a two phase that means liquid and vapor as you know from the T s diagram under the critical temperature and pressure is that what you get is the liquid and vapor. So, this is my vapor pressure line and on this if I give this point is nothing but 4.2 Kelvin and 1 atmosphere which is a normal boiling temperature of helium. So, what you have here is a vapor and what you have this as a critical point and here comes a different line which is nothing but solid hydrogen what you have is a liquid helium over here. So, now you can see that I got three phases I got liquid helium over here I got vapor helium over here and what I have here is a solid helium. It means that the liquid and vapor are coexisting together solid and liquid are coexisting together, but the solid liquid and vapor are not coexisting together and this is a very important aspect of helium. From the adjacent figure helium has no temperature and pressure at which solid liquid vapor can coexist it means that it has no triple point and this is why we say that if you go on reducing the temperature of helium it will still remain in liquid state it will not reach the solidification point. Now, this is a lot of physics associated with it helium has a very high zero point energy and thing like that it has got very involved physics and therefore, I do not want to really go into the details of those physics aspects for engineers it is important to understand that helium does not have a triple point as most of other caravans have. Now, what happens of course solid helium does exist. So, if I want to convert something to solid helium what I will do I will have to pressurize this to 25.3 bar to solidify. So, saturated liquid helium must be compressed to 25.3 bar to solidify. So, this point where I can get solid minimum pressure is 25.3 bar. On this curve you can see that this pressure has not been given in the scale because this is one bar the pressure associated with this is around 2.5 bar and this pressure I am talking about is now 25 bar. See if I really want to get solid helium I will have to compress the saturated liquid to 25.3 bar in order to get solid helium. Now, as liquid helium is further cooled below a particular temperature this is very specific temperature of 2.17 Kelvin which is over here. See if I go on cooling this liquid further in this direction let us say a new liquid phase liquid helium 2 emerges out. This is something different what you see as compared to all other caravans. So, here liquid helium 2 emerges out and therefore what I call these 2 phases as is liquid helium 1 and liquid helium 2 or helium 1 and helium 2. So, I just pointed out to you in earlier slide you got different versions of putting helium in that is helium 3 and helium 4 which are nothing but isotopes. Again I am putting something which is helium 1 and helium 2 actually this is liquid helium 1 and liquid helium 2 but in a colloquial language I will always say helium 1 and helium 2. So, what is helium 2? Helium 2 is a phase of liquid helium which comes into existence when you go on cooling helium 1 and this new phase emerges when you go below 2.17 Kelvin which is a very specific temperature. So, what is this all we are talking about? The 2 different liquids now are called liquid helium 1 and liquid helium 2. So, this is clear from this diagram. Now, these liquid phases are distinguished on the basis of viscosity. So, I got some viscosity associated with helium 1 and I got some viscosity associated with helium 2 and on the basis of that I am doing this differentiation. Normally liquid helium 1 is normally called as normal fluid and helium 2 is called as super fluid. You possibly must have heard about this that helium exist in 2 fluid form 1 is a normal fluid and 1 is a super fluid form and what is this super fluid form and this is what you see from this. What I am giving you here is a line which is joining 2.17 Kelvin up to this point which divides helium 1 and helium 2. This phase separation line is called as lambda line. So, imagine this is a 2.17 Kelvin touching up to this solid liquid line at this point and this what I call as lambda line and this point is called as lambda point. So, the point of intersection of phase separation line with saturated line the intersection of phase separation line which is this and where it hits the saturated line at this point is what we call as a lambda point. So, this is lambda point. Now, this is a complete phase diagram of helium and again I summarize what you have on the right side of this dividing line is helium 1, what you have on the left side of this line is helium 2. Helium 1 liquid helium 1 is called as normal fluid and liquid helium 2 is called as super fluid. The difference is happening as we go on cooling liquid helium 1 below 2.17 Kelvin depending on what pressure you have. The line which divides this 2 helium 1 and helium 2 is what we call as lambda line and the point where this intersect the saturated vapor line is the lambda point. This is very important to understand and this is very important that a cryogenic engineer is expected to draw this diagram immediately to understand. Liquid helium 2 is called as super fluid because it exhibits properties like zero viscosity. We made a statement earlier that this difference of helium 1 and helium 2 is owing to the viscosity of the liquids. This new phase which emerges as helium 2 from helium 1 is basically because of the viscosity differences between these two fluids. So, helium 2 is called super fluid. It is called super fluid because it exhibits properties like zero viscosity. What I am talking about is helium 2 has got very close to zero viscosity. While helium 1 is like a normal fluid, it has got its own viscosity. What does it mean? It will never have effect like pressure drop, friction. It can move in any direction. It is like mercury basically and it can run in any direction. It can run through small little channels. You do not have to really bother about the pressure drops that are happening in helium 2 and this is very important. The other aspect of this, it has a very large thermal conductivity. Now, these two aspects make it very important features of helium 2. Low viscosity or zero viscosity or we also call it zero entropy. As you come down to zero Kelvin, it has become much more order. See, the most order thing is solid. You have got all the lattice crystalline structure. You have got a very defined position. While in helium, what you have got is liquid helium is a very helium 2 is becoming ordered liquid. It is not solid exactly. It is as ordered as solid and therefore, what we call is as zero entropy in this case. So, it has got zero viscosity and it has got a very large thermal conductivity. Now, these two aspects are very important of helium 2. In addition to that, it has got very funny properties. See, lot of research is being done on helium 2 to understand the behavior of helium 2. This is called super fluid. Because of its very high thermal conductivity, because of its zero viscosity, it has got different applications. It ensures that all the super conducting accelerators have got magnets. For example, in CERN, all the magnets are cooled at 1.8 Kelvin. 1.8 Kelvin is nothing but super fluid. What does it ensure? It ensures fantastic heat transfer, because it has got a very large thermal conductivity. At the same time, it has got zero viscosity. So, whatever cracks are there, whatever ways are there, whatever paths are there, helium 2 will go and occupy the place. It will not worry about the pressure drops happening over there, because of absolute minimum or zero viscosity. The other property is this fluid expands on cooling, which is a very funny property. It cannot be well defined, but it is very funny property of helium 2. Owing to its low viscosity, the fluid below the lambda line, that is, liquid helium 2 flows through the narrow slits and channels very rapidly. This is a very important aspect of helium 2, that it can really flow through very narrow slits and channels and within no time. Otherwise, you have to do pumping or something like that. No, what if you want a mixture of helium 1 and helium 2, helium 2 of this mixture, which immediately go through a slit or a channel, but helium 1 will not be able to go through. We will find lot of applications of this in the next lecture, because we have got very specific experiments one can do on helium 1 and helium 2. Because of this property of zero viscosity, helium 2 can flow through narrow slits and channels very rapidly. What happens? When one goes from helium 1 to helium 2, what actually happens is there is some kind of a phase transformation. This is called a phase transition. Although one can see that it is only liquid on either side. So, in reality, there is no phase transition that means there is a liquid to liquid phase transition. So, it is a completely different kind of a phase transition in this case. One has to understand what is the physics behind this. Till now, what we have understood is what is the helium phase diagram look like. We also concluded from here that solid, liquid vapor never touch or never coexist and also when we cool liquid helium, it has got one more transition happening below the lambda point temperature, which is 2.17 Kelvin and a new phase emerges called helium 2. Now, what I am going to talk about is what is this transformation or transition of helium 1 into helium 2 is all about. Let us see that in small details. Again, the physics behind this is very, very big and I am not going to discuss that. What I am going to do is only some important aspects of this phase transition. Now, when I talk about phase transition, we have got a first ordered phase transition and we have got a second ordered phase transition also. This is the equation which talks about Gibbs free energy. In thermodynamics for any reaction, what you have is a Gibbs free energy equal to we have got some internal energy E, we have got P V pressure and volume variations here P V and then we got a T S. So, G is equal to E plus P V minus T S. This is a very standard equation which comes from Gibbs free energy equation. Now, this Gibbs free energy if I differentiate with respect to pressure and if I take the first derivative of first order derivative of this at constant temperature, it will give density. So, if I see the variation of Gibbs free energy with respect to pressure at constant temperature and constant pass that means, whenever there is a phase transition happening at constant temperature and at constant mass what you get is a density. This is the first order derivative of Gibbs free energy with respect to pressure at constant temperature it gives density. This density which is the first order derivative of the Gibbs free energy under grows an abrupt change leading to discontinuity. So, whenever this kind of phase transition happen of first order nature, this is the first order derivative of Gibbs free energy. Whenever this happens the density undergoes an abrupt change leading to a discontinuity called Gibbs first order discontinuity of or first order transition. I am basically going to explain to you what is the first order transition and what is the second order transition. In this case which is the first order transition what you see is whenever the transitions of this nature happens, this happens at constant temperature and the density goes through a abrupt change that means, if I see the right side density and the left side density I will get a big discontinuity at a point where this transformation happen at a temperature where this transformation happens alright. The density undergoes an abrupt change leading to a discontinuity called Gibbs first order discontinuity or this transformation is called as first order transition in this case. What are the features of this transition? This transition involve latent heat. So, whenever a phase transition of first order happens it happens with a involve energy it involve energy either the energy is taken in or the energy is given out the temperature of the system however remains constant alright. What is I am pointing at is such a transition of first order is nothing but from gas to liquid or from solid to liquid. So, whenever you see conversion from liquid to gas what has gone into it? Latent heat it is a latent heat of conversion the temperature remains constant, latent heat is get involved and the density changes abruptly alright. If I see liquid to gas conversion there is a involvement of latent heat and there is a abrupt increase in density when I go from gas to liquid or reverse will happen when I go from liquid to gas and this is what is called as the first order transition where the phase changes from solid to liquid or from liquid to gas or from gas to liquid and from liquid to solid alright. This is what I am going to talk about. For example, the first order transition is nothing but solid to liquid or liquid to gaseous transition the latent heat is absorbed at constant temperature and these are the features that are involved in the first order transition ok. Now, we will see what is the second order transition and this is what happens in when you get transformation from helium 1 to helium 2. These transitions are continuous in the first order but exhibit discontinuity in the second order alright. So, if I differentiate second time now gives free energy function if I differentiate with respect to some other parameter 2 times then I will get discontinuity there and that is why this is called as second ordered phase transition. So, the second order derivative of gives free energy with respect to chemical potential because there is a chemical reaction happening some kind of reaction is happening and in the chemical potential associated with that transition. If I differentiate give free energy the equation of which I had given earlier what I will get is the second derivative of this energy is nothing but specific heat. In the first derivative what I had got was density in the second order phase transition what I get is specific heat and this variation of specific heat in liquid helium is abrupt in this case and possess a discontinuity at the lambda point. So, what we see in helium 1 and helium 2 is the specific heat change drastically because this is the second order phase transition alright. In the first order phase transition what we had was density variation in the second order derivation second order phase transition what we have is specific heat changes or the discontinuity at the lambda point temperature which is 2.17 Kelvin and you will see what it happens. So, this figure really gives you what exactly happens at lambda point. You can see on the y axis what I have plotted is the specific heat on the x axis what you have is the temperature and you can see here that the specific heat variation is suddenly random at this point and literally this is an infinite kind of thing. So, the big change in specific heat capacity at the temperature of lambda point which is 2.17 Kelvin and what can you conclude from the shape of this line alright. This point is called as lambda point and why it is because of the shape of this curve at 2.17 this looks like a Greek letter lambda a Greek letter lambda denotes the specific heat variation at the lambda point where the second order derivative of the Gibbs free function is discontinuous and this is what discontinuity we are talking about at the lambda point and this is why this is called as lambda transition sometimes there is no energy involved is lambda transition as I said in the earlier case first order transition what you had was a latent heat conversion we had gas to liquid conversion we had liquid to solid conversion or solid to liquid or liquid to gas where latent heat is given in or latent is taken out. So, there is a addition of heat or removal of heat were involved in this case there is no energy involved there is smooth transition from one phase or one condition to another condition one liquid helium 1 to helium 2 what changes at this point is the abrupt change in the specific heat capacity at this lambda point, but there is no energy involved in this lambda transition and these are nothing but the characteristics of the second order phase transition which is what is involved in the helium 1 to helium 2 transition. The specific heat at is infinite at lambda point almost infinite at lambda point and it is called as second order transition. So, one can call it as lambda transition as far as helium specific is concerned or we can always call it second order transition in this case. So, what we saw just now was what is the first order transition and what is the second order transition and what we have to understand is the first order transition density changes happen second order transition Cp or the specific heat abrupt changes are happening this is what is very specific of helium and if you understood that we will go to the next part to understand what is this super fluid helium. So, this curve is basically giving you the viscosity versus temperature as I talked to you earlier the helium 1 to helium 2 phase change the helium 1 to helium 2 phase transition is basically because there is some viscosity change also. In addition to viscosity what has changed was this discontinuity which happened at of Cp at lambda point, but how do I differentiate between helium 1 and helium 2 is basically because of it is own viscosity. Now, here you can see the viscosity how does it change for helium 1 and helium 2 on the right side of lambda point or on the left side of the lambda point. Capitza was a person who did lot of work on helium low temperature physics and specific to the helium 1 and helium 2 transition. So, Capitza stated that viscosity for flow through thin channels is independent of pressure drop and is only a function of temperature. So, here you can see that viscosity is absolutely constant as far as normal helium was considered, but as soon as you got a super fluid. So, you got a normal viscosity associated with this as soon as you came down below lambda point the total viscosity decrease drastically this is what you can see from this figure alright. How to understand this? This has to be understood that you had very high viscosity up to lambda point and suddenly below the lambda point the viscosity changed that means you had some different things happening below this. What is this? To explain this one only a 2 fluid model is being used. What is this 2 fluid model? Here I got a different behavior below lambda point this is my lambda point temperature 2.17 Kelvin and below 2.17 Kelvin I got 2 curves which is giving me the density variations in the super fluid and a normal fluid. In the 2 fluid model which is what proposed by Capitza the liquid is assumed to be composed of 2 fluids that is a normal fluid and super fluid. So, on the left side of lambda point what you have got is some normal fluid and some super fluid. As you go on reducing the temperature at 0 Kelvin what you got is all the super fluid. As you go up to the lambda point what you got is all the normal fluid that means what you have in between the lambda point and 0 Kelvin is a mixture of normal fluid and super fluid and this is what the 2 fluid model suggest that the fluid between the temperatures of lambda point and 0 Kelvin has some density contribution coming from the super fluid and some density contribution coming from the normal fluid and this is what the 2 fluid theory is all about. Mathematically I can write density at any point at this between below 2.17 Kelvin is rho n plus rho n rho s where rho is the total density and rho n is a normal density and rho s is a super fluid density. So, the total density at any point below 2.17 Kelvin is a contribution from a normal density that means from the normal helium and from the super fluid helium or a density component coming from the super fluid. So, at any temperature below 2.17 Kelvin what you have is a contribution coming from normal fluid and contribution coming from super fluid. What you can see from this figure is as you go below 2.17 Kelvin rho n by rho it is a rho n by total density the density of normal fluid divided by total density is becoming absolutely 0 which means that the contribution of rho n is becoming absolute 0 it is coming to 0 while the rho s by rho starts increasing up below the 2.17 Kelvin and it almost becomes equal to 1 which means that rho s is equal to rho in this case same thing is being given over here. At less than temperature of 2.17 Kelvin the contribution of as you go down from 2.17 Kelvin towards 0 Kelvin the contribution of rho s is going to increase given as per this line while as you go on the right side the contribution of rho n will start increasing alright and at lambda point what you got is a 100 percent rho n or rho is equal to rho n in at the lambda point the figure shows the temperature dependence of density below the lambda point what you can see it as temperature equal to 0 you got rho is equal to rho s that means it is a 100 percent contribution of the super fluid in this case at a temperature more than or equal to 2.17 what you have is a rho n and between the temperature 0 to 2.17 Kelvin you got a component coming from normal fluid and coming from super fluid. So, rho in this case is equal to rho n plus rho s this is a 2 fluid model which explains to you the total fluid viscosity safely compared to what we see in the viscosity the super fluid component goes on increasing below 2.17 Kelvin and therefore the total viscosity almost reaches 0 at 0 Kelvin while at lambda point you got all the components in the normal helium and therefore rho n contributes to that and therefore the normal viscosity will come into picture. If we talk about heat transfer we just talked about viscosity the heat transfer in super fluid helium that is liquid helium 2 is very very special when the pressure about liquid helium 1 is reduced by pumping the fluid boils vigorously. So, if I remove the pressure the boiling of liquid will happen of liquid helium 2 will happen when the pressure above liquid helium 1 is reduced by pumping the fluid boils vigorously during pumping the temperature of the liquid start decreasing. So, I got some liquid helium 1 and I remove the pressure over it what will happen the temperature of the liquid will decrease and the part of the liquid is boiled away all right. But as soon as the temperature of the liquid reaches less than lambda point temperature that is that means less than 2.17 Kelvin the apparent boiling of the fluid stops that means what was vigorously boiling earlier which you could see from outside suddenly will come to stand still and a very quiet and apparent boiling which you could see from outside will stop suddenly which is happening at T less than lambda point temperature why does it happen the liquid now at a temperature less than lambda point temperature it becomes very clear and quiet even though it is vaporizing rapidly all right. So, vaporization happening the boiling is happening however it has become very clear and quiet and not vigorous as it was when the temperature was above the lambda point this is difference as soon as in boiling in boiling as soon as the liquid comes below the lambda point why it happens because the thermal conductivity of liquid helium 2 is very very large it is very large and that the vapor bubbles do not have time to form within the body of the fluid before the heat is quickly conducted to surface. Now this is the real reason what happens below the lambda point temperature below the lambda point temperature the thermal conductivity of helium 2 is so large that before the bubbles reach in the surface which is what happens in normal boiling heat gets conducted because of this very high thermal conductivity of helium 2 and therefore because the bubbles do not rise up that vigorous boiling stops the liquid apparently looks very quiet and clear and that is why the word which we had used earlier that apparent boiling phenomena stops you cannot see boiling happening over there but boiling is happening. So, you can see from this table how the thermal conductivity changes if one goes from helium 1 to helium 2 you can see here that helium was has got thermal conductivity at 0.024 watt per meter Kelvin while helium 2 has got a 86,500 watts per meter Kelvin thermal conductivity. So, you can see relative difference between these two conductivities easily and can understand why that apparent boiling which I talked about stops as soon as helium 1 goes to helium 2 state below lambda point temperature. Similarly, you can see what happens to the viscosity which is in minus 10 to the power minus 6 right in this region while it has gone to 10 to the power minus 7 to minus 12 depending on the slit size the viscosity will now show changes the viscosity will be different for a bulk flow and for a flow through small pipes or small slits. These two property changes of thermal conductivity and viscosity make helium 1 and helium 2 as two different fluids two complete different fluids and therefore, their utilities also could be different because of these changes properties all right. So, this is what we talked about of helium 1 and helium 2 and also about the phase transition. Just an additional information I want to add to this lecture is that Kapitza of which you talked about we talked about he was awarded Nobel prize in physics in the year 1978 for his basic inventions and discoveries in the area of low temperature physics all right this is what we talked about and its contribution to the super fluidity of the helium all right. This is my end of lecture and what you have got is a self assessment exercise it give us given after this slide again please kindly assess yourself for this lecture very honestly this will give you a feedback about this lecture. These are different questions over here of which you are expected to answer yourself I have given the answers although also at the end of this thank you.