 So, welcome to the lecture number 40 on cryogenic engineering under the NPTEL program. In the earlier lecture, we have seen the importance of instrumentation in cryogenic engineering and various properties like pressure, temperature, liquid level. These are the properties which we want to study in this lectures, etcetera are monitored for safe operation. Every cryogenic operation needs to monitors these parameters. There are various parameters, but mostly pressure, temperature, liquid levels are very important parameters which are generally monitored. So, we started with temperature to begin with and we are still continuing with temperature. So, we discussed about the thermocouples and the metallic RTD resistance temperature dependent parameters in the previous lecture. We found that T type, K type, E type are the different types of thermocouples that are normally used. And we talked about platinum RTDs Pt 100 and Pt 1000s where 100 and 1000 are the resistances of this sensor at 0 degree centigrade and these are normally used some of the commonly used RTDs in cryogenics. So, we talked about thermocouple, we talked about RTDs or platinum based RTDs that are used for temperature measurements. Now, in this particular lecture, we will take the temperature topic ahead and we will talk about measurement of thermo physical properties that is temperature and we will continue with that. And we will go to lastly the measurement of liquid level at the end of this lecture. So, in the earlier lecture, we have seen a metallic RTD in which the resistance of a conductor changes with temperature, this is what we have seen. We found that as the temperature decreases, the resistance decreases as far as these RTDs are considered. Similarly now, in non-metallic sensors, many times we prefer to have a non-metallic sensors also because of various other reasons because we can actually make a kind of sensor which we want. So, non-metallic sensors like silicon diode, Cernox and ruthenium oxide, they also exhibit this temperature dependent properties. So, we had a metallic sensors earlier and now we have a non-metallic sensors like silicon diode, Cernox, ruthenium oxide exhibiting such property where the resistance also changes, resistance changes with temperature again. So, we know what is a diode. So, a diode is a two terminal electronic component which is most commonly made of silicon. So, we have talked about silicon diode. The properties of diode you know basically allows the current to go to only in one direction while it does not allow the current to go in opposite direction. Also, it has got some temperature resistance dependent current properties also and that is what we utilize for temperature detection. The I versus V characteristics or IV variations of it, the current voltage variation of a diode can be changed by adding impurities or dopants like germanium, arsenic etc. And therefore, we can have the kind of properties we want at various temperatures. You can add dopant to diode and you can change the characteristics or the IV variation of these diodes. In these sensors, a constant current supplied typically in microamps, very small current. In earlier case, we had a milliamp current now. But in these diodes, in Cernox, we have got a constant current supply typically in microamps is fed across the sensor. That means you want a very low current flowing through it and therefore, we got a very low heat generation in the sensor also. The I square R also is very, very small and therefore, the errors involved are also going to be very, very small in these cases. With the decrease in the temperature, the resistance of the device increases. So, if you remember in case of PT100 for example, with the decrease in temperature, the resistance of the device or the RTD had increased. While in these cases, with the decrease in temperature, the resistance of the device increases as the temperature decreases. So, it is important to note that this property is in reverse to the characteristic of metallic RTD. In metallic RTD, what happened? The temperature decreases, the resistance came down. This resistance change is calibrated against the temperature change. So, as it was in the metallic RTDs, in these cases also, resistance change becomes a function of temperature and one can do a calibration that can fit and curve so that the resistance changes with temperature can be calibrated properly. So, let us come to the non-metallic sensors. Few of the commonly used non-metallic sensors are silicon diodes. Silicon diodes, the sensor consists of a small silicon chip with a repeatable resistance temperature property. So, typically a sensor would look like this, a diode would look like this. It has got two outputs or two wires coming out of this and a small casing in which silicon chip is kept, which is having cover and some kind of sealing also. So, this will come down on this and this will constitute a silicon diode, alright. So, this is what predominantly will be used. Then you got a CERNOX, a similar local CERNOX like a silicon diode. So, CERNOX is a better deposited thin film resistor. You know thin films basically. So, these thin films are having a particular IV characteristics, alright. So, you can make thin film, you can have thick films and they have a different characteristics. CERNOX is a basically a trademark. It is a trade name for lecture company, but typically it represents sputter deposited thin film resistor. CERNOX is a trade name for zirconium oxynoitride manufactured by lecture USA. So, typical CERNOX would look like this. Again it has got a chip which is going into this or a thin film going into this and again it is housed in a small you know kind of a casing. And then we got a third category also which is ruthenium oxide. It is a thick film resistor which is widely used in magnetic field applications. So, whenever you got a high magnetic field environment, ruthenium oxide will be preferred. It works in a similar principle as a change of temperature will result in change of resistors. So, typically we have got a three different kinds which we discussed there are plenty of other things also. You got germanium, we got a you know gallium, aluminium, arsenide and thing like that. All the dopants could be used. But typically most commonly that the sensors which are used are silicon diodes CERNOX and CERNOX. So, let us study silicon diodes in little bit details. Alright, so you can see a silicon diode. The adjacent photograph shows a casing which houses a silicon diode. We saw the photograph of silicon diode earlier and it is a very small thing and it is very costly. And therefore, normally one did not touch the silicon diode directly. It is always kept in some kind of casing. So, you can see a copper casing over here and but it has got a small hole also with which you can actually have a brass you know nut kind of it is screw kind of a thing with which it can be attached to the surface of which the temperature has to be measured. And these are the wires which will come out. This casing is actually housing the silicon diode. The packing is a ceramic hermetically sealed casing with the lowest self fitting errors alright. And the casing is designed to withstand the mechanical fatigue occurring due to the temperature change. So, all those properties have to be taken into account to find out particular casing for the silicon diode. Normally one should not buy the silicon diode only one should buy the silicon diode with these cases. So, that handling become very simple. You are not touching the silicon diode directly and also the placement of the silicon diode on the surface of which temperature has to be measured can be connected. It can be in good thermal contact with the area of which the temperature has to be measured. The 4 wire connection is recommended for accurate sensor reading. Very often these sensors are provided with signal conditioner and display temperature controller. So, I am showing a lecture temperature controller and these wires will be connected to these. And you can see the kind of sensor you have bought. One can select the kind of sensors on this particular display and the calibration curves are normally fade. So, calibration curve for a particular diode which we are using can directly be fade to this temperature controller and you can have a display as shown over here alright. So, before I go to silicon diode I just want to show the picture. I do not I want to show the silicon diode here and you can have a look at this silicon diode. So, what I just showed to you we can actually see the entire thing over here. So, you got a silicon diode which is put in this casing and the 2 wires the 4 wires are coming from here and these this is a hole through which a nut can be you know screw can be put it and if I want to measure the temperature of this I can just put it down over here and get a good thermal contact with the surface of which the temperature requires to be measured alright. Let us go back to the slide. So, if I see now the silicon diodes and its temperature characteristics they look like this the adjacent figure shows the variation of voltage with temperature for a silicon diode. And you can see this is the voltage on the y axis and the temperature here on the x axis. If you remember in case of PT 100 this curve was coming down like this the voltage was higher and as you come down the temperature it was in opposite direction. Well in silicon diode you can see that it is opposite direction that is as the temperature decreases the voltage increases. So, the sensitivity can be negative over here alright. Also you can see that as you go down the temperature up to let us say 50 Kelvin it is going in a linear fashion in one line with a some different slope and there also you can see some linear variation below 50 Kelvin also you got a linear variation. So, you can have a good linear variation that means the measurement you can have a very good line fit in order to get a good calibration curve for such diodes. It is clear that the gradient of the curve is very steep for the temperature below 30 Kelvin. So, let us say this is 30 Kelvin and you can see how the gradient has increased as compared to the restored temperature range. Therefore, it is most preferred in this range for good accuracy. So, what we want is basically a steep change. So, that the sensitivity increases alright. So, below 30 Kelvin that means as you come down lower the temperature these are the sensor which should be preferred when it comes to comparison for against PT 100 or thermocouples. So, at lower and lower temperatures silicon diodes are most preferred. So, below 30 Kelvin I will always prefer to have a silicon diode and not PT 100 and not thermocouples because of such characteristics of the silicon diode. So, therefore, it is most preferred in this range for its good accuracy. The figure shows the variation of sensitivity dv by dt with temperature for a silicon diode. So, based on what we saw earlier the sensitivity remains constant is actually a slope of what we saw earlier alright. Slope remains constant up to a particular level and the slope increases. The sensitivity remains constant up to 30 Kelvin this is what you can see and suddenly the slope increases. It increases with the decreasing temperature below 30 Kelvin hence it is most preferred for that means the sensitivity is higher for lower temperatures. For the sensitivity it is still higher actually from room temperature till around 30 Kelvin alright, but it increases below 30 Kelvin. The following table gives some of its properties. We can see that the range for which the silicon diodes are used is 1.4 Kelvin to 475 Kelvin. So, quite low temperature you can come almost close to 1 Kelvin and you can go up to 475 Kelvin while using silicon diode. The excitement current is 10 micro amps is a very small current. The repeatability is very good 10 millikelvin at 4.2 Kelvin, 16 millikelvin at 7.7 75 millikelvin at 273. So, repeatability is very good actually in the range of 10 millikelvin at lower temperature because of high sensitivity. The accuracy is around plus minus 50 millikelvin or better. So, this is a very good accuracy as far as temperatures you know at low temperatures are considered. Sensitivity is very high minus 33.6 millivolt per Kelvin at 4.2 Kelvin. We can see the sensitivity is high at 4.2 Kelvin as compared to what it is at 77 Kelvin. So, sensitivity is just minus 1.91 millivolt per Kelvin at 77 Kelvin. These are some you know some figures which we have taken from various references. Most of the silicon diodes would have their values around these values only they are all demonstrative just representative values basically ok. The advantage of a silicon diode are the activation current is in the order of micro amps we saw just 10 micro amps. Therefore, the i square losses are negligibly small just clear. It exhibits a linear response over the entire operating range and repeatability and accuracy. So, we got a linear response which is what is expected from a good sensor and silicon diode that showed these characteristics. What is the disadvantage? The disadvantages of a silicon diode are errors are induced in magnetic field and this is a very important disadvantage which has to be considered because most of the cryogenic operations happen in some kind of magnetic field. So, if you got a atmosphere or environment of magnetic field when the temperature measurement is carried out then the silicon diode will not give good results alright. So, you got a got to have a very small magnetic field but you could have some magnetic field it will show some you know weird readings basically alright. So, silicon diode cannot be used in magnetic field active places and the second disadvantage is the diodes are of course costly. I mean these sensors are much costlier as compared to thermocouples and Pt 100. So, when as to really justify if you want to measure 4.2 Kelvin, 10 Kelvin or a temperature below 30 Kelvin and that to more most accurately then such sensors need to be placed. Silicon diode has to be thought about for 4.2 Kelvin or if you are working with helium cryogenics levels alright below 20 Kelvin and so. The representative prices are let us say calibrated silicon diode would cost 39000 rupees. This is just the cost of sensor then we got to cost the casing if you want to have then cost of course transport and packaging and thing like that. And non calibrated ones will be almost half the cost but then you have got to calibrate it also alright. So, depending on what you want what temperatures you want to measure one should buy silicon diodes. So, the next is Cernox as mentioned earlier Cernox is a thin film RTD it is manufactured by lecture U.S. trade name and which is very also which is very commonly used sensor for helium temperature levels. It exhibits a good temperature sensitivity over a wide range of operating temperatures. One of the most important characteristics of this sensor is its accuracy in magnetic field. Now this is a very important characteristics and as I said most of the cryogenic experiments cryogenic measurements are done in the magnetic field environment. For example, if you are working with MRI, NMR you know you have got a magnet you have got a superconducting magnet many times where you want to do temperature measurements and therefore your sensors will be always be surrounded or it will always be in some magnetic field. And therefore for accurate temperature measurement Cernox is a good solution. Also these sensors exhibit a fast response time at low temperature alright. So, Cernox is always preferred at low temperatures when the magnetic field environment is prevalent. Cernox are packaged in a robust hermetically sealed casing similar to silicon diodes. So again you have got to buy them in casing or you preferred it is preferred that Cernox is get packaged in a robust hermetically sealed casing. The following table gives some of its properties as we saw for silicon diode. Similarly, we got a properties of Cernox. Now the range you can see from 0.3 Kelvin to 325 Kelvin by silicon diode from 1.4 to 475 a representative value of course in this case we can come down below 1 Kelvin for Cernox. Again the excitations of the order of 10 microamps the accuracy is plus minus 5 milli Kelvin at 10 Kelvin while the repeatability also is plus minus 3 milli Kelvin at 4.2 Kelvin. These are some of the property specifications for Cernox. The advantages of Cernox are these RTDs offer excellent stability over the entire operating range. Similar to silicon diodes Cernox exhibits a linear response for temperatures. So behavior is similar to what we saw silicon diode. Cernox diodes are not affected by the magnetic field and this is what is one of the most or the biggest disadvantages of the Cernox sensor. So typically non-metallic sensor the three important differences between a non-metal and a pure metal sensor. The non-metallic sensors what we saw are the Cernox and silicon diode and the pure metal sensor what we saw were the thermocouple and Pt100. It comes of sensitivity. The sensitivity of a non-metal sensor is more than pure metal at any temperature. So basically non-metal is what we are talking about semiconductor. Diode is a kind of semiconductor. Sensitivity of a semiconductor always is more than pure metal at any temperature. Temperature coefficient. The coefficient of temperature resistivity of a non-metal sensor is negative. This is what we saw. When temperature decreases the voltage increases. Therefore the coefficient dv by dt of a non-metal sensor is negative whereas for pure metal for Pt100 for example dv by dt was positive. Temperature decreases voltage decreased. This is a major change when you go from a metal to non-metal. Resistivity. Resistivity of a non-metal sensor is very high. It is very important. Resistivity high as a result a non-metal sensor has a small length and relatively a large area. So because the resistivity is very high and you are talking about variation of resistivity with temperature. Variation of resistance with temperature and resistance depend on the resistivity length area etc. So because the row parameter or the resistivity parameter is very high you can have a non-metal sensor as a small length and small and relatively large area because area will come in the denominator. So rho into L by A if you have you can have the resistance parameter and resistivity is very high in those cases. So if I want to compare silicon diode and Cernox this is the table where you can see that silicon diode normally will be used from 1.4 Kelvin to 475 Kelvin while Cernox will be used from 0.3 to 325. You had excitation of 10 microamps, 10 microamps. Accuracy is 50 millikelvin, 5 millikelvin at 10 Kelvin and the repeatability also is plus minus 3 millikelvin which is good and plus minus 10 millikelvin at 4.2 Kelvin for silicon diode. So this is just to have a some representative facts, some comparative data which I have taken from various references to compare a silicon diode with Cernox. So various thermo physical properties which we wanted to study and we want to measure in cryogenic engineering. There are various thermo physical properties that are measured or monitored in cryogenics. They are temperature, liquid level, pressure, mass flow rate, viscosity and density, electrical and thermal conductivity. These are very important properties that normally one needs to monitor in cryogenic experiments. However, we are going to talk about the top three temperature, liquid level and pressure. Offish till now we have talked about temperature measurement that can be done by using thermocouple, Pt100 and silicon diode, Cernox etc. We will now go to know what is this liquid level measurement. So cryogen level is a very important parameter and we will talk about that now. We will talk about liquid level measurement or cryogen level measurement. In this topic only the first three properties are covered which are very important. I am taking only three properties which are normally very very important to be measured in cryogenic engineering and therefore now we will go for liquid level. So liquid level measurement, it is important to monitor the liquid level in a close cryogenic condition. Now this is very important because you got to plan your experiments in cryogenics and you got to know what is the liquid nitrogen level you have. That means how many liters of liquid nitrogen you have, how many liters of liquid helium you have and accordingly it is important that the cryogenic containers are never emptied. For example, you got a cryostat and you always retain some liquid helium at the bottom and before it gets finished completely, you should have the next lot of liquid helium cold in that basically, alright. So topping up has to be done when there is some liquid helium is left at the bottom. Many times for superconducting magnet also you should ensure that the magnet does not become normal or the magnet does not quench and it is very important therefore to monitor the liquid helium level or liquid nitrogen level in such applications. This is a very important parameter which is always all the liquid nitrogen containers, divorce, liquid helium divorce, they will always have a level gauge over there. It tells you it monitors how many liters of liquid helium or nitrogen is left there and therefore correspondingly you can have your experiments planned. So the liquid level monitoring is very important to avoid overflow of cryogen that is A to know the amount of cryogen left at any time. This is very important. Now various electronic measuring devices techniques are available in order to monitor the liquid level. So various ways of monitoring because it is not a very quite different from monitoring other liquid levels but do not forget that these measurements are going to be done at very very low temperature. For example, liquid nitrogen minus 196 degree centigrade or 77 Kelvin, liquid helium 4.2 Kelvin. So whatever device you use whatever technique you use you have to understand that the sensor is going to see very very low temperature and therefore new sensor has to be designed for monitoring the liquid level of cryogenic conditions. The level of the liquid inside the container is often expressed as a percentage of total volume. Normally you will say 100% field, 50% field and thing like that and you know that entire thing can have 200 liter or 500 level. So from there you can calculate how much percentage of liquid, how many liters of liquid has been there in the container. The measuring device technique that are used in cryogenics are deep stick measurement. I mean the approximate liquid level can be understood for common cryogen like nitrogen. You cannot do of course this technique cannot be used for helium for example but for nitrogen this can definitely be used and this is still being used just to an approximate level of what is the liquid level of nitrogen available in the open container. Then we got a hydrostatic gauge. We got something like electric resistance gauge and we know that the resistance changes at lower and lower temperatures. So these are the facts that are used to indicate the level in cryogenic, cryogenic containers. Capacitance liquid gauge. So you got a resistance gauge, you got a capacitance liquid gauge, you got thermodynamic liquid level gauge, you got superconducting liquid helium level gauge. So you got a various ways to have this liquid level measurement. One can use any kind of this level gauge depending on what cryogen level you want to identify. Certain things cannot be used for helium or certain techniques cannot be used for nitrogen for example. So one has to really you know understand which level gauge should be used to monitor a particular cryogen. Well dipstick is a very simple technique that is still being used when you want to have approximate level indication. So let us see what dipstick technique is. It is one of the oldest and simplest ways to check the liquid level. As soon as you got a empty tube actually which could be of you know stainless steel or it could be of anything any material basically and you start inserting that liquid dipstick in the liquid or a container of which you want to measure the level. So as soon as the open stick you know touches the liquid the boil off happens because your stick is going to be at 300 Kelvin. So as soon as it touches nitrogen a boil off would happen and this boil off would come through this tube up. So as soon as it touches the liquid level you can hear a bubbling sound first or a boil off and that is the indication where the thin open tube is dipped into the liquid. So you can see now at what point the liquid level is and that will give an approximate understanding about the liquid level in the cryogen. The following video demonstrated this technique for liquid nitrogen. This video will make it absolutely clear how the dipstick technique works. So let us have a look at this video which shows the working of the dipstick which is normally used in a lab atmosphere. So what you see here is a container of around 1.5 litre of liquid nitrogen and what you see in this my student's hand is a dipstick which is just a hollow tube of a small diameter running for around let us say 2 meter or 1 meter or 2 feet kind of a length. But what is important is a small hole and now let us insert this tube or dipstick in this liquid level or to measure the liquid level of this container. So around 1.5 litre and you get a small containers and you see as he has dipped this and suddenly you can see that the boil off has started occurring alright. So you can see a very important thing that as soon as it touches the liquid level the boil off starts coming out this tube which is basically because of the heat because of the boil off that occurs as soon as this touches and now I can take it out and I can see corresponding outside how much liquid is there in this container alright. So you can measure using a simple scale and corresponding you know that you know vertical height of this means 1.5 litre and therefore this will this much of height will be something like that. So if I can also see approximately how much liquid there. So you can see that this much amount of liquid from bottom is going to be there let us say around 0.75 50% is going to be there and this is the way a dipstick would function. So very approximate indication of liquid nitrogen level. So having seen the video now let us go to the next gauge which is called hydrostatic gauge. So consider a closed cryogenic vessel as shown in the figure. So this is the liquid level and the sensor is going to be dipped in this and it will monitor at what point what is the level of this liquid is. Let Lf and Lg are be the heights of the liquid and the gas column. So you have got a liquid level over here you got a gas column over here because the gas in this which is the boil off of this liquid basically and you can see that you got a Lf and Lg are the heights of the liquid and gas column respectively and we have L is equal to Lf plus Lg simple. Pressure tapings are provided at top and bottom of the vessel as shown. So this there are two pressure tapings here and here and this pressure tapings are now connected to a pressure gauge also. Tapings are connected across a differential pressure measurement device as shown over here alright. As the name suggests now the hydrostatic name the hydrostatic differential pressure is calibrated in terms of liquid level. Therefore the pressure difference delta P can be written. Now this is the pressure gauge basically and this pressure is going to actually show a delta P pressure difference at this point and this point which actually is indicative of the level alright. So the pressure differential delta P can be written now in terms of Lf and Lg. Lp is equal to rho Lg for gas and rho Lg for so rho f Lfg which is this column this vertical pressure plus so the pressure at this point actually at this point is equal to rho f Lfg plus rho g Lg g at this point while the pressure at this point would be atmosphere. So the pressure difference is actually going to major the pressure at this point which is a function of Lf and Lg alright. So pressure difference therefore is actually going to see the pressure difference at this point and at this point and the delta P therefore will be rho f Lfg plus rho g Lgg. Using L is equal to Lf plus Lg, which is what we know. The above equation can be rearranged as, so I am just replacing this Lg as L minus Lf and put this equation and this manipulator. The terms what you get ultimately is delta P is equal to rho f minus rho g Lfg plus rho g L into g, alright. By putting this value of Lg as L minus Lf here, you get this. The density of vapor is negligible as compared to that of liquid. So in the equation what we found, you got a term called rho f minus rho g and you can see that rho g is going to be very small as compared to rho f. Therefore, what we can write is this equation what we have, delta P is equal to rho f minus rho g Lfg plus rho g Lg Lg and we just said that the density of vapor which is rho g is going to be very small as compared to rho f. So rho f minus rho g can be written as rho f only and this can be neglected in front of this term. So by this assumption that rho g is very small as compared to rho f, you can get delta P is equal to rho f Lfg. And therefore, we can write Lf is equal to which is this height. The liquid level height is equal to delta P upon rho fg. Rho fg is constant and therefore, we can say that Lf is directly proportional to delta P. So whatever delta P is shown here at this point, it can be calibrated straight away in terms of Lf. So when you got a 100 percent Lf, you got some delta P. You got 50 percent, you got something and you can have a calibration function fade to this pressure gauge and when you can compute whatever pressure difference is shown here, correspondingly one can compute this pressure difference as a function of height over here. The pressure gauge is directly calibrated in terms of height of the liquid. The sensitivity of the gauge is directly proportional to the difference in the liquid and vapor density which is just of rho f minus rho g. If you could neglect that, then that is possible. If we cannot neglect this, then it is not possible. And just wanted to compare with these different fluids. So you got a density is over here. For nitrogen, you got rho L is equal to 808 while that is rho f we are talking about and rho g is 0.65. If we say rho L minus rho g for nitrogen, all right, rho g is very small as compared to rho L and therefore, one can neglect for nitrogen rho g as compared to rho L. But for hydrogen and helium, the liquid density itself is very small while in case of nitrogen, the liquid density is very, very high. So because the liquid levels are liquid densities are very low values, rho L is equal to just 70, rho L is just 124. So in front of this, your rho g cannot be neglected, right. So rho L minus rho g becomes a parameter, it is an important parameter and therefore, for hydrogen and helium, because of the low density of liquid, hydrogen and liquid helium, you cannot use such technique. Hydrostatic gauge cannot be used because I cannot neglect rho g in front of rho L. In the cases of hydrogen and helium, rho g cannot be neglected in comparison to rho L. This assumption what we had was rho g is very, very small as compared to rho L, does not hold good for hydrogen and helium. Hence, these gauges cannot be used for hydrogen and helium, but of course, they can be used for nitrogen. Then we go to the next kind of a gauge, which is electrical resistance gauge and this gauge is movable actually. Let us see how it works. So the schematic of a movable electrical resistance gauge is as shown in the figure and here you can see that is a movable gauge here. In this arrangement, a movable resistor is connected across the voltmeter. So you can see you got a movable resistor, you can go up and down. Again, you got a liquid level at this point and you got a boil of gas in this region. So you can, you can push this sensor down and you can see what happens at the interface when the sensor enters from the gaseous region and enters the liquid region. This movable, the movable sensor element is heated by using a very small current. What I do is I just heat it small before I want to measure the level. Just heat it, therefore the temperature of the sensor increases because it gets heated by I square r value, alright. And now that the heat transfer, because this heated surface and the heat transfer from this resistor to the gas or resistance to the liquid depending on where it is, alright. It is clear that the wire temperature is high when it is above the liquid level. So when it is in the gaseous region, you got a heat transfer by convection to the gas here and this heat transfer is going to be very, very less as compared to more as compared to when it is in the liquid state, alright. So temperature in this case is going to be very high while the temperature in this case is going to be low. So if you move this at a particular point, there is a sudden change of temperature that will happen and therefore voltage change will occur and therefore from that you will come to know that the level lies at this point. So if you take it up and start coming down at a particular point, because the heat transfer characteristic in the gas and heat transfer characteristic in the liquid, there is going to be some temperature change which is going to be shown as a change in value of V and therefore you can calibrate with the movement of this sensor at what point it happens and that will indicate indirectly the level of the cryogen. The heat transfer coefficient of the liquid is nearly twice that of vapor and therefore there will be good heat transfer in the liquid and therefore temperature will be low in this case while the temperature will be higher in this case, alright. As a result, when the wire is dipped into the liquid, the temperature of the wire drops momentarily and therefore there is a change of resistance that will occur, change of voltage that will occur, which can be monitored as a level indicator. The electrical resistance thereby the voltmeter reading undergoes a sudden change which is actually calibrated. This sudden change is the indication of the liquid vapor interface. So this is what constitutes in a movable electrical resistance gauge. Now let us see electrical resistance gauge. When it is in movable, that means there is no movement happening of the sensor as what we did earlier. This method was first devised by Laxler and Cox in the year 1956. Unlike in the earlier arrangement, this arrangement has a fixed resistor along the total height of the cantilever. So what you see here? A fixed resistor. So you can see in the earlier case, I had a resistor only up to this and I will go up and down or I will move the electrical resistance while here I got a resistance coming down from the 100 percent liquid to the 0 percent liquid and there is a resistor running from top to bottom and ultimately it is connected to some voltmeter, alright. And if I want to measure the liquid level now, I do not have to move this up and down because it is occupying the entire space, entire the vertical space in the container. The resistance is connected across a voltmeter as shown in the figure. The resistance element is fed by very small current. If I want to measure the liquid level now, I just press a button here which will pass a current, a very small current to the circuit. So there is a circuit over here and therefore, there is a effective resistance of this circuit which is what is indicated to the voltage here. With the change in the level of the liquid, the resistance of the wire changes. So as we know that this much part is in the vapor region, this much part is in the liquid level. So depending on how much part is going to be in the gaseous region and how much part is going to be in the liquid region, you got a heat transfer which is what we just have seen. So the temperatures will be different at this point and correspondingly, the resistance of the voltage shown will indicate at what point this liquid develops. How much part is dipped in liquid? How much part is there in gas? That can be calibrated and indirectly, the voltage shown at this point will be representative of what is the cryogen level over existent over here. So with the change in the level of the liquid, the resistance of the wire changes. This change in resistance now, this change in resistance thereby, the change in voltmeter reading is calibrated as a function of liquid level. So here I have got a immovable unit and as soon as the liquid level changes, the voltage will show that change. Now what is the difference? You got a immovable unit and therefore, this unit is always dipped over here and which will also cause some losses in assist because this will have some conductive losses brought it from 300 Kelvin down and then of course, you are dipping an outside foreign body in the liquid which will cause some extra boil off. Not only that, it is getting some conduction heat from outside in addition and therefore, such sensor actually are producing continuous boil off at the advantage of being immovable. You do not have to move the sensor in these cases. The advantage of such sensor therefore, is the system does not involve any moving component. So I do not have to worry about any extra mechanism of how to move this sensor up and down. So system becomes simple in this case. The gauge has a continuous induction of liquid level. So because the gauge is always dipped over here, one can have a continuous display of the liquid level also if one wants to. The disadvantage is continuous energy is dissipated leading to excess boil off. So because the system is actually all the time dipped in liquid helium, in the earlier case, it was not and it will also bring therefore, some conduction happening across it. Therefore, it will cause some extra boil off. So continuous energy is dissipated leading to excess boil off. This is the disadvantage of such assist. In a similar way now, we can have various other gauges working on similar principle. For example, we got a capacitance liquid gauge. Again you got a capacitance over here in gaseous region and capacitance exists in the liquid level and again they can be actually calibrated to indicate the level. In this arrangement, the level probe consists of a two concentric cylindrical electrodes as what we see here, placed vertically as shown. The dielectric constants of liquid and the vapour are different. We know that the dielectric constant for gas is Cg, the dielectric constant for the liquid is Cf and this is going to be different for gas and different for the liquid. Let them be denoted by Cf and Cg respectively. The net capacitance Cnet is a function of Cf and Cg, which in turn are function of liquid and vapour heights. So depending on what is my Lv is, what is my Lg is corresponding to that you got a Cf and Cg and therefore, you got a Cnet, net capacitance and therefore, I can have net capacitance calibrated with the level over here with Cf actually over here. So net capacitance can be calibrated as level indicator. It will indicate the level directly depending on the calibration. With the change in liquid level, the net capacitance changes. This property is used to calibrate the liquid level instead of this. So capacitance liquid level also actually is going to be dipped all the time. So it is also going to bring some dissipative energies energy over here, but then this is what the principle of the capacitance liquid gauge will be. The advantages are again the system does not involve a moving component. The gauge has a continuous indication of liquid level and disadvantages again it will bring in some extra load on a system. Going to the next type of liquid level gauge is thermodynamic width gauge. The schematic of a thermodynamic level gauge is as shown in the figure. It works on a principle that you can see the gauge over here. So what you can see is your capillary running from top to bottom in some kind of dead space over here where the gas is stored and you put a pressure indicator at this point. So it works on a principle that liquid undergoes a large change in the volume when it is evaporated alright. So this is the principle on which it works. So when the gas becomes liquid, there is a large change in the volume happens. For example, when the condensation happens, the volume decreases. The gas will occupy all the volume. The liquid undergoes a large change in volume when it is evaporated. So when liquid becomes gas or gas becomes liquid, there is a huge change in volume and therefore there is the pressure loss alright. So this is the indicative of the level that is the principle they want to use. The probe consists of a thin capillary tube which is a hollow kind of a thing and a pressure gauge via a buffer volume. So you got a buffer volume, you got a buffer volume connected to a capillary tube and at the top you got a pressure gauge. The capillary is attached to a pressure gauge through a dead volume at an ambient temperature. So you got a dead volume which is at ambient temperature. The gauge is charged with a measured amount of gas of the same time as that of the storage vessel. If you want to measure liquid nitrogen or liquid helium, you will charge in nitrogen or helium gas respectively depending on what fluid you have. If you have nitrogen, you will charge nitrogen gas. If you got helium, you will charge helium gas. So the same gas will be there in this capillary tube and staying in this dead volume or volume at room temperature at ambient temperature. As the capillary tube is immersed into the liquid, now you got a capillary tube. Some part of the capillary tube is in the gaseous phase. So in the gaseous part of the boil of gas is stored while the other part of this capillary tube is dipped in liquid. So the gas that going to be in the liquid region is going to get condensed because it has got a boiling point just above this and therefore this gas will get condensed while this gas will remain in the gaseous phase because the temperature of this gas around is going to be more than its boiling point. If I got a nitrogen gas over here, the nitrogen gas and outside temperature is going to be 77 Kelvin. So nitrogen gas in this height depending on how much portion of this capillary is below or is in this liquid region, this gas would condense and accordingly there will be pressure changes happening and this is the principle. So as the capillary tube is immersed into the liquid, the gas in the immersed portion of the tube is condensed alright. So this gas in the capillary tube which is immersed in the liquid will get condensed and therefore there will be a change of volume that happen. The change in the volume of the gas during condensation reduces the gas pressure. So as soon as the condensation will occur, your pressure will decrease and therefore this pressure can indicate how much condensation has occurred and how much condensation occurs will depend on how much part of this capillary is below the liquid level. So depending on the gas which is below the liquid level that will condense and depending on that the pressure would change and therefore this pressure can directly be calibrated as a function of liquid level alright. So changing the volume of the gas during condensation reduces the gas pressure within the capillary and at dead volume. This drop in pressure is used as an indication of the liquid level inside the container. So there is direct calibration between the drop in pressure and the liquid level here. So this is the way the thermodynamic liquid gauge would work. Similarly we got one more level gauge which is normally will be used for liquid helium only. So we got a superconducting liquid helium level gauge. Because it has got a superconducting wire it uses some superconducting material now it is going to be little costlier as compared to the other gauges. It is normally preferred because it is more accurate and simple. So the schematic of a superconducting liquid helium level gauge is as shown in this arrangement and immovable superconducting element is dipped in the liquid helium. So you can see the element of this material which becomes superconducting at liquid helium temperature and whatever part is dipped below in the liquid helium will turn superconducting. And whatever part is above the liquid helium in the gaseous region it will not be superconducting to normal. And therefore depending on whatever part is immersed voltage will vary alright. This is the principle on which superconducting liquid helium level gauge would work. The sensor is connected to a voltmeter and is fed with a small current. Some small current this is the circuit over here and some small current is fed through. This sensor measures the liquid level by measuring the resistance of the measuring filament. So you got a measuring filament running from top to bottom and the resistance or when i flows through this the current flows through this you got a some resistance across this which is what will be indicated by the voltage. Now depending on how much part is below the liquid level because this much part which is below the liquid level is going to be superconducting and therefore the resistance in this region is zero. So whatever voltage is shown will be going to be corresponding to the resistance offered by the material which is normal state. The superconducting state will show zero resistance and this is what can be calibrated as a function of level as far as working of a superconducting liquid helium level gauge is considered. This superconducting filament is housed inside a teflon protective tube. The portion of filament in liquid remains in the superconducting state and exhibits zero resistance alright. So this much part will show zero resistance. Therefore the resulting voltage along the sensor filament is proportional to the length of the filament above the liquid helium. So whatever resistance is offered actually is offered by this normal material in the alright. So this can be therefore calibrated accordingly to show the liquid collagen layer. It is a very important type of level gauge which is used in helium containers. This sensor provides a continuous measure of the helium and again you can press a button when you want to measure things. Current is passed and accordingly voltage can be seen and this can be calibrated in terms of the liquid level. Four wire techniques is used to eliminate the errors resulting in variation in the length of the leads. The small amount of heat generated in the probe is dissipated primarily in the helium gas rather than in the liquid. So when you pass the current through it the heating is going to happen only in this part because this is a superconducting part and therefore there is no extra heating that is or there is no I square are associated with this region. Whatever I square R happens is only in the gaseous or the in the boil of region only. So the heat dissipation in this case amounts to only the part which is in the gaseous space which is the boil of which is the boil of gas not for the part which is dipped in the in the cryogen. So the summary of the lecture therefore is so the commonly used non-metallic sensors are silicon diodes, serenox and rutheninoxide. Silicon diodes have negligible I square R losses exhibit a linear response, good repeatability and accuracy. The I is in microamps and therefore the losses are minimum for these non-metallic sensors. The serenox RTDs offer high response time and have low magnetic field induced errors. So whenever you got a magnetic field environment serenox are most preferred sensors. Sensor used to monitor liquid level are dipstick hydrostatic gauges, electric resistance or capacitance liquid level gauge, thermodynamic level gauge and superconducting liquid helium level gauge. So we have seen the working of all these sensors and they work for the way you want. For example dipstick works for giving an approximate indication of the level for nitrogen while superconducting will be used for liquid helium level and other could be used for nitrogen, neon, hydrogen etc. Thank you very much.