 Hello everyone, my name is Aurob Tiwari, I am PhD student at IIT Bombay. I am also course T of this work. In the previous lecture, you have studied about the various method through which you can store hydrogen in different phases. Also you have studied in the previous lecture, the various method of compression of hydrogen using different type of compressors. In this lecture, we will go in more detail by taking some of the examples, how the hydrogen will be compressed or how the volume of storage will change when the hydrogen will be stored in different phases. So in the first question, we have to calculate the volume required to store 1 kg of hydrogen. First the first question is that what amount of volume we require to store in gases form at normal temperature and pressure and when we pressurize it up to 352 bar to 700 bar. Then we will store, we will try to find out the volume when the hydrogen will be stored in liquid form at 20 Kelvin, then in the solid state at room temperature. Then we compare all these 3 cases of storage and finally we will comment on the hazard related issue when leakage occurs from liquid hydrogen storage tank. So we will start with the first. So the amount of hydrogen to store is 1 kg. We will start with the first case at NTP density of hydrogen gas is 0.089 kg per meter cube. So at NTP the volume required to store 1 kg of hydrogen is which gives us 1 by 0.08 9 around 11.24 meter cube which will convert into litre gives us 11240 litre. This is the first case. When you pressurize this hydrogen up to a pressure of 350 bar at 350 bar the density of hydrogen gas will change and it will change up to 23.65 kg per meter cube. Now if we calculate volume from this, this comes out because when you pressurize the gas the amount of volume required will be less. So now the volume comes out to be 0.042 meter cube which is around 42.28 litre to be exact. After that we will see at 700 bar the density of hydrogen gas is around 40.2 kg per meter cube which will gives the volume to be 1 by 40.2 which comes out to be 0.025 meter cube and in litre it is 25 litre. So from here we have seen that when the pressure is increasing from NTP to 350 bar up to 750 bar the volume to store 1 kg of hydrogen will be at NTP is 11240 litre it is 11240 litre at 350 we have calculated as 42.28 litre and at 750 it is 25 litre. So as we increase the pressure we have seen that the volume requirement will continuously go on decreasing. So this is the, this is one of the method to store hydrogen. In the second question it is given that we have to store this 1 kg of hydrogen in liquid form. So in case B at liquid form liquid phase the density of liquid hydrogen is 70.8 kg per meter cube this will give us the volume required to store 1 kg of hydrogen as 1 by 70.8 which is 0.0148 meter cube which is around 14 litre. Now in the case C in the question C we see that at solid state storage density of hydrogen comes out to be 100 kg per meter cube which will give us the volume of around 0.01 meter cube which is around 10 litre. Now in the case D we have to compare all these type of storage system that in different phases. So we have from the first of the calculation we have seen that as when we want to store hydrogen in gases form the volume required is high as compared to the liquid phase and the solid state storage. Now if we can, if we just compare that the volume required in solid state to store 1 kg of hydrogen versus when we store the same amount of hydrogen in the liquid phase. So this comes out to be in solid state storage the volume required is 0.7 time of what is required in the liquid form. If we compare the another case if we compare that to store the same amount of energy at during the gas phase form the volume required and to store the same amount of energy in the liquid phase when you then we have seen that this comes out to be 802.85 this is a very big number. So if we want to store hydrogen gas if we store hydrogen in gas phase form then the volume required is 802 times of what we want in liquid phases in liquid phase. In the next part it is seen that what is the hazardous condition which will create when the hydrogen will be leaked in from the liquid phase. So this is from last answer we have seen that the volume required to store gases form is 802.85 times of Vl. So when they if we have a tank of tank in which the liquid hydrogen is stored and if there is some leakage from this portion. So hydrogen will be hydrogen will be liquefied at a temperature of around 20 Kelvin. So when there will be some leakage this will continuously go on the outer portion in the atmosphere and this will produce a cloud of liquid hydrogen in this portion. Then after forming a cloud at 20 Kelvin this will continuously go on evaporate because when it comes in the contact of atmosphere as temperature goes on increasing then there will be evaporation converted into gaseous hydrogen. If there is no ignition and there will be delayed conversion of liquid hydrogen into the gaseous hydrogen the volume occupied by this gaseous hydrogen is around 802 times. So what we have seen is if there is a tank in which the liquid hydrogen is present and there will be leakage of liquid hydrogen so there will be initially the cloud of liquid hydrogen then it will start expanding which is known as the expansion ratio and it will expand up to a point of 802.85. This times the expansion of volume is 803 times as compared to what is seen when it converted into the gaseous forms. So this will prove that the how much the hazardous is the gaseous hydrogen when the liquid hydrogen is converted into gaseous phase. In the next question after seeing that what the volume is required to store a certain amount of hydrogen it is also sometime important to compress hydrogen up to a higher pressure so that there will be requirement of less volume in it. So the compression of hydrogen is also a very important topic that is covered in the last lecture by Professor Pratibha Sharma. So for doing a small calculation how the compression is being done the question is we have to calculate the work done to compress 1 kg of hydrogen from 1 bar to 16 bar at standard temperature and pressure by assuming hydrogen as an ideal gas. If this compression after that if this compression we will done in 2 stage compression that is initially we will go from 1 bar to 9 bar and then from 9 bar to 16 bar then we have to calculate the work done in this case also and then we compare the what which one is which way is better to compress hydrogen up to this bar. So initially it is given that for the for single stage compression for single stage P 1 is given as 1 bar and P 2 is given as 16 bar we have to compress it isentropically. So the work required to compress hydrogen isentropically is given by gamma by gamma minus 1 R T 1. This is how the isentropically work will be for isentropically compression of hydrogen will be described as the work done. So the value of gamma is 1.4 because it is a diatomic gas. So if we put this value as 1.4 by 0.4 into 8.314 this is kilo joule per kilogram Kelvin multiplied by if it is an atmospheric temperature then 25 degree taken as 298 Kelvin P 2 is given as 16 bar and this one is 1 bar calculating it as 0.4 by 1.4 minus 1. If we if we just if we if we solve this values we have found that this is this is what we have seen from single stage compression for 2 stage compression isentropic work will be given by gamma by gamma minus 1 R T 1 P 2 by P 1 gamma minus 1 gamma minus 1 plus gamma by gamma minus 1 R T 1 P 2 by P 1 gamma minus 1 by gamma minus 1. Here this one is P 3 by P 2. So initially we have to compress it from 1 bar to 9 bar and then from 9 bar to 16 bar. So in this case P 1 is equal to 1 bar P 2 is equal to 9 bar and P 3 is given by 16 bar. So now any now after that we have to put the value of these it is 1.4 by 0.4. Similarly the R value is 8.314 T is 298 P 2 initially the P 2 is we have to compress it from 1 bar to 9 bar. So P 2 is 9 gamma minus 1 is 0.4 1.4 minus 1. After compressing it from 1 bar to 9 bar we have to compress it from 9 bar to 16 bar. So this is given by 1.4 298 16 by 9 0.4 1.4 minus 1. When we solve this equation this W isentropic comes out to be 9122.420 kilojoule. This is the single when the compression will be done by single stage this is the amount of work done. When we have to done for the two stage compression this is the work done that is being required. So for one stage compression W isentropic is given by 10476.72 kilojoule and for two stage compression W isentropic is given by 9122.42 kilojoule. If we from here to see that if we want to compress hydrogen from 1 bar to 16 bar and if we will done into by using the two stage compression the amount of work done required is lesser in case of two stage compression as compared to the one single stage compression. If we see how much amount is this increment is there. So the percentage of less work in two stage compression it is nearly about 14 percent. So if we want to compress hydrogen from 1 bar to 16 bar there will be 14 percent less work we have to done in two stage compression as compared to the one single stage compression. The next question is also about the compression if the process is isothermal that there is no change in temperature. So what is the amount of work that need to be done to compress 1 kg of hydrogen isothermally at standard temperature and pressure such that the final volume will reduce to one fourth of the initial volume. We have to also find out the amount of heat evolve and change in internal energy. So here it is given that the such as the final volume reduces to one fourth of the initial volume. So if we see that the final volume is one by fourth of the initial volume. So the temperature at we are assuming at 298 Kelvin the value of R is around 8.314 kilo joule per kilogram Kelvin we want to compress 1 kg of hydrogen. So the isothermal work to compress this if hydrogen is assumed to be as ideal gas is given by RT ln V2 by V1. From here V1 is given by 4 V2 so if you put this value in it it comes out to be 8.314 into 298 into ln V2 by 4 V2. If you solve this equation we will get a value of now we have to find out the amount of heat evolve and the change in the internal energy also. This will be so from here we have found out we are able to find out the work required to compress hydrogen from when the final volume is one fourth of the initial volume. Now from the first law of thermodynamics DQ is given by Du plus Dw. Now it is given that the process is isothermal so the change in internal energy comes out to be 0. So from here is given by Dw. Now the work done is this, this is the amount of energy that is being evolved when the hydrogen will be compressed from 1 by 4 to the initial volume of the final volume. So this is the method of compression of hydrogen from by different methods which is isentropically and isothermally also. We have also seen that how the how the value how the storage volume is changing when the hydrogen is stored in the different phases like in liquid phase in solid phase and in the gases phase. We have also seen that there will be a problem when the hydrogen will when the there will be leakage in the liquid hydrogen tank and the there will be expansion of expansion of volume when the liquid hydrogen is converted to gases hydrogen by 803 times which is very hazardous in our case. Thank you.