 The last topic that we're going to cover in this lecture is that of a refrigeration cycle that enables very, very low temperatures and it can enable liquefaction of gases. Let's all begin by writing out a process schematic as well as a process diagram. Before I do that, however, liquefaction of gases, sometimes as I mentioned earlier for cryogenic applications, you might want liquid oxygen or liquid nitrogen. This would be the cycle that you would use to get those and typically what we'll do is we'll just use air and when you liquefy air, depending on the temperature, you can pull off the different components that are in air. So there are many different reasons why you'd want liquid nitrogen, liquid oxygen, liquid hydrogen. Liquid hydrogen is used for rocket propellants and liquid helium is used for superconductivity studies and liquid nitrogen is used quite often in any kind of scientific or industrial applications, liquid oxygen as well in the medical community in many different places. So what we'll do now is we'll take a look at the cycle, both the process diagram as well as the process schematic for liquefaction of gases. So what we have here is the TS diagram as well as the process schematic for liquefaction of air and you can see for the most part what we're dealing with. Usually when we're dealing with air, we deal with it in the gas phase, ideal gas. However, we're going to temperature as whereby we start to enter into the two phase region and that's why we have the two phase region on the TS diagram. But going through this process, what we do is we have multi-stage compression. So at multi-stage compression, we begin at state 8 as shown here and we go through compression cooling, compression cooling, compression cooling. We do that multiple times and we come out at state 1 after going through that and so then in terms of our schematic we would be here. We then go into an after cooler and that after cooler will drop us down to a temperature at 2 and at that point we then go into a heat exchanger and that heat exchanger will drop us from 2 down to 3 and the heat transfer is going with air from another part of the cycle going from state 5 up to state 6. And so that exchange, that is going that way, that's going that way and we have heat exchange going between those two fluid streams, enabling us to cool down to state 3. We then go into a throttling process which brings us into an area whereby we're in the two phase or multi-phase region for air and what we then do is we then flow the fluid into a separator and we knock out the liquid and the vapor then goes to state 5. So the liquid there would be coming off at state 9 as shown here and here and state 5 is where we go back into the heat exchanger. Notice we have makeup air coming because we are pulling mass out of the system and so we continually have to make it up but then we go then again into the multi-stage compression process. So that is the cycle for liquefaction of a gas. It's using multi-stage compression and then kind of an ingenious approach to doing heat exchange, throttling and separation of the gases and liquids as you go through the process. So that's the final system that we'll be looking at for this lecture. In the next lecture what we'll do is we will go on into the air refrigeration or gas refrigeration cycles. We've looked at the vapor refrigeration cycles here. Now we will go on to just gas refrigeration cycles.