 We're now going to work on an example problem involving a gas refrigeration cycle. So what I'll do is begin by writing out the problem statement. So there's the problem statement that we're dealing with. What we have is a gas refrigeration system, ideal gas refrigeration system, and we're maintaining our space at minus 23 degrees C. The surrounding medium is at 27 degrees Celsius, and we're told that the pressure ratio in the compressor is 3. And what they want us to do is determine the maximum and minimum temperatures in the cycle, the coefficient of performance, and the rate of refrigeration, the amount of cooling or heat transfer that we actually had, and knowing the mass flow rate of 0.15 kilograms per second. So that is the problem statement. What we'll do, I'll write out what we know and what we're looking for, and then we'll go on to solve the problem. So that's what we know and what we're looking for. And now what I'll do is I'll write out the process schematic as well as the process diagram, and then we'll start working through the problem solution. So there we have our process diagram as well as our schematic. Now one of the things that the question states is the surrounding temperature. Let's go back and look at our data. It says the surrounding temperature is 27 degrees Celsius. And so we have to think about that a little bit as we're looking at the solution to the problem. If the surrounding is at 27 degrees Celsius, what that is telling us is that the temperature at the end of our heat rejection process cannot be lower than the surrounding. So it cannot be less than 27 degrees Celsius. So that is basically specifying temperature 3 in our cycle. The other thing it is telling us is that the refrigerated space will be at a temperature of minus 23 degrees C. So that's the other piece of information. So if the refrigerated space is at minus 23 degrees C, that means that our temperature 1 cannot go above that. So that has to be minus 23 degrees C. Because if our cooling, we won't be able to cool if we go above that temperature. And so realistically, you might want to be a little bit below. But what we'll do is we'll consider it to be minus 23 degrees C for our analysis. So that is kind of an indirect way of giving us information that they've done in this problem. And that's how we can determine it. So what we'll do now, we'll go ahead, we'll determine states and then go through and solve the problem. So what we're going to do here is we're going to go into the tables in the back of the block, the air tables. And given that process one, we have information about state one, and we have some information about state three, we don't have information about state two or four. And so that's what we need to determine process one through two, notice it's an isentropic process as is three through four, we're dealing with an ideal cycle here. And so with that, what we can do is we can use the relative pressure from the tables in the back of the block. And I'll get the enthalpy as well, I'll am at it. And then I'll get relative pressure for state three. So with the relative pressure, the other thing that we know with the problem statement, we know the pressure ratio. And so if we know the pressure ratio, looking at our TS diagram, we know then the pressure ratio is between one and two, as well as three and four, and that pressure ratio is three. So we can use that and our relative pressures in order to get the missing state information. So knowing the relative pressure at state two, we can then go into the tables and look up the temperature, we have to do an interpolation here. And similarly, between three and four. So there we have all the state information, we can now go ahead and start answering the different questions that have been posed to us for the problem. The maximum temperature in our cycle is going to be the temperature of T two. And the minimum temperature is T four. Coefficient of performance would be the desired effect, which is cooling. And the cooling process is between states one and four. And then what we do is we look at the work and minus the work out of the turbine. So the work in is into the compressor. We subtract off the work out of the turbine. And finally, what we want to determine is the amount of cooling that we're providing. So those are the answers to the problem. We have our max, our mid-temperature, the coefficient of performance, as well as the amount of cooling that we get from the cycle knowing the mass flow rate. And so that concludes the problem of dealing with the gas refrigeration cycle.