 What we're going to do now is we're going to take a look at the equation that was just derived. That is for reversible work of a steady flow system. And we said that if we're looking at a pump or a compressor, it would have the positive in front. It's the specific volume multiplied by an integral with respect to the pressure change. Now what we're going to do is look at compression work or compressors. Compressors are used in many different mechanical engineering applications and many different processes use them. So compressors and gas compression is relatively important area within a mechanical engineering discipline. Now the amount of work in a compression process is dependent upon the type of process itself and really what it comes down to is the way that the particular compressor is designed. So let's take a quick look at a couple of different types of compressors. One compressor we're going to look at is a very small compressor like you would use for pumping up your car. Let's see if you're driving and you have a flat tire. It's a single cylinder compression device and it is relatively low power input. And we will also look at a three cylinder compression device used for a jack hammer that I saw earlier this year when I was in China. So let's take a look at those videos. So you can see first of all they're very very different compressors and in terms of size, noise, and what they can do. But when we look at the details of the way that the compression process is actually occurring we do find that there are significant differences depending upon how a particular compressor is designed. So what we're going to do is we're going to look at three different types of compression processes and we're going to look at this on a PV diagram. And part of the compression process we're going to be going from a lower pressure P1 up to a higher pressure P2. And we'll start at the original state down here, state one. And we're going to look at first of all a process whereby our compressor for example would be wrapped in insulation. And that would be an adiabatic and if it was reversible then it would be an isentropic compression process. And on the PV diagram it might look something like this. And so I'll denote here that is isentropic. And an equation for that we can write it that P specific volume raised to the power k where k is the ratio of specific heats and that is equal to a constant. Let's remember that is for an adiabatic compression process where we have no heat transfer from the cylinder device. At the other extreme we have a process that looks like this. That process is isothermal. So that would be a compressor whereby we were cooling the gas as it was being compressed. And you would have to do a lot of cooling in order to keep the gas at a constant temperature. In reality we would never see a compression process like that. What we actually see with real compressors is some place between isentropic and isothermal. And it's what we call a polytropic compression process. And so it would be some place in the middle here. So that is a polytropic compression process and it can be described by an equation that looks like this where n is some power that is going to range from one to the ratio of specific heats. So those are three different processes. Now when we're looking at compressor work sorry I made a mistake it should be compressor work. When we're looking at compression work what we can do is we can come back to our equation up here and notice what this one is we have the specific volume integrated with respect to dp. So I'm going to write out a differential element on one of our curves. So we'll call this here dp for a change in pressure. And the specific volume in our reversible work equation we'll sketch down that would be a value down here. So what we can see this equation the reversible work in equation represents is actually the area to the left of the curve because we would be integrating from pressure one to pressure two. So essentially what we are doing is we are evaluating an integral in this curve here. So our reversible work in equation is evaluating the area to the left of our compression curve. Now what we can do we can take the different pressure relationships and specific volume relationships and integrate them and come up with expressions for the work for either an isentropic, a polytropic or an isothermal compression process. I'm not going to do that however that is in your textbook. So if we evaluate those integrals we will get relationships for the amount of work done for different compression processes and what we find after doing that is the isothermal process requires the smallest amount of work while the isentropic requires the most. And that actually makes sense again if we sketch out our PV diagram and we had the curves for isentropic and isothermal. So this one here was isentropic and this one was isothermal and we said that the work was equal to the area to the left. Well just by sketching that we can see the work for isothermal and then if we sketch out the work for isentropic it's a much larger area and consequently it is rather intuitive and it makes sense that isentropic would have the largest amount of work. Now one thing that is often done in order to make the compression process more efficient is we go through a stage called an inter cooling stage and there are different reasons for cooling gases after compressing. Sometimes the the gas temperature will be very hot and you want to cool it before it goes into whatever device it could be a tank or could be going into a pipeline. In the case of a pipeline you want to lower the temperatures that you do not have an impact on the coating but sometimes what you'll have is a multi-stage compression process whereby you compress and you cool and you compress and you cool. And the number of intercooling stages required it comes out to be a bit of a trade-off between the savings that you'll get through the compression process which I'll show you in a moment and the additional economics of having to have the complexity of multiple compression processes. So let's take a look at the PV diagram and we'll look at what the intercooling process looks like. So P and our specific volume there again we're going from a lower pressure to an upper pressure and what I'll do is I'll sketch out the bounds to begin with our isentropic process and then isothermal. And so a real world compression process would be in the middle somewhere it's a polytropic process or polytropic. The way that you figure out the polytropic power the the end value is by doing experiments on whatever compressor you may have. Okay so what we have here this was isentropic this here was isothermal and we have polytropic. Okay so what we're going to do we're going to go along the polytropic line and we're coming along coming along coming along and maybe we get to a point here where what we do is we take the gas out of our first stage compression and we go through an air to air heat exchanger or air to gas depending on the gas that you're compressing and when you go into the heat exchanger what we're doing is we're cooling and when you cool a gas what happens is a specific volume goes down and so that process is in indicated here because if you recall density is P over RT specific volume is 1 over rho which that would be RT over P so if we are to cool the gas and we're dropping the temperature down what will happen is our specific volume will go down so that's why we're moving to the left on that curve and we go through this intercooling so first of all the first stage here is polytropic and then we do intercooling and then what we do is we go into a second stage compression process sorry about that and it'll look something like that again it's supposed to follow the line that we had for the polytropic process but our gain by doing this is that we have a savings and work performed and the amount of work saved is this area here because remember I said the work done for a compression process is the area to the left of the curve so what we have indicated here and this would be the work that is saved so if you hear somebody referred to intercooling as part of a compression process that's essentially what they're talking about you can have more than one stage compression and intercooling and again it will come down to the economics of it how many stages you'll actually have so what the intercooler effectively does is it reduces the temperature and it is often a gas to air or gas to liquid heat exchanger so that is compression work for the three different processes as well as intercooling