 Now the most popular well-known vapor power cycle is referred to as being the Rankin cycle. And so that's what we'll start with. And we'll be looking at the conventional Rankin and then derivatives or modifications to that. So what I'll do to begin is I'll write out the process schematic as well as the process diagram for the Rankin and then we'll go through and apply the first lot at each of the individual components in this cycle. So what we have with the Rankin cycle, you can see the schematic on the left and we have a pump. The fluid comes out of the pump goes into a boiler where we have heat addition. It converts into steam. The steam then goes into a turbine, produces work. The steam comes out of the turbine and we condense it back into a liquid phase and then bring it back into the pump. So what we're going to do now is let's represent that in the diagram, the process diagram in the TS. So we always start off on the saturated liquid line and that will be state one, which is where we then go into the pump. And when we go through the pump, what we're doing is we're raising the pressure of the fluid, taking us to state two. And then we have a constant pressure line because we will assume that the operation in the boiler is a constant pressure. We'll see later that that's a bit of an approximation, but it's one that we'll use for now. And then once we go through the pump, so we're doing work in here, so we'll represent that. We then go into the boiler taking us from state two up to state three, which brings us into the superheated region. And in order to do that, we need to have heat addition. So that is what is going on in the boiler. We are then a superheated steam and we go into the turbine and we then drop down through the turbines for dropping in pressure. And ideally what will happen is we will end right on the saturated vapor line at state four. And in the process of doing that, we are producing work. And then finally, from state four, returning to state one, we go into the condenser. And in the condenser, what we do is we are rejecting thermal energy to the environment as all heat engines need to do. So that is the process diagram for the Rankin. So what we're now going to do is we're going to take a look and apply the first law to each of the individual components that are in the Rankin cycle. So let's begin by writing out an equation for the network. We can say the network is going to be the work out minus the work in. And that can also be expressed in terms of the heat transfer, the heat in minus the heat out. So we're now going to apply the first law to each of the components. And we'll assume them to be steady flow components or steady flow devices. And consequently, we'll use the steady flow version of the first law. So expressing or writing out the first law for a steady flow device, we have the following for heat transfer. Now we're usually dealing with a device that's stuck to the ground, it's not moving. And consequently, we will take kinetic and potential energy and neglect those. So the first component that we will look at will be the pump. And in the pump, if you look back to the process diagram and the schematic on the previous slide, in the pump, we're going from state one up to state two. And so let's take a look at that. Now in the pump, we can assume that there is no heat transfer. So Q will be zero. And with that, when we come back to our first law, what we will have is the following for the pump. It's basically just the change in enthalpy. So we need a way to be able to express the change in enthalpy in the pump from the exit to the inlet. And in order to get that expression, what we'll be doing is we'll be using the steady flow work equation that we saw in an earlier lecture. And if you recall, this is the one that had the specific volume multiplied by the change in pressure of the fluid as it went through the device. Now, in coming up with this equation, what we're going to assume is that the enthalpy at state one, we will determine that by the enthalpy of a saturated liquid at pressure one, which makes sense. We go into the steam table and we can get enthalpy there. But the question, how do we handle the specific volume and the convention that we will use is the specific volume will be the specific volume also at state one, which would then be the specific volume for a saturated liquid at pressure one, P one. So that would be the pressure going into the pump and you determine your specific volume there. You usually know the pressure differential and from that you can determine the work that you're putting into the pump. So let's move on to the next element that we have in our cycle. And that is the boiler. So let's apply the steady flow version of the first lot to the boiler. So here we're going from state two to three. Now in the boiler, unlike the pump, we said there is no heat transfer in the boiler. There's a lot of heat transfer. That's what's making it work. However, there's no work in the boiler. So we can write work is equal to zero. And then the steady flow version of the first law turns out to be the following. So it's pretty simple. It's just the change in enthalpy that we have going across the boiler between state three and state two. Now the next item that we will look at is the turbine. Now in the turbine, we're going from state three to state four. And in the turbine, just like in the pump, we're going to assume that there is no heat transfer. And the only thing going on in the turbine is we're getting work out. And the way that we will quantify that is going to be the change in enthalpy of the fluid going through the turbine. So looking back at our TS diagram, it will be H3 minus H4. So that difference is how we can then determine the work in the turbine. And that'll be pretty easy because we can get those enthalpy values out of the superheated steam tables, assuming we end right on the saturated liquid line. If we go into the two phase region, then you have to look at the two phase characteristics there to get the enthalpy at state four. The final thing that we have is the condenser. And for that, we're going from state four to state one going back here. So this is the operation of the condenser. It's basically heat rejection. We're going through a phase change in an ideal world. We go from saturated liquid, sorry, saturated vapor down to saturated liquid. And consequently, there's no work in the condenser. However, there is heat transfer. The heat transfer is leaving the system. And that would be the enthalpy at four minus the enthalpy at one. So those are all the different equations we can use to examine each of the individual components or devices within the rank and cycle. And with that, the final thing that I want to say is that the thermal efficiency can be calculated with the following. So if you're given a rank and cycle, you can go through, determine all the different enthalpies, plug them into these equations. You can get work net. So you'd have to evaluate both of the work terms, the turbine out in the pump in, the heat in, or if you know Q out and Q in, you can also determine the thermal efficiency for that. And that is the equation that we can use to determine thermal efficiency of the rank. So what we're going to do now is we're going to go into a little more detail looking at each of the individual components and how they operate. So we'll spend a little bit of time looking at the performance of each of the components within the rank and cycle.