 What we'll do now is we will apply the first law to the closed feed water heater in a very similar manner to what we did for the open feed water heater. So with this, we'll assume that the feed water heater is insulated, there are no moving boundaries or no moving parts for work. The other thing is kinetic energy and potential energy of both the exit and the inlet streams will be neglected. And with this, we get a similar form of the first law that we saw for the open feed water heater, basically just the mass flow rate of the fluid stream's exiting multiplied by the enthalpy is equal to the mass flow rates of the fluids coming in multiplied by their enthalpies. So for the feed water heater, let's go back here and take a look at our schematic. This was what we were looking at, and we had the enthalpy coming in, so we were at state two, and we also had fluid coming in at state seven, and then it was exiting at state three and state nine. So with that, we can write, taking into account the fact that we have mass fractions here, because not all of the mass is going in each of the streams. So that's what we get for the feed water heater, and the other thing that we have, we have a mixing chamber, which is something that's different from what we looked at before. Mixing chamber is basically just a T elbow, it could be as simple as a T elbow, where you have two inlets in one exit and a piping system. So let's look at applying the first law to the mixing chamber. Now our fluid streams that we have, we have fluid stream nine coming in and four coming in and five going out, so two in and one out. And what is exiting is that the full flow rate, so we have one for the premultiplier. So that would be the representation of the first law for both the closed feed water heater as well as the mixing chamber. Now sometimes what we do is we can get away without having to have pump number two by using what is called a trap. And when you use the trap, instead of sending the fluid through pump two, what you do is you send it through a throttling valve, whereby the fluid pressure drops down to the condenser pressure. The thing about this, you're losing, well actually we're not even gaining energy here, so it's a way of doing this in a slightly more economical manner and that you don't need this second pump. So we sometimes use a trap, sometimes also called a throttling valve. Now what we're doing is we're throttling the liquid to a lower pressure and this is a constant enthalpy process. So what we're going to do, we'll take a look at a process schematic and a process diagram for the closed feed water heater using a trap. So what we have here is the process schematic as well as the process diagram for our closed feed water heater, assuming that we have what is called a trap. So we don't have two pumps, we only have one pump here and we have this trap device. Now traps or throttling processes are characterized as being constant enthalpy processes and consequently what we can say is that in the trap H3 equals H8. So it's a constant enthalpy process, the enthalpy will not change. And with that if we can determine H3, we then know H8 and from that we can then get the quality at 8 and that is assuming that we know the pressure within the condenser. So that's one thing we can do here and then the other thing is looking at the first law or basically the energy exchange in the condenser. We have a slight change where we would have Q out. So we would have that for Q out of the condenser. 1 minus Y times H6 minus H8 which is reflecting the change in this stream with this stream and then plus H8 minus H1. So that would be the heat transfer out of the condenser. This is the way that we determine conditions through the trap. So that is if you have regenerative rank in with the closed feed water heater and a trap. So with that, that concludes the efficiency games that you can play with the rank in. We looked at rank in with reheat and we've looked at regenerative rank in two types, both open and closed feed water heaters.