Okay, hopefully you were thinking about one of the general carriers that we have. We talked about this at the beginning of the course. So, there's coal, there's natural gas, there's oil, there's nuclear. Those are kind of the standard players. And of course, there's more and more sustainable energy that's coming online. So, a couple of things. You're starting to get the tools to understand the magnitude of what we're talking about. So, our example we had a power plant that was about 36% efficient. That was our example, 30 to 40% efficient. And that's pretty typical for Rankine power plant. We don't quite know how much power generation though, our power plant is going to make. Was it a 1 megawatt facility? Was it a 1 gigawatt facility? That's something that we're going to cover today in this unit. So then, the question is, okay, so we're starting to get some perspective for these numbers. What's the likely carrier? Well, it's not just going to be cost of fuel. That should be a very obvious thing that you thought of. Okay, what's the cheapest fuel? But, the regulations, particularly on air toxic emissions and water pollution that are associated with the power plants add significant cost to the power generation. And there's some really interesting articles, if you want to follow up, on how power in the United States is more costly than a lot of nations because of the after treatment that's required for the air toxic emissions. So, it's not just fuel costs, it's also emission costs. And within the United States natural gas power plants are the most efficient. And natural gas is very clean burning. And right now, natural gas is very inexpensive. So that's the triple whammy. So in the United States, I would expect natural gas to be the primary energy carrier for the next generation of power plants, which is a shift away from coal. It's not going to shift very quickly. But there will be a shift more towards natural gas. Okay, let's get back to our example. So last time we calculated the cycle efficiency of our power plant. So now, what I want you to do is, again, let's get some absolute numbers. Everything there was done in terms of a normalized mass flow rate. We didn't have a mass flow rate calculated. Let's assume we want our power plant to generate 500 megawatts of power. What mass flow rate of steam is required to meet that target? And I'll tell you 500 megawatts is not a typical, that's not super big and that's not super small. Obviously, it's a stationary power plant type capacity. This isn't one that you're going to use in your back yard and it's probably bigger than anything that an industrial manufacturing facility might need. So, that's a good sized power plant, but it's also reasonable. Okay, and our efficiency is also typical and reasonable that we determined. So let's go ahead and do that calculation. Okay. So we have a net power of 500 megawatts, we have a net power that we want to generate, a 500 megawatts. So, that's net. So that's 500 megawatts and that's on a rate basis and again that's net. So that's work out and including the losses associated with powering the pump. And so, that's going to be, in this case, the work from these two stages of the turbine which again, those values will both be positive. And then, we have the cost associated with operating the pump and there's just one pump in our system and, of course, all of our analysis was done on a per mass flow rate basis like this. Okay. So, these numbers are simply the enthalpy differences for all of the turbines. So, or alternatively, I'm doing this analysis on the power side. We could have just as well used the net heat transfer to do this calculation as well, and we already determined that. So, I'm going to write that down here for you. So, we already determined the net heat transfer for cycle. Remember, we used that for our efficiency analysis. So, we could have just as easily determined the mass flow rate from that calculation. But I want to see what these numbers look like, I want you to see it, more specifically, what these numbers look like for the specific work. These are all specific work values for the two stages of the turbine and for the pump. So, if we go through and we plug in the appropriate enthalpy balances for each of these components. What we see is, for the first stage of the turbine, we have h1 minus h2 were the enthalpy at state one minus the enthalpy at state two. For the second stage of the turbine, we have enthalpy at state three minus the enthalpy at state four. Plus we have the pump, which is enthalpy at stage 5 minus the enthalpy at stage six. Again, each of these are specific enthalpies, so we multiply them by the mass flow rate in order for us to get a power basis. And we are, ultimate we're going to solve for this, this mass flow rate, but I want to look at each of these numbers so you can see each of them. And what we find is for the first stage of the turbine we develop 476.8 kilojoules per kilogram. For the second stage of the turban we developed 930.4 kilojoules per kilogram. And the pump costs us 9 kilojoules per kilogram, and again it's a negative number as we would expect because this is the pump. So this is less than 0, greater than 0, greater than 0. And what we see here is that, you know, the majority of the energy is developed at the second stage of the turbine. And that the pump doesn't cost us too much, less 10% of the energy in the cycle, which is a good thing, right? because we don't want the pump to be too costly. And again, all of this has to be multiplied by the mass flow rate. Well that's, of course, what we're trying to solve for in this part of the question. And if we go ahead and do the substitution, watch your units. These are megawatts here. These are kilojoules per kilogram here. If we go ahead and let's determine the mass flow rate here in kilograms per hour to be very specific. What we determine is that the mass flow rate is 1.29 times 10 to the 6 kilograms of steam are required per hour. In order for us to produce 500 megawatts of power. Okay, so now we have some real numbers that we can look at. So this is a 500 megawatt power plant. So that's a pretty respectable size for a power plant, and as we can see, it requires quite a bit of fresh water in order for us to operate that power plant. Now, we could take the average temperature of the heat addition and the average temperature of the heat rejection. We could calculate a Carnot efficiency and we could determine how close does our power plant come to that Carnot efficiency. And there are other techniques that we could use to improve the efficiency of our power plant. We could add more stages of reheat. We can ad intercooling, there are other types of hardware that we could include, but in general my steam power plant. I might get it up to 50% thermal efficiency, but that's about the numbers that we have for power plant generation thermal efficiency for a steam power plants. Okay, let's take a look at one other key characteristic before we leave this specific example. How much heat did we waster by rejecting the heat to the environment? So very specifically, what I want to know is, what fraction of the heat in, ends up being heat rejected to the environment. In other words, how much of the heat in to the cycle, ends up being heat out of the cycle. So, we're going to look at that number. We're going to call that a waste metric. We'll use aeta like it's an efficiency, but let's just see what that looks like. And specifically what I want to know is how much heat is out of the system compared to how much heat was brought into the system. And we already calculated these numbers in our previous cycle efficiency calculations. We'll just go ahead and drop those right in. So there's the heat transfer out of the system. That's the heat rejected to the environment. And then, remember we had two components to heat transfer in, one and two. The steam generator and the reheater. And if we plug those numbers in, what we find is that 63% of the heat added to the system is in fact rejected to the environment. That's a whole lot of energy that's not being used in a productive way. And that's going to be the basis for us to make some pretty major improvements in the way we use and generate power. Okay, so, what I want you to think about just as again, thought exercise here is the different categories of power generation that we have in the United States. The power grid is powered in the United States by a combination of what we refer to as baseline, load-following, and peaking power plants. I want you to answer these questions. What category of power plant do you think generates the most power on an absolute basis and which has the highest capacity? The capacity means different things in different communities. In this case, what I want you to think about is capacity when it's a fraction of time the power plant is online, is being used at its maximum capacity. So in other words, if you have a power plant, how many days of the year is it in use and how much, like if it's a 500 megawatt power plant, how much of that 500 megawatts capacity is being used 365 days of the year? And so, pick which of those categories you think that falls in. And then I want you to also think about which category would you think could be the power plant that can respond most quickly to transient demands. We'll keep piling on here. And then I want you to think about which category where you'd place a wind farm, and which category where you'd place solar power tower. Some of you may be very familiar with those, some of you may not. Here's a good chance for you to go look those up on the internet. But then, come back and tell me are they baseline, load-following, or peaking power plants. And that's where we'll start next time.
