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Efficiency of a Nuclear Power Plant

Patrick Ford
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Hey guys, so let's get started with our example here. Now I want to mention right off the bat, we're gonna see some units in here that are a little bit different than the ones that were used to, for example, 250 megawatts of power or 550 megawatts out to the surrounding environments. But ultimately what we wanna do is we want to calculate the thermal efficiency of this power plant. So let's just go ahead and get started here. What we want to calculate is E. So we have a couple of of equations for E. We've got the work over Qh or the Q. C over Q. H. I'm just gonna use the simplest one here. This work over Q. H. So this is E equals work divided by the heat that flows into this nuclear power plant here. However, what we have here is not the work, what we have is the amount of power that it produces. Now remember that power is really just work divided by delta T. So here's what's going on here. And some problems where you're given units of power instead of work, remember that the efficiency equation does not depend on time. So whenever you have these kinds of situations, you can still unit when you use this equation, when you're giving units of power instead of jewels or something like that. So basically what's going on is that you can take this work over Qh equation and you can turn it into basically a unit of, of power or in terms of the rate of energy. So for example, you can say this is going to be W over delta T divided by Q. H. Over delta T. So what's going to happen is that your delta T. Is ultimately are going to cancel. They don't really actually do anything to this equation. But this is sort of just how this how this is working out, you can use those variables. So basically what's going on here is this power is 250 MW and now all we have to do is figure out the amount of power or energy that flows into this nuclear power plants. So basically we're gonna have to figure out what is Q. H. Now we're told here is that this expels 550 megawatts out of the surrounding environment, that's going to be the cold reservoir. So this here really represents Q. C. So if I want to calculate Q. H, what I have to do is I have to go here and I have to use my W equals Q H minus Q. C. Equation. Now again you can still use this even though we're working with units of power. So one way you can kind of think about this is that in one cycle this nuclear power plant will produce 250 mega jewels and expel 550 mega jewels out of the environment. But if you just run it continuously then you can also express this in units of power. Alright, so that's kind of what's going on here. So my Q. I really need to figure out what this Qh is. So I'm gonna move this Q. C over to the other side, we're gonna get the W plus Q C. Is Q. H. So in other words, the 250 megawatts of power that I produce, that's the useful energy that you get out of it, plus the 550 that gets expelled out to the environment. And what you'll see here is that Q. H is equal to 800 megawatts. So what's going in here is if you sort of like if you, if you sort of draw the energy flow diagram like this, Then we're going to see here that this QH is equal to 250 MW, this QC. Is 550 MW. And the amount of work that you get out of it, this w here, I'm sorry, this is the 800 this is the 800 megawatts and the work that you get out of each cycle is 250 megawatts. Alright, so that's how you can kind of see what's going on here as the energy flow diagram. So now this is basically what we plug into this efficiency equation. So you have the 2 50 divided by the 800 megawatts and what you're gonna get here is an efficiency, that's equal to um It's going to be 31.3%, so that is your final answer. Alright? So hopefully that makes sense here guys, because you may see some questions like this later on in the future, so that's it for this one.