A nuclear power plant generates 3000 MW of heat energy from nuclear reactions in the reactor's core. This energy is used to boil water and produce high-pressure steam at 300℃. The steam spins a turbine, which produces 1000 MW of electric power, then the steam is condensed and the water is cooled to 25℃ before starting the cycle again. b. What is the plant's actual efficiency?

Video transcript

Hey, everyone. So this problem is dealing with heat engines. Let's see what it's asking us. We have a coal fired power plant prototype. The coal is burned in a boiler which produces 7, 2750 watts of heat. The heat from the burning coal is used to boil water and then that steam causes the blades of a turbine to spin. As a result. 220 watts of electrical power is generated. We're asked to determine that the prototypes power this prototype power plants efficiency. Our multiple choice answers are a 8% b 18% c 82% or D 93%. So the key to solving this problem is we're calling the equation for efficiency denoted by a which is equal to our work divided by our total heat. And so we're told in the problem that our work, the amount of power that comes out is 220 watts or jewels per second. And so if we're going to look at this whole problem adds the efficiency in one second, we can list that as 220 jewels. Similarly, for our total heat that is 2750 watts. Again, looking at this in one second of time, that would be a heat of jewels. And so we can plug that into our calculator and we get 0.08 which is of course, 8%. So that is the efficiency of this power plant. And that aligns with answer choice A that's all we have for this one. We'll see you in the next video.