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Problem 8 Easy Difficulty

A typical nuclear fission power plant produces about 1.00 GW of electrical power. Assume the plant has an overall efficiency of 40.0% and each fission produces 200. MeV of thermal energy. Calculate the mass of $^{235} \mathrm{U}$ consumed each day.

Answer

2.63 $\mathrm{kg}$

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Top Physics 103 Educators
Andy C.

University of Michigan - Ann Arbor

LB
Liev B.

Numerade Educator

Farnaz M.

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Meghan M.

McMaster University

Video Transcript

this question, we will find out how much you run into a tree fires needed to sustain a nuclear fission power planned. So we know that the powered as being produced it's actually one gigawatts. But the problem is that it's not 100% of should see. There's some energy days being lost, and this is only 40% off it says were given their The efficiency is 40%. So what we want is the total amount off energy on the total power there is actually being produced by all deficient reactions and that you will have to multiply by. Divide it right by 41 flight by hundreds, right? This is, ah, actual energy that is being produced, and now we want to consider the amount off energy produced in a D. I just want to find out what's the mask on somebody So energy total in one day, that is, we take Peter toe, multiply by the number of seconds in a day since peace in terms off per second number of seconds a day will be $3.600 part by four or get these so this devalue in terms off juice. But since our our energy for the fusion reaction is in terms off M E V. He'll be convenient if you can. Competent to Emily, you can do that very simply by dividing everything by 1.6 times 10 po minus 13 50 commission factor from Jews to MTV and we should get 105. It's 10 post seven every view. So does the energy that's required to be ah, released by the fission directions in a day. And from this we can co create. What is the number of fission reactions? Quiet. Take this energy divide by the energy released profession. Just 200 MTV. So give us 6175 times 10 voted for. And since each reaction consumes one uranium to terrify atom, this is also the number off union to Chief I atoms that is consumed. Finally, we can't get a mess. Miss off uranium to five that is consumed. There'll be 6.5 times 10 party for we divide debt by abogados constant 6.0 to 2 time step belt entry to find a number off Moores and then we multiplied by its more alarmists, which is 235 grams pummel. Get 2.6 tree instead, Poetry Gramps, which is 2.63 kilograms

National University of Singapore
Top Physics 103 Educators
Andy C.

University of Michigan - Ann Arbor

LB
Liev B.

Numerade Educator

Farnaz M.

Other Schools

Meghan M.

McMaster University