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Problem 64 Hard Difficulty

(a) Calculate the energy (in kilowatt-hours) released if 1.00 $\mathrm{kg}$ of 239 $\mathrm{Pu}$ undergoes complete fission and the energy released per fission event is 200 $\mathrm{MeV}$ . (b) Calculate the energy (in electron volts) released in the deuterium-tritium fusion reaction
$$
\frac{2}{1} \mathrm{H}+_{1}^{3} \mathrm{H} \rightarrow_{2}^{4} \mathrm{He}+_{0}^{1} \mathrm{n}
$$
(c) Calculate the energy (in kilowatt-hours) released if 1.00 $\mathrm{kg}$ of deuterium undergoes fusion according to this reaction. (d) What If? Calculate the energy (in kilowatt-hours) released by the combustion of 1.00 $\mathrm{kg}$ of carbon in coal if each $\mathrm{C}+\mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}$ reaction yields 4.20 $\mathrm{eV}$ . (e) List advantages and disadvantages of each of these methods of energy generation.

Answer

a. $2.24 \times 10^{7} \mathrm{kWh}$
b. 17.6 $\mathrm{MeV}$
c. $2.34 \times 10^{8} \mathrm{kWh}$
d. 9.36 $\mathrm{kWh}$
e. Coal is cheap and abundant but its combustion results in greenhouse gases that leads to global warming. Pu-238/D-T nuclear reactions have high energy density (energy released per kg) but Pu-238 results in radioactive by-products, while D-T fusion requires high ignition temperature due to coulomb repulsion between the two positive nuclei.

Discussion

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Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

LB
Liev B.

Numerade Educator

Zachary M.

Hope College

Meghan M.

McMaster University

Video Transcript

So for the first question, we are completing the energy released by one kilogram off plutonium every night. Given that each efficient event GVC by each plutonium fission event is 200 MTV. So we can we just you find how many clients they are? You should tell us how many fusion reactions can co and from David Can Coke a waste to energy daughter energy V's. Right. So number off, Tonio, new clients. That is one kilograms you fight by the mass Elvish off to you, Tonio, that is 239 points. You fight you and then we multiply by the conversion factor to covering two kilograms. You should get 52 times 10 to 4 to this tunnel. Nuke rights, which is also total offish in reactions that cannot cope. So the total energy that's released would be de number off your kites type by D energy per reaction nineties will give us in terms off M E V to convert from MTV To blow hours, you multiply by 4.44 times 10 off a minus 20. Kiddo. What hours put on TV so issues get through 0.24 I'm simple. Seven people will always next. You want to find the energy with these poor reaction profusion, Reaction off deuterium beef Treat him. Use us helium for and a neutral. So to find what is the energy released majestic you value. We need to take the mass difference between the initial reluctance and you find a product might right by C squared. So that is mass off Jeriome thus mess off. Treat him minus the mess off in full minus mass softy by C squared. It's really mess off to you. This two point for once your to you myself treat you so much. Sure miss off here for finally mess off the neutral and became wanted by C squared using sees grass 91 point before night. For if we put you I see it We are dealing with the mess units. We should get our Q value to be 17.6 MTV perfusion reaction No, You want to find What is the energy released by one kilogram off? Deuterium Simple. We do the same process esti plutonium. You must find how many What is the number? Number of deuterium in one kilogram. So did take one program. Divide by D mess off individual you claim. So that is two points You 14 a club Russian defector. Nobody for you. Two kilograms. You should kids number off you go a school. It is. And he will know. From here we can find the energy total energy by taking the number of deuterium. What a play by the energy, which we co created. Profusion that is 17.6 and feet Demi comfort from MTV to get about always doing the same conversion Fekter ahead Final and so p 0.3 full absent. Paul off it one hours, Stevie on. Look at cold, right commission off. Cool. First we find the number off carbon atoms. I didn't want to program fight by mess. Just shelf you on my body commission factor neighborhood aces and see for no Debbie. Tick and see, given that each off the combustion reaction Useful point to e v. So Toto, total energy from the coven movie and see want to play by for two Very much apply by t accomplishing defector. So for this we should get nine point six. You know what I was can see That is pretty low compared to our inshore fusion reaction and also D if you should sanction eight. And so what is? The advantage is that I'm going to split them up into the nuclear energy, which is our plutonium and do TV she to action and the other would be cool. So far, you nuclear energy, the advantage is dead. It has very high. And she testy, right? You get very, uh, get very large amount off energy for a small model mess, right? One kilogram, you get a lot more energy to compare to call. So it's very high energy density. But the T seven teach right for plutonium two feet? Yes, that is radioactive interactive site products that we don't want and this waste products that we have to be disposed off properly. If not, it will cause damage to the environment for deuterium tritium reaction CD 70. She's dead. You quite a very high starting temperature, more ignition temperature, right. And this costs a lot off energy to sustain right to sustain the temperature enough to allow the efficient reaction to occur spontaneously and at a high enough efficiency to generate energy on our the hand for cool. The advantage would be dented this very cheap days. Very abundant amounts off Karpin's on earth so you can get the energy almost from anyway. However, decision very obvious disadvantage is dead. It produces co two, which is a greenhouse gas. This is pollution you to our environment and close this greenhouse warming.

National University of Singapore
Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

LB
Liev B.

Numerade Educator

Zachary M.

Hope College

Meghan M.

McMaster University