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Problem 54 Hard Difficulty

Approximately 1 of every 3 300 water molecules contains one deuterium atom. (a) If all the deuterium nuclei in 1 $\mathrm{L}$ of water are fused in pairs according to the $\mathrm{D}-\mathrm{D}$ fusion reaction $^{2} \mathrm{H}+^{2} \mathrm{H} \rightarrow^{3} \mathrm{He}+\mathrm{n}+3.27 \mathrm{MeV}$ , how much energy in joules is liberated? (b) What If? Burning gasoline produces approximately $3.40 \times 10^{7} \mathrm{J} / \mathrm{L}$ . State how the energy obtainable from the fusion of the deuterium in 1 $\mathrm{L}$ of water compares with the energy liberated from the burning of 1 $\mathrm{L}$ of gasoline.

Answer

a. $2.65\times 10^9 \mathrm{J}$
b. Fusion reaction would release 78 times more energy than the same volume of gasoline.

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Top Physics 103 Educators
Elyse G.

Cornell University

Christina K.

Rutgers, The State University of New Jersey

Andy C.

University of Michigan - Ann Arbor

Meghan M.

McMaster University

Video Transcript

two studies question. We will need to find the put a number off YouTube nuclear that we have in one litre of water so that we can find home. Any fusion reactions can occur and finally, to get the total amount of energy that can be released from this fusion reaction in one detail water. So first off in one liter water, you wanna find number off terrible accuse and that we can't find by taking you know, that one liter, the mess off the density off water is Cuban s one kg polyta right? Or 1000 grams per liter. We take the mess So these elements of water divided by the molar mess off water. Which is it? When's your grams football Terry multiplied by our graduates number to get these older noble all accuse I will go to its number is six points. You're to two times 10 oppo off a tree so we get number official molecules is 3.4 step part of five. We are given that one off 3000 Chetumal accuse There will be one due to you and ah nuclei and so number of deuterium that's quite handy. Would be trip what you for? Multiply by one off 3300. And these leaves asked me at 1.1 time. Standard politics too do to you in new Kreiss. So the number of fusion reactions can occur is half off this value because each fusion reaction actually takes in two deuterium. All right, so the fusion you should involving two tier of IHS to duty rooms to keep us a human tree. That's a neutron. That's the energy, right? So the number of fusion reactions PND you got it by two. And there is 5.7 time set apart. Anyone you see no more reactions. And finally, we can get the total energy from the fusion reactions by multiplying this number fusions by the energy release profusion, which is 3.27 MTV. And we would like to accommodate to juice, right since why do large amount off energy and to call it into Juicy multiplied by 1.6 time State Department 13 juice for MTV. If this should get 2.65 instead, pop off nine Jews. So this is the amount of energy that can be released from the deuterium in just one deter off water, comparing it to gasoline. But the energy release Pour gasoline for each litre. It's actually only 3.4 times 10 part seven juice and can see that by taking the fraction off and your fusion you better by the energy off gas, we get about 78. So amount of energy released by the fusion reaction in the same volume. Right? One liter off water compared to one it off gasoline, Exactly 78 times more steady energy from burning the gasoline. So it's much more energy. Shouldn't Lisa's a lot more energy? Then yesterday?

National University of Singapore
Top Physics 103 Educators
Elyse G.

Cornell University

Christina K.

Rutgers, The State University of New Jersey

Andy C.

University of Michigan - Ann Arbor

Meghan M.

McMaster University