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Problem 58 Hard Difficulty

(a) Calculate the energy (in kilowatt-hours) released if $1.00 \mathrm{kg}$ of $^{289} \mathrm{Pu}$ 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 $$_{1}^{2} \mathrm{H}+_{1}^{3} \mathrm{H} \rightarrow_{2}^{4} \mathrm{He}+_{0}^{1} \mathrm{n}$$
(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 kilowatthours) 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) $22 \times 10^6 \ \text{kWh}$ b) $17.6 \times 10^6 \ \text{eV}$ c) $2.3 \times 10^8 \ \text{kWh}$ d) $9.38 \ \text{kWh}$

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Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

LB
Liev B.

Numerade Educator

Aspen F.

University of Sheffield

Meghan M.

McMaster University

Video Transcript

question 50 is multiple parts. Each part is really but they're kind of different each month. So excuse me for part A. We'll calculate the energy and could long hours if one kilogram of petroleum to 39 other ghost vision. And we're told each fission event polices 200 MTV of energy. Okay, so I only need to do. I'm kind of flipping back and forth between the queue for energy. Me not to stick with E because he was the energy released in reaction but to believe display energy in terms of the But I'll save 60. So learn to Germany. Total energy is need to know the energy per reaction times a number of reactions and quite simply, to find the number reactions based on mass, we can use the relationship. It's the mass over mullah mass times avocados number. So you go ahead and do that. Eso for nd these provisional reaction. That's 200. And maybe her reaction That number of reaction will cancel with the units of this term. So if you have one kilogram of course 1000 grams for simplicity, EMS gonna call the mass Muller Mass to be to 39 exactly it shouldn't really affect my results. Thanks, but no tears. Times 10 to the 23. And I would convert this into jewels to get a program of energy. But since it does ask for energy in terms of kilowatt hours, I want to look up the conversion to and maybe to kill hours. I know that one. MTV is the Kremlin before 10.45% generated play kilowatt hours. So I take a 4.45 Don't you got 4.45 times tends in native 20 kilowatt hours per and TV. I can go ahead and packages out. They're higher. Yes, that's right. So the night with this I was playing on my energy and killed what hours is 22 point for times 10 26 kilowatt hours. Barbie is based on the reaction shown here where you have deuterium in trillion views to create Helima tonight. Neutron, begin. Want to find the energy excited electron volts released in the fusion reaction. The result for this me? Just look at what's composed in our reaction. We have a deuterium. So the master deuterium is 2.1 for why don't to you plus the mass of treaty, um, 3.1 six before nine minus the massive healing for my is the mass of the neutron that's always use to you. And this time we convert to energy using this expression 91.5 temps into the six e v for you because you want it to be like our bolts, not anything that we normally do. And this way, if I in each reaction that produces 17.6 I was 10 to the six electron volts or 17.6 MBD. Proxy now asks to calculate the energy and kilowatt hours. If so, energy killing errors. If the above reaction uses one kilogram of deuterium, so using its reaction having the massive deuterium, how much energy is released so really the above reaction, I should label it as energy per reaction. It's just that if you want to find the total energy using the energy, her reaction times, the number of reactions and basically we hadn't part a we could read that represent the number of reactions with this term here because we were given a massive deuterium, someone who had just used us directly and since you want energy and killed what hours? I'll leave my value for now in electron volts. See? 10 6 Any reaction times 1000 grams of deuterium divided by the molar mass of deuterium, which this time I will put in as 2.1 for one or two grand formal times have a god rose number have is probable. And this time again, we want energy and kill What hours? So I don't want, um I don't want, um excuse me. My energy delectables needed in kilowatt hours. Sort of convert for this. I am employers by 4.45 times. Tend to native 26 kilowatt hours per electron volt. So if I just didn't this before, But just to be sure, I'm gonna check my units. Electrical cancels out, the number of atoms cancels out within here, Grams cancels, purples, cancels and you're left with just kill hours. And with this, we can find that the amount of kilowatt hours produced for this reaction is 2.3 times 10 to the eighth kilowatt hours. Great in party finally does asked to calculate the energy again, killing what and where's if we can combust? One kilogram of carbon in the following reaction. We're told each reaction produces 4.2 old electron volts. Again, I'll use E is my energy term. So it's really the same equation as we have here. So I'm not gonna write out the equation of simple you guys 4.0 electron volts Prevent mostly by the mass of carbon. Here is 1000 grams. The more massive carbon is exactly 12. No approximation there again, we'll explain. My Afghan does something end for a number of atoms per mold because they cancel out previously, Excuse the end again converting two kilowatt hours from Electron Golds tendon in 26. You know what hours per electron gold we find that the energy released would be 9.38 kilowatt hours saying go. Each of these questions is essentially based on this relationship in which you can find the number of particles using our chemistry knowledge. That I get the number of particles is mask over more mass times, avocados

Carleton University
Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

LB
Liev B.

Numerade Educator

Aspen F.

University of Sheffield

Meghan M.

McMaster University