Calculating Break-Even Point of Muon-Catalyzed Fusion

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In summary, the concept of "break-even" point is important in fusion as it is reached when the energy output equals the energy input. For muon-catalyzed fusion, the rest energy of a muon is 106 MeV and it takes 6.022 reactions to reach the break-even point. However, for more significant figures, the number of reactions needed may be slightly higher.
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xinlan
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Homework Statement



When discussing attempts to make any type of fusion into a workable power source, an important concept is the "break-even" point. The break-even point is reached when the fusion process generates as much energy as was initially put in (i.e., the energy output equals the energy input). The rest energy of a muon is 106 MeV. If this is the only energy input necessary to initiate muon-catalyzed fusion, how many reactions must a muon catalyze to attain the break-even point?


Homework Equations





The Attempt at a Solution



from the previous question, I got the energy per reaction is 17.6 MeV
so, the number of reactions needed = 106 / 17.6 = 6 reactions
but the feedback says that "This is very close to releasing the same amount of energy as was input, but we want more energy than was input."
I'm totally confused..

please help me..
 
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  • #2
I think they want you to round up.
 
  • #3
the real answer is 6.022,
I already rounded up to 6..
 
  • #4
xinlan said:
the real answer is 6.022,
I already rounded up to 6..

No, you rounded down. ;)
 
  • #5
oh my.. thank you so much to Phlogistonian.. :)
 
  • #6
Based on your answer, I guess they just wanted more significant figures. We didn't use these computer things when I was in school. We just used books, pencil, and paper. :)
 

1. How is the break-even point of muon-catalyzed fusion calculated?

The break-even point of muon-catalyzed fusion is calculated by comparing the energy output of the fusion process to the energy input required to sustain it. This is done using a formula that takes into account the fusion rate, energy released per reaction, and energy required to produce and maintain the muons.

2. What is the significance of the break-even point in muon-catalyzed fusion?

The break-even point is significant because it represents the point at which the energy output from the fusion process is equal to the energy input required to sustain it. This is a crucial milestone in the development of muon-catalyzed fusion as a potential energy source.

3. How does the break-even point of muon-catalyzed fusion compare to other forms of nuclear fusion?

The break-even point of muon-catalyzed fusion is significantly lower than other forms of nuclear fusion, meaning that it requires less energy input to sustain the fusion reaction. This makes it a more promising candidate for practical energy production.

4. Are there any challenges or limitations to accurately calculating the break-even point of muon-catalyzed fusion?

Yes, there are several challenges and limitations to accurately calculating the break-even point of muon-catalyzed fusion. These include uncertainties in the muon production and confinement processes, as well as the difficulty in accurately measuring the fusion rate and energy output.

5. What are some potential applications for muon-catalyzed fusion once the break-even point is reached?

If the break-even point of muon-catalyzed fusion is reached, it could potentially be used as a clean and sustainable energy source to power homes, businesses, and even vehicles. It could also have applications in space travel and other advanced technologies that require large amounts of energy.

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