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my question is simple. How can we calculate the temperature needed in order to do the nuclear fusion things , and also the temperature after the reaction successful.

enter image description here

If you can describe it, it would be really cool. I just want to know about it


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marked as duplicate by John Rennie, Kyle Kanos, Brandon Enright, Qmechanic Apr 7 '14 at 13:44

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Firstly, fusion doesn't happen in the way depicted in the question. Four protons don't participate in a 4-body reaction. Instead there are many intermediate steps:

enter image description here

Each step has its own reaction rate. The overall reaction rate is determined by the rate limiting step. The proton-proton reaction is the rate limiting step in this case.

It is important to think in terms of the rate at which a reaction occurs, rather than whether or not it will occur.

The reaction rate will depend on temperature and pressure. In the Sun, pressure is ~265 billon bar, so the reaction can proceed at 10-15 million K. The rate of reaction is actually very low, the center of the Sun only produces energy at rate of ~277 Watts per cubic meter. On Earth, we can not built a reactor with pressure this high, so higher temperature is needed. Different reactions such as starting with deuterium or tritium are used to avoid the need for the proton-proton reaction. Then fusion could be achieved in the ~100 million K range for example.

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