Another physics question.. (E=MC^2 and Fusion)

[ExampleFlamer]

Ok so this is where I'm a bit stumped.

I'm trying to figure out where the speed of light comes into the equation E=mc2, in regards to fusion reactions.

So correct me if I'm wrong, but if I take 1kg of Hydrogen isotopes and create a fusion reaction I will get 9x10^16 J.

(1 x (3x10^8)^2).

But where does the speed of light come into this? You can understand the mass being relevant in the equation, being the amount of Hydrogen there is to begin with, but there is nothing in that simple concept/theory that mentions the speed of light.

A lot of people have been telling me that it is just a constant and was there due to other equations being relevant to it - that still doesn't explain why it's used.

For example, if I was to replace the speed of light with gravity (let's say gravity is effecting the reaction), we know gravity's a constant and is 9.8m/s. You can understand why it is used in the equation, because gravity is a factor in the fusion reactor. But again, there's no mention of the speed of light in the theory. From what I understand (excuse my naivety), the speed of light has nothing to do with fusion reactions.

It can't be anything to do with the atoms themselves, they have mass... Therefore, no speed of light. Is it something to do with photons interacting with the atoms on a micro-scale, because that's the only thing I can think of...

So people have also been telling me that it's just a conversion factor. So, being a conversion factor means yea sure, 3 days = 72 hours but it also equals 24x3, 24 being the conversion factor. However that still doesn't explain why "9x10^16" is used in the equation, being in a different form or not.

[swansont]

 

So correct me if I'm wrong, but if I take 1kg of Hydrogen isotopes and create a fusion reaction I will get 9x10^16 J.

 

That's what you'll get if there is a 1 kg reduction in mass

But where does the speed of light come into this? You can understand the mass being relevant in the equation, being the amount of Hydrogen there is to begin with, but there is nothing in that simple concept/theory that mentions the speed of light.[/size]

 

For example, if I was to replace the speed of light with gravity (let's say gravity is effecting the reaction), we know gravity's a constant and is 9.8m/s. You can understand why it is used in the equation, because gravity is a factor in the fusion reactor. But again, there's no mention of the speed of light in the theory. From what I understand (excuse my naivety), the speed of light has nothing to do with fusion reactions.[/size]

g is actually 9.8 m/s^2

 

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A joule is a kg-m^2/s^2 so whatever the conversion factor is, it has to have units of (m/s)^2, because that's how you get from mass to energy. It has to have units of speed, squared. It also has to be a constant, meaning it has to be proportional to c anyway — what if the equation was E = 4mc^2? Then you could say that the constant is 2c. Any value it might have, and you could still ask the question, "why does it have that value?" Ultimately, we don't know. You can't derive the universe from first principles. You observe what happens and figure out the rules.

 

You can, however, look at a derivation of the equation, and light is involved, and the momentum of light is E/c. That's where the constant enters the picture.

[Enthalpy]

For example, if I was to replace the speed of light with gravity, we know gravity's a constant and is 9.8m/s. But there's no mention of the speed of light in the theory. From what I understand, the speed of light has nothing to do with fusion reactions.

 

It can't be anything to do with the atoms themselves, they have mass... Therefore, no speed of light.

 

1/c² is just how heavy energy is. Any form of energy, not just nuclear one. Kinetic energy has that mass, and this includes heat. Electrostatic energy has this mass, and this includes nuclear fission: when uranium splits, the fragments get their speed from the electric repulsion of the protons. The energy of strong interaction, which attracts protons and neutrons together in a nuclear fusion, has this mass. Even gravitation energy has...

 

But nuclear energy is more concentrated than chemical or thermal energy, at our usual human scale (gravitation can be more concentrated than nuclear energy at astronomical scale). So concentrated that the relative variation of mass is easily measured, like 0.1%, while it is far less with other forms of energy. That's why the mass variation is commonly used to compute energies of nuclear or particle reactions but not elsewhere. Just a matter of usable quantities, not of nature.