It's widely known that nuclear weapons that rely on fission or fusion are vastly more powerful than chemical explosives, and that nuclear power is vastly more powerful in all ways than chemical energy, such as combustion or the rapid break of chemical bonds that occurs in explosives like TNT.

I was trying to get some figures on just how much more powerful it was, and wanted someone to check my figures to see if I'd erred.

A rule of thumb is that one ounce of mass contains roughly one megaton's worth of energy, and to release one megaton's worth of enerfy with TNT using chemical reaction level energy would take one million tons of mass, or 32 billion ounces, so I determined that chemical energy reactions only release 1/32,000,000,000 of the total energy in a mass.

Now, a thermonuclear fusion reaction liberates about 0.7% of the energy in a mass. This seems to suggest that as a powersource, fusion is about 22,400,000,000 times more powerful than chemical reaction power as it releases that many times more energy from a given mass.

Am i correct here? I may be writing something that deals with energy sources and how much more powerful nuclear energy sources are, and how much more energy they will give people to do things with.

You are in the right order of magnitude for the total energy content of matter.

Einstein's famous equation shows that a gram of matter has about 9x10^13 joules of energy.

A metric ton of TNT has a yield of about 10^9 calories, or 4.18 billion joules. Crunching the numbers shows that the total energy of a given mass is about 21 billion times the yield of an equal mass of TNT.

The fusion of ordinary hydrogen into helium has a yield of about 0.7% of that grand total, or about 150 million times that of TNT. I don't know what the yield is for the fusion of lithium⁶ deuteride and tritium, the typical main charge of a thermonuclear bomb.

The detonation of TNT is not the most energetic chemical reaction. It just happens to be a high explosive. I once estimated that the burning of coal has a yield of about 1 part in ten billion of the total mass of the reactants. I will need to look up the heat of combustion to check my work.

Hmm, I was using the famous science fiction writer's rule of thumb about an ounce of mass equalling a megaton of energy, looks like it's way off. Damn.

Thanks for the correction, my point was to show just how much more energy you get from nuclear energy processes than from molecular level reactions, I would like to get the best figures possible on that but am uncertain where to look, so I came to a place where I know the people are knowledgeable and helpfully inclined.

Oh! I just remembered something relevant here: In combustion, some of the mass comes from atmospheric oxygen too, not just the mass in the coal, so be sure to factor that in.

I did just that. I looked up the heat of formation for carbon dioxide and did the number crunching. It takes about 2.7 billion grams of carbon combining with 7.3 billion grams of oxygen, yielding 10 billion grams of carbon dioxide, to yield as much energy as the total conversion of 1 gram.

Coal is not pure carbon, but we should be fairly close.