Hello. I’m trying to understand the nature and amount of force generated in an explosion. Take, for example, the explosion that results from the complete annihilation of one gram of matter, releasing 8.9876E+13 Joules. Let’s say that the initial volume of the explosive material is one cubic centimeter, shaped into a sphere with an area of .2244 square meters. Working through the inverse square law I end up with an output of 4.0050E+14, and this is where I begin to get confused. I get that having an area measuring less than 1.0 means that my final energy value will be greater than my original energy value, but while this might be mathematically correct it doesn’t reflect what would happen in the real world (making an explosive smaller does not make it more powerful). I suspect I’m missing something fundamental here, but being neither a mathematician nor a scientist I’m not sure what it is. My second point of confusion has to do with something I came across when I was reading up on the inverse square law. In the description I found the following statement: "At large distances from the source (compared to the size of the source)…”. What I’m wondering is what constitutes a “large” distance compared to the source. Is it twice the size? Ten times? Thank you for any help you can give me.
Welcome to PF; I don't follow the calculation you have done. If your explosive releases X joules of energy, then that is how much energy it releases. No amount of fiddling with geometry changes that. But the energy flux per unit area can be higher, the closer to the center of the explosion you get. "measuring less than 1.0" is irrelevant - that depends on the size of the units you use and has nothing to do with the physics. Depends on the context. The idea is that an approximation has to be justified. Note: inverse square law is not specific to explosions.
The power of an explosion depends on how fast the energy content is released. The force of the explosion depends upon how it is confined ... In the open air it is carried by the supersonic blastwave. For the perfect matter-antimatter explosion hypothesized here ... you would get a lot of gamma rays. The intensity would fall off as the inverse square of the distance from the center; there would be a single pulse travelling outward at the speed of light. This pulse would appear as a thin shell ... the thickness depending on how long the anhilalation took.