Kinetic energy, riddle me this

[quadcatfly]

Imagine two experiments A and B.

In experiment A I load a gun with a cartridge and shoot a bullet. Total energy in this experiment will be E(heat) + E(projectile). I include recoil in E(projectile). E(heat) in its turn will heat the muzzle and some air. Done.


In experiment B I do everything the same, except the is no bullet (e.g. no projectile). Same gun, same cartridge and the amount of gunpowder in it. So I pull the trigger. Total energy of this system will be E(heat) which will amount to the same level as in experiment A since I am burning the same amount of gunpowder under the same conditions.

I can't quite wrap my head around it.It turns out that in my experiment A I got E(projectile) out of nothing? Since it obviously didn't convert from E(heat) as clearly demonstrated by the experiment B.

Someone please enlighten me !

 

[willem2]

In experiment B I do everything the same, except the is no bullet (e.g. no projectile). Same gun, same cartridge and the amount of gunpowder in it. So I pull the trigger. Total energy of this system will be E(heat) which will amount to the same level as in experiment A since I am burning the same amount of gunpowder under the same conditions.

No you're not, there's no bullet in experiment B. In both cases you create high-pressure gas, which is going to expand. In the first case, most of the energy will go to the bullet, in the second case, all of the energy will end up moving the air in and in front of the barrel, and this energy will eventually up as extra heat.