The thermodynamics of a gun are unique for a
couple reasons. One is that it is a combustion process
that is known to have too little oxygen for complete
combustion. This is because within the chamber of
the gun, there is not enough volume to hold the
propellant and the correct amount of air. For this
reason, oxidizer has to be included in the propellant.
Along with the oxidizer, there must be fuel in the
gunpowder. The fuel comes from charcoal and sulfur.
The charcoal provides carbon to the reaction, and the
sulfur provides fuel, as well as lowers the ignition
temperature of the gun powder. Charcoal (C) has an
ignition temperature of 350oC, whereas sulfur (S) has
an ignition temperature of 200oC. The oxidizer used
in gun powder is potassium nitrate (KNO3), which
allows the combustion to happen in the absence of
air. A basic balanced equation is as follows:
In order to set off the gun powder, it must be
ignited. This is the function of the primer. The
primer contains a small amount of lead styphnate,
which is an extremely sensitive explosive. It is so
sensitive that a change in pressure can set it off.
When the firing pin hits the primer, the lead
styphnate gets pressed between the anvil and the new
indentation made by the firing pin. This sends flame
through the cartridge and ignites the gunpowder.
Gunpowder has about 3MJ of energy per kg,
which comes out to 3000 joules per gram. One gram
is equal to roughly 15.43 grains, which is the unit
gunpowder is measured in. A standard .45 ACP
round has between 4.5 and 6 grains of powder. This
means a standard .45 ACP load has between 875 and
1166 joules of energy inside of the casing. Looking
back at the first section for the kinetic energy of the
bullet, ~477 joules, we can, roughly, determine the
efficiency of the system. This gives the system an
efficiency between 41% and 55%.