Question

An airsoft pellet gun uses air pressure to launch a small plastic pellet .
The working gas (air ) is initially compressed and stored in a small capsule,
connected to the barrel by a valve, with the pellet directly on the other side of the
valve. When triggered, the valve opens and allows the high-pressure gas to expand
into the barrel while pushing the pellet out of the barrel, against the atmospheric
pressure on the open end.
a) Assume the barrel is 6 inches long, with an internal diameter of 6 mm. The
volume of the charge capsule is 10% of the volume of the barrel. What
pressure do you need to fill the capsule with before the shot so that the
barrel pressure right before the pellet exits is 2 atm? Assume that the gas
expands adiabatically as the pellet moves through the barrel, and that no gas
escapes between the pellet and the barrel walls.
b) If the pellet weighs 0.2 grams, what kinetic energy will it acquire when it
leaves the barrel, and how fast will it be moving? ( hint: assume that the
pressure on the “open” end of the barrel remains precisely at 1 atm. In
reality, it will rise slightly as the pellet is pushed forward, as it will tend to
compress the air directly in front of it. Also, ignore the friction between the
pellet and the barrel).
c) If the temperature is 300K immediately before the shot, what will be the
temperature of the gas in the barrel right before the pellet leaves?

Feel free to introduce/define additional
parameters as you see necessary.

Answer 1