The internal ballistics of a firearm or artillery piece considers the pellet, bullet, or shell motion while it is still inside the barrel. In general, deriving the muzzle speed of a gunpowder firearm from first principles is difficult because powder combustion is fast and it very rapidly raises the temperature of gas (generated by gunpowder "deflagration," or burning), which greatly complicates the analysis. A simple case is provided by air guns, for which we can make reasonable approximations that permit a derivation of muzzle speed. It is perhaps surprising that muzzle speed depends upon barrel length (artillerymen debated this dependence for centuries, until it was established experimentally and, later, theoretically). Here we see that a simple physical analysis, accessible to high school or freshmen undergraduate physics students, not only derives realistic muzzle speed but also shows how it depends upon barrel length.