I'm not sure that the basic thermodynamic envelope look at the system is very instructive when it comes to the amount of useful work done on the bullet itself. I think looking it as pressure-volume work is probably more useful for examining effects on the bullet, which is really all we care about. The bullet only really cares about the force it sees on its base minus the drag force of the barrel interface, and whatever inertial force is exerted by the air in the barrel being forced to move by the bullet (probably pretty small).
To get a view of the whole, you'd probably be looking at something like the integral of the force curve at the base of the bullet (product of pressure and area) minus the integral of the barrel drag force curve (both with bullet barrel time on the X). Or something like that, too lazy to crack the books on my day off. At any rate, I could see how geometric changes to the powder burning chamber might affect flow during combustion, rate of combustion, and therefore the pressure curve as experienced by the bullet.