The approximations for pressure change calculated as a ratio of volume are OK for a general understanding where it is assumed that temperature of the powder gas is constant. However, the actual pressure would also have to include differences in temperature. Those who have worked with compressible fluids know that expansion of a compressed fluid causes a temperature drop. Clearly, the expansion between a 12 bore and 10 bore is different. Therefore, we would not expect for "T" to be exactly constant. I'd say that the actual change in pressure would be, directionally, more than the simple volume ratio indicates. Beyond this, it gets quite complicated; I will, however, be will to discuss if anyone really wants to.