The amount of gas produced is not linear with the temperatures produced. The other point that I’m making is there are other things that affect the temperature of combustion such as atmospheric conditions. In Spearfish SD the temperature changed from -30 to +40 degrees in 15 minutes. If firing during this period there would be other conditions that have affected the pressure and temperature of the firing of the cartridge. Normally these things can be considered constant as long as the temperature of things like the ammo is constant. Density of air, temperature of ammo etc.
When the ammo is hotter the the combustion is faster. The pressures increase due to the faster combustion. Yet the amount of gas produced is the same as long as there is complete combustion. The bullet will come out of the barrel faster due to the time the bullet is in the barrel there is higher pressure.
However the temperature and the pressure of two solids becoming gases are not linear. You are sticking with your thermo-dynamics story with how gases behave while ignoring the realities of the chemical properties of the different materials changing from solids to gases.
The amount of gas produced and the time it takes for complete combustion is different for different materials.
I am saying that powder “A” can produce the same velocity as powder “B” yet the temperature produced can be different all other things being equal.
