Calculating Deflagratio Pressure in a Closed Vessel

[lukebeadgcf]

Forgive me because I'm not a math or physics wiz but I'm at a dead end trying to calculate the pressure generated by a deflagration inside a cylinder. I have been searching for a formula but I've come up with nothing.

Here is an example scenario:

I have a cylinder with a height of 9cm and a diameter of 13.7cm. Inside the cylinder is a gaseous mixture of 2/3 hydrogen and 1/3 oxygen at atmospheric pressure. The cylinder has been preheated to a temperature of 900 degrees Celsius (before oxidation). When the hydrogen oxidizes (either spontaneously or with a catalytic spark), the energy generated will be 7.9kJ (am I right?). So what is the resulting pressure on the cylinder and how do I calculate it?

Thanks for your help!

 

[Chestermiller]

The reaction is $$2H_2+O_2=2H_2O$$So the reaction mixture is stoichiometric. The heat of this exothermic reaction at 900 C can be determined from the heat of the reaction at 25 C and the heat capacities of the reactions and product. This heat of reaction goes into raising the product to a higher temperature, which can be determined using the heat capacity of the product mixture. The number of moles of gas decreases from 3 to 2. Both the higher temperature and reduced number of moles can be used in conjunction with the ideal gas law to establish the final pressure. Consideration might have to be given to non-ideal gas behavior a postiori.