Temperature change of air
I am trying to fact check a manufacturer of residential security containers (AKA cheap safes that don't meet the standards of a real safe) on their claim of fire protection. To do this, I need a question answered that I think some people here can probably help me with.
They use a half inch of a 2300F ceramic board with a thermal conductivity of about 1.03 BTU-in/hr/ft^2/degF @ 1,200F. According to my calculations (which could be wrong) a safe with a total surface area of 50ft^2 with that thermal conductivity and an exterior temperature of 1,200F and an interior temp of 70F there will be approximately 115,000 BTU/hr added to the interior of the safe.
I used the following equation: Qh = kADT/L = 1.03*50ft^2*1130F/0.5in
This of course is all over simplified assuming the temperature difference is the same on all sides etc. That is fine. I'm not looking for exact, just ballpark.
So my question is this: What would be the temperature change of 25 ft^3 of air that was 70F after adding 115,000 BTU? What about 60k BTU (roughly half an hour)? You can assume the area is perfectly insulated for simplicity to give a worst case scenario. If it really matters, you can use a relative humidity of 45% @ 70F.
This guy is claiming it will keep the temperature below 350F for an hour at 2,300F using a half inch of this stuff. I don't think he is trying to be misleading, I think he is just very ignorant of how this stuff actually works. I definitely don't believe his claim, but wanted to see how far off it was.