# determine temperature at which pita bread will expand in a toaster

suppose you have a pita pocket of radius 5cm or .05m. We will model the pita pocket as consisting of disk with a layer of air of volume V which is contained by the surface of the bread. We will assume that no cracks or perforations exist in the pita pocket. supposing the thickness of the pocket is d = .5cm = .0025m. we can calculate the volume from the radius and thickness of the disk

$V_{pita}$ = $\pi r^2d$

suppose that the pita contains a volume of air inside

$V_{air} = \frac {V_{pita}}{5}$

and that the rest of the volume of the pita is a solid. Model the forces and pressure that cause the pita to expand. at what temperature will the air pressure inside be able to break the bonds holding the top sides of the bread together and allow it to expand under your models assumptions? rough order of magnitude estimates are fine--- but all answers should agree with experimental values of pita expansion as a function of Temperature

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i suppose you would need an accurate oven thermometer and a full package of pita to do testing –  Timtam Aug 10 '11 at 10:11
i think what happens is that the air inside the pita gets hotter than the air around the pita because the solid part of the bread conducts heat better than the air in the chamber and the air inside the pita is surrounded on all sides by this conductor whereas the air outside the pocket is only exposed to one side of the conductor, or something like that lol –  Timtam Aug 10 '11 at 10:14
Can you provide an experimental temperature vs. pita bread expansion curve? Unbelievably, I don't seem to have that data on hand. –  Richard Terrett Aug 10 '11 at 12:59
the goal would be to predict the temperature at which the chemical bonds that hold the top and bottom together are overcome by the pressure differential of the hotter air inside the bread from first principles... and THEN to compare with experiment –  Timtam Aug 10 '11 at 20:02

Some obscure thermal conductivity effect might heat the air inside to double the temperature, thereby doubling its pressure, but if the air expands and the pita doesn't let new gas in, it will not be able to expand more than a factor of 2 before the pressure is the same as outside. The expansion observed is a factor of a ten or more, so it's gas production.

I think that the explanation is production of steam, and the critical temperature is close to the boiling point of water, give or take the effects of solutes in water trapped in the pita. Steam production gives as much expansion as you want, and also, when I cut the pita open, I notice that it is full of steam.

(I don't think its such a terrible question either)

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interesting i hadn't even thought of that... but you are right, I think the steam production probably is the cause. –  Timtam Aug 13 '11 at 4:21
i would predict then that when inside of the pita reaches around 373Kelvin we should start to see expansion--- i'm gonna go buy a thermometer and some pita bread--- will report back –  Timtam Aug 13 '11 at 4:31