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This is a know rule when baking:

Don't open the oven until your cake is finished, otherwise it will "fall".

Why/how does this happen?

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A cake will rise because of a combination of chemical leavening (baking powder, baking soda) and steam. The gases released from these things (carbon dioxide or steam) inflate tiny air bubbles in the batter.

These air bubbles need to set. A protein mesh, generated from gluten (created when flour and water come into contact), is what actually holds the bubbles in place in the baked good. But gluten takes time to set correctly and when it's hot, it's still very soft and can easily collapse.

So, you have outward pressure of hot gasses in tiny air bubbles suspended in this very soft, elastic protein matrix. When you expose it to a sudden shock of cold air, the bubbles contract (cold gas takes less volume than hot gas, you can see this by inflating a balloon and then sticking it in the freezer -- it will shrink) and the protein matrix isn't firm enough to remain. So the bubbles collapse and you lose any leavening you worked hard to get.

That said, I have never had a cake fall by opening the oven door. I have, however, had it take a lot longer to bake because opening the door dropped the temperature. So perhaps the real motivation is so you don't extend the baking time. After all, who wants to wait longer for cake?

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I understand why the bubbles collapse, but why don't they expand again, when the oven is closed and the cake is heated again? Since air has very low volume heat capacity, after the oven is closed, the cold air should get very quickly heated to the original temperature by the solid parts of the oven. – Petr Pudlák Jun 18 '13 at 12:52
The cold air could set the proteins in the batter at some point either during/after the collapse and once gluten sets, it doesn't get very elastic again. So no amount of gas expansion would re-inflate the bubbles. – tpg2114 Jun 18 '13 at 12:55
It's also possible that the gas escapes (which happens anyway) and there is just less gas left behind to re-inflate the bubbles. – tpg2114 Jun 18 '13 at 12:56
Thanks, I'm just curious, why would the gas escape? Cooling the gas inside the bubbles means its pressure drops (and so the bubbles collapse), so the pressure of the gas should be equal or even less (if the protein mesh opposes the force) than the pressure of the surrounding gas. – Petr Pudlák Jun 18 '13 at 13:08
I've also never had a cake fall by opening the oven door, though for entirely different reasons. – Emilio Pisanty Oct 28 '13 at 16:12

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