# The amazing vacuum microwave

Happy Easter everyone. Sorry for lack of blog activity – lots of marking has been building up that I’ve needed to get through.

Yesterday we experienced the vacuum-packing ability of a clip-container in a microwave. In this case, it was being used to cook some vegetables for Benjamin’s dinner. The veges were placed in the microwave, the lid put on, and then zapped for a few seconds. The problem was then taking the lid off, since it had sealed tightly shut.

I’ve had a comment on my blog about this before, from someone who’s experienced it. I think what’s happening is that, as the contents heat up the air inside expands. It is able to push it’s way out through the seal. The mass of air on the inside is then rather less than what it was to start with. Once the heating has stopped, however, the temperature reduces and the air contracts. However, this time the seal doesn’t let air back in – instead the lid is sealed and the air inside reduces pressure. Consequently we are left with lower pressure on the inside than the outside.

Just how big a pressure difference do we have? Suppose the air inside is heated to 100 C, as opposed to the 20 C that it is on the outside. At constant pressure, volume scales as absolute temperature, so we have a volume increase of about (100 + 273) / (20 + 273) =  1.27 times. That is, about 30% of the air is pushed out in the heating process. This air doesn’t get back in during the cooling. Therefore, once cool, the container has 30% less pressure inside (pressure being proportional to volume at constant temperature).

What does this equate to in everyday terms? Air pressure is about 100 kPa, meaning a force of 100 thousand newtons over an area of 1 metre squared. 30% of this would be 30 000 newtons over a metre squared. Since a kilogram weighs about 10 Newtons, that’s about the equivalent of 3000 kg spread over a metre squared.

Now, the little container wasn’t a metre squared in area. It’s about 10 cm times 6 cm (approximately) , which is 60 cm2 or 0.006 or a metre squared. Multiply that by 3000 kg per metre squared, gives us 18 kilograms. That is to say, the force due to the air pressure is equivalent to sticking about 18 kg of mass on top. Little wonder it was tough opening.

This calculation has a few assumptions in it, not least that the air had cooled back to room temperature (it hadn’t). The reality I think is that it would be rather less force. I managed in the end to get a flat knife under the seal and let some air in – that got the lid off.