illuminating science

Everyone probably knows that old science trick: how do you get a whole, boiled egg into a bottle whose neck is too small for it to fit? The answer, of course, is to light a piece of newspaper and shove it into the bottle. Quickly place your egg on top, and when the flame goes out - *thwup*, your egg is magically sucked into the bottle.

The was the activity being run by an established science demonstration group at a fair I went to recently. This demo was made famous (in Australia, at least!) by Julius Sumner Miller, of Why is it so?, a science show back in the 80’s, and countless kids (and adults!) have successfully duplicated the feat. (It takes a little work to find the right size bottle - the opening must be just “a little” smaller than the egg - 330mL glass juice bottle (Golden Circle, etc) work well!)

But one thing that’s a little hazy is the physics involved. The usual answer is that the flame uses up the oxygen in the bottle, creating a (partial) vacuum which sucks the egg in. Unfortunately, that doesn’t quite hold water - yes, the flame does use up oxygen in the bottle (that’s why it goes out eventually!) but it also produces new gasses - mainly carbon dioxide, but also some carbon monoxide (which is toxic to us). In fact, it can actually produce slightly more gas than it uses, which should push the egg out of the bottle! (One molecule of oxygen O₂ can become one molecule of carbon dioxide CO₂ or two molecules of carbon monoxide, 2CO.)

In fact, the real physics is what happens to gases when they heat up - they expand. Cool them down, and they shrink. You can see this by putting a tiny bit of water in a balloon, then putting the balloon in the microwave - the water turns into steam, which heats up and expands! (Just be careful - it can be hot! Also, don’t run your microwave too long when it’s almost empty, or it can damage it. Putting a saucer of water inside is a good idea)

So, when the paper burns, it heats up the air which expands. The extra air pushes the egg out of the bottle, and escapes out the sides - but the egg doesn’t fly away because gravity holds it down (it would be really cool to try this in zero gravity!) Then, when all the oxygen is used up, the flame goes out, the air cools down, shrinks, and sucks the egg into the bottle!

A fellow physicist, however, was a little skeptical - could the heat from a single match be enough to expand/contract the air enough to suck it into the bottle? So I did a little back of the envelope calculation: a match, apparently, releases about 1BTU of heat, which in proper SI units is 1000 Joules. Let’s assume that all that heat is released by a match dropped in the bottle. Say I have a 330mL=0.00033m³ bottle, and all the heat goes into the air of the bottle. The specific heat of air is approximately 1000 Joules per kilogram per degree and the density of air is approximately 1kg per cubic metre, at room temperature. So, I have 1kg/m³*.00033m³ = .0003kg of air, which receives 1000 Joules, and so increases by 1000 degrees Celsius!

Given that the volume of gas doubles when you double the temperature, this is more than volume change to suck the egg in. (There’s a subtlety here - the gas is initially at 300 Kelvin, a scale that starts at absolute zero but has the same spacing as Celsius. That means the temperature has tripled, and so does the volume.) Even allowing for the fact that some heat escapes from the bottle, less heat from the match, etc, this seems like expansion and contraction of gas, rather than “using up the air” is the true explanation of the “Egg in the bottle” trick.