Sometimes one can demonstrate very profound and remarkable physics with very simple, even mundane, tools. Last week I received the tools to perform one such demonstration by mail:
This pair of iron hemispheres, with handles attached and a valve on one side, are a small scale model of one of the earliest and most dramatic displays of the power of atmospheric pressure. They are now known as the Magdeburg hemispheres, and they still work as a great demo to this day.
Curiously, the hemispheres are not named for a person, but a place: Magdeburg, Germany. The spheres were designed by the German scientist (and mayor of Magdeburg) Otto von Guericke (1602-1686) in 1654 to show off his newly-invented vacuum pump and the concept of atmospheric pressure.
The premise is simple: with the hemispheres pressed together, air is pumped out of the interior, creating at least a partial vacuum. This seals together the hemispheres with a remarkable force.
Guericke first demonstrated this force in 1654 for the Emperor Ferdinand III. Thirty horses, in two teams of 15, were unable to pull apart the evacuated hemispheres! He performed a smaller scale performance in 1656 in his hometown of Magdeburg, using two teams of eight horses. This latter performance was immortalized in a famous sketch by the scientist Gaspar Schott in a 1657 book, Mechanicahydraulica-pneumatica.
So how do the spheres stay together? Simply put: atmospheric pressure! All objects within the atmosphere are under constant bombardment from air molecules traveling every which way; this atmospheric pressure is not noticeable to us because our bodies have an internal pressure that matches and balances it. (Though you won’t explode if exposed to a vacuum, movie tropes notwithstanding.)
When the hemispheres are first placed together, the air pressure within them balances the air pressure outside, and they are easily pulled apart. When air is removed from the interior of the hemispheres, however, there is no longer any force pushing outward: the atmospheric pressure outside dominates, pushing the hemispheres together and keeping them from being separated.
An attentive reader may have already noticed a similarity between the Magdeburg hemispheres and a very common, everyday object: a suction cup!
A suction cup gets its sticking force by the same action as the Magdeburg hemispheres: when one pushes the cup against a smooth wall, one forces the air out of the cup, allowing atmospheric pressure to hold it to the wall. We could say that the Magdeburg hemispheres are an early primitive form of suction cup (though suction cups apparently have a history that goes back much further)!
A good set of Magdeburg hemispheres, however, can provide suction forces significantly stronger, as Guericke’s original horsepower demonstration shows. In mathematical terms, the force holding together a pair of hemispheres of radius can be shown to be
where is the pressure difference between the interior and exterior of the hemispheres. My pair of hemispheres have a radius of 5 cm; assuming conservatively that my hand vacuum pump can reduce the interior pressure to half of atmospheric pressure (atmospheric pressure being ), I find that the hemispheres will stick together with a force of 392 Newtons, or 88 lbs! Guericke’s hemispheres had a radius of about 25 cm; if he had almost completely evacuated them of air, they would provide a force of about 4400 lbs!
For those not willing to spend some $60 for a metal set of hemispheres, it is possible to perform a simple version of Guericke’s demonstration at home with readily available supplies. You will need:
- two identical glasses
- a candle
- a damp piece of paper that covers the opening of a glass
Put the candle in one of the glasses, and light it. Place the other glass on the top of the first, with the wet piece of paper between them; this paper will help form an airtight seal between the glasses. The candle will slowly consume all of the available oxygen in the glasses, and be extinguished. If you have done things correctly, you will find that the glasses are strongly stuck together due to the drop of atmospheric pressure inside! If you have set up a really good seal, it might be impossible to pull the glasses apart by hand — they can be twisted apart in this case.
Obviously, the seal between the two glasses is key: I’ve only been able to get a weak seal on my preliminary home experiments; a heavier piece of paper should work better than a lighter one.
How does the home experiment work? It looks like several factors can play a role in reducing the pressure within the glasses. For one, a candle burns by combining the oxygen in the air with hydrogen present in the candle to produce water vapor and carbon dioxide. Less CO2 gas is produced than the amount of O2 consumed (thanks to the creation of water, as well); when the water vapor condenses, this results in a pressure drop inside the glasses, serving as a crude form of vacuum pump. Another aspect: the candle heats up the air within the glass, causing it to expand. When the candle goes out, the temperature drops, causing the pressure to drop within the glass as well. The more I look at this simple setup, the less simple it seems to be!
The Magdeburg experiment is a delightful glimpse of the hidden and powerful atmospheric forces that are with us at all times. It is just as fascinating today as it was some 350 years ago!
Update: revised my calculations for the force of attraction of the hemispheres! Also, related to comments below, I revised my explanation of the “candle effect”; it looks like it is another experiment in which a number of factors can play a role!